Yield and Crazing in Polymers

The present article discusses yield and crazing in polymeric materials. After introducing the definitions of stress and strain states, we present a brief summary of the general stress–strain responses for polymers under uniaxial tensile and compressive loading. We introduce the various regimes of behavior, from almost linear elastic through the nonlinear response to rubber-like behavior. We also include the concepts of necking and cold drawing and the Considere construction for determining whether a material will undergo either of these processes. The history of the development of yield criteria and models is then examined in some details. Yield criteria, which may be considered as macroscopic criteria relating the applied stress state to a critical value for yielding, are first discussed and the modifications for pressure dependence introduced. These criteria, while useful from an engineering point of view in that they offer a method to estimate the likelihood of failure for a given loading situation, provide no insight into the microscopic or molecular mechanisms that give rise to yield. Early theories of yield (eg adiabatic heating and strain induced dilatation), though now considered incorrect, are mentioned in their historical context. A number of models are then presented which consider yield as an activated process. In these models, resistance to yielding is considered as being due to inter- and/or intramolecular forces. Application of stress (or the associated strain) affects the energy landscape of the material such that the energy barrier for this resistance is reduced and yield can occur. More complex models are then presented which address not only the yield of the material but the subsequent strain-softening and strain-hardening events that are observed. We conclude the section on yield by some brief, general observations on dislocation plasticity, the ultimate shear strength, dilatometry and calorimetry, computer modeling, and finally some discussion of yield in semi-crystalline materials. The second section of the current chapter discusses the phenomenon of crazing. Crazing is a microscopically localized phenomenon, which involves a large degree of localized plastic deformation. Yet, crazing is generally the precursor to macroscopically brittle failure at low craze densities. An overview of craze morphology is first given to familiarize the reader with the main structural features of crazes. The development of a craze can be conveniently subdivided into three stages—initiation, growth, and failure—and each stage is examined separately. As with the yield section, craze initiation is examined in an historical context and the development of theories considering, variously, a critical cavitation stress, a critical strain, or the presence of inherent microvoids which can grow under the applied local stress or strain are discussed. There is general consensus on the mechanisms for craze growth. Craze tip advance is thought to occur by the Taylor meniscus instability mechanism, while craze thickening is due to the drawing in of material from the bulk–fibril interface. Both these mechanisms are presented and the dependence on, for example, molecular weight and cross-link density discussed. Craze failure is examined in terms of either fibril failure or failure at the bulk–fibril interface. The section is completed by considering other factors for craze formation and failure (effect of cross-tie fibrils, environmental-stress cracking, and fatigue failure). Keywords: Craze; crazing; failure; mechanical properties; plastic deformation; polymer; amorphous polymer; semicrystalline polymer; yield; yield criteria; yield stress