Stress Transfer Mechanics: Models that Should be the Basis of Life Prediction Methodology
Authors: McCartney LN 
Published: March 2009

The initiation and growth of damage in composite materials are phenomena that precede the failure event where a material sample or component separates into two pieces. In fatigue, the damage grows slowly and leads to a gradual deterioration of mechanical properties. For the prediction of the fatigue behavior of unidirectional and laminated titanium composites, it is necessary to be able to take account of the effects on the thermoelastic constants of matrix cracking that is induced by fatigue stress cycling. The values of the thermoelastic constants for microcracked composites are determined by the way in which stress is transferred between fiber and matrix in unidirectional composites, and between neighboring plies in laminates, as a result of microcrack formation in the matrix.

A summary is given of the recent progress that has been made at the National Physical Laboratory (NPL) on the development of analytical stress transfer models for unidirectional and laminated composites. The models are each based upon just a single assumption concerning the stress field that leads to stress and displacement solutions for which the Reissner energy function, used in a variational calculation, has stationary values. The use of the Reissner function allows both applied traction and displacement conditions to be imposed on the fiber/matrix interface and external boundary. In contrast to other applications of variational techniques, the models provide both the stress and displacement distributions at every point in the composite. Thus, complete solutions can be derived that satisfy exactly the equilibrium equations, the interface conditions, the stress-strain relationships apart from one, and the boundary conditions involving tractions. The remaining stress-strain relationship and boundary conditions involving displacements are satisfied in an average sense. For unidirectional composites, both perfectly bonded and frictionally slipping interfaces (such that the interfacial shear stress is a constant) are considered; while for laminates, consideration is restricted to interfaces that remain perfectly bonded in the presence of transverse cracks. The analytical stress transfer models are of high quality to the extent that they represent the best models that can be derived subject to the single assumption on which they are based. The models do, therefore, offer life prediction methodologies the opportunity of confidently making use of analytical methods that obey the important principles of mechanics.

The estimation of effective stress intensity factors for bridged matrix cracks that occur in titanium composites subject to fatigue loading at modest load levels is an important element in the prediction of composite performance. Assuming that fibers remain intact, the paper makes use of the stress transfer models to predict the dependence of stress intensity factors (for long cracks) on the applied stress and crack separation, for bridged cracks in both unidirectional and laminated composites. The effects of crack interaction are determined, and the new model predictions are compared to those of shear-lag theory modified to take account of residual stresses arising from thermal expansion mismatch effects. It is also shown how predictions can be made for the dependence of the thermoelastic constants of unidirectional and laminated titanium matrix composites on the nonuniform spacings of matrix cracks that can be encountered in practice.