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## Simultaneous Observation of Phase-Stepped Images for Photoelasticity Using Diffraction Gratings

### Experimental Mechanics (2013) 53: 1343-1355 , October 01, 2013

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Phase-stepped photoelasticity is a powerful method for full-field stress analysis, but sequential collection of the multiple required images limits the technique to static loading applications. We have developed a system that utilizes diffraction gratings to collect four phase-stepped images simultaneously with a single camera for transient loading applications. Two adjacent, perpendicularly oriented, 1D Ronchi rulings are placed after a transparent sample to split the light into equal intensity beams for each diffraction order. The four beams that are diffracted once in the x direction and once in the y direction transmit through arrays of analyzing polariscope elements, with different combinations of fast-axis orientations for four phase-stepped images. The mirrors and imaging lenses in the system work in concert to focus each beam onto separate quadrants of the same CCD. We demonstrate the system for stress analysis of compressive loading of a Homalite-100 disk and of a Homalite-100 plate with a central hole. This system has the potential for photoelastic analysis of time-dependent materials and of dynamic events, when equipped with a high-speed camera.

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## Stress Monitoring of Post-processed MEMS Silicon Microbridge Structures Using Raman Spectroscopy

### Experimental Mechanics (2012) 52: 1341-1353 , November 01, 2012

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Inherent residual stresses during material deposition can have profound effects on the functionality and reliability of fabricated Micro-Electro-Mechanical Systems (MEMS) devices. Residual stress often causes device failure due to curling, buckling, or fracture. Typically, the material properties of thin films used in surface micromachining are not well controlled during deposition. The residual stress; for example, tends to vary significantly for different deposition methods. Currently, few nondestructive techniques are available to measure residual stress in MEMS devices prior to the final release etch. In this research, micro-Raman spectroscopy is used to measure the residual stresses in polysilicon MEMS microbridge devices. This measurement technique was selected since it is nondestructive, fast, and provides the potential for *in-situ* stress monitoring. Raman spectroscopy residual stress profiles on unreleased and released MEMS microbridge beams are compared to analytical and FEM models to assess the viability of micro-Raman spectroscopy as an *in-situ* stress measurement technique. Raman spectroscopy was used during post-processing phosphorus ion implants on unreleased MEMS devices to investigate and monitor residual stress levels at key points during the post-processing sequences. As observed through Raman stress profiles and verified using on-chip test structures, the post-processing implants and accompanying anneals resulted in residual stress relaxation of over 90%.

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## An apparatus for tensile testing of concrete

### Experimental Mechanics (1979) 19: 109-111 , March 01, 1979

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This paper describes a test fixture and alignment jig used for testing small concrete or rock cylinders in uniaxial tension. The fixture may be easily modified to test cube specimens and is adaptable for use in any standard universal testing machine. A testing procedure is described and results presented for 3 in. × 6 in. (76 mm × 152 mm) concrete cylinders. The main virtues of the fixture are its ease of construction, simple alignment procedure for the test specimen, and accuracy comparable to that obtained from the standard compression test of concrete cylinders.

## On the measurement of Poisson's ratio for modeling clay

### Experimental Mechanics (1971) 11: 402-413 , September 01, 1971

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Resonance testing of Plasticine clay indicates that, for small strains (≤10^{−5}) in the frequency range 100–3000 Hz, the material can be considered to be a linear viscoelastic solid with parameters which depend on temperature, frequency and prior large-strain history. In order to measure Poisson's ratio, it is necessary to take special precautions to eliminate large straining between small-strain tests of different tensorial character. A simple but effective test configuration for measuring Poisson's ratio is described and test results are displayed.

## An automated biaxial sheet tester

### Experimental Mechanics (1972) 12: 155-157 , March 01, 1972

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A mechanical system is described which can stretch a sheet of solid propellant in two directions as a function of time. The sheet displacements along each of the two directions are independently controlled from a computer tape. Two load cells record the instantaneous resulting loads. Biaxial strains are measured by means of a 70-mm camera, which also is operated by the tape. The instrument is designed to stretch a 10-cm square by 0.25-cm-thick sheet to 50-percent strains at cross-head rates from quasi-static to 150 cm/min.

## Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

### Experimental Mechanics (2005) 45: 344-350 , August 01, 2005

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A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.

## Pulsatile flows in a lateral aneurysm anchored on a stented and curved parent vessel

### Experimental Mechanics (2004) 44: 253-260 , June 01, 2004

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We present particle tracking velocimetry measurements and flow visualization of pulsatile flow fields in a stented cerebrovascular lateral aneurysm model with a wide ostium anchored on a curved parent vessel. Among the stent parameters, the blocking ratio*C*_{α} ranging from 0% to 75% was selected to study its effect on the changes of intra-aneurysmal hemodynamics for the reference of minimally invasive endovascular aneurysm treatment. The Womersley number was 3.9 and the mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 850, and 300, respectively. The results are characterized in terms of velocity vector field, coded streak images, region averaged velocity, vorticity, and wall shear stress. A critical range of*C*_{α} related to the inflow location as well as the shape and number of intra-aneurysmal vortices is identified. The intra-aneurysmal flow activity, vortex strength, and wall shear stress are found to decrease with increasing*C*_{α}. Among the*C*_{α} examined,*C*_{α}=75% is the most favorable in attenuating the risk of aneurysmal rupture and promoting intra-aneurysmal thrombus.

## Using Carrier Fringes to Study the High Temperature Deformation Behavior of a BGA Package Under Extended Dwell Times

### Experimental Mechanics (2008) 48: 355-365 , April 29, 2008

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There is a compelling need to experimentally understand solder joint deformation behavior at high temperatures over an extended period of time. Accordingly, the deformation behavior of solder joints in a Ceramic Ball Grid Array (CBGA) package mounted on an organic FR4 board under extended dwell time at a high temperature has been studied using laser moiré interferometry. The warpage and the in-plane horizontal deformation of the ceramic substrate and the organic board as a function of time were determined. The variation of the normal strains and shear strains in the solder joints with time were also investigated. It was found that increased sensitivity was necessary to accurately determine the strains in the small sized solder joints. A new method utilizing carrier fringes to increase the sensitivity of the moiré interferometry system is proposed and has been used to determine the strains in the small sized solder joints. Increased sensitivity can be obtained merely by changing the incident angle of the laser light on the surface of the specimen, thereby making it unnecessary to use expensive phase shifting apparatus with the traditional laser moiré system.

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## Determination of stress-intensity factors by the method of caustics in anisotropic materials

### Experimental Mechanics (1995) 35: 137-143 , June 01, 1995

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This paper studied the applicability of the method of caustics to anisotropic materials under Mode I and mixed-mode static-loading conditions and introduced the procedure to obtain stress-intensity factors (SIF) in anisotropic materials by the method of caustics.

The mapping equations for initial and caustic curves in anisotropic materials were introduced and their computer graphical images were compared to the experimental ones to check the validity of the mapping equations proposed in this paper. The agreement between them was found to be satisfactory.

Two kinds of equations to determine SIF in anisotropic materials by the method of caustics are proposed in this paper. Corroborative experiments carried out by using the orthotropic materials under various loading conditions are presented. In the case of Mode I loading condition, the SIF's obtained by this paper's methods were found to be close to the results by another method, i.e., boundary-element method (BEM). And in the case of mixed-loading condition, the SIF's by this paper and BEM show little differences, (2.2–24.4 percent) with respect to the slanted angle of crack.

## Stresses in spheres with concentric spherical cavities under diametral compression by three-dimensional photoelasticity

### Experimental Mechanics (1966) 6: 244-250 , May 01, 1966

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This paper presents the experimental solution of the problem of a sphere with a concentric spherical cavity under diametral compression using the three-dimensional photoelastic method and calculations of the complete stress distributions along lines of interest using Golecki's analytical series solution. The experimental procedure, the stress distributions along different lines as well as the comparison with the theoretical results and a discussion of Golecki's solution are included.

## Continuous monitoring of fatigue-crack growth by acoustic-emission techniques

### Experimental Mechanics (1974) 14: 71-81 , February 01, 1974

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The application of acoustic emission to the detection of fatigue-crack propagation in 7075-T6 aluminum and 4140 steel is investigated. The relationship between crack-growth rate, cyclic stress-intensity factor, load-cycling rate and observed acoustic-emission behavior is presented. Crack-growth rates of less than 10^{−6} in./ cycle could be detected, and acoustic-emission counts per cycle were shown to be closely related to the energy released by crack extension per cycle. A quantitative relationship for the threshold conditions for detection of fatigue-crack growth is presented which agrees with experimental test results. The results also showed that fatigue-crack growth occurs in an accelerating and decelerating manner, even though the stress-intensity range remains uniform, and that the count rate posses through a peak that is believed to be associated with a plane strain-plane stress transition. The effects of instrumentation sensitivity and frequency bandpass are also investigated. The results obtained indicate that acoustic-emission techniques should be suitable for in-service monitoring of a variety of cyclically loaded structures, even in the presence of high background noises.

