The Effect of Strain-Softening Cohesive Material on Crack Stability

Citation

Ungsuwarungsri, Tawach (1986) The Effect of Strain-Softening Cohesive Material on Crack Stability. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/sqjv-pf95. https://resolver.caltech.edu/CaltechETD:etd-02242004-152909

Abstract

Part I

Failure mechanisms of materials under very high strains experienced at and ahead of the crack tip (such as the formation, growth and interaction of microvoids in ductile materials, microcracks in brittle solids or crazes in polymers and adhesives) are represented by one-dimensional, nonlinear stress-strain relations possessing different post-yield softening (unloading) behaviors. These reflect different ways by which the material loses capacity to carry load up to fracture. A DCB type specimen is considered in this study. The nonlinear material is confined to a thin strip between the two elastic beams loaded by a wedge. The problem is first treated as a beam on a nonlinear foundation for which the pertinent equation is solved numerically as a two-point boundary value problem for both the stationary and the quasi-statically propagating crack. A finite element model is then used to model the problem in more detail to assess the adequacy of the beam model for reduction of the experimental data.

It is found that the energy release rate G = 2(γb) = {3P²δ)²/EI}^1/3 derived by assuming the built-in conditions at the crack tip could be used to calculate the fracture (surface) energy more accurately and conveniently than the conventional scheme even in cases where the built-in assumption is invalid. Results for the deformations of the beam prior to or during crack growth suggest ways to approximately characterize the complete material stress-strain behavior, including loading and strain-softening characteristics.

Part II

This study investigates the effects of nonlinear fibril behavior on the mechanics of craze and crack growth. We developed a numerical method for determining the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement (P-V) behavior, including strain softening characteristics.

The problem formulation is based on the superposition of the relevant elasticity Green's function. The solution is effected by using Picard's successive approximation iterative scheme. Both field equilibrium and the Barenblatt condition for vanishing stress and strain singularities (K_I = 0) are satisfied simultaneously, rendering the craze tip profile cusp-like as observed experimentally. The formulation allows the stress distribution profile and the corresponding P-V relation to be computed from experimentally measured craze/crack contours with certain advantages over the methods proposed to date.

Further numerical investigations indicate that only certain classes of the fibril P-V relations are consistent with realistic craze profiles, i.e., profiles with nonnegative displacements at all points. In addition, it is found that for a given P-V relation, nontrivial solutions -- the 'trivial solution' refers to the solution corresponding to a fully closed craze, i.e., zero displacements throughout or, simply: no craze exists -- exist only for certain ranges of craze lengths depending on the P-V characteristics under consideration.

Quasi-static growth of a craze with a central crack is analyzed for different nonlinear P-V relations for the craze fibrils. A 'critical crack tip opening displacement' (CTOD) or more precisely, 'critical fibril extension' is employed as the criterion for fracture. The P-V relation is further assumed to be invariant with respect to the craze and crack lengths. For comparison purposes, the results are compared and contrasted with the Dugdale model. The craze zone size and the energy dissipation rate are shown to approach asymptotic values in the limit of long cracks.

The problem of craze growth from a precut crack under increasing far-field loading is then studied. Instability is shown to occur in the case where the P-V relation is monotonically softening: The crack could start to grow unstably before the crack tip opening displacement reaches its critical value.

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