Handbook of mathematical fluid dynamics. / Vol. 2 by Susan Friedlander; D Serre

By Susan Friedlander; D Serre

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By Susan Friedlander; D Serre

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G. a small-scale yielding situation (fig. 5) Dynamic Fracture Theory 57 o .. • K r I J I - 1/2 e :E . I J elasto-plastic boundary Fig. 19, lllustration of a small-scale yielding situation. Let us adopt a strain rate dependent plasticity theory of the form discussed in section 12 with an exponent n > 1. The singular stress field will then be characterized by ~ and the From material models of fracture it appears that the cleavage singular strain field by mode of failure is chiefly governed by the stress state.

18) does not depend on the crack growth history. 18) is subject to the same restrictions as was described above. We can, however, obtain some interesting results. Suppose that a crack tip has been propagating in a finite body. Imagine now that the tip is stopped at some time instant to· Then under a time interval limited by the first reflection of wave emitted from the tip at to. the stresses in front of the tip can in principle be obtained from the instantaneous state of the body at to . Denote the end-point of this interval1c:J.

18) can then be inverted for each specific form of q(p). It is seen that the timedependence of K1 is simply given by the convolution between q(t) and the inverse of the factor within brackets. e. a) denotes generalized binomial coefficients. 21) for any given tis a finite series, it gives the exact result for K1. In fig. 22) (h(l-2v)) f1 15 10 K I (t)/ Klqs 5 5 10 15 Fig. 7, The stress intensity factor for the strip problem. K1 (t) oscillates around the quasi-static result (t/to) K1qs with -~diruinishing amplitude.

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