Small-Scale Yielding Calculation of Transition Temperature and Toughness.
ARMY MATERIALS AND MECHANICS RESEARCH CENTER WATERTOWN MASS
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Toughness and a toughness transition temperature for a crack-like notch are calculated for small-scale yielding corresponding to K sub Ic test conditions using a macroscopic material failure representation. This transition is the point about which the failure posiition changes from the notch tip to a subsurface position or vice versa. In lieu of an exact solution for stresses, three cases are treated to provide reasonable bounds. Case II appears to be quantitatively exact at sufficient distances from the crack tip. Case I. Stresses are from usual elasticity theory. Case II. Stresses are from usual elasticity theory, but strains are from a two-straightline stress-strain relationship and deformations and boundary movement may be large. Case III. Strains are from usual elasticity theory on the argument that even in the yielded region they are substantially contained within a fairly rigid elastic mass. The transition is found to be independent of the tip radius. Because of its simiplicity and consequent clarity, Case I is most extensively discussed. However, if the work-hardening rate of the notch material is very low, Case II must be employed. Author
- Numerical Mathematics