A. Chudnovsky

Strain‐energy effects on dynamic fragmentation

Grady’s model of the dynamic fragmentation process, in which the average fragment size is determined by balancing the local kinetic energy and the surface energy, is modified to include the stored elastic (strain) energy. The revised model predicts that the strain energy should dominate for brittle materials, with low fracture toughness and high fracture‐initiation stress. This conclusion is not borne out, however, by limited experimental data on brittle steels, even when the kinetic‐energy density is small compared with the strain‐energy density.

Fractal dimension––a measure of fracture roughness and toughness of concrete

Abstract The quantitative description of rough surfaces and interfaces has been an important challenge for many years. This paper addresses the potential application of fractal geometry to characterize the fracture surface and to determine whether there is any correlation between fracture properties and the roughness of the fracture surface. Fractured surfaces of three different size wedge-splitting specimens, dimensions varying from ( width × total depth × thickness ) 420×420×50 mm to 1680×1680×200 mm with four different maximum aggregate sizes of 9.5, 19, 38, and 76 mm, were analyzed using a modified slit-island technique. It was found that fractal dimension, i.e., roughness, increases with an increase in both specimen and maximum aggregate size. A clear correlation exists between roughness (fractal dimension) and fracture toughness: the tougher the material, the higher the fractal dimension.

Elastic interaction of a crack with a microcrack array—I. Formulation of the problem and general form of the solution

Abstract Elastic interactions of a crack with an array of microcracks located near the tip is considered. The analysis is based on the potential representations (known also as representation of cracks by dislocations) and approximation of tractions on the microcracks by polynomials.

A probabilistic model of brittle crack formation

Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set Ω of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability P(X) that crack penetration depth exceeds X is expressed as a functional integral over Ω of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather nonrestrictive assumptions we reduce the integral to solving a diffusion‐type equation. A new characteristic of fracture process, ‘‘crack diffusion coefficient,’’ is introduced. An illustrative example is then considered where the integration is reduced to solving an ordinary differential equation. The effect of the crack diffusion coefficient and of the magnitude of strength fluctuations (ratio of minimal and mean values of the strength field) on probability density of crack penetration depth is presented. Practical implications of the propo...

Interaction of a crack with a field of microcracks

Abstract Crack propagation in brittle materials is of ten accompanied by intensive microcracking; being a major energy sink,this phenomenon can strongly affect the fracture process. A two-dimensional problem of elastic interaction of a macrocrack with a field of microcracks is considered in the article. Consideration is based on the self-consistent method, generalized with the account of strong non — uniformity of the stress field in the vicinity of the macrocrack. The technique of double layer potentials is used. A closed form solution for the effective stress field is constructed.

Effect of damage dissemination on crack propagation in polypropylene

Kinematic measurements of Fatigue Crack Propagation (FCP) in thick compact tension polypropylene specimens shows that the rate of FCP does not increase monotonically as predicted by conventional laws of fracture mechanics. Specifically, crack deceleration occurs with increasing crack length. Microscopic examination indicates that crazes (damage) disseminate around and ahead of the main crack, thus controlling its rate of propagation. Accounting for damage dissemination, in terms of the crack layer theory, shows that the rate of FCP is controlled by the shape of the active zone and by its size, in addition to the crack length. Abrupt changes in the first two parameters are directly related to the observed crack deceleration.

Energy analysis of crack interaction with an elastic inclusion

This paper gives an energy analysis of an elastic solid with a crack which penetrates an elastic inclusion. The purpose of our work is to evaluate the energy release rates (ERR) associated with crack tip extension while the inclusion is stationary, and to evaluate the ERR due to inclusion translation, rotation and expansion with respect to the crack tip. Reduction and increase in the crack ERR caused by an inclusion (shielding and amplification effects of the inclusion) are expressed in terms of the inclusion elastic properties normalized by Youngs modulus of the bulk material. The variation in ERR as a crack approaches and passes through a circular inclusion is also examined.

Thermodynamics of translational crack layer propagation

AbstractRecognizing that fracture in many materials propagates as a crack preceded by intensive damage, a theory is presented to model the crack and the preceding damage as a single thermodynamic entity, i.e., a crack layer (CL). The active zone of the CL may propagate by translational, rotational, expansional and/or distortional movements. Concepts of irreversible thermodynamics are employed to derive the law of CL propagation by translational mode as:

Correlation between crack tortuosity and fracture toughness in cementitious material

\dot l = \frac{{\beta J_1 \left\langle d \right\rangle }}{{\gamma ^ * R_1 - J_1 }}