Numerical Verification of a Procedure for Calculation of Elastic Constants in Microcracking Composite Laminates

Abstract

In two recent papers Gudmundson and Östlund have presented a simple to use theory for calculation of reduced thermoelastic constants in composite laminates with matrix cracks. The theory is valid for two- and three-dimensional laminates of arbitrary layups and is asymptotically exact for dilute and infinite microcrark densities. Further more, the theory is based solely on ply property data and matrix crack densities. No ex perimentally determined or unknown theoretical parameters are required. The theory pre dicts changes in all coefficients of the elastic stiffness and thermal expansion coefficient tensors. In previous papers the accuracy of the present theory has been investigated for cross ply laminates by comparisons to experimental results from the literature and two-dimensional finite element calculations. However, in order to become a powerful tool in the analysis of cracked composite laminates the theory must be verified at intermediate crack densities also for angle ply laminates. Unfortunately no useful experimental results for such lami nates have been found in the literature and numerical methods must be considered for the verification. In the present paper the approximate theory is compared with three- dimensional finite element calculations of cracked thick [⊖, - ⊖ ] M glass fiber reinforced epoxy laminates for a wide range of different matrix crack densities. The finite element calculations can be considered as exact for all crack densities within the present formula tion, and errors are due only to the numerical algorithm. It is found that the dilute theory in combination with the theory for infinite crack densities to a surprisingly good accuracy cover all ranges of crack densities.