## Tensile testing of materials at high rates of strain

### Experimental Mechanics (1981) 21: 177-185 , May 01, 1981

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A tension version of the split Hopkinson bar or Kolsky apparatus is developed for conducting tests in tension at high rates of strain up to 10^{3} s^{−1}. A number of aluminum, titanium, and steel alloys tested in tension show increasing degrees of rate sensitivity above 10 to 10^{2} s^{−1}. Tests on 6061-T651 and 7075-T6 aluminum show measurable strain-rate sensitivity in tension at the highest strain rates, although similar tests in compression in the literature show essentially no strain-rate sensitivity. Details of the apparatus and instrumentation and guidelines for its use are presented.

## High-temperature low-cycle fatigue: Survey of british work

### Experimental Mechanics (1968) 8: 309-318 , July 01, 1968

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## Fatigue damage accumulation around a notch using a digital image measurement system

### Experimental Mechanics (2004) 44: 241-246 , June 01, 2004

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A digital image measurement (DIM) system is used to study the plastic damage accumulation around a notch under conditions of low-cycle fatigue. This system incorporates a contrast correlation method to evaluation the level of plastic damage at each point of the studied area from two images acquired before and after the introduction of fatigue deformation. A compact tension specimen of 304 stainless steel with a notch radius of 1 mm is analyzed during the stages of fatigue crack initiation and growth. The results obtained using this measurement system are compared with those attained by means of a recrytallization technique.

## Enhanced sensitivity residual-stress measurements using taper-hole drilling

### Experimental Mechanics (1995) 35: 124-129 , June 01, 1995

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A novel method for enhancing the strain sensitivity of the hole-drilling method for measuring uniform residual stresses is examined. Such enhanced strain sensitivity is important because it improves the accuracy of the residual-stress evaluation. The new method involves enlarging the effective hole size by drilling a reverse taper hole. A simple practical technique for drilling reverse taper holes is described. The strain sensitivity for this new method is compared with that of the conventional hole-drilling method. Experimental results show excellent correspondence with theoretical results. The reasons for the sensitivity improvement are explained.

## A Shear-Corrected Formulation for the Sandwich Twist Specimen

### Experimental Mechanics (2012) 52: 17-23 , January 01, 2012

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The sandwich plate twist test method involves torsion loading of a panel by application of concentrated loads at two diagonally opposite corners and supporting the panel at the other two corners. Compliance measured in this test can be used to extract the shear moduli of monolithic, composite and sandwich plates, and it may also be employed for determination of the twist stiffness, *D*_{66}. Previous studies of the plate twist specimen have shown that classical laminated plate theory does not adequately predict the compliance of sandwich panels with a low density/modulus core, as a result of transverse shear deformation. This work proposes a “shear-corrected” model for accurate prediction of the plate twist compliance by incorporation of the transverse shear stiffnesses of the core. This model was used to extract the transverse shear modulus of a range of low density PVC foam cores from the measured panel twist compliance. Good agreement with published PVC foam core shear modulus values was obtained.

## Biomechanical study of the constitutive laws of vascular walls

### Experimental Mechanics (1974) 14: 440-444 , November 01, 1974

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Static mechanical behaviors of three different arterial walls were examined through changes in external radius due to distending pressure. In order to examine the distensibility of these vessels, distension ratio was defined as the ratio of eternal radius at each pressure to that at zero pressure. Linear relations were observed between the logarithmic pressure and the distension ration, and they were described by on exponential function. Two parameters used in this equation were related quantitatively to the area fraction of elastin or collagen component occupied in the cross section of wall. Stress-strain relation was then determined from their pressure-diameter data by using finite-deformation theory. An exponential function was established between tangential stress and tangenital strain. These results can be used to study the resistance of arterial walls to cardio-vascular disease.

## Photoelastic analysis of the stress field surrounding a fatigue crack

### Experimental Mechanics (1974) 14: 64-68 , February 01, 1974

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A photelastic analysis was carried out on plane polyester specimens containing a fatigue crack, in order to study the effect of plastic yielding around the crack tip on the elastic stress distribution in the vicinity of the crack. In general, results were in good agreement with values calculated for the case of a sharp-tipped crack. However, very near the crack tip, principal stresses obtained experimentally were slightly lower than calculated stresses, probably due to the bluntness of the fatigue crack. Also lines of constant stress tended to move behind the crack tip, in contrast with the calculated stresses, which occurred further forward over the field of investigation.

## An Experimental Technique for Spalling of Concrete

### Experimental Mechanics (2009) 49: 523-532 , June 26, 2009

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The spalling strength of concrete is measured by examining the strain wave profiles in a polymer buffer bar behind the slender concrete bar specimen placed between a large diameter (*Φ*100 mm) Hopkinson bar and the buffer bar. The experimental results indicate that the spalling strength is related to not only the compressive strength of concrete but also the impact velocities (the loading rates). The rate effect of spalling strength mainly results from the different cracking paths in concrete under different impact velocities. However when the input compressive stress to specimen exceeds the threshold required to trigger the compressive damage, the spalling strength decreases due to the evolution and cumulation of compressive damage in concretes. The repeated impact loading experiments indicate that damage plays an important role in the spallation process of concrete. The high speed video of the spalling fracture process shows that multiple spalling fractures may occur in the scab and damage accumulation resulting from stress wave propagation in scab is the main reason for the producing of multiple spallations.

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## Stress waves in pyramids by photoelasticity

### Experimental Mechanics (1968) 8: 289-299 , July 01, 1968

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The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.

## An optical method to assess electromechanical coupling in ferroelectric ceramics

### Experimental Mechanics (2005) 45: 290-294 , June 01, 2005

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A new technique is described, which allows the assessment of elastic and inelastic regions around a macroscopic defect in ferroelectric-ferroelastic ceramics. The accuracy and robustness of the method are demonstrated on a PZT plate with a centered hole subjected to uni-axial compressive stresses. From the electrical potential distribution on the sample surface, the mechanical response of the material is obtained at different load levels.

## Radial Inertia Effects in Kolsky Bar Testing of Extra-soft Specimens

### Experimental Mechanics (2007) 47: 659-670 , September 19, 2007

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Impact responses of extra-soft materials, such as ballistic gelatins and biological tissues, are increasingly in demand. The Kolsky bar is a widely used device to characterize high-rate behavior of materials. When a Kolsky bar is used to determine the dynamic compressive response of an extra-soft specimen, a spike-like feature often appears in the initial portion of the measured stress history. It is important to distinguish whether this spike is an experimental artifact or an intrinsic material response. In this research, we examined this phenomenon using experimental, numerical and analytical methods. The results indicate that the spike is the extra stress from specimen radial inertia during the acceleration stage of the axial deformation. Based on this understanding, remedies in both specimen geometry and loading pulse to minimize the artifact are proposed and verified, and thus capture the intrinsic dynamic behavior of the specimen material.

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## Apparatus for Testing Concrete under Multiaxial Compression at Elevated Temperature (mac2T)

### Experimental Mechanics (2006) 46: 387-398 , June 01, 2006

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This paper describes a new test facility for determining material mechanical properties of structural concrete. The novel facility subjects 100 mm cubic concrete specimens to true multiaxial compression (*σ*_{1} ≠ *σ*_{2} ≠ *σ*_{3}) up to 400 MPa at temperatures of up to 300°C. Forces are delivered through three independent loading frames equipped with servo-controlled hydraulic actuators creating uniform displacement boundary conditions via rigid platens. Specimen deformation is calculated from displacements measured to an accuracy of 10^{−6} m using a system of six laser interferometers. The combination of stiff loading frames, rigid platens, an accurate and reliable strain measurement system and a fast control system enables investigation of the material response in the post-peak range. The in-house developed control software allows complex multi-stage experiments involving (i) load and temperature cycling, (ii) small stress probes and (iii) arbitrary (pre-defined) loading paths. The program also enables experiments in which the values of the control parameters and the execution of the test sequences depend on the response of the specimen during the test. The capabilities of the facility are illustrated in this paper by experiments determining the effects of different heat-load regimes on the strength and stiffness of the material and tests identifying the tangent stiffness matrix of the material and the associated changes in the acoustic tensor under multiaxial compression.

## Determining the contact force during the transverse impact of plates

### Experimental Mechanics (1987) 27: 68-72 , March 01, 1987

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The contact force during the transverse impact of a plate is determined from dynamic strain-gage measurements made on the plate. Experimental results for the impact of an aluminum plate are presented, and comparisons are made with finite-element predictions and measurements from a force transducer.

## Determination of natural frequencies of vibration of a sandwich plate

### Experimental Mechanics (1967) 7: 490-493 , November 01, 1967

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In this paper, an expression is derived for the natural frequencies of vibration of a simply supported sandwich plate. Experimental procedures and results for the subject problem are presented. The experimental data obtained are in good agreement with the theoretical results.

A literature survey^{1, 2} shows that no work has been done on the experimental determination of natural frequencies of vibration of sandwich plates. A general analysis of flexural vibrations of elastic sandwich plates was presented by Yu in Ref. 3. The vibration analysis based upon this theory is, in general, very complicated due to the high order of the equations. It was then simplified^{4} for low-frequency ranges and for ordinary sandwich plates.

