A study of damage mechanics in continuous fiber composite laminates with matrix cracking and internal delaminations

Abstract

A cumulative damage model for predicting the stiffness loss in crossply graphite/epoxy laminates is obtained by applying a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach wherein the distributed damage is characterized by a set of second order tensor valued internal state variables. The internal state variables represent globally averaged measures of matrix cracking and internal delaminations. The resulting model represents a set of damage dependent laminate plate equations. These are developed by modifying the classical Kirchhoff plate theory. The effect of internal delamination enters the formulation through modifications of the Kirchhoff displacements. The corresponding internal state variable is defined utilizing the kinematics of the internal delaminated region and the divergence theorem. This internal state variable represents the components of the out-of-plane displacement modes created by the delamination. A local anisotropic stiffness is then defined to couple these out-of-plane displacements with the in-plane forces. The effect of the matrix cracking enters the formulation through alteration in the individual lamina constitution. The internal state variable is related to the surface area of delamination by employing linear elastic fracture mechanics. This leads to a relation between the strain energy release rate and the internal state variable. Thus, as long as the s train energy release rate can be defined the model is applicable for predicting the response of general laminate plate behavior. The model is demonstrated by predicting the relative axial stiffness loss due to internal delamination in crossply laminates with very good results.