Characterization of random microstructural stresses and fracture estimation

In this paper, the analytical approach to quantitative characterization of random microstructural residual stress field in brittle elastic materials is presented. The analysis consists of two parts. First, we expound the basic features of random microstructural stresses and show how the eigenstrain approach (of “classical” micromechanics) can be extended to the situations where randomness of the initial eigenstrains has to be taken into account. The second part of the paper deals with the effects of random microstresses on crack growth phenomena. The stress intensity induced by random dilatant transformation eigenstrains and by thermally-induced random microstresses are treated in detail, including numerical and graphical illustrations of specific crack problems.