## On the dynamic elastic limit

### Experimental Mechanics (1982) 22: 270-276 , July 01, 1982

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The fact that the elastic limit of some solids increases with increasing stress rate has been qualitatively and semiquantitatively established for many decades. Well known experimental difficulties have impeded reliable quantitative measurements of the magnitude or, in some solids, even the existence of such an increase of the elastic limit with stress rate.

The present paper describes a simple method for accurately measuring the dynamic elastic limit in any solid which has a linear-elastic domain at small strain, including high-strength structural metal alloys. This method has the advantages of laboratory simplicity, a minimum of complex assumptions, and a close parallel with the manner in which the quasistatic elastic limit generally is determined.

Although it is subsidiary to the main focus of this paper, evidence is presented here that a knowledge of the dynamic elastic limit firmly established by experiment, can be of considerable value for subsequent research in the continuum mechanics of solids, particularly with respect to the existence and properties of two distinct yield surfaces during impact loading.

## Holographically determined isopachics and isochromatics in the neighborhood of a crack in a glass composite

### Experimental Mechanics (1980) 20: 53-56 , February 01, 1980

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The isochromatic and isopachic fringes are obtained holographically in the neighborhood of a central crack in a tensile, orthotropic glass-composite plate. The general inability to separate the principal stresses or strains from such information alone under anisotropic conditions is discussed, as are the results relative to fracture-mechanics implications.

## An Energy Based Fatigue Life Prediction Framework for In-Service Structural Components

### Experimental Mechanics (2011) 51: 707-718 , June 01, 2011

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An energy based fatigue life prediction framework has been developed for calculation of remaining fatigue life of in service gas turbine materials. The purpose of the life prediction framework is to account aging effect caused by cyclic loadings on fatigue strength of gas turbine engines structural components which are usually designed for very long life. Previous studies indicate the total strain energy dissipated during a monotonic fracture process and a cyclic process is a material property that can be determined by measuring the area underneath the monotonic true stress-strain curve and the sum of the area within each hysteresis loop in the cyclic process, respectively. The energy-based fatigue life prediction framework consists of the following entities: (1) development of a testing procedure to achieve plastic energy dissipation per life cycle and (2) incorporation of an energy-based fatigue life calculation scheme to determine the remaining fatigue life of in-service gas turbine materials. The accuracy of the remaining fatigue life prediction method was verified by comparison between model approximation and experimental results of Aluminum 6061-T6. The comparison shows promising agreement, thus validating the capability of the framework to produce accurate fatigue life prediction.

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## Letter from the technical editor

### Experimental Mechanics (2005) 45: 477 , December 01, 2005

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## Two-dimensional moiré method and grid method using Fourier transform

### Experimental Mechanics (1989) 29: 399-404 , December 01, 1989

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Formerly, the authors presented one-dimensional strain analysis by a moiré method using a Fourier transform. In the present work, the method is extended to two-dimensional strain analysis. The analysis is completely automated by introducing digital image processing. All of the laborious and subjective procedures required in the classical and conventional moiré method, such as separation of the two gratings, fringe-sign determination, fringe ordering and fringe interpolation, are completely eliminated; and objective, fast and accurate analysis can be made.

## Stress concentrations around horizontal circular tunnels

### Experimental Mechanics (1968) 8: 474-478 , October 01, 1968

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The problem of axial variation of stress concentrations at the periphery and normal to the axis of a circular tunnel is solved by means of the three-dimensional photoelasticity technique, under the following conditions: 1.

The center lines of two horizontal tunnels of equal diameter (2*r*) are separated by a distance*K* and include an angle α.

*K* and α assume values of 0, 3*r*, 7/2*r*, 4*r* and 30 deg, 60 deg, 90 deg, respectively.

The tunnels are located in a uniform, uniaxial stress field normal to the axes of the tunnels.

## Development of a measuring system for segmented ship models

### Experimental Mechanics (1989) 29: 101-108 , June 01, 1989

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The use of segmented ship models to test and study various ship responses in model scale poses a challenge to instrumentation and test engineers. In recent years, the authors have developed a segmented ship model to study and trace ice loads acting on the ship hull. The model contains three segments at the bow. Each segment is supported at multiple points which enable the resolution of the location, magnitude, and direction of the external loads. The typical segment support system consists of four vertical, two transverse, and one longitudinal support points with uniaxial compression pression transducers. Stabilization of the segment is achieved by using three specially designed tension links acting in the vertical, transverse and longitudinal directions, respectively. The system is subjected to several levels of calibration which include individual transducer calibration, calibration using internal loading applied by the tension links, external calibration using a specially designed and built calibration rig capable of exerting normal and inclined loads, and calibration of the effects of buoyancy changes in a floating model. The results of calibration and ice-breaking tests indicate that position prediction of the external load can be made within 20 mm. The normal load of less than 100 Newtons can be determined within a few percentage points but the frictional load magnitude and direction are found to be subject to greater errors particularly for low friction factors of the order of 0.1.

## A simplified optical method for measuring residual stress by rapid cooling in thermosetting resin strip

### Experimental Mechanics (1986) 26: 185-192 , June 01, 1986

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This paper presents a simplified optical method for measuring the residual stresses by rapid cooling in thermosetting resin strips. First, the fundamental equations for calculating the residual stress from the residual birefringence were obtained by the linear photoviscoelastic theory. The specimens were then subjected to rapid cooling. After rapid cooling, the residual stress was measured by two methods, the simplified optical method mentioned above and the well-known layer-removal method. The effectiveness of the simplified optical method was discussed by comparing results of the two methods.

## Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

### Experimental Mechanics (2010) 50: 1313-1321 , December 09, 2010

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In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at *α* < 15°, forming a small separation bubble, and full separation occurs at *α* ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at *α* ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.

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## Optical strain determination at transient high temperatures in stainless steel

### Experimental Mechanics (1964) 4: 320-327 , November 01, 1964

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Type 304 stainless-steel plates 0.24×2.25×4 in. in size were subjected to stagnation heating in an oxyacetylene-flame apparatus. Transient thermal strains at temperatures up to 2000°F were measured with a water-cooled Tuckerman optical strain gage shielded from heat transfer by a cooled radiant-heat shield. The general equations of thermoelasticity are used for a flat homogeneous plate which is subjected to a particular transient three-dimensional temperature distribution. The optically measured strains on the unheated surfaces of the specimens were in close agreement with the thermal strains from the analytical solution using experimentally obtained temperature distributions in the specimens.

## Experimentally determined stress-intensity factors for single-edge-crack round bars loaded in bending

### Experimental Mechanics (1978) 18: 280 , July 01, 1978

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## Photoelastic stress analysis of an elliptical hole in a thick plate subjected to uniform in-plane compressive Loading

### Experimental Mechanics (1985) 25: 105-114 , June 01, 1985

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A three-dimensional photoelastic analysis was conducted to determine the stress distribution and concentration around the periphery of a centrally located elliptical hole in a plate of finite thickness. The edge of the plate was subjected to a uniformly distributed compressive uniaxial in-plane load. The principle of superposition was employed to study the effect of uniform biaxial loading.

Elliptical holes with five different major/minor axis ratios (β) ranging from 1.0 to 2.64 were investigated. Among the results of this study, it was established that the variation of the principal stresses at the edge of the hole is not linear across the plate thickness. It was also found that in loading the plate in a direction parallel to the major axis of the ellipse, the value of the maximum tangential principal stress (σ_{η}) occurs in a plane other than the middle plane of the plate. However, in loading the plate in a direction either parallel or perpendicular to the major axis, the maximum transverse stress (σ_{z}) occurs at the middle plane. In addition, the maximum value of (σ_{z}) was about 20 percent of the maximum value of the tangential stress for all models tested. Furthermore, the effect of the bixial loading has reduced the value of the maximum tangential stress at the periphery of the hole as compared with uniaxial loading.

As a three-dimensional theoretical solution does not exist for this problem, the present findings were correlated with the well established two-dimensional solutions.

## Recent research activities in experimental mechanics in China

### Experimental Mechanics (1982) 22: 171-173 , May 01, 1982

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A brief review is presented of the recent activities in the field of experimental mechanics in the People's Republic of China.

The current research work covers the following subjects: (1) photoelastic phenomena, such as the classical three-dimensional photoelasticity, the scattered-light technique, birefringent coatings, birefringent materials; (2) holography, holographic interferometry, speckle interferometry and their applications; (3) moiré method; (4) strain-gage techniques and strain indicators.

## The dependence of yield stress on strain rate as determined from ball-indentation tests

### Experimental Mechanics (1966) 6: 87-92 , February 01, 1966

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A ball-indentation experiment was conducted to explore the possibility of using this test for the investigation of strain-rate dependence of yield properties of materials. The initial velocities of indentation used were between 0.0002 and 3 ips. Force and depth of penetration were measured continuously during a test. Using these and the results given in a previous report, the dependence of yield pressure of the indentation test on penetration velocity is shown for a range of velocities from 0.0002 to 300 ips. Results are presented for annealed C1018 steel, annealed 1100 F and annealed 6061-T6 aluminums. For all materials tested, the dependence of yield stress on strain rate seems to be derivable from the ball-indentation results by using Tabor's empirical formulas and an equation relating strain rate and velocity of penetration. The increase of yield pressure over the range of indentation velocities is 100 percent for steel, 30 percent for 1100 aluminum and 20 percent for 6061 aluminum.

