โ Scribed by G. C. Sih
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Recent activities of research work on the analytical aspects of fracture mechanics at Lehigh University have been concerned with an improved theory of plates with application to the fracture thickness problem and.the interaction of stress waves with a running crack. A s,,mmaryof the work is given as follows:
(i) Using a variational principle, a system of equations is derived for the theory of extension and bending of elastic plates. The equations take into account the stress variations across the thickness of the plate which depend on the characteristic dimensions arising in a given problem such as the crack size, plate thickness, etc. For illustrative purposes, the problem of the uniform extension of an infinite plate containing a โข through crack is solved by application of integral representations. One of the significant and new features of the solution which differs from that found from the customary equations Of generalized plane stress is that the stress intensity factor depends on the plate thickness/crack length ra~io, and a dimensionless parameter characterizing the stress distribution ~ across the thickness. The results show that the stresses local to the crack tip increase rapidly when the plate thickness/crack length ratio i s pe'rt~rb~d slightly from zero. Efforts are also being made to incorporate a p~as~ยข zone length parameter into the problem in a manner similar to the Dugdale strip yield model for two-dimensional crack problems.
(2) Continuing a series of investigations concerned with dynamic crack propagation, the problem of the interaction of stress waves wi~h a ,~ running crack has been recently studied. More specificslly an analysis of the scattering of horizontally polarized shear waves by a finite crack extending at constant velocity is carried out. The distortion of th 9 ~ocal stress pattern due to the motion of the crack is determined for incide~ waves impinging on the crack in an arbitrary direction.
It is fou~d~h~t ~ the dynamic stress intensity factor depends sensitively upon the sp~ed of crack propagation, the frequency of the incoming waves, and the angle &f incidence. As the crack speed is increased at normal incidence, ~h~ pe~ks of the stress intensity factor curves tend to decrease and to occur at lower wave numbers. Similar conclusions can also be obtained for the ` qas~i of diffraction of plane harmonic compression and vertically polarizsd s~ea~ waves by an advancing crack. The knowledge gained
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