Discrete Damage Modeling of Matrix Dominated Failure Including Random Spatial Variation of Strength

Abstract

Discrete Damage Modeling (DDM) was applied to strength prediction of three types of composite tape specimens exhibiting rather brittle behavior. These were transverse tensile coupons, three-point bend 90° coupons and NASA LaRC Clamped Tapered Beam sub-element. The performed strength predictions are sensitive to the value of the transverse tensile strength Yt. Deterministic strength predictions required different values of Yt for realistic prediction of strength for the three specimen categories. Weibull scaled seeding of transverse tensile strength was introduced to address this problem. Cohesive Zone Method (CZM) in the field of random initiation strength distribution was examined and revealed that a finite seed length is required in order the reproduce brittle behavior. A 0.4mm seed length window was applied and resulted in realistic predictions of strength in all three specimens based on the Yt=64MPa measured on standard ASTM 90° coupons and Weibull modulus of α=13. INTRODUCTION Laminated composite materials are used in a variety of aerospace, automotive, and sports equipment applications. In designing these parts, coupon tests are performed to determine the material properties to be used in the design. However, manufacturing and material variation cause significant strength variations within a single part in all three material directions. Significant amount of work was devoted to measurement and characterization of variation of basic stiffness and strength properties of tape composites, and in-situ transverse tensile strength in particular. The subject literature is very extensive and the reader is referred to recent experimental work [1] including ______________ 1 Institute for Predictive Performance Methodologies, University of Texas Arlington Research Institute, 7300 Jack Newell Blvd. S., Fort Worth, TX, 76118 2 Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Woolf Hall, Room 211, Box 19023, Arlington, TX 76019 references. While the mechanism and interlay of strength controlled initiation and fracture mechanics controlled propagation as a function of ply thickness are well understood, it is pointed out that additional brittle strength scaling concepts are required to explain the entire spectrum of results. Understanding the implications of input property variation and scaling is also critical to application of progressive damage analysis (PDA) to design and certification of composite structures. Thus recently performed simulations of failure initiation and propagation in Clamped Tapered Beam (CTB) specimens [2] showed good agreement with experimental data for ply level transverse strength parameter obtained by using 3 point bend (3PB) test method [3] whereas the results obtained by using an almost two times lower value resulting from tensile testing of 90° coupons [4] resulted in 30% underprediction of the peak load. The goal of the present work is to introduce spatial scatter of transverse strength parameters into simulations and attempt to predict the strength of all categories of coupons. i.e. 90° tension, 3PB and CTB specimens with a single set of input parameters. The Discrete Damage Modeling (DDM) method utilizing Regularized Extended Finite Element Method (Rx-FEM) was used for simulation [5]-[7]. Two aspects of this mesh independent cracking methodology are affected by random distribution of transverse strength. One is the randomization of the crack initiation location, and second is the cohesive zone methodology based propagation with nonuniform variation of release pressure. The fracture toughness in the mode I and II were not varied in the present study. The cohesive zone model response with random seeding of initiation strength was theoretically investigated first and showed that a finite physical dimension based seeding is required to reproduce the Weibull type weak link failure load scaling with the nonuniform field of initiation strength. Namely if the initiation strength is seeded based on the integration point the global behavior is not brittle. Next the minimum dimension of the seed was evaluated by modeling 3PB and standard tensile coupons and finally the CTB revisited.