Most procedures for experimental stress evaluation rely on the measurement of elastic
strain followed by point-wise calculation of stress based on continuum elasticity
assumptions despite the fact that the real purpose of the investigation is to
characterise the state of stress everywhere in the object to the greatest possible
detail. Using the example of residual elastic strain measurements in a bent titanium
alloy bar taken by means of high energy synchrotron X-ray diffraction, an
interpretation technique is here introduced based on the variational eigenstrain
analysis. An analytical framework is presented for the solution of the direct problem
of eigenstrain, that is, the calculation of residual elastic strain distribution within an
inelastically bent beam containing a known distribution of eigenstrain. An inverse
problem about closest matching between the model and experiment is then cast in a
form that allows determination of the underlying eigenstrain distribution from a
single noniterative solution of a linear system. Subsequently the complete stress state
can be reconstructed everywhere within the object in the form of continuous
functions. The value of the approach lies in the fact that subsequent deformation
modelling can be carried out with the effects of residual stresses (and their
evolution) naturally incorporated. The extension of this approach to more
complex geometries within the framework of the finite element method is briefly
discussed.
