Rate Process Theories of Fracture

An argument to resolve the discrepancy between the failure envelopes obtained for different modes of straining is indicated by the work of Blatz, Sharda, and Tschoegl [42]. These authors have proposed a generalized strain energy function as constitutive equation of multiaxial deformation. They incorporated more of the nonlinear behavior in the constitutive relation between the strain energy density and the strain. They were then able to describe simultaneously by four material constants the stress-strain curves of natural rubber and of styrene-butadiene rubber in simple tension, simple compression or equibiaxial tension, pure shear, and simple shear. 

The continuous viscoelastic models discussed in this section make use of the theory of rubber elasticity and of the time-temperature superposition principle. 

They implicitly very well recognize the molecular origin of the viscoelastic behavior of a material — but explicitly they do not refer to noncontinuous quantities such as the discrete size, structure, and arrangement of molecules, the anisotropy of molecular properties, or the distribution of molecular stresses or stored strain energy. If individual molecular events or discontinuities of stress or strain are either not discernible or not of particular importance, a representation of a solid as a continuum is quite adequate. 

As opposed to the continuum mechanical theories, molecular rate process theories of fracture recognize the presence of discrete particles or elements forming the material body. Rate process theories intend to relate in a straightforward manner breakage, displacement, and reformation of these elements to deformation, defect development, and fracture of the structured material. 

One of the early applications of the theory given by Glasstone, Laidler, and Eyring [43] was the prediction of the flow and diffusion behavior of liquids. From the original concept of flow, the thermally activated jump of molecules across an energy barrier, various fracture theories of solids have emerged. Tobolsky and 

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Statistical, Continuum Mechanical, and Rate Process Theories of Fracture... 

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