Present state of experimental stress analysis by strain gages in Japan

This paper describes the present state of strain gages, measuring devices and stress-cycle counters in Japan. Details are given to the following items: (1) electric-resistance-wire strain gages, (2) vibrating-string gages, (3) magnetostriction gages, and (4) stress-cycle counters. Items (1) and (2) manufactured in Japan are comparable to those manufactured in other advanced countries. Item (3) was specially developed in Japan. Research on item (4) is now in progress.This Field Report is based on a paper presented, by title only, at the 1960 SESA Spring Meeting held in Indianapolis, Ind., on May 18–20.     

Filtering of the experimental data in plane stress and strain fields

The paper presents a filtering algorithm which corrects the results of measurements of strain and stress fields in order to satisfy the fundamental equations of the continuum. It is proved that the algorithm is very efficient and requires small computational time. The developed filter can be used to correct the measuring data from any experiments provided some additional information about the measured system is available.     

Radio telemetry in experimental stress analysis

This report describes in detail, for the potential user, the evaluation and application of an FM/FM radio-telemetry system designed to transmit strain and temperature data from rotating parts. Three resistance-strain-gage transmitters, one thermocouple transmitter, and two receivers were thoroughly checked in the laboratory and evaluated in a number of field measurements. The laboratory investigation showed that strain and temperature data could be accurately transmitted with the telemetry equipment, and several field applications confirmed that the data obtained using the telemetry equipment were in good agreement with theoretical calculations.     

Use of electrical-resistance strain elements in three-dimensional stress analysis

A method for constructing resistance-wire strain gages which may be imbedded in a plastic model without materially altering the stress pattern in the model is presented. The methods used to calibrate the gages and the photoelastic tests made to investigate the effect of the gages on the stress pattern are described. The application of this new three-dimensional technique to evaluate the stress distribution in a thick-walled cylindrical pressure vessel is discussed. Correlation between experimental data and calculated values is given.     

Assessment of flow stress and plastic strain by spectrum analysis

The relation between the angular distribution of the reflected-plus-scattered light intensity (scattered field) from a metallic surface and the flow stress, plastic strain the material has experienced is experimentally and theoretically investigated. A scattered field, which is obtained by illuminating a specimen surface using a laser beam, carries surface-feature-related information. Experimental evidence suggests that surface correlation length of a material decreases in proportion to the flow stress and plastic strain that the material experiences. A theoretical derivation based on Huygens-Fresnel principle, Fraunhofer approximation, and Wiener-Khintchine theorem shows that the correlation length may be obtained by performing a Fourier transform to the scattered field from the surface. This leads to the development of a noncontact, nondestructive, and remote technique for measuring flow stress and plastic strain.     

FE analysis of stress and strain fields in finite random composite bodies

In this paper the mechanical behaviour of finite random heterogeneous bodies is considered. The analysis of non-local interactions between heterogeneities in microscopically heterogeneous materials is necessary when the spatial variation of the load or the dimensions of the body, relative to the scale of the microstructure, cannot be ignored. Microstructures can be periodic but generically they are random. In the first case, an exact calculation can be performed but in the second case recourse has to be made either to simulation or to some scheme of approximation. One such scheme is based on a stochastic variational principle. The novelty of the present work is that a stochastic variational principle is projected directly onto a finite-element basis so that all subsequent analysis is performed within a finite-element framework. The proposed formulation provides expressions for the local stress and strain fields in any realization of the medium, from which expressions for statistically-averaged quantities can be derived. Then an approximation of Hashin-Shtrikman type is developed, which generates a FE-based numerical procedure able to take account of interactions between random inclusions and boundary layer effects in finite composite structures. Finally, two examples are presented, namely a cylinder with square cross-section subjected to mixed boundary conditions of different types on different faces and a rectangular body containing a centre crack. The results show that in the vicinity of the boundary or close to the crack tip, the strain and the stress in the matrix and in the inclusions differ considerably from those obtained by the formal application of conventional homogenization.     

Hybrid stress analysis of perforated composites using strain gages

A strain gage hybrid method is described for determining individual stresses on the boundary and in the neighborhood of cutouts in orthotropic composites. Results agree with independent measurements and finite element analysis. Few measured strain data are needed, and the measured strains originate away from the hole. Ability to determine the stresses on the edge of a cutout from nonboundary measurements recognizes the difficulties in obtaining reliable measurements very near an edge while circumventing the challenge of attempting to bond gages to the transverse curved surface of a small hole or notch. The method also alleviates the problem of not knowing a priori where the most serious stress will occur on the geometric boundary and, hence, where to locate strain gages.     

Application of ultrasonic-pulse-spectroscopy measurements to experimental stress analysis

We apply the technique of ultrasonic pulse spectroscopy to measure the interference effects between two shear waves propagating in specimens loaded in uniaxial compression. We show that the power spectrum of an echo containing both fast and slow components of a shear wave will exhibit periodic minima. The periodicity exhibited in the spectrum is 1/Δτ, where Δτ is the difference in arrival time between the fast and slow waves. A change in the state of stress which produces a change in the two shear velocities results in a stress-dependent change in wave-arrival times. Because of this velocity change, the frequency at which a particular minimum occurs in the spectrum changes, and this can be used to indicate the state of stress in the material. Our results indicate that, if the spectrum minima frequencies could be resolved to within 10 kHz, the principal-stress differences within 36 psi (0.251 MPa) could be measured in specimens of aluminum 1 in. (2.54 cm) thick. Inherent in analyzing and measuring echo-interference effects is a single-echo requirement. Thus, transducer coupling effects are minimized and measurements in highly attenuating materials or at high frequencies in normal attenuating materials are possible. This technique shows considerable promise as a means of measuring and monitoring the applied stresses in materials.     

The importance of attending to details in experimental stress analysis

After justifying the title and classifying likely objectives in carrying out experimental stress analyses, methodical job specification and design of experiments are outlined. Some problems arising in the above and in the manufacture and testing of models are described in the hope that some of the author's experiences may assist others. Paper was invited lecture at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

Various forms of the strain-displacement relations applied to experimental strain analysis

The purpose of this paper is to present the strain-displacement relations in a general way and to develop modified forms for three special cases which have application in experimental strain analysis:

1. 1.
   Small rotations—large strains     
   
   

Strictly conjugate stress and strain tensors

a subclass of strictly conjugate tensors, namely, the tensors that satisfy the requirement for transformation by the same law upon rigid motion of the neighborhood of a material particle, is separated into the class of work-conjugate stress and strain tensors. The advantage of the use of strictly conjugate stress and strain tensors in formulating the variational principles for bodies from a hyperelastic material is shown. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 149–154, May–June, 2000.     

Acoustical birefringence and the use of ultrasonic waves for experimental stress analysis

Stress-induced optical birefringence in transparent materials has long been a common technique of stress analysis. Although stress-induced acoustic birefringence was discovered more than 20 years ago, its development and actual applications are still limited. This paper will look at the similarities and differences between the propagation of light waves in photoelastic materials and the propagation of ultrasonic waves in deformed solids. Critical comparisons of the experimental methods employed in photoelasticity with those available in modern ultrasonic measuring technique show why previous studies on ultrasonic measurement of stresses were not very successful. A new experimental technique is devised for using ultrasonic waves for stress analysis. The technique employs a single rotatable 10-MHz shear transducer as the transmitter and receiver of ultrasonic pulses. The enlarged display of the 10-MHz modulated-pulse pattern of reflected echoes provides a convenient way to determine the directions of principal axis of the stress within ±3 deg. The pulse-echo-overlap method is used to measure the absolute velocities of the two principal shear waves. The difference in principal stresses is then calculated from the velocity measurements. Test results of common structural-aluminum and steel specimens under uniaxial compression show a linear relation between the velocity changes and the applied stress. Ultrasonic measurements of stress distribution in a 6.35-cm diameter, 1.9-cm-thick aluminum disk under diametric compression are also reported. Paper was presented at Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13–18, 1973.     

The singularity analysis of the stress and strain fields for Mode I fracture in elastic-plastic state

The stress and strain singularities of power hardening material for Mode I fracrure are analysed according to the fundamental equations of elastic-plastic mechanics. It is found that the singularities of all stress and strain components do not change in the thick direction, and neither the six stress components nor the six strain components have the same singularity.     

Finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress

A new method is developed to determine the dominant asymptotic stress and deformation fields near the tip of a Mode-I traction free plane stress crack. The analysis is based on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. We show that the dominant singularity of the near tip stress field is governed by the asymptotic solution of a linear second order ordinary differential equation. Our method is applicable to any hyperelastic material with a smooth work function that depends only on the trace of the Cauchy-Green tensor and is particularly useful for materials that exhibit severe strain hardening. We apply this method to study two types of soft materials: generalized neo-Hookean solids and a solid that hardens exponentially. For the generalized neo-Hookean solids, our method is able to resolve a difficulty in the previous work by Geubelle and Knauss (1994a). Our theoretical results are compared with finite element simulations.     

A new notation for stress and strain

This note is concerned with a new notation for the stress and deformation gradients. It is intended to be both clear and elegant.     

Coaxiality of stress and strain in anisotropic no-tension materials

For an anisotropic no-tension material there exist at least two rotations such that stress and strain become coaxial. The same result holds for any hyperelastic material whose response is expressed in terms of the small strain tensor and whose stress function is a continuous positively homogeneous degree 1 function.     

Coaxiality of strain and stress in anisotropic linear elasticity

For a linearly elastic anisotropic body there are at least two rotations of the principal axes of strain such that the stress and strain tensors become coaxial. These rotations correspond to critical points for the stored energy, viewed as a function of the relative orientation between the body and the strain tensor.Supported by Gruppo Nazionale per la Fisica Matematica of C.N.R. (Italy).