A computational damage approach towards three-dimensional ductile fracture

Metal forming processes lead to a phenomenon called damage which reduces the metal’s strength and eventually to fracture. This thesis aims at developingmodelling tools to predict the evolution of damage and fracture in its full three dimensional complexity. It addresses in particular crack propagation, which is the last phase of the fracture, in a continuum damage context. For this purpose, necessary developments have beenmade, in terms of finite element technology, remeshing and transfer and finally the geometrical treatment of crack initiation / propagation. A special tetrahedral mixed element tailored to deal with incompressible plasticity has been developed and verified for large strain elasto-plastic damage behavior. This element uses a linear interpolation for the displacement, hydrostatic stress and nonlocal damage driving variable. Although a nonlinear bubble shape function is used to enrich the displacement, still one integration point is utilized. This displacement enrichment is simplified by regarding it as a small-strain elastic contribution embedded in the finite strain elasto-plastic damage behavior represented by the conventional part of the discretisation. Finite element discretisation need to be more refined where the deformation is localized and the damage rate is high. This is done to make sure that the quality of the elements and accuracy of the solution is maintained throughout the deformation. A procedure is designed in order to transfer state variables from one mesh to another with a minimum of error and inconsistency. This scheme is particularly tailored to the developed mixed element. Point wise and global consistency is maintained by transferring a minimum set of variables and reconstructing the remaining fields via the constitutive and balance equations. If the damage exceeds a critical value, a crack is initiated either on the surface of the geometry or inside the body. This is done using adaptive insertion and opening of the crack surface in the weakest region inside the body. The crack front is a curve in three dimensional space which in each increment of crack growth propagates towards a new curve which is the new crack front. The propagation vector for each point lying on the crack front is obtained by sampling the nonlocal damage driving variable ahead of that point. By sweeping the old crack front curve towards the new one (in the direction of the propagation vectors), an extension of the three dimensional crack surface is obtained. A discontinuity is introduced on this surface by splitting the nodes on the crack surface. The proposed methodology is applied to several examples, including double notched specimen and tensile test on a rectangular specimen. These examples demonstrate the viability and the three dimensional features of the algorithm both for initiation and propagation of cracks.