The Effect of Material Shear Nonlinearity on the Predictive Capabilities of Failure Criteria for Multidirectional Laminates

Abstract

The objective of this study is to evaluate predictive capabilities of the typical failure criteria for the failure predictions of cross ply, angle ply and [0⁰2/±θ⁰]S laminates. It is implemented through comparison of numerically predicted failure curves between linear shear stress-strain analysis and nonlinear shear stress-strain analysis. Finally, the numerical predictions are compared with experimental results obtained from biaxial static tests of E-glass/epoxy. In this study, secant shear modulus instead of initial shear modulus or tangent shear modulus is used for accurate shear stress-strain relations. The implementation of nonlinear constitutive law is accomplished through the Ramberg-Osgood model. The modulus values are recalculated every time when the combined load is changed. The nonlinearity is considered throughout the process of initial and final failure analyses. In the first ply failure analysis, no matter the laminate is unidirectional or multidirectional, fracture curves are generated from the maximum stress, Tsai-Wu and Puck criteria for E-glass/epoxy reinforced composites. After the implementation of these three criteria, two property degradation methods combined with their corresponding failure criterion, e.g. utilization of the ply discount degradation method in the maximum stress criterion and utilization of the gradual stiffness degradation method in Puck criterion, are performed to generate the final fracture curves. Similarities and discrepancies between the numerical calculations and the experiment data are observed. In the initial failure comparisons, the influence of material shear nonlinearity can be observed clearly in the utilization of the maximum stress criterion. The influence will generally lead to a larger size of initial failure envelopes if shear failure belongs to either one of failure modes from the linear and nonlinear analyses based on the maximum stress criterion. In the final failure comparisons, failure modes and failure sequences are the determinants of the size of safe regions. Usually the same failure modes will lead to similar failure stresses. Among the failure modes, the fiber failure means that the laminate reaches the maximum bearing load values in case different failure modes exist between the two analytical models. Inter-fiber failure C that leads the maximum bearing load values in the remaining failure modes except fiber failure. Considering the influence of the material nonlinear property on the initial failure envelopes, the limit and separate mode failure theories, such as, the maximum stress criterion and Puck criterion could provide an enlarged region, especially for σ1-σ2 biaxial failure envelopes. For comparative analytical results involved in the final failure envelopes, the failure stresses in the consideration of the material nonlinear property almost are the same as the stresses from the linear analysis based on the limit failure theory. The failure curves generated from the nonlinear analysis show enlarged safe regions depend on the failure modes and failure sequences based on Puck criterion. Besides, the trend of the failure curves generated from the nonlinear analysis well match the experimental data for [±55⁰] laminates based on the Puck criterion.