## Surface topography by multisource moiré patterns

### Experimental Mechanics (1968) 8: 82-87 , February 01, 1968

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Moiré patterns produced by interference of a series of periodically arranged linear light sources with a line-specimen grating of similar pitch are located at a plane parallel to the sources and the specimen grating and at some distance away from these planes. A transparent or reflecting specimen located at a distance from the specimen grating distorts the image of the multisource projected on the specimen grating due to its surface irregularities and forms a moiré pattern. This pattern yields the partial-slope contours of the topography of the specimen along a direction normal to the lines of the grating. Two such contour patterns taken at mutually perpendicular directions are sufficient to yield the complete topographic picture of the surface.

The method was used for determining gradients of thickness variations in two-dimensional specimens due to lateral contraction. The technique is highly accurate in determining the values of thickness in such cases, since the integration of the slope of thickness variation along any traverse of the specimen is a steady and accurate process.

## The Potential of MEMS for Advancing Experiments and Modeling in Cell Mechanics

### Experimental Mechanics (2009) 49: 105-124 , January 20, 2009

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Response to mechanical stimuli largely dictates cellular form and function. A host of extraordinary yet unexplained responses have been identified within the hierarchical cell structure. As experimental and model-based investigations in cell mechanics advance, the underlying structure-function mechanisms dictating these responses emerge. Here we explore the potential of microelectromechanical systems (MEMS) for advancing understanding of cell mechanics. To motivate the discussion, existing experimental techniques are summarized. Interrelated model-based approaches, which aim to interpret or predict observed results, are also outlined. We then focus on a representative set of MEMS-based devices designed for investigations in cell mechanics and point to the fact that, while these devices have yet to maximize their functionality through higher levels of sensor/actuator integration, they are highly complementary to existing techniques. In closing, novel MEMS sensor and actuator schemes that have yet to materialize in this field are discussed to motivate the next generation of MEMS for investigations in cell mechanics.

## On the measurement of residual-stress gradients in aluminum-alloy specimens

### Experimental Mechanics (1978) 18: 269-276 , July 01, 1978

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The assessment or prediction of fatigue life or strength improvement due to residual stresses requires knowledge of their magnitude and distribution. This paper presents an extension of the modified hole-drilling technique (MHDT) to the measurement of stress gradients in a biaxial-residual-stress field. This is achieved by taking a series of ‘point’ measurements and evaluating the stress profile with due consideration to the effects of hole location, the interaction between holes and the redistribution of stress due to hole drilling.

An application to the measurement of residual stresses induced in 2024-T3 aluminum-alloy specimens by edge-dimpling technique is described and the method of compensation for the effect of redistribution of stress is explained. The experimental results are shown to be in good agreement with those obtained elsewhere by an analytic-numerical solution.

## Authors' closure

### Experimental Mechanics (1965) 5: 127 , April 01, 1965

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## Review of Experimental Investigations on Compressibility of Arteries and Introduction of a New Apparatus

### Experimental Mechanics (2012) 52: 895-902 , September 01, 2012

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Arterial tissue incompressibility is a common notion used in numerical simulations and analytical studies. However, only a few experimental investigations have been performed to characterize arterial tissue incompressibility. Such studies have used various approaches, ranging from the initial purely mechanical measurements in 1954 to the more recent image-based analyses (2004). The results of these studies are rather diverse because different arteries have been tested (human/dog/mouse, carotid/pulmonary/iliac). This has therefore made accurate comparisons between studies challenging. In the first part of this report, a review of the experimental investigations on the compressibility of arteries is presented, with particular focus on the test rigs that have been used. In the second part of this report, a novel simple apparatus to test samples under physiological or supra-physiological conditions is described. Recommendations for a testing procedure are also provided. Finally, preliminary results on porcine renal arteries indicate significant levels of compressibility are possible (>10 %), thereby suggesting the need for further investigation.

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## On residual-stress measurements in light truck wheels using the hole-drilling method

### Experimental Mechanics (1985) 25: 54-59 , March 01, 1985

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An investigation of the effect of drilling speed, milling-cutter wear, drilling mode, and applied drilling force on residual-stress measurements in a light truck wheel using a milling guide manufactured by Measurements Group, Inc. is described. The milling variables chosen were used to minimize the residual stresses induced by the introduction of a hole into the wheel material. An improved hole-drilling procedure was developed and found to be successful in the residual-stress measurements for a light truck wheel.

## Study of three-dimensional deformation of a pallet using phase-shiff shadow moiré and finite-element analysis

### Experimental Mechanics (2005) 45: 9-17 , February 01, 2005

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We present the results of a comparative study on the static deformation of a pallet, made from oil-palm fiberreinforced composite material, using the phase-shift shadow moiré method and finite-element analysis (FEA). The pallet was designed and analyzed using a commerical software package. The effect of various joint types on the deformation profile was studied to obtain a simplified model to represent the actual design. A one-fifth scale model of the pallet was fabricated and the deformation due to static loading was measured using the phase-shift shadow moiré method. The comparison between the measurement and FEA results on the deformed profile showed a maximum difference of 13.7% at the center of the some of the deck boards, but a smaller difference at other deck boards. The FEA results also produced a larger deformation gradient compared to the measurements.

## A photoelastic-model study of stress distribution and rock fracture around mining excavations

### Experimental Mechanics (1969) 9: 75-81 , February 01, 1969

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A three-dimensional photoelastic-model study of two horizontal mining excavations with a central pillar is described. Details of experimental techniques used are given and stress distributions, rock-fracture initiation zones and the directions of subsequent fracture propagation around these excavations are determined. It is shown that the techniques adopted for this investigation offer realistic means for comparative design studies of best shape and layout of mining excavations.

## Experimental critical loads for perforated square plates

### Experimental Mechanics (1968) 8: 69-74 , February 01, 1968

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Experimentally determined critical loads are presented for simply supported square plates with a circular central hole under the action of uniform edge displacements for hole diameters varying up to seventenths the dimension of the plate. The critical load is defined as the inflection point on the load-deflection curve as measured by a set of dial gages at the edge of the hole. Least-squares-curve fitting techniques are used for reducing all experimental data and the entire set of computations is carried out on the electronic digital computer. Finally, it is shown that the experimental results agree well with the theoretical critical loads as determined by the Ritz energy method.

## Experimental and analytical investigation of the modified wyoming shear-test fixture

### Experimental Mechanics (1994) 34: 10-15 , March 01, 1994

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The interaction between the isopescu shear-test specimen and the modified Wyoming shear-test fixture was investigated. This involved three areas of study. First, strip strain gages were applied to the specimen contact surfaces to measure strains induced by the fixture. While it has generally been assumed that the fixture induces an asymmetric load into the specimen, the measured strains indicated a nonasymmetric loading. Second, the effect of an out-of-plane moment, externally applied to the fixture, on gage section shear strains was observed. The shear strains observed were small leading to the conclusion that the fixture is very resistant to out-of-plane moments. Finally, the effect of fixture misalignment on the observed shear modulus was determined. The results indicate that the observed shear modulus increased significantly for slight amounts of misalignment. Therefore, experimental techniques should be modified to include a check for misalignment. Beyond this, it is suggested that the fixture design be modified to prevent misalignment and to achieve an asymmetric loading of the specimen.

## An Energy-Based Torsional-Shear Fatigue Lifing Method

### Experimental Mechanics (2012) 52: 705-715 , September 01, 2012

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An energy-based fatigue-life prediction framework for the determination of full-life, remaining-life, and critical-life of in-service structures subjected to torsional-shear loading has been developed. This framework is developed upon the existing foundation of energy-based fatigue models crafted for the axial, uniaxial bending, and transverse-shear loading cases, which state: the total strain energy density accumulated during both a monotonic event and a cumulative cyclic process is the same material property. The modified energy-based torsional-shear fatigue-life prediction framework is composed of the following entities: (1) the development of a torsional-shear fatigue testing procedure capable of assessing strain energy density per cycle in a pure shear stress state and (2) the determination of the remaining-life and critical-life of in-service aluminum (Al) 6061-T6 structures subjected to shear fatigue through the application of the energy-based prediction method. Experimental data was shown to be affected by load-frame misalignment which was estimated and successfully incorporated into the validation results. Close correlation between adjusted experimental results and the full-life and critical-life predictions stemmed from a 3-to-2 shear-to-axial biaxial loading assumption, which was supported by crack path comparisons. Results of the study effectively demonstrated the versatility of the energy-based lifing method.

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## Experimental investigation of longitudinal wave propagation in an elastic rod with coulomb friction

### Experimental Mechanics (1970) 10: 137-144 , April 01, 1970

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This paper presents the experimental results obtained from the propagation of a compression stress wave generated by the longitudinal impact of two cylindrical elastic rods. One of these rods is subjected to a uniformly distributed coulomb-friction force. In order to determine the stress-wave shape and the decay rate, the rod is subjected to longitudinal impact for different values of coulomb friction. As the stress wave propagates along the rod, it is measured at strain-gage stations located on the stationary rod.

