The paper describes an algorithm of photoelastic tomography and its application for residual stress measurement in glass articles of complicated shape. The algorithm is based on a linearized solution of the equations of integrated photoelasticity. The problem of tensor field tomography is decomposed into several problems of scalar field tomography for normal stress components of the stress tensor. The method is implemented with an automated polariscope supplied with a rotary stage. Software for the control of tomographic measurements and for the calculation of the stress fields has been elaborated. Several examples illustrate application of the method.
The paper describes analgorithm of photoelastic tomography and its application for residual stress measurement in glass articles of complicated shape. The algorithm is based on a linearized solution of the equations of integrated photoelasticity. The problem of tensor field tomography is decomposed into several problems of scalar field tomography for normal stress components of the stress tensor. The method is implemented with an automated polariscope with a rotary stage. Several examples illustrateapplication of the method.
General algorithm of integrated photoelasticity is complicated and leads to nonlinear relationships between the stress components and measurement data. It is shown that effective algorithms for determining completely the axisymmetric state of stress and for measuring normal stress distribution in an arbitrary 3-D model, can be constructed if birefringence is weak. In the case of strong birefringence stresses can be determined only if rotation of the principal stress axes is absent or weak. In the general case of strong birefringence curious optical phenomena take place and integrated fringe pattern becomes ambiguous.
Integrated photoelasticity, a nondestructive method of three-dimensional stress analysis, is treated as optical tomography of the stress tensor field. Distinguishing features of the optical tensor field tomography are considered. Since in the general case the measurement data is in a nonlinear way related to the stress field, two particular cases are considered in detail: (1) weak birefringence, (2) constant principal stress directions. In these cases it is possible to measure two line integrals of the components of the stress tensor. It is shown that the general problem of stress tensor field tomography can be reduced to a problem of scalar field tomography for a single component of the stress tensor. The other stress components can in some cases be determined using equations of the theory of elasticity. The paper is illustrated by some examples of application of the method.
Possibilities to apply integrated photoelasticity for residual stress analysis in glass specimens of complicated shape are considered. In the general case algorithms for the interpretation of experimental data in integrated photoelasticity are complicated. However, if birefringence of the specimen is weak, simple integral relationships can be used for stress calculations. It is shown that normal stress distribution can be determined in a plane of a specimen of arbitrary shape. In the case of an axisymmetric specimen residual stresses can be completely determined using a combination of integrated photoelasticity and of a tomographic technique. Several examples illustrate application of the methods developed.
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