Effect of the yield stresses in uniaxial tension and pure shear on the size of the plastic zone near a crack. (March 2018) - Revil-Baudard, Benoit; Cazacu, Oana; Chandola, Nitin
Abstract: In this paper, we make use of complex potentials for the problem of an elliptic hole subject to far field uniaxial tension to obtain the elastic stress distribution in the vicinity of a crack. Unlike the classical Westergaard stress distribution, the new stress field obtained is not axisymmetric in the crack plane. Using this new elastic stress field, it is possible to assess the effect of the particularities of yielding on the extent of the plastic zone near a crack. Analysis is done considering yielding governed by von Mises, Tresca, and Drucker yield criterion, respectively. It is demonstrated that the ratio between the yield stresses in uniaxial tension and pure shear of a material has a great influence on the size of the plastic zone around the crack. Specifically, the larger this ratio the larger is the plastic zone. Finite-element calculations confirm the theoretical predictions. Moreover, we derive new analytic relations between the length of the plastic zone, measured from the crack tip in the crack plane, and the external applied load for the case when yielding is governed by the von Mises and Tresca criterion, respectively. Highlights: New solution for the elastic stresses near a central crack under uniaxial tension. Shown effect of ratio of yield stresses in tension and shear on the plastic zone size. Developed new analytic relations for the size of plastic zone. Largest plastic zone is obtained for yielding according to Tresca criterion.