Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

Photonics and fracture toughness of heterogeneous composite materials

Fracture toughness measures the resistance of a material to fracture. This fundamental property is used in diverse engineering designs including mechanical, civil, materials, electronics and chemical engineering applications. In spite of the advancements made in the past 40 years, the evaluation of this remains challenging for extremely heterogeneous materials such as composite concretes. By taking advantage of the optical properties of a thin birefringent coating on the surface of opaque, notched composite concrete beams, here we sense the evolution of the maximum shear stress distribution on the beams under loading. The location of the maximum deviator stress is tracked ahead of the crack tip on the experimental concrete samples under the ultimate load, and hence the effective crack length is characterised. Using this, the fracture toughness of a number of heterogeneous composite beams is evaluated and the results compare favourably well with other conventional methods using combined experimental and numerical/analytical approaches. Finally a new model, correlating the optically measured shear stress concentration factor and flexural strength with the fracture toughness of concretes is proposed. The current photonics-based study could be vital in evaluating the fracture toughness of even opaque and complex heterogeneous materials more effectively in future

The simulation of transport processes in cementitious materials with embedded healing systems

A new model for simulating the transport of healing agents in self-healing (SH) cementitious materials is presented. The model is applicable to autonomic SH material systems in which embedded channels, or vascular networks, are used to supply healing agents to damaged zones. The essential numerical components of the model are a crack flow model, based on the Navier-Stokes equations, which is coupled to the mass balance equation for simulating unsaturated matrix flow. The driving forces for the crack flow are the capillary meniscus force and the force derived from an external (or internal) pressure applied to the liquid healing agent. The crack flow model component applies to non-uniform cracks and allows for the dynamic variation of the meniscus contact angle, as well as accounting for inertial terms. Particular attention is paid to the effects of curing on the flow characteristics. In this regard, a kinetic reaction model is presented for simulating the curing of the healing agent and a set of relationships established for representing the variation of rheological properties with the degree of cure. Data obtained in a linked experimental programme of work is employed to justify the choice and form of the constitutive relationships, as well as to calibrate the model’s evolution functions. Finally, a series of validation examples are presented that include the analysis of a series of concrete beam specimens with an embedded vascular network. These examples demonstrate the ability of the model to capture the transport behaviour of this type of SH cementitious material system

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily overconsolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as the critical distance. This fracture criterion is known as the Point Method, and is part of the Theory of Critical Distances, which is utilized in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, ó0, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, óc and ót. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (óc/ót=3-50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low confining stresses.The work presented was initiated during a research project on “Structural integrity assessments of notch-type defects", for the Spanish Ministry of Science and Innovation (Ref.: MAT2010-15721)