Photoelastic Tomography as Hybrid Mechanics

Abstract

Abstract. Photoelastic tomography is a non-destructive method of 3D stress analysis. It permits determination of normal stress distribution in an arbitrary section of a 3D test object. In case of axial symmetry also the shear stress distribution can be determined directly from the measurement data. To determine also the other stress components one can use equations of the theory of elasticity. Such a combined application of experimental measurements and numerical handling of the equations of the theory of elasticity is named hybrid mechanics. It is shown that if stresses are due to external loads, the hybrid mechanics algorithm is based on the equations of equilibrium and compatibility. In the case of the measurement of the residual stress in glass the compatibility equation can not be applied. In this case a new relationship of axisymmetric thermoelasticity, the generalized sum rule can be applied.

Polarization tomography for residual stress measurements in a hexagonal single crystal

“…The results are formulated as modified sum rules (Appendix C). Some variants of the generalised sum rule have been published earlier [26,32,33]. These results open up the possibility for experimental determination of the thermal residual stresses in hexagonal single crystals, also in the presence of the axial stress gradient.…”

“…We have in these cases a smaller number of unknown components, the reconstruction of the stresses is simplified accordingly. The field of experimental mechanics that employs both analytical and numerical methods has recently been named hybrid mechanics [26], which is based on simultaneous analyses for optical tomography and elasticity. Compared with isotropic objects, the application of the integrated photoelasticity becomes much more difficult in the case of single crystals due to the occurrence of natural anisotropy.…”

Whole-field measurement of three-dimensional stress by scattered-light photoelasticity with unpolarized light

“…Three-dimensional Photoelasticity has been performed by the scattered-light method [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], the speckle technique method [23,24], integrated photoelasticity [4][5][6], and the frozen stress method [25], which is a destructive method. Up to the present time it is difficult to measure nondestructively the stress state in a 3-D photoelasticity with general rotation of the principal stress axes except for the scattered-light photoelasticity.…”