In order to correlate the experimental results, the solution of the modified wave equation with coulomb friction is obtained for the longitudinal impact of two semi-infinite rods.

## A Simple Methodology to Measure the Dynamic Flexural Strength of Brittle Materials

### Experimental Mechanics (2011) 51: 1325-1334 , October 01, 2011

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A simple methodology is proposed for measuring the dynamic flexural strength of brittle materials. The proposed technique is based on 1-point impact experimental setup with (unsupported) small beam specimens. All that is needed is a measurement of the prescribed velocity as a boundary condition and the fracture time for a failure criterion, both to be input in a numerical (FE) model to determine the flexural strength. The specimen was modeled numerically and observed to be essentially loaded in bending until its final inertial failure. The specimen’s geometry was optimized, noting that during the very first moments of the loading, the specimen length does not affect its overall response, so that it can be considered as infinite. The use of small beam specimens allow large scale testing of the flexural strength and comparison between static and dynamic loading configurations. Preliminary experiments are presented to illustrate the proposed approach.

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## Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices

### Experimental Mechanics (2003) 43: 256-268 , September 01, 2003

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The mechanical properties of ultrananocrystalline diamond (UNCD) thin films were measured using microcantilever deflection and membrane deflection techniques. Bending tests on several free-standing UNCD cantilevers, 0.5 μm thick, 20 μm wide and 80 μm long, yielded elastic modulus values of 916–959 GPa. The tests showed good reproducibility by repeated testing on the same cantilever and by testing several cantilevers of different lengths. The largest source of error in the method was accurate measurement of film thickness. Elastic modulus measurements performed with the novel membrane deflection experiment (MDE), developed by Espinosa and co-workers, gave results similar to those from the microcantilever-based tests. Tests were performed on UNCD specimens grown by both micro and nano wafer-seeding techniques. The elastic modulus was measured to be between 930–970 GPa for the microseeding and between 945–963 GPa for the nanoseeding technique. The MDE test also provided the fracture strength, which for UNCD was found to vary from 0.89 to 2.42 GPa for the microseeded samples and from 3.95 to 5.03 for the nanoseeded samples. The narrowing of the elastic modulus variation and major increase in fracture strength is believed to result from a reduction in surface roughness, less stress concentration, when employing the nanoseeding technique. Although both methods yielded reliable values of elastic modulus, the MDE was found to be more versatile since it yielded additional information about the structure and material properties, such as strength and initial stress state.

## An experimental study of the elasto-plastic behavior of certain grid frameworks

### Experimental Mechanics (1965) 5: 120-125 , April 01, 1965

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An experimental investigation of the elastoplastic behavior of certain torsionless grid frameworks is presented. The purpose of the test program was to determine the significance of the stiffness criterion in the evaluation of collapse loads of interconnected beam systems. The load-deflection relationships in the various members, the sequence of hinges and moment redistribution are studied. The test values are used to verify the theoretical values obtained by the application of the simple plastic theory.

## The Evolving Role of Experimental Mechanics in 1-D Nanostructure-Based Device Development

### Experimental Mechanics (2011) 51: 1-9 , January 14, 2011

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Future generations of transistors, sensors, and other devices maybe revolutionized through the use of one-dimensional nanostructures such as nanowires, nanotubes, and nanorods. The unique properties of these nanostructures will set new benchmarks for speed, sensitivity, functionality, and integration. These devices may even be self-powered, harvesting energy directly from their surrounding environment. However, as their critical dimensions continue to decrease and performance demands grow, classical mechanics and associated experimental techniques no longer fully characterize the observed behavior. This perspective examines the evolving role of experimental mechanics in driving the development of these new devices. Emphasis is placed on advances in experimental techniques for comprehensive characterization of size effects and their coupling, as well as assessment of device-level response.

## Use of mixed-mode stress-intensity algorithms for photoelastic data

### Experimental Mechanics (1984) 24: 300-307 , December 01, 1984

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A generalization of irwin's method and a new algorithm, called ‘quadratic,’ are proposed for the extraction of mixed-mode stress-intensity factors (SIF) in three-dimensional cracked-body problems. These new algorithms are evaluated along with the existing ones of Smith, Sanford-Dally and Theocaris-Gdoutos, and their SIF results compared.

It is shown that all these algorithms deliver SIF values in good agreement and that they all can be applied reliably to near-tip photoelastic data.

## Techniques for measuring stress-strain relations at high strain rates

### Experimental Mechanics (1966) 6: 395-402 , August 01, 1966

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The qualitative dependence of the mechanical behavior of some materials on strain rate is now well known. But the quantitative relation between stress, strain and strain rate has been established for only a few materials and for only a limited range. This relation, the so-called constitutive equation, must be known before plasticity or plastic-wave-propagation theory can be used to predict the stress or strain distribution in parts subjected to impact stresses above the yield strength.

In this paper, a brief review of some of the experimental techniques for measuring the stress, strain, strain-rate relationship is given, and some of the difficulties and shortcomings pointed out. Ordinary creep or tensile tests can be used at plastic-strain rates from 10^{−8} to about 10^{−1}/sec. Special quasi-static tests, in which the stress- and strain-measuring devices as well as the specimen geometry and support have been optimized, are capable of giving accurate results to strain rates of about 10^{2}/sec. At higher strain rates, it is shown that wave-propagation effects must be included in the design and analysis of the experiments. Special testing machines for measuring stress, strain and strain-rate relationships in compression, tension and shear at strain rates up to 10^{5}/sec are described, and some of the results presented. With this type of testing machine, the analysis of the data requires certain assumptions whose validity depends upon proper design of the equipment. A critical evaluation of the accuracy of these types of tests is presented.

## Comparison of measurement of piston deformation using holographic interferometry and finite elements

### Experimental Mechanics (1993) 33: 336-342 , December 01, 1993

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Holographic interferometry was used to measure the thermal expansion of a diesel-engine piston and the results are compared with those predicted by a finite-element model. Various assumptions were made in the generation of the model and the holographic results provided a means of assessing the effects of these assumptions on the deformed profile of the piston. A holographic rig has been developed that enables one to measure simultaneously the deformation on the front and rear surfaces of the piston using a single holographic plate and hence detect any body displacement. A simple ‘mirror’ concept is introduced that can be used to measure in-plane and out-of-plane displacements simultaneously. The holographic results showed expansion values of ten-percent greater than the predictions of the model at midskirt level of the piston. A closer agreement of the results were observed at other levels of the skirt.

## Holographic velocimetry for flow diagnostics

### Experimental Mechanics (1988) 28: 402-408 , December 01, 1988

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Currently, there are a number of flow diagnostic tools available for the evaluation of fluid dynamic systems. In spite of its great potential, holographic velocimetry is one technique which has not been widely used. It does, however, have great potential in this area due to its inherent three-dimensionality. As demonstrated in this study of fully developed turbulent flow in a pipe, full three-dimensional mapping can be achieved at any instant in a flow cycle. Comparisons of holographic results with analytical predictions and laser-Doppler-anemometry (LDA) measurements demonstrate the accuracy of the technique as well as some of its advantages and disadvantages relative to LDA. Although relatively poor spatial resolution is obtained, the fact that holographic velocimetry is both an instantaneous and full volume measuring tool makes it useful for a range of complex and high-speed flow-measurement applications.

## On the history of some recent measurements described in Experimental Mechanics

### Experimental Mechanics (1977) 17: 359-360 , September 01, 1977

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## Characterization of the Grain-Level Mechanical Behavior of Eglin Sand by Nanoindentation

### Experimental Mechanics (2014) 54: 871-884 , June 01, 2014

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Characterization was made on the structure and grain-level mechanical behavior of Eglin sand (Quikrete #1961 sand quarried in Pensacola, FL). The as-received assorted sand was sorted to six grain sizes: 0.60 mm, 0.50 mm, 0.42 mm, 0.30 mm, 0.212 mm, and 0.15 mm. The sand chemical constituents and crystalline structures were determined using energy dispersive X-ray spectroscopy, X-ray diffraction and transmission electron microscopy. The Young’s modulus and hardness were determined using nanoindentation with a Berkovich tip, and the fracture toughness was measured using a cube-corner tip. The median Young’s modulus, hardness and fracture toughness were determined as 90.4 GPa, 12.8 GPa and 2.32 MPa⋅m^{0.5}, respectively. The mechanical properties were analyzed statistically and the parameters of the Weibull distribution were determined. The grains show highly ductile behavior under nanoindentation due to confinement by high pressure induced by Berkovich tip. An inverse problem solving approach using finite element method (FEM) with the consideration of the Ramberg-Osgood model was used to determine the stress–strain relationship for individual sand grains.

