Crack propagations in quasi-static fracture are studied theoretically. The Griffith theory is applied to discuss a crack extension condition and motion of crack tips in straight propagations. Stability of the straight propagations is investigated based on the simple assumption that a curvature near the crack tip is determined by a singular shear stress. It is shown that straight propagations be...

The scattering of SH-waves by a Griffith crack in an infinitely long elastic strip situated at an asymmetric position has been analyzed. Applying Fourier transform, the mixed boundary value problem has been reduced to the solution of dual integral equations which finally has been reduced to the solution of a Fredholm integral equation of second kind. The numerical values of stress intensity fac...

Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is co...

To model elastic wave scattering from fatigue cracks in metals, studies were conducted of wave scattering from artificial cracks using ultrasonic spectroscopy. The cracks are of two dimensional planar strips oriented at various angles and embedded in diffusion bonded titanium alloy. The crack is assumed to behave as a Griffith crack and expressions (derived by Achenbach1) to describe diffracted...

A major contribution to the study of general anisotropic elasticity was made by Eshelby et al. (1953), who showed that, by making an appropriate linear transformation of the coordinate axes, the governing equations of the plane problem could be reduced to Laplacian form, thus permitting solutions to be written down in terms of analytic functions of the complex variable. This method was elaborat...

1 Physics and analytical solution The growth rate of microcracks in a brittle material can be discribed by a mesoscopic equation. Here the specialized version for uniaxial loading is presented. ∂f(l, t) ∂t = − 1 l2 ∂lvl(l, t)f(l, t) ∂l , (1) f(l, t) is the distribution function for the crack length l at time t, vl = l̇ is the growth velocity of the cracks. A Rice-Griffith-like dynamic is assumed...

RESTRICTIONS on the quasi-static extension, or healing, of Griffith cracks are developed in the framework of irreversible thermodynamics. It is emphasized that thermodynamics requires that (G 2r)I > 0, where i is crack speed, G the Irwin energy release rate, and 2y the work of reversible separation of the surfaces to be fractured. Implications for ‘lattice trapping’ models of cracks and for the...

A recently introduced method of crack representation as a distribution of three-dimensional Volterra dislocations is used in conjunction with two-dimensional dislocation dynamics simulations to study the brittle to ductile transition behavior of Ferritic Steels. The crack-tip plasticity zone is represented as an array of discrete dislocations emitted from crack-tip sources. The dislocations shi...

In this paper, the dynamic responses of cracked beams under different moving forces, including moving load, moving mass, moving oscillator, and four-degrees-of-freedom moving system, are investigated. Structural elements such as beams are designed to withstand the predicted loads, but unfortunately, they are always exposed to unpredictable damage such as cracks. Several factors may cause these ...

The phase field method integrates the Griffith theory and damage mechanics approach to predict crack initiation, propagation, and branching within one framework. No crack tracking topology is needed, and complex crack shapes can be captures without user intervention. In this paper, a detailed description of how the phase field method is implemented with explicit dynamics into LS-DYNA is provide...