A Numerical Procedure for Predicting Creep and Delayed Failures in Laminated Composites

Abstract

A numerical procedure is described for predicting the viscoelastic response of general laminates. A nonlinear compliance model is used to predict the creep response of the individual laminae. A biaxial delayed failure model predicts ply failure. The numerical procedure, based on lamination theory, increases by increments through time to predict creep compliance and delayed failures in laminates. Numerical stability problems and experimental verification are discussed. Although the program has been quite successful in predicting creep of general laminates, the assumptions associated with lamination theory have resulted in erroneous bounds on the predicted material response. Delayed failure predictions have been conservative. Several improvements are suggested to increase the accuracy of the procedure.

Time Dependent Behavior of Laminated Composites at Elevated Temperatures

“…Expressions for nonlinearly viscoelastic unidirectional plies have been proposed by Schapery and Lou [18,19] and by Dillard and his colleagues [22,23] for the case when temperature is constant. Here, we describe a model which can be applied to nonlinearly viscoelastic unidirectional plies when the temperature varies with time.…”

“…At room temperature T = To, Q = 6. and a., = 1. Two additional parameters appear in Equation (22), gi, and ~,2. both of which depend on stress and temperature.…”

“…Equations (22)(23)(24)(25)(26)(27)(28)(29) provide the viscoelastic stress-strain-time relation. These expressions contain a number of constants which must be determined by tests.…”

“…The A, B, and D matrices are defined as [36] In Equations (44-46), the summation convention applies for the indices i and j. T-,,ij is the transformation tensor from the on'-axis (m,n) to the on-axis (i,j ) coordinates [36]. Si; is the on-axis compliance matrix By utilizing Equations (11), (20), (22), and (31) we obtain (see Appendix A)…”

“…(a) For 0 ~ t < tA , we have By substituting Equations (B-6) and (B-7) into Equation (22), we obtain the viscoelastic strain er e (b) For t,,, :5 t < tB , we have By substituting Equations (B-9) and (B-10) into Equation (22), we obtain the viscoelastic strainer e The superscript A indicates the values from time 0 to tA, the superscript B from time t,, to tB . If a7 is zero, Equations (B-6) and (B-7) correspond to Equations (71) and (72) in the text.…”