On the Significance of Effective Modulus Solutions for Fibrous Composites

Abstract

The concept of effective moduli is widely used in the analysis and design of structural fibrous composites. In this approach, composite bodies are treated as laminated systems in which each layer is represented as a homogeneous anisotropic material. This approach, however, breaks down in the presence of non-uniform macroscopic stress fields. In this work, we attempt to examine the physical significance of effective modulus solutions in such cases by comparison with solutions in which the microstructure is recognized. While the meaning of a non-uniform stress field predicted by the effective modulus approach is generally ambiguous, we find, at least in the problems treated here, that the respective stresses averaged over dimensions comparable to fiber spacing agree quite well with corresponding exact averages. An example is presented which demonstrates that the effective modulus stress field cannot predict the correct physical response while the average stresses are at least qualitatively correct. Finally, an elementary approximate theory for the determination of average interlaminar normal stresses in the laminate free-edge problem is developed.