Va. Buryachenko et Ws. Kreher, INTERNAL RESIDUAL-STRESSES IN HETEROGENEOUS SOLIDS - A STATISTICAL-THEORY FOR PARTICULATE COMPOSITES, Journal of the mechanics and physics of solids, 43(7), 1995, pp. 1105-1125
We consider a linearly elastic composite medium, which consists of a h
omogeneous matrix containing a homogeneous and statistically uniform r
andom set of ellipsoidal inclusions. Because of the differential therm
al expansion, a microstructural residual stress state arises. By means
of the ''multiparticle effective field'' method we first derive the f
unctional relation between the stored elastic energy and the thermoela
stic constants of the components. Using this result an exact estimatio
n of all components of the statistical second moment tenser of the str
ess fields is given. Furthermore, an expression for the second moment
of the stress in the matrix in the vicinity of the ellipsoidal inclusi
on and a correlation function of internal stresses is obtained. The ap
plication of the theory is demonstrated by some numerical results for
a WC-Co composite.