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## Ultimate tests of thick shells

### Experimental Mechanics (1974) 14: 290-296 , July 01, 1974

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Experimental investigation of the elastoplastic and ultimate load response of thick hemispheres with cylindrical skirts is presented. A shell with a hinged boundary condition, loaded symmetrically, and one having a fixed edge, with unsymmetric lateral load, were tested. Electrical-resistance bonded foil strain gages and photoelastic surface coatings were used in monitoring the strain response while spring-activated dial gages were used in recording displacements. Both panchromatic and color still photographs were utilized in observing the photoelastic patterns, while the failure mode of one model was recorded by means of high-speed motion pictures.

## A new application of differential interferometry for stress analysis

### Experimental Mechanics (1984) 24: 277-285 , December 01, 1984

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In the past, differential interferometry has found interesting applications in gas dynamics. The gradients of density could be measured in gas flows. Now, a first trial is made to extend this method to the experimental treatment of stress problems. A Wollaston prism with polarizing elements is used in the optical arrangement. This prism combines two beams of light which have penetrated the model at locally separated points. A field of interference fringes can be produced behind the Wollaston prism. The deflections of the different conjugated light beams, which are caused by the deformed elements of the model, lead to a shifting of the interference fringes. A Stress Differential-interferometer Law is derived theoretically in order to interpret the optical data According to this theory, the optical effect caused by the deflection in this arrangement is proportional to the gradient of the sum of principal stresses. A calibration test is performed by using a circular disk, this method is applied to a circular ring for measuring the stress gradients. Under special conditions, interference fringes could be produced which represent the loci of equal stress gradient. Plexiglas plane models are loaded diametrically by single loads. The experimental results verify the statements of the developed theory.

## Strain-field investigations with plane diffraction gratings

### Experimental Mechanics (1965) 5: 233-238 , July 01, 1965

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The development of means for producing small, separate, plane diffraction gratings as integral parts of the surfaces of flat metal specimens has led to modification of the method of Bell and to the investigation of strain fields by study of diffraction phenomena. Choice of a particular diffraction-strain relationship and the use of master gratings in conjunction with diffraction gratings to be used as strain gages permits use of simple optical instrumentation. The diffraction phenomena from multiple gages at the same orientation may be photographed simultaneously during loading for subsequent analysis, and instrumentation in the form employed permits resolving strain increments of magnitude 0.0008 in the range 0.0030 to 0.030.

## A sensitive thrust-measuring device

### Experimental Mechanics (1975) 15: 365-368 , September 01, 1975

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A centilevered beam with mounted strain gages is used to indirectly measure the velocity of a stream of drops by measuring the thrust produced by this stream. A design procedure is explained and implemented to determine a suitable geometry for this device. Sensitivity, frequency response and fragility are the factors considered in the design. Laboratory-test results show the usefulness of this device.

## Strain distribution measurement in a coarse-grained titanium alloy

### Experimental Mechanics (1993) 33: 320-325 , December 01, 1993

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Strain distributions in a coarse-grained titanium alloy under tensile loading were measured using a moiré-interferometry method. Analysis of the interferograms show that variations of more than 25 percent away from the mean level are present, most noticeably in the direction transverse to the loading axis.

## Monitoring Fatigue Crack Growth in Compact Tension Specimens Using Piezoelectric Sensors

### Experimental Mechanics (2008) 48: 247-252 , March 19, 2008

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This paper aims to report the results of an experimental study on the application of piezoelectric dynamic strain sensors for crack length measurement in fracture mechanics specimens. The performance of the piezoelectric sensors was assessed through fatigue crack propagation tests in compact tension (CT) specimens. Sensors of polarized polyvinilidene fluoride polymer (PVDF) were bonded to the back face of CT specimens, in the same manner as the electrical resistance strain gages installed for crack length measurement in the back face strain technique. The results showed that, mainly due to its high sensitivity to strain, the use of piezoelectric materials as dynamic strain sensors can contribute to the experimental investigation in the field of fracture mechanics.

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## Poisson's ratio variations in concrete

### Experimental Mechanics (1976) 16: 154 , April 01, 1976

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## Effects of thermal impact on a thin spherical cap

### Experimental Mechanics (1962) 2: 303-306 , October 01, 1962

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Because of the importance of thin shells as structural elements in all aircraft and missile vehicles, the response of the shell to transient thermal loads is of extreme interest. At very high heating rates, as can be produced by the absorption of intense radiation energy, dynamic mechanical response of the structure may be produced. This paper describes a brief exploratory investigation of the effects of short-duration, high-intensity thermal radiation exposure of a thin-shell structure. Exposure of a spherical cap in a arc-image furnance failed to produce buckling under the test conditions. Rapid thermal rupture, however, did result in interesting failure surfaces.

## Phase-measuring profilometry using sinusoidal grating

### Experimental Mechanics (1993) 33: 117-122 , June 01, 1993

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When a sinusoidal amplitude grating is projected on an object, the surface-height distribution of the object is translated to a phase distribution of the deformed grating image. In this paper, two algorithms developed for phase acquisition of such images are presented and compared. The phase-acquisition algorithms are sufficiently simple that high-resolution phase maps using a highresolution area detector array can be generated in a short time. The average detection error is within 30 mm, which can be reduced further by changing the period of the projected grating and the angle offset between the projection and the observation optics.

## Balanced Biaxial Testing of Advanced High Strength Steels in Warm Conditions

### Experimental Mechanics (2013) 53: 1681-1692 , November 01, 2013

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The main purpose of the present work is to measure the stress–strain behavior under warm conditions (about 100 °C) of advanced high strength steel (AHSS) sheets up to large strains compared to uniaxial tension. The test equipment consists of two main parts, i.e., a hydraulic bulge tester and a heating device. A mechanical system is attached to the test equipment for measuring the membrane stress and thickness strain at the bulge pole. The stress–strain curves were measured for three kinds of AHSS sheets with the proposed test method for various initial temperatures (10, 50 and 100 °C). The proposed method does not provide isothermal stress–strain curves because the specimen temperature increases during the test due to the effect of deformation-induced heating. A numerical scheme using thermo-mechanical finite element (FE) simulations is suggested to deconvolute the isothermal stress–strain curves.

## Moiré interferometry at VPI & SU

### Experimental Mechanics (1983) 23: 203-210 , June 01, 1983

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A relatively easy technique for producing high-frequency gratings on specimens extends moiré techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moiré interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.

## A new look at the bending strength of gear teeth

### Experimental Mechanics (1980) 20: 217-225 , July 01, 1980

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This paper reports on an extensive two-dimensional photoelastic study of the basic deformation behavior of gear teeth under load. Limitations of existing bending-strength design procedures are used to formulate a test program which considers the magnitude of the critical root-fillet stresses, the effects of varying the load position on the flank, the effects of friction forces at contact and the relationship between bending and shearing deformations. Particular interest is devoted to a study of the observed movement of the maximum-stress position around the fillet as load moves up the tooth flank and to the associated variation in stress-concentration factors (around the fillets) due to radial, bending and shear loads. Note is also made of the problems associated with observed ‘proximity effects’ and of the procedures carried out in an attempt to qualify the nature of the effect.

The results of the program have been used to, explain certain anomalies observed in earlier three-dimensional photoelastic model tests^{1.7} and reference is made to the development of a new design procedure for the bending strength of helical gears.

## Experiments on tension measurement in manufacturing processes

### Experimental Mechanics (1982) 22: 106-110 , March 01, 1982

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Today's demand to preserve energy, to optimally utilize limited resources and to still increase quality calls for more-precise measurements in virtually all manufacturing processes.

One such field is the measurement of tension in, for instance, paper machines, printing presses, machines for the manufacturing of rubber, plastics, fabrics, etc.

Newspaper-printing presses produce today an impressive number of paper breaks. Measurement of the web tension at critical positions could give an early warning when the tension in the paper is growing to dangerous values.

In a paper macnine, it is necessary to introduce webtension measurements at many positions to optimize quality, to prevent paper breaks and to reduce wear.

Measurements have been carried out with a particular force transducer that can be easily built into an existing, as well as a new machine. Several installations, mainly in paper machines and newspaper-printing presses, show that

- the number of paper breaks are drastically reduced

- a more-uniform quality of the paper can be achieved

- the lifetime of machine parts, such as wires and felts, can be increased.

## Separation of the isochromatics-isopachics patterns by use of retarders in holographic photoelasticity

### Experimental Mechanics (1976) 16: 146-150 , April 01, 1976

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By double passing the object beam in photoelastic-holographic interferometry, separation of the isochromatic-isopachic patterns can be achieved. The object beam must then interact with a suitable polarizing element between the first and second pass.

This problem is analyzed using Jones' matrices. This analysis shows that, apart from active and passive rotators, half-wave and quarter-wave retarders can also be used as polarizing elements. Possible experimental arrangements of the method are reviewed and experimental verifications are presented.

## Measurement of residual stresses by the hole-drilling method: General stress-strain relationship and its solution

### Experimental Mechanics (1990) 30: 33 , March 01, 1990

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## A Linearized Method to Measure Dynamic Friction of Microdevices

### Experimental Mechanics (2009) 49: 395-401 , June 01, 2009

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We propose and evaluate a linearized method to measure dynamic friction between micromachined surfaces. This linearized method reduces the number of data points needed to obtain dynamic friction data, minimizing the effect of wear on sliding surfaces during the measurement. We find that the coefficient of dynamic friction is lower than the coefficient of static friction, while the adhesive pressure is indistinguishable for the two measurements. Furthermore, after an initial detailed measurement is made on a device type, the number of trial runs required to take the data on subsequent devices can be reduced from 200 to approximately 20.

