Strip Of Elastic Material Research Articles

Effect of T-stress on the cleavage crack growth resistance resulting from plastic flow

Crack growth is studied numerically for cases where fracture occurs by atomic separation, so that the length scale of the fracture process is typically much smaller than the dislocation spacing. Thus, the crack growth mechanism is brittle, but due to plastic flow at some distance from the crack tip, the materials show crack growth resistance. It is shown here that the resistance is strongly dependent on the value of the non-singular T-stress, acting parallel to the crack plane. The numerical technique employed makes use ofa thin dislocation-free strip of elastic material inside which the crack propagates, with the material outside described by continuum plasticity. Thus the width of the strip is a material length scale comparable to the dislocation spacing or the dislocation cell size.

Two finite length cracks moving between strips under plane extension

The problem of the two coplanar uniformly propagating finite cracks in the strip of elastic material is solved. Two specific conditions of loading on the strip with finite width are discussed. In the first case the rigidly clamped edges are pulled apart in opposite directions. In the second case equal and opposite tractions are applied to edges of the strip. By the use of Fourier transforms we reduce the first problem to solving a set of triple integral equations with cosine kernel and a weight function. These equations are solved by using finite Hubert transform techniques for large values of h where 2 h is the width of the strip. Finally, numerical values for dynamic stress intensity factors are presented graphically. It is shown that the solution of the second problem can be obtained in a manner similar to the first case.

Influence of Rotatory Inertia on Steady-State Crack Propagation in a Finite Plate Subjected to Out-of-Plane Bending

A dynamic stress-intensity factor and energy release rate are obtained for a running semi-infinite crack traversing a strip of elastic material subjected to out-of-plane bending. It is shown that the maximum ratio of crack tip velocity to shear wave velocity is identical to the maximum ratio of flexural wave velocity to shear wave velocity in the limit of vanishingly small wavelength. The dynamic stress-intensity factor is written as the product of a static stress-intensity factor multiplied by a function of Poisson’s ratio and crack tip velocity the function decreasing monotonically with increasing crock tip velocity. The energy release rate is shown to be independent of crack tip velocity for this type of problem.

Crack propagation in a strip of material under plane extension

The problem of a uniformly propagating finite crack in a strip of elastic material is solved using the dynamic equations of elasticity in two-dimensions. Two specific conditions of loading on the strip with finite width are discussed. In the first case, the rigidly clamped edges are pulled apart in the opposite directions. The second case considers equal and opposite tractions applied to the crack surface. By varying the strip width to the crack length ratio, the amplitude of the dynamic stresses ahead of the running crack is determined as a function of the crack velocity. The local dynamic stresses are found to be lower than the corresponding static values for the displacement loading condition and higher for the stress loading condition. This effect becomes increasingly more important as the crack length to strip width ratio is enlarged. Numerical results for the dynamic crack opening displacement are also presented.

Approximate Analysis of Elastic Stress Distribution in Thin Strip Material

The general problem of the two-dimensional state of stress in a strip of elastic material under normal loading is considered. A series expansion of displacement functions generated along lines suggested by Mindlin and Medick [1] for dynamical questions arising in plate theory is employed in the solution. The variational procedure generates a set of variational equations of motion. In order to obtain useful results the series is truncated in such a way that the analysis gives an approximate solution valid for ratios of loaded length to plate thickness greater than unity.