A cohesive segments method for the simulation of crack growth

Abstract

A numerical method for crack growth is described in which the crack is not regarded as a single discontinuity that propagates continuously. Instead, the crack is represented by a set of overlapping cohesive segments. These cohesive segments are inserted into finite elements as discontinuities in the displacement field by exploiting the partition-of-unity property of shape functions. The cohesive segments can be incorporated at arbitrary locations and orientations and are not tied to any particular mesh direction. The evolution of decohesion of the segments is governed by a cohesive law. The independent specification of bulk and cohesive constitutive relations leads to a characteristic length being introduced into the formulation. The formulation permits both crack nucleation and discontinuous crack growth to be modelled. The implementation is outlined and some numerical examples are presented.Keywords Crack growth, Fracture, Cohesive zones, Partitions of unity IntroductionIn conventional engineering fracture mechanics, crack growth is assumed to occur by the extension of a single dominant crack. However, there are a wide variety of circumstances where the fracture process involves the nucleation and growth of multiple crack-like flaws. For example, in heterogeneous materials, multiple cracks that initiate and grow in one phase may link up by nucleating cracks in another phase or by propagating across phase boundaries, e.g. [1]. Another example is the transition from subsonic to intersonic crack speeds via the nucleation of a micro-crack ahead of the main crack, [2]. Also, in quasi-brittle materials micro-cracking in front of the main crack tip plays a key role in setting the fracture toughness [3]. Hence, a need for analysing discontinuous crack growth arises in a wide variety of contexts.A cohesive surface methodology has emerged which permits the analysis of fracture processes in which there is no dominant flaw. In fact, an initial crack-like defect is not required since crack nucleation can occur naturally during the loading history. The basic assumption of the cohesive surface framework is that the separation process is confined to a set of discrete planes (or lines in a two-dimensional context). A constitutive relation is then specified for each cohesive surface that allows separation to occur.The cohesive approach to fracture was pioneered by Barenblatt [4], Dugdale [5] and Hillerborg et al. [6]. In these formulations, a dominant flaw was assumed present as in conventional engineering fracture mechanics, but a cohesive zone was introduced ahead of the existing crack tip. The relation between the work expended in this cohesive zone and that in the crack tip field is typically such that the stress singularity is cancelled and the near tip stresses are finite. The slip weakening model of Andrews [7] introduced in the geophysics literature did not require crack growth to be continuous. The cohesive framework was extended to finite deformations and to situations without an initial crack in [8]. Subsequ...

A large deformation formulation for fluid flow in a progressively fracturing porous material

“…In the spirit of previous works on crack propagation in a single-phase medium [11,12,13,14] the interpolation of each component of the displacement field of the solid phase is enriched by discontinuous functions:…”

“…The opening of this plane is governed by a traction-separation relation. In order to allow for the nucleation and the propagation of cracks in arbitrary directions, irrespective of the structure of the underlying finite element mesh, the model exploits the partitionof-unity property of finite element shape functions [10], see also [11,12,13,14]. At the fine scale the flow in the crack is modelled as a viscous fluid using Stokes' equations.…”

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

“…Crack propagation in heterogeneous materials and also fast crack growth in more homogeneous materials is often characterized by the nucleation of (micro)cracks at several locations, which can grow, branch and eventually link up to form macroscopically observable cracks. To accommodate this observation, the concept of cohesive segments has been proposed [45], in which, again exploiting the partition-of-unity property of finite element shape functions, crack segments equipped with a cohesive law are placed over a patch of elements when a loading criterion is met at an integration point. Since the cohesive segments can overlap in elements, they can also behave macroscopically as a single, dominant crack.…”

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

“…The eXtended Finite Element Method (X-FEM) is a proven technology in solid mechanics and has as an important advantage compared to the previously mentioned fracture models; a fracture can grow in arbitrary directions without the need to remesh [18]. In X-FEM a fracture is modelled as a discontinuity in the displacement field by exploiting the partition-of-unity property of finite element shape functions [19].…”