ABSTRACT
Similar to the elastic bulk response, the fracture toughness of rubbery polymers can be rooted in statistical micro-mechanics. The occurrence of macroscopic fracture of rubbery polymers is a result of the failure of the network at the molecular level. When a rubber-like material is deformed, the network constituents change their conformation and polymer chains align according to the above mentioned bulk models. At a critical load level, rupture of one first molecule occurs, inducing the overload and breakage of neighboring chains. Further loading of the body involves rupture of additional chains and finally a macroscopic
1 INTRODUCTION
The prediction of failure mechanisms due to crack initiation and propagation in rubberlike materials is of great importance for engineering applications. Practical applications are the modeling of fracture phenomena in tires, seals, medical devices, conveyor belts and base isolations of buildings. A rubbery polymer may exhibit a very complicated inelastic behavior at finite strains. In this work on fracture of rubber, we focus on crack propagation in rubbers with an idealized purely elastic response. This is typically achieved for very slow deformation processes, where viscous effects can be neglected. For this scenario, we outline a new phase field approach to crack propagation, which embeds micro-mechanically based network theories of both the elastic bulk response as well as the crack toughness. The elastic bulk response of rubbery polymers is dominated by an extreme reformability and can be well explained by statistical micro-mechanics, see for example Treloar (1975) for an introduction. The dominant contribution to the elastic response of rubber-like materials is due to changes in conformations of network constituents, yielding the so-called entropy elasticity theory. Entropic elasticity of chain molecules is well established
crack is generated. Early investigations of failure of rubbers were performed in a sequence of papers by (Rivlin & Thomas 1953, Thomas 1955, Greensmith & Thomas 1955, Greensmith 1956). Here, a critical macroscopic fracture toughness or tearing energy for rubbers was defined in the sense of a critical energy release rate in line with the classical approach to fracture by Griffith (1921).
