Shape and energies of a dynamically propagating crack under bending
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We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen’s thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.
I. INTRODUCTION
The shape of a crack in a body is a key parameter in understanding critical situations associated with crack propagation. While the basic state of singular stresses is not shape- or size-dependent, the amplitude of the stress singularity or the strain energy release rate is dictated by the geometry and the loading. Therefore the shape of the crack and the driving force for its propagation in various geometries and under different external loadings are of critical importance. This subject has been thoroughly investigated over the last three decades for elastostatic cracks, and a number of handbooks have been published describing numerous geometries, crack shapes, and loadings, as well as the distribution of their stress intensity factors.1–3 Most of these calibration functions were calculated by linear-elastic and static finite-element analysis of bodies containing cracks. The situation is different in fast-propagating cracks, and no assessment of the quasistatic strain energy release rate (SERR) in rapidly propagating cracks was given, especially for cracks with complicated shapes. The aim of this paper is to describe the exact shape of the crack in thin plates with a high width-to-thickness ratio when subjected to bending deformation and to calculate the associated strain energy along the crack loci. There are many calculations of the stress intensity factors for plates containing elliptical cracks under bending,4–8 all are based on the finite-element analysis of linear elastic, isotropic materials, and stationary cracks, but none are related to dynamically propagating cracks. We have J. Mater. Res., Vol. 18, No. 10, Oct 2003
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developed a procedure to determine the exact shape of such cracks, where the width-to-thickness ratio is high, and the associated quasistatic SERR. The procedure involves the fracture of various types of brittle materials under monotonic loading of a three-point
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