Transient analysis of crack in composite layered medium subjected to dynamic loadings

Abstract

A semi-in® nite crack in a layered medium subjected to antiplane dynamic loading is investigated. In analyzing this problem, the fact that the re¯ections and diffractions of stress waves by the interface boundary and by the crack will generate an in® nite number of waves must be taken into account. A useful fundamental solution is proposed, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the application of exponentially distributed traction (in the Laplace transform domain) on the crack faces. Cagniard's method for Laplace inversion is used to obtain the transient solution in time domain. The ® nal formulations for the stress intensity factor are expressed explicitly and the dynamic effect of each wave is presented in a closed form. The results are valid for an in® nite number of waves that are scattered from the crack tip and re¯ected by the interface. Numerical calculations of dynamic stress intensity factors are evaluated and discussed in detail.

Transient Analysis of Mode III Fracture in Anisotropic Layered Media

“…Then it will approach its corresponding static value after the first nine waves have passed through the crack tip. Moreover, it is also found that the stress intensity factor decreases as the value of β (1) increases for this single-strip problem. The reason is that the width of the strip after linear coordinate transformation will be widened with the increment of β (1) .…”

“…Figure 3 shows dynamic stress intensity factors of a single strip for different values of β (1) . It can be seen that the transient response jumps first from zero to a constant value, which corresponds to the appropriate static stress intensity factor of a cracked anisotropic infinite plane as indicated in Eq.…”

“…2. It is noted that the width of the strip is changed from 2l to 2β (1) l, whereas the location of the concentrated loading is unchanged. Relations between the anisotropic problem and the corresponding isotropic problem have been established and discussed in the preceding section.…”

“…Since τ (1) yz (x, y, t) = τ (1) Y Z (X, Y, t), as indicated in Eq. (18), the stress intensity factor in the transformed coordinates (X , Y , Z ) is exactly the same as that in the original coordinates (x, y, z).…”

“…First, the interfaces remain straight, continuous, and parallel to each other; that is, no gaps or overlaps are generated along the interfaces. Second, the thickness of the middle strip becomes 2β (1) l instead of 2l. Finally, the X axis is coincident with the x axis even after the transformation, which means that the crack still lies on the negative X axis after the transformation.…”