Crack Propagation in a Nonlinearly Viscoelastic Solid With Relevance to Adhesive Bond Failure

Abstract

The problem of crack propagation through a material possessing nonlinearly viscoelastic material response is considered, including the influence of stress-induced free-volume changes on the rheology, as well as the formation of voids as material failure is approached. This particular material response is confined to a thin layer along the crack propagation axis, while the bulk of the material behaves in a linearly viscoelastic manner, thus simulating the situation arising in the growth of a crazeled crack, or the failure of a bonded joint with a thin adhesive layer strained uniformly across its thickness. The nonlinear material behavior thus governs simultaneously the stress and strain distribution at the crack tip as well as the crack speed solely in dependence on the applied load (stress intensity factor). Only quasi-static motion is considered, the velocities being understood to be “reduced” by temperature according to a time-temperature superposition principle. Comparisons with a model based on linearly viscoelastic considerations and rate-insensitive properties of the damaged material are presented.

Time-dependent craze zone growth at a crack tip in polymer solids

“…Their deformation and failure processes are time-, temperature-and rate-dependent. The effects of viscoelasticity on crack growth have been treated by a number of workers, among them are Williams [3], Knauss [4,5], Schapery [6], and McCartney [7]. To describe the work of these authors is clearly beyond the scope of this paper.…”

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

“…More generally, we could express the mixed-mode evolution as D ∆ ,T 0 , q , where q represents any state variables. As a simple example, we might choose an evolution relation, taking a scalar argument, that incorporates the exponential "tail" of the universal binding energy curve [80] 48) where δ c represent a characteristic opening to failure. One problem with an evolution relation of this form is that traction magnitude evolves, but the direction remains the same in the local frame.…”

“…Although much research has focused on modeling the rate effects in the bulk behavior of materials, fewer works have addressed rate effects in cohesive crack growth. Knauss and Losi [48] proposed a rate-dependent cohesive surface relation incorporating viscoelasticity and damage. In addition, Knauss [48] addressed crazing in thermoplastic polymers within the context of the model.…”

“…Knauss and Losi [48] proposed a rate-dependent cohesive surface relation incorporating viscoelasticity and damage. In addition, Knauss [48] addressed crazing in thermoplastic polymers within the context of the model. Yoon and Allen [98] proposed a cohesive relation in the form of a single hereditary integral for a linear viscoelastic material.…”

A note on the role of dilatation in the fracture of viscoelastic elastomer

“…The reason for the remaining lack of precision is that the dilatation varies spatially in the crack tip region and only a numerical analysis would render a close estimate in the manner that Knauss and Losi (1993) have pursued analytically for a similar material. 6 The limitations underlying the current estimate are delineated further below.…”