Bifurcation phenomena in cohesive crack propagation (original) (raw)

Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone

International Journal of Fracture - INT J FRACTURE, 1998

Numerical solutions of a dynamic crack propagation problem are presented. Specifically, a mode III semi-infinite crack is assumed to be moving in an unbounded homogeneous linear elastic continuum while the crack tip consists of a nonlinear cohesive (or failure) zone. The numerical results are obtained via a novel semi-analytical technique based on complex variables and integral transforms. The relation between the properties of the failure zone and the resulting crack growth regime are investigated for several rate independent as well as rate dependent cohesive zone models. Based on obtained results, an hypothesis is formulated to explain the origin of the crack tip velocity periodic fluctuations that have been detected in recent dynamic crack propagation experiments.

A rate-dependent cohesive crack model based on anisotropic damage coupled to plasticity

International Journal for Numerical and Analytical Methods in Geomechanics, 2006

In quasi-brittle material the complex process of decohesion between particles in microcracks and localization of the displacement field into macrocracks is limited to a narrow fracture zone, and it is often modelled with cohesive crack models. Since the anisotropic nature of the decohesion process in separation and sliding is essential, it is particularly focused in this paper. Moreover, for cyclic and dynamic loading the unloading, load reversal (including crack closure) and rate dependency are essential features that are included in a new model. The modelling of degradation is based on a 'localized' version of anisotropic continuum damage coupled to inelasticity. The concept of strain energy equivalence between the states in the effective and nominal settings is adopted in order to define the free energy of the interface. The proposed fracture criterion is of the Mohr type, with a smooth transition of the failure and kinematics (slip and dilatation) characteristics between tension and shear. The chosen potential, of the Lemaitre-type, for evolution of the dissipative processes is additively decomposed into plastic and damage parts, and nonassociative constitutive equations are obtained. The constitutive equations are integrated by applying the backward Euler rule and by using Newton iteration. The proposed model is assessed analytically and numerically and a typical calibration procedure for concrete is proposed.

Generalizations and specializations of cohesive crack models

Engineering Fracture Mechanics, 2003

This paper presents an overview of the cohesive crack model, one of the basic models used so far to describe the fracture of concrete and other quasibrittle materials. Recent developments and needs for further research are discussed. The displayed evidence and the discussion are based on considering the cohesive crack model as a constitutive assumption rather than an ad hoc model for the behaviour ahead of a preexisting crack. Topics addressed are fracture of unnotched specimens, mixed mode fracture, diffuse cracking, anomalous stress-strain curves, size effect and asymptotic analysis, and strength of structural elements with notches.

On singular points in mixed-mode cohesive crack propagation

1994

The non-linear behaviour of concrete-like materials in tension is characterised by strain-softening. One of the models most widely used to study this kind of behaviour is that of the cohesive crack. When applying this evolutive model to mixed-mode problems it is possible to meet with a number of singular points: this paper examines possible ways to cope with two of them: the singularity of the stiffness matrix and the loss in directