## ABSTRACT

of talk for presentation at

Workshop on

Modeling the Development of Residual Stresses During Thermoset Composite Curing

## A Brief Review of Residual Thermal Stresses: Micromechanics to Structural Mechanics

### M. W. Hyer

Virginia Polytechnic Institute and State University

This talk will review the calculation of residual thermal stresses in laminated fiber-reinforced composite materials, starting with the micromechanical level and proceeding to the structural level. The discussion begins with the classic concentric cylinders model, which is based on an elasticity solution, and the prediction of fiber, matrix, and interface stresses with this model. The basic assumptions and some results from the model will be presented. A comparison with more rigorous finite element models is used to evaluate the validity of results from the concentric cylinder model. The discussion then proceeds to the layer level and the use of smeared thermoelastic properties. The influence of layer geometry on residual thermal stresses is demonstrated by first considering a single cylindrical layer. An elasticity solution is used to examine the potential for orthotropic material properties leading to thermally-induced stresses within a single cylindrical layer, even for a spatially uniform temperature change. The stresses within multiple layers are then studied with the same elasticity approach. The low magnitude of the through-the-thickness components of thermal stress in the cylinder problems provides motivation for the next topic, namely the classical lamination theory approach for computing residual thermal stresses at the layer level. The assumptions of this well-known theory are reviewed and to evaluate the accuracy of the theory, classical lamination theory is used to re-compute the stresses in the previously discussed cylinder problems. Comparisons between the classical lamination theory predictions and the more refined elasticity solution predictions are presented. The residual stresses in flat laminates are next considered. The influence of through-the-thickness thermal gradients on stress calculations is briefly discussed, as is the influence of temperature-dependent material properties. The limitations of classical lamination theory are underscored by focusing on thermally-induced stresses at the free-edges of laminates. Finally, several structural level problems are addressed to illustrate other important points regarding the influence of geometry and boundary conditions on residual thermal stresses at the layer level.