Constitutive Relationships for Laminates with Ply Cracks in In-plane Loading

Abstract

A theoretical framework which allows determining the whole set of 2-D thermomechanical constants of a damaged laminate as a function of crack density in different layers is presented. In this approach, closed-form expressions, which contain thermoelastic ply properties, laminate layup, and crack density as the input information are obtained. It is shown that the crack opening displacement (COD) and crack face sliding displacement, normalized with respect to a load variable, are important parameters in these expressions influencing the level of the properties degradation. They are determined in this paper using generalized plain strain FEM analysis results for noninteractive cracks. The strong dependence of the COD on the relative stiffness and thickness of the surrounding layers, found in this study, is described by a power law. The methodology is validated and the possible error introduced by the noninteractive crack assumption is estimated by comparing with the 3-D FEM solution for a cross-ply laminate with two orthogonal systems of ply cracks. Experimental data and comparison with other models are used for further verification.

Physical interpretation of parameters in synergistic continuum damage mechanics model for laminates

“…An exact expression for stiffness of a general symmetric laminate with intralaminar cracks in plies was derived in [12,13] […”

“…The 4 drawback of this approach is that these expressions does not account in a proper way for the constraint of surrounding layers on COD and CSD [12].…”

“…A theoretical framework establishing unique link between the damaged laminate thermo-elastic properties and the microdamage parameters COD and CSD was developed in [12,13]. It was shown that the details of the relative displacement profile along the crack surface are not important: only the average values of these quantities enter the stiffness expressions.…”

“…The normalized COD dependence on geometrical parameters of the laminate and on the material properties was studied experimentally using optical microscopy of loaded damaged specimens in [10,11]. FE studies were performed to understand which material and geometry parameters affect the COD and CSD [12,13]. Based on this analysis simple empirical relationships (power laws) were suggested.…”

“…The objective of the presented paper is to use the general framework for analysis of damaged laminates developed in [12,13] to identify the physical meaning of material constants in the CDM model [2] and to give exact expressions for their calculation. We will present transformation expressions for these constants when the layer orientation angle changes.…”