Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

A review of experimental data and elementary theoretical formulas for compressive failure of polymer matrix fibre composites indicates that the dominant failure mode is by plastic kinking. Initial local fibre misalignment plays a central role in the plastic kinking process. Theoretical analyses and numerical results for compressive kinking are presented, encompassing effects of strain-hardening, kink inclination, and applied shear stress. The assumption of rigid fibres is assessed critically, and the legitimacy of its use for polymer matrix composites is established.

http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/38.pdf

Compressive failure of fibre composites

A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.

Cohesive models for damage evolution in laminated composites

This article attempts to review the progress achieved in the understanding of scaling and size ef­ fect in the failure of structures. Particular emphasis is placed on quasi brittle materials for which the size etTect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, non local finite element models and discrete element models. Extensions to com­ pression failure and to the rate-dependent material behavior are also outlined. The damage con­ stitutive law needed for describing a microcracked material in the fracture process zone is dis­ cussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber compos­ ites, rocks and ceramics are presented. There are 377 references included in this article.

/pdf/scaling-of-structural-failure-2e1poilpdy.pdf

Scaling of Structural Failure

Compressive Failure of Fiber Composites

Resistance to delamination in composites can be enhanced by a variety of bridging mechanisms. The bridging zone size is usually several times the lamina thickness, so it is questionable to think of delamination resistance as a material property independent of specimen size and geometry. When measured with slender beams, the plateau resistance is found to be independent of the beam thickness. However, the steady-state bridging zone size increases with the beam thickness. Further implications of the large-scale bridging are studied using a family of steady-state, mixed-mode delamination beams, in conjunction with an idealized damage response. The complete solution is obtained for the model, which allows the R-curves to be constructed for given model parameters. The significance of the steady-state cracking, which is crucial in understanding delamination R-curves, is elucidated by contrasting double-cantilever beams loaded by moments and by wedge forces. As an inverse process, it is recommended that R-curves be used as an experimental probe to study localized damage response, such as polymer craze and interface separation.

Delamination R-curve phenomena due to damage

The role of material orthotropy in fracture specimens for composites

Orthotropy rescaling and implications for fracture in composites

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Papers

Delamination R-curve phenomena due to damage

The role of material orthotropy in fracture specimens for composites

Orthotropy rescaling and implications for fracture in composites