Numerical simulations of material mismatch and ductile crack growth
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Both the global geometry and inhomogeneties in material properties will influence the fracture behaviour of structures in presence of cracks. In this thesis numerical simulations have been used to investigate how some aspects of both these issues affect the conditions at the crack-tip. The thesis is organised in an introduction chapter, summarising the major findings and conclusions, a review chapter, presenting the main aspects of the developments in the field of fracture mechanics, and three research papers. Paper I considers the effect of mismatch in hardening exponent on the local near-tip stress field for stationary interface cracks in bi-materials under small scale yielding conditions. It is demonstrated that the stress level in the weaker material increases compared to what is found in the homogeneous material for the same globally applied load level, with the effect being of increasing importance as the crack-tip is approached. Although a coupling between the radial and angular dependence of the stress fields exists, the evolving stress field can still be normalised with the applied J. The effect on the increase in stress level can closely be characterised by the difference in hardening exponent, Δ n, termed the hardening mismatch, and is more or less independent of the absolute level of hardening in the two materials. Paper II and III deal with the effects of geometry, specimen size, hardening level and yield stress mismatch in relation to ductile crack growth. The ductile crack growth is simulated through use of the Gurson model. In Paper II the effect of specimen size on the crack growth resistance is investigated for deep cracked bend and shallow cracked tensile specimens. At small amounts of crack growth the effect of specimen size on the crack growth resistance is small, but a more significant effect is found for larger amounts of crack growth. The crack growth resistance decreases in smaller specimens loaded in tension, whereas the opposite is the case in the deep cracked bend specimens. The effect is most pronounced for low levels of hardening. Ductile crack growth in mismatched specimens introduces the possibility of crack growth deviation away from the initial crack plane. This is mainly found to be controlled by the hardening level and mode of loading. Crack growth deviation is promoted by low hardening, and the effect is stronger in the deep cracked bend specimens. Paper III focuses on the effect of ductile crack growth on the near-tip stress level. In homogeneous specimens the peak stress level increases with ductile crack growth, with the most pronounced effect for small amounts of ductile crack growth. No unique stress field exists in front of the growing cracks, and both specimen size and global geometry influences the stress field, with the strongest effect for low hardening materials. In case of mismatch it is demonstrated that if the crack is forced to grow along the interface between the two materials, the effect of mismatch on the stress field is similar to the one found for stationary cracks. If crack growth deviation is allowed for the mismatch effect on the peak stress level is reduced, however, the highest stress level remains at or near the interface, and is not found in front of the current crack tip.