Thermal loading in multi-layered and/or functionally graded materials: Residual stress field, delamination, fatigue and related size effects

Abstract

The stress field and fracture propagation due to thermal loading in multi-layered and/or functionally graded composite materials are extensively analysed. Regarding fracture, we have focused the attention on delamination between the layers due to brittle or fatigue thermally induced crack propagations. The statically indeterminate stress analysis is solved coupling equilibrium, compatibility and constitutive equations. Fracture analysis is based on the classical GriffithÕs criterion rewritten for composite structures under thermal loading. As an example, a two-layer prismatic structure is considered, each layer being composed by a different functionally graded material. The solution is particularized for the case of a linear grading. The size and shape effects are discussed and an optimization procedure is proposed. A numerical application of the findings to hard metal and diamond based cutters concludes the paper.

Thermo-elastic mismatch in nonhomogeneous beams

“…The longitudinal displacements w of two adjacent layers i and i + 1 at the ith common interface can be computed as follows (see also [23]), i = 1, . .…”

“…To fix ideas, let us consider as a representative example the case of two layers, which was also analyzed in [23]. In this case, we have only one compatibility equation:…”

“…Concerning the analysis of thermo-elastic stresses in FGMs, recent studies deal with the behavior of thick plates with nonhomogeneous composition along their thickness [22]. The problem of thermal loading in bi-layered and/or FGM beams was investigated in [23]. Special emphasis was given to the analysis of the residual stress field induced by a hot bonding.…”

“…In this paper we propose a generalization of the analytical approach recently developed in [23] for the thermoelastic stress analysis of multi-layered and/or FGM beams. With respect to the previous contributions, the proposed analytical approach based on the multi-layered beam theory permits to deal with a generic number of layers with an arbitrary grading on the Young's modulus and on the thermal-expansion coefficient.…”

Numerical analysis of fracture mechanisms and failure modes in bi-layered structural components

“…Residual stresses are instead generated during the bonding process and are usually caused by a uniform temperature distribution. From the theoretical point of view, it is important to notice that the problem of residual stresses induced by a hot bonding of two material components during the fabrication process can be considered equivalent, neglecting the algebraic sign, to the problem of thermal stresses induced by a temperature increase in a bonded two-material structure [35]. As a consequence, the problem of residual stresses induced in the elements by a temperature increase T can be studied as the problem of thermal stresses due to a temperature decrease of the same absolute amount.…”