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## Stress analysis by combination of holographic interferometry and boundary-integral method

### Experimental Mechanics (1983) 23: 196-202 , June 01, 1983

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The paper describes a hybrid experimental and numerical method analysis of bodies. It consists of the experimental method of double-aperture speckle interferometry and the boundary-integral method. The interference patterns allowing evaluation of the displacement vector are obtained by the speckle interferometry. The boundary displacements obtained experimentally are conveniently used for the calculation of stresses in the body by the boundary-integral method. Some examples bear witness of the effectiveness and accuracy of the hybrid technique.

## Service-simulation tests to determine the fatigue life of outside-diameter-notched thick-wall cylinders

### Experimental Mechanics (1982) 22: 96-100 , March 01, 1982

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Simulation specimens were used to model the fatigue behavior of outside-diameter-notched internally pressurized cylinders of alloy steel. Results from continuum mechanics and finite-element analyses are described for use in selection of simulation-test conditions. The effects of notch depth and residual stress on fatigue life are determined from the simulation tests.

## The rapid deposition of moiré grids

### Experimental Mechanics (1971) 11: 375-377 , May 01, 1971

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This technical note describes a simple method for using the nickel meshes with up to 2000 lines/in. (lpi) as masks for producing moiré grids. The main advantages, when compared with other methods, are the substantial increase in the speed of application and the precision of the reproduced grid.

## Strain-history effect on isotropic and anisotropic plastic behavior

### Experimental Mechanics (1972) 12: 264-271 , June 01, 1972

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An experimental investigation was performed to evaluate the effect of strain history on an initially isotropic material. A hot-rolled 2.5-in.-diam bar of SAE 1045 steel provided all the test specimens. Axial and circumferential compression data indicated that the steel was isotropic. Additional tension and torsion data indicated that the steel was an isotropic-hardening von Mises material; this was also confirmed by proportionate loading of thin-walled cylinders such that the ratio of axial to circumferential stresses was either 0, 1/2, 1, 2 or ∞. Two additional sets of cylinders were preloaded either in simple axial tension or as closed-ended cylinders to an effective plastic strain of 0.006 before they were proportionately loaded. The preloading had a pronounced effect on yield surfaces for reloading if the effective plastic strain on reloading was only slightly greater than that for the preloading. The effect of preloading on the yield surfaces was small when the effective plastic strain was three to four times that for the preloading. Hill's anisotropic theory was used to predict stress-strain relations for several of the reloaded cylinders. Good agreement was obtained between theory and experiment.

## Photoelastic determination of stresses in the tube plate of a 70-mw steam generator

### Experimental Mechanics (1969) 9: 449-455 , October 01, 1969

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This article describes the examination, by three-dimensional photoelasticity, of the tube plate of a sodium steam generator. The tube plate is flat on the side of the tube bundle (121 tubes) and spherical (concave) on the other side.

The photoelastic model was made by precision casting, there being no glued joints at the points which are important from the point of view of stresses, such as the tube-tube plate junctions.

Both the stress distribution along important sections and the stress concentrations in different types of tube-tube plate junctions due to the internal pressure were determined.

The investigation described in this article was carried out in the framework of the Association—Euratom TNO/RCN on Fast Reactors, on behalf of the TNO—Neratoom Sodium Technology Project.

## Dynamic-stress-data management for aeromechanical testing of turbomachinery

### Experimental Mechanics (1977) 17: 207-212 , June 01, 1977

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Aeromechanical testing of turbine engines is an important benchmark in the development of today's modern aircraft propulsion systems, and detailed dynamic-strain gaging of the engine's compressor and turbine are required to provide insight to the integrity of these engine components. Comprehensive real-time visualization of the compressor/turbine dynamic stress is necessary for safe engine operation and rapid posttest data-editing/processing systems are essential for day-to-day test-program direction.

This paper reviews the evolution of on-line data-monitoring and posttest data-processing/analysis techniques that have been utilized at the Arnold Engineering Development Center to support dynamic strain-gage test programs. The transition from hardwire single-channel analog analysis equipment to the incorporation of digital computers for aiding on-line data monitoring, bulk processing of test data, and rapid editing/analysis of test results is discussed. The present on-line monitoring and posttest processing/analysis systems are presented, and refinements for improving the on-line data monitoring and posttest data-processing capabilities are discussed.

## Electronic techniques in isodyne stress analysis: Part 1. Basic relations

### Experimental Mechanics (1997) 37: 33-38 , March 01, 1997

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The purpose of the study was to develop electronic techniques for collecting, processing and evaluating information in experimental isodyne stress analysis. The original technique involved chemical photography recording and manual evaluation of the normal and shear isodyne functions and their derivatives, which are proportional to the stress components. One objective of the reported study was to show that it is feasible to reliably reconstruct isodyne surfaces which contain information on the internal force intensities and the components of the stress tensor. It is shown that the new technique satisfies all the theoretical conditions and constraints imposed by the theory of the analytical and optical isodynes. Thus another objective of the reported study was to demonstrate that the isodyne stress analysis allows one to obtain reliable data on the actual three-dimensional stresses in a cost-effective manner. The procedure developed to date and presented in the paper is a hybrid electronic-manual procedure. It involves electronic recording of the isodyne fields, manual determination of the isodyne orders in chosen sections, and electronic determination of the indicated and load-induced isodyne functions and of the isodyne surfaces. It is shown that the developed techniques are more reliable, accurate and cost-efficient than the traditional techniques of photomechanics. Pertinent data are illustrated by examples presented in Part 2.

## A simple method for determining principal-stress directions in embedded-polariscope models

### Experimental Mechanics (1970) 10: 390-393 , June 01, 1970

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A disadvantage of the embedded-polariscope method is the inability to observe isoclinics because the embedded Polaroid sheets are fixed within the model. Perforating the embedded active layer with an array of small-diameter holes allows observation of stress trajectories in the layer from the isochromatic patterns. Further, it is shown that the full-field fringes are little disturbed by the presence of the small perforations. The techniques of model fabrication are described, as well as an extension of the method to reveal bending-stress trajectories in plates loaded out of plane.

## Holding characteristics of fasteners in bone

### Experimental Mechanics (1971) 11: 363-369 , May 01, 1971

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A satisfactory method was developed for evaluating the holding characteristics of fasteners in bone. Using this method in over 100 tests, the ultimate pull-out forces and shear stresses were determined for two sizes of sheet-metal type of screws with various interference fits, for a commercial orthopedic self-tapping screw, and for two sizes of machine screws in tapped bone, each at five sections of equine metacarpus. The ultimate pull-out force was maximum at the midlength of the bone, and minimum at the distal end. In general, the failure mechanisms were bone-thread shear for low pull-out forces, bone splitting at intermediate pull-out forces, and bone fragmentation at high pull-out forces. The failure mechanisms of the bone indicate that orthopedic fasteners should possibly not be designed for maximum holding force.

## An analogue technique for determining torsion and flexure functions of uniform beams

### Experimental Mechanics (1969) 9: 117-122 , March 01, 1969

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This paper describes an extremely simple, and yet accurate technique, based on electric analogy, for determining torsion and flexure functions of beams of uniform section, acted upon by terminal loads. Equations governing the torsion and flexure of such beams have been expressed to state the problem as a Neumann-type boundary-value problem; thus, the problem reduces to finding a function (or functions), which is harmonic within the cross section of the beam, and whose normal derivatives at the boundary of the section are prescribed.

Prescribed current densities are introduced at the boundary, and consequent voltages are obtained as the analogue of required functions. Instrumentation is very simple and, once what has been described here as the “influence matrix” of voltages is obtained, both torsion and flexure functions can be obtained simply by multiplying the “influence matrix” by vectors of appropriate normal derivatives at the boundary. None of the usual drawbacks of membrane analogy arise here. Use and accuracy of the technique have been demonstrated by a number of examples.

## Automated measurement of birefringence: Development and experimental evaluation of the techniques

### Experimental Mechanics (1989) 29: 252-257 , September 01, 1989

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Traditional photoelasticity has started to lose its appeal since it requires a well-trained specialist to acquire and interpret results. A spectral-contents-analysis approach may help to revive this old, but still useful technique. Light intensity of the beam passed through the stressed specimen contains all the information necessary to automatically extract the value of retardation. This is done by using a photodiode array to investigate the spectral contents of the light beam. Three different techniques to extract the value of retardation from the spectral contents of the light are discussed and evaluated. An experimental system was built which demonstrates the ability to evaluate retardation values in real time.

## Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

### Experimental Mechanics (2006) 46: 137-154 , April 01, 2006

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A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (*K*_{ID}) and crack-tip velocity (
$${\mathop a\limits^ \cdot }$$
) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar
$${\mathop a\limits^ \cdot }$$
-*K*_{ID} relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

## Using Depth-of-Penetration Tests to Design Transparent Armor

### Experimental Mechanics (2013) 53: 47-51 , January 01, 2013

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The depth-of-penetration (DOP) test has been modified for application to transparent armor materials. Armor materials to be tested are bonded to a polycarbonate substrate and penetration into the substrate measured. The tests can be used both for comparing armor materials and for evaluating laminate parameters. Materials tested were all armor-grade transparencies: borosilicate glass, soda-lime glass, glass ceramic, and spinel. For blunt projectiles, armor material performance is inversely correlated with density. For hard, sharp projectiles, material strength is most important, with spinel providing the best performance. The efficiency of spinel-glass laminates was only weakly dependent on the spinel thickness. Linear scaling can reconcile data obtained with different size projectiles. Relatively thick bond layers do not adversely affect the efficiency of laminates. DOP tests can be used to evaluate effects of damage from single cracks and multiple hits, and results also provide an estimate of optimal armor design against the threat used in the DOP experiments.

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## Measurement of Orthogonal Stress Gradients Due to Impact Load on a Transparent Sheet using Digital Gradient Sensing Method

### Experimental Mechanics (2013) 53: 97-111 , January 01, 2013

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A full-field optical method called Digital Gradient Sensing (DGS) for measuring stress gradients due to an impact load on a planar transparent sheet is presented. The technique is based on the elasto-optic effect exhibited by transparent solids due to an imposed stress field causing angular deflections of light rays quantified using 2D digital image correlation method. The measured angular deflections are proportional to the in-plane gradients of stresses under plane stress conditions. The method is relatively simple to implement and is capable of measuring stress gradients in two orthogonal directions simultaneously. The feasibility of this method to study material failure/damage is demonstrated on transparent planar sheets of PMMA subjected to both quasi-static and dynamic line load acting on an edge. In the latter case, ultra high-speed digital photography is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those based on the Flamant solution for a line-load acting on a half-space in regions where plane stress conditions prevail. The dynamic measurements, prior to material failure, are also successfully compared with finite element computations. The measured stress gradients near the impact point after damage initiation are also presented and failure behavior is discussed.

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## Application of the diffraction-grating strain-gage technique for measuring strains and rotations during elastic impact of rods

### Experimental Mechanics (1974) 14: 509-512 , December 01, 1974

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Experimental results are presented which establish the applicability of the diffraction-grating strain-gage technique to the measurement of dynamic elastic strains and rotations on the surface of axially impacting metallic rods. A strain resolution of 2.2×10^{−4} is achieved. The smallest detectable angle of surface rotation is 10^{−4}. The accuracy of the DGSG technique for elastics-strain measurements is confirmed by the agreement of the far-field DGSG-measured strains with the theoretical prediction of elementary rod theory.

## Full-field separation of principal stresses by combined thermo- and photoelasticity

### Experimental Mechanics (1996) 36: 318-324 , December 01, 1996

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The combined use of thermoelastic stress analysis and full-field reflection photoelasticity based on the phase-stepping technique has been developed for twodimensional problems. The first method determines the sum of the principal stresses, the latter evaluates the difference of the principal stresses. Thus the principal stresses were separated at each point in the field of view without reference to neighboring points. An evaluation of this approach has been performed using a tensile plate with a central circular hole. The results show that the analysis carried out combining thermo- and photoelasticity incurred errors no larger than those of each system working independently.

## Characterization of the Damping Behavior of a Nanoindentation Instrument for Carrying Out Dynamic Experiments

### Experimental Mechanics (2008) 48: 571-583 , August 29, 2008

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A new displacement modulation based dynamic indentation method is demonstrated and shown to be effective for viscoelastic characterization of a glassy polymer. The analysis of dynamic experiments requires a complete understanding of the measuring system’s dynamic characteristics especially the damping. Accordingly, an improved method, based on the use of a wire spring, is developed for determining the damping characteristics. In general, damping in an indentation instrument is contributed by two elements: the eddy current damping from the electromagnetic loading coil and the squeeze film damping from the capacitive displacement transducer. Therefore, a method to determine the relative contribution from the different damping elements present in the system is demonstrated and the results are compared with the calibration obtained from the wire spring method. Finally, dynamic indentation tests are carried out on a glassy polymer to obtain the complex modulus; the values of which are compared with those obtained from bulk dynamic mechanical analysis (DMA) tests. Storage modulus values are found to be in good agreement with bulk data but some divergence in the case of loss modulus is observed. The calibration procedure of the measuring instrument is critically examined in view of these observations. Overall, displacement modulation based dynamic indentation is shown to be a promising method for viscoelastic characterization at the micron length scales.

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## Effect upon shock spectra of the dynamic reaction of structures

### Experimental Mechanics (1961) 1: 145-151 , May 01, 1961

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Attempts to use fiducial limit curves of a set of classes of shock spectra as a basis for the design of structures have shown that the design spectra obtained by the combinatorial analysis of many shock spectra tend to be overconservative. This paper presents a possible explanation for this. It exhibits some experimental evidence to show that the values of interest in a shock spectrum plot tend to lie in the valleys of that plot and not upon the peaks, whereas fiducial limit curves are controlled by the peaks of the individual shock spectra.

## Delamination of a high-temperature sandwich plate

### Experimental Mechanics (2002) 42: 206-213 , June 01, 2002

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This paper describes the development of a method for determining the fracture toughness of the core/faceplate bond in high-temperature sandwich plates. The tensile deformation behavior of a sandwich element was also determined. The results from the latter experiment were used in a beam on elastic foundation analysis of the fracture specimen. The faceplate/core toughness was determined at 23 and 180°C. The room temperature toughness was slightly higher and, in both cases, the toughness decreased with crack length. The higher toughness was associated with a greater degree of interlaminar failure in the faceplates, as opposed to core-pullout.

## Experiments in mechanical and optical coincidence in photoplasticity

### Experimental Mechanics (1961) 1: 43-47 , February 01, 1961

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In the extension of the shear-difference method to the separation of interior principal stresses in the elasto-plastic state^{1}, a basic question arises whether the optical isoclinics give the directions of the principal stresses, i.e., whether optical coincidence exists. Experiments are described aiming to answer this question, and preliminary results are given for cellulose nitrate as a model material. Experiments are also described dealing with mechanical coincidence.

## Axisymmetric vibrations of a cylindrical resonator measured by holographic interferometry

### Experimental Mechanics (1975) 15: 81-88 , March 01, 1975

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A circular, cylindrical, ultrasonic resonator excited at one of its resonant frequencies is studied by holographic interferometry. Displacement distributions associated with the axisymmetric oscillations of the resonator are measured with the aid of time-average holograms, and are compared with a simple one-dimensional theory of rod vibrations, corrected for radial inertia. Analysis shows the overall error bounds on measured displacements to be ±9 percent of the maximum displacement at the resonator tip. Although the accuracy of measurements could be increased by refinements in experimental techniques, the work reported here represents substantial improvement in measuring the vibratory motion characteristics of ultrasonic devices over the point-by-point technique used heretofore.

## Stress Measurement Using EBSD Analysis of Grains in Copper Foil

### Experimental Mechanics (2012) 52: 493-502 , June 01, 2012

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A cyclic biaxial stress measurement method using electrodeposited copper foil was examined. The crystallographic orientations of individual grains that undergo grain growth in copper foil subjected to cyclic loading were analyzed by electron backscatter diffraction (EBSD). One of the slip directions in most of the grains corresponded to the direction of maximum shear stress when the biaxial stress ratio was negative. However, the number of grains with other orientations gradually increased as the biaxial stress ratio approached zero. On the basis of these features, we propose biaxial stress measurement using EBSD analysis of grown grains in copper foil. Our new method has excellent resolution compared with other stress-strain measurement methods since it can measure the average biaxial stress ratios in an area of 500 μm × 500 μm.

## Using Micro-Raman Spectroscopy to Assess MEMS Si/SiO2 Membranes Exhibiting Negative Spring Constant Behavior

### Experimental Mechanics (2013) 53: 593-604 , April 01, 2013

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We introduce a novel micro-mechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures exhibit unstable buckling and require additional moving components during deflection to avoid deforming out of its useful shape. In Micro-Electro-Mechanical Systems (MEMS) devices, buckling caused by stress at the interface of silicon and thermally grown SiO_{2} causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The 1 mm^{2} membrane structures presented here utilizes this effect but overcome this limitation and empirically demonstrates linearity in both regions. The Si/SiO_{2} membranes presented deflect ~17 μm from their pre-released position. The load deflection curves produced exhibit positive linear stiffness with an inflection point holding nearly constant with a slight negative stiffness. Depositing a 0.05 μm titanium and 0.3 μm layer of gold on top of the Si/SiO_{2} membrane reduces the initial deflection to ~13.5 μm. However, the load deflection curve produced illustrates both a linear positive and negative spring constant with a fairly sharp inflection point. These results are potentially useful to selectively tune the spring constant of mechanical structures used in MEMS. The structures presented are manufactured using typical micromachining techniques and can be fabricated *in-situ* with other MEMS devices.