# The Stress Analysis of Cracks Handbook, Third Edition

By
Washington University
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Paul C. Paris
Paul C. Paris
Washington University
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George R. Irwin
George R. Irwin
University of Maryland
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ISBN-10:
0791801535
No. of Pages:
698
Publisher:
ASME Press
Publication date:
2000

The following pages are devoted to strip yield model solutions (sometimes called the “Dugdale-Barrenblatt model”; e.g., Barrenblatt 1962). This model is useful in assessing the effects of finite configuration size and high net section stresses on the plastic zone size accompanying a crack tip. It does give plastic zone size estimates with some improvement over the small-scale yielding analysis represented by Eq. (27) (p. 1.11), but falls short of a full plasticity solution. Consequently, the formulas on these solution pages should be regarded as improved estimates of plastic zone size, l , as directly comparable to rp of Eq. (29) (p. 1.11).

The strip yield model replaces the actual crack and its plastic zone, Fig. 30-1 (a), with the superposition of two elastic crack solutions Fig. 30-1 (b) and (c). The crack length in the model, (b) and (c), is taken to be the actual crack length plus the plastic zone size, l As in Fig. 30-l(c), the plasticity effects are modeled by applying closing flow stresses, σY, over the portion of the model crack surface where plasticity is occuring for the actual crack. At the new model crack tip the stresses must be finite; therefore the total crack tip stress intensity in the model must be zero, that is
$totalK=appleidK+flow=0K$
This relationship is used with the appropriate elastic stress solutions for the model cracks to determine £ and other features of the solution.
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