Separation of principal stresses in dynamic photoelasticity

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved. Concurrently published in the Chinese Edition of Acta Mechanica Sinica, Vol. 26, No. 1, 1994     

Separation of principal stresses by SOR technique over arbitrary boundaries

A computerized method is presented that generates a grid mesh within the digitized boundary of a photoelastic specimen as it appears in the single viewing through an overhead polariscope. The second-order partial differential equation for the first linear invariant of stress which satisfies the Laplace equation is solved from the boundary values for the digitized domain by the finite-difference method. Connectivity and the weighting functions that are required for the iterative solution of the systems of linear equations are generated from the digitized information along the boundary. Isochromatic values at each nodal point within the boundary are estimated from the digitized fringe patterns by a scanning technique, and the individual values of principal stresses are determined. To enhance convergence, the method of successive over relaxation is applied with an optimum accelerating factor determined in the course of the solution process. The accuracy and the speed of the solution are tested with three different examples. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

On the effect of rotating secondary principal stresses in scattered-light photoelasticity

The lack of understanding of the effect of the rotation of secondary principal axes has been a severe limitation of the scattered-light method. The method of Poincare's equivalent system has been applied in order to develop a general formula for scattered-light intensity. Relationships among the orientation of eigenvectors and their phase retardation and stresses have been found. The method is illustrated by the solution of the problem of a circular rod loaded by a combination of torsion and axial load. An experimental procedure has also been suggested.     

Coordinates of principal stresses for elastic plane problem

I.IntroductionInelasticmechanics,thereisakindofproblemsthatcouldbesolveddirectlybyequilibriumequations,i.e.,whenal1oftheboundaryconditionsaretheknownstressesorforcessuchasthestressfunction.Becausestressfunctionsmustsatisfyharmonicequationorbi-harmonicequa…     

On the determination of the sum of the principal stresses in two-dimensional problems

The well-known principle of the determination of the sum of principal stresses in plates by measuring thickness changes is applied in this paper to “frozen” plates and to models made with low-modulus materials, such as rubbers, deformed inside portable frames. It is shown that a sufficiently precise measurement of thickness changes is possible with a machine-shop comparator, rather than with the more delicate laboratory-type instruments. The necessary corrections to be introduced to the comparator readings when rubber models are used are described in the Appendix. Two other methods based on moiré fringes, using the same two kinds of models, are also presented. The use of moiré on “frozen” specimens yields patterns of large response. Gratings on rubber models also yield precise moiré patterns that can be combined with isochromatics to separate the principal stresses. Two ways of conducting the moiré analyses are presented. The advantages and limitations of the several alternative methods are pointed out, and applications are given.     

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

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.     

主应力方向余弦的计算公式

从教学目的出发, 在前人工作的基础上, 采用"逐次筛分法" 求解主应力方向余弦的联立方程式, 推导了实用的主应力方向余弦计算公式.     

Separation of dynamically induced low-frequency stresses in rods and pipes

Expressions are evaluated with which the separation of oppositely propagating axial-stress components in rods and pipes can be achieved from stress waveforms obtained at different locations on the rod or pipe. The corresponding measurement/processing procedures can produce either the power spectra or the waveforms of these components. Simplifications of basic procedures for waveform evaluation are formulated whenever possible.A few experiments are described which verify the analytical results obtained theoretically and which also demonstrate the applicability of the separation procedures.     

Determination of uniaxial stresses in steel structures by the laser-ultrasonic method

This paper describes the experimental implementation of the laser-ultrasonic method for diagnosing mechanical compression and tensile stresses in steel structures, based on the acoustoelasticity effect. The special laser-ultrasonic transducer that provides the laser excitation and highly sensitive piezoelectric detection of head (longitudinal subsurface) ultrasonic waves is developed. It is shown on the example of R65 rail samples of various quality that, regardless of the structural phase state of the rail, there is one and the same linear relationship between the relative variation of the velocity of head ultrasonic waves and the absolute value of uniaxial compression and tensile stresses acting in the rail.     

Hole-drilling strain-gage method of measuring residual stresses

The hole-drilling strain-gage method of measuring residual stresses in elastic materials can be termed semidestructive if holes of very small diameters are used. The method permits the magnitudes and principal directions of residual stresses at the hole location to be determined. This is accomplished by means of an emirpically determined relation between the magnitudes and directions of the principal stresses and the strain relaxation about the hole as the hole is drilled. This relation was obtained for a nondimensional model of the hole-gage assembly in order to make the results independent of hole size. A generalization was postulated to extend the use of this calibrated solution to the measurement of residual stresses in all elastic, isotropic materials.I. Vigness was HeadPaper was presented at 1966 SESA Spring Meeting held in Detroit, Mich. on May 4–6.     

Examination of the ring method for determination of residual stresses

A semidestructive method for determining residual stresses on the surface of an isotropic material is examined. The method requires that a ring be cut around the point where residual stresses are to be found. Calibration is done by using a specimen with a known residual-stress distribution. Sensitivity of the technique is found to be much better than that of the conventional semidestructive method of hole drilling.     

Another method to separate principal strains in photoelastic coatings

It is shown that the combination of a prism and a reflection polariscope provided with a Babinet-Soleil compensator offers a simple practical solution to the problem of separation of the principal strains in photoelastic coatings.