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.
Highlights
Tomography is a powerfull method for the analysis of the internal structure of different objects, from human bodies to parts of atomic reactors [1]
Let us mention that Schupp [5] has developed a method for 3D stress field tomography based on interferometric measurement of the absolute optical retardation
Since Radon inversion for the tensor field does not exist, the problem of stress field tomography can be solved if we can reduce it to a problem of scalar field tomography for a single component of the stress tensor
Summary
Tomography is a powerfull method for the analysis of the internal structure of different objects, from human bodies to parts of atomic reactors [1]. Experimental data g(l,θ*) for different values of the angle θ* are called projections. If f(r,φ) is the function that determines the distribution of a certain parameter of the field, the experimental data for a real pair l, θ* can be expressed by the Radon transform of the field,. When projections for many values of θ* have been recorded, the function f(r,φ) is determined from the Radon inversion. The question arises whether it is possible to determine tomographically the stress fields in
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