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As it was pointed out in the Introduction, the source of residual stress appearance lies in the initial strain eij0 that fails to meet the equations of strain compatibility. This strain is connected by the Hook’s law to the elastic strain eij - eij0 emerging in the body (where eij are full strains corresponding to the general solution of the problem with external loads missing). Residual stress is adjusted for equilibrium inside the body after eliminating the impacts that caused it.  In the theoretical study of residual stress, either the initial incompatible strain eij0 or the sequence of changes in force/temperature conditions of loading that leads to initial strains eij0  are assumed to be known. 

   The approaches to the study of residual stress that are presented in this chapter belong to destructive methods. Yet, in contrast to the known investigation techniques that involve notching, these methods do not assume any apriori correlation between distribution of residual stress to be found, on the one hand, and the stress-strain state of the investigated part after notching, on the other, the latter being determined experimentally.

   Below are given experimental design methods of determining the continuous distribution of residual stress in flat parts of arbitrary shape by measured parameters of stress-strain state close to notches made.   Such parameters can be represented by stress/strain tensor components or those of displacement vector, as well as by some of their functionals (e.g. the 1st invariant of stress tensor) that retain the attribute of linear dependence on residual stress to be found.

              The problem of determining residual stress from measured parameters of stress state in the vicinity of a created notch belongs, by the manner of posing, to the class of inverse problems.  The observed picture of the stressed state is a response of the residual stress that is relieved along the notch line and must be restituted by this response.  Inverse problems are distinguished by being ill-defined in most natural (with regard to practice) spaces (C and L2) which incorporate initial data and target distributions of residual stress [1]. These problems are ill-defined because close distributions of observed stressed state parameters (close within measurement error limits) can be matched against significantly different distributions of residual stress along the notch line. Consistent procedures of determining residual stress can be based on regulating algorithms for various solving integral equations.  Let us consider 2 variants of obtaining consistent derivation procedures with differently posed problems.  

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