Strength Prediction of Random Fiber Composite Beams using a Phenomenological-Mechanistic Model

Abstract

A phenomenological-mechanistic model, referred to as a lamini model and reported in a previous paper [8] for homogeneous stress states, is used to predict random fiber composite beam strength in this paper. This model divides a random fiber composite panel into a stack of thin transversely isotropic layers (laminas) with each lamina constructed from a series of unidirectional layers (laminis). As the number of laminis and laminas approach infinity, the convergence of the extensional stiffness matrix [A] and the bending stiffness matrix [D] is proved. These two stiffness matrices also satisfy the relationship established for isotropic materials, thus ensuring the transverse isotropy typical of random fiber composite plates (and beams). Due to the difficulty in determining lamini post-peak stress-strain behavior, in this paper only bounds on the damage growth and ultimate strength of a random fiber composite beam have been determined. The lower bound is obtained by assuming the stress falls to zero immediately after it reaches its peak value, i.e., zero residual strength in the failed layers. The upper bound is based on the assumption that the stress remains constant after the peak value is reached. This is analogous to a perfectly plastic material. Both bound predictions follow the four point bend load-strain experimental curves closely until the failure process begins to dominate with the lower bound predicting failure load approximately 39% below the experimental results while the upper bound predictions are approximately 37% higher. The model also quantitatively predicts the failure initiation and damage growth behavior in the composite beam which were observed in the previous high sensitivity laser Moire interferometry experiments [6].