Multi-Scale Approaches for Progressive Failure Analysis using Continuum Damage Mechanics Model

Abstract

In this paper, predictions of failure strength of carbon-fiber laminate composites are attempted using an improved continuum damage mechanics (CDM) model with emphasis on the material nonlinearity of the fiber, shear stiffness reductions, the damage contribution of matrix cracks in adjacent layers and the multi-scale approaches for PFA due to constituent material characteristic and fiber defects. The Weibull parameter to establish a CDM model was extended to five parameters to satisfy multi-scale compatibility and inter-lamina effects. These five Weibull parameters, which serve as coefficients of a damage evolution function, were investigated using a statistical model of progressive tensile fiber failure in a composite laminate. The Newton-Raphson method was utilized to formulate a damage-estimation method via a progressive failure analysis (PFA) procedure. A continuum damage analysis based on the Matzenmiller-Lubliner-Taylor (MLT) model was revised to add the statistical characteristics of the material strength. The proposed CDM method was also used to solve laminate tension problems with various stacking sequences. The damage model, nonlinear shear model and nonlinear elastic model of fiber are implemented in IPSAP, which is a general structural analysis program developed at Seoul National University. An implicit integration procedure for the proposed material and degradation model also was developed. The Newton-Raphson method for equilibrium calculations was adopted in IPSAP. Also, an improved continuum damage mechanics (CDM) model is proposed, which takes micro-scale phenomena into account. It includes degradation due to the damage initiation and development, overloading on fibers in the neighbor of a broken fiber. Two-parameter Weibull distribution which is obtained through Kolmogorov-Smirnov test is used to find an approximate model of single fibers strength distribution. A three-dimensional representative volume element model-based multi-scale approach is presented for applying degradation mechanism due to fiber defects. The present model reveals that composite failure which is controlled by defected fiber breakage and their clustering determines the post failure behavior after initial failure occurs. Macro-scale degradation factor for CDM is derived from the results. Developed models for PFA were used to solve open-hole tension and compression problems about IM7/8552, AS8552 and CP150NS/K.015 materials. The results have been shown accurately predict the failure strength of the laminates under room temperature dry, cold temperature dry and elevated temperature wet condition.