Constitutive ply damage modeling, FEM implementation, and analyses of laminated structures

The present work is concerned with the modeling of progressive damage in fiber reinforced polymer (FRP) laminates and the FEM implementation as constitutive material law. The objective is to predict damage evolution and material degradation due to matrix dominated failure modes (‘matrix cracking’). Secondary failure modes (e.g. micro-crack induced delamination) and their interactions are not considered. In a previous work [

1

], a ply-level continuum damage model based on ply failure mechanisms postulated by the Puck failure hypothesis [

2

] has been presented. In its original version, the model is restricted to loading scenarios where the fracture plane orientation predicted by Puck’s failure criterion does not change during loading. In the current work, the damage model is adapted for arbitrary loading paths to be used as a constitutive law with the finite element method (FEM).

The model uses a phenomenological scalar evolution law to describe the increase of damage with load. The effect of damage on ply stiffness is imitated by a 4th order tensor relation derived from a mean field method. By this approach, the complete elasticity tensor of a damaged ply is predicted in a thermodynamically consistent way, reflecting the non-isotropic nature of damage in FRPs and coupling of different components. Additionally, effects like stiffness recovery and degradation under in-plane transverse compression due to slanted matrix cracks are captured. At the same time only a relatively small number of model parameters is required, which can be identified from standard test methods.

The damage model is implemented as constitutive material law into the FEM package ABAQUS (ABAQUS Inc., Pawtucket, RI). This way, complex structures can be analyzed and their damage behavior including load redistribution due to damage can be studied. To demonstrate the utilization of the damage model in structural analysis, it is applied to some example problems. Based on comparisons between modeling results and experimental data the validity of model assumptions is discussed. It is shown that the agreement is very good at low and moderate loads where secondary failure mechanisms have not yet developed. The analysis of such loading conditions is the main objective of the presented model.