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**Science**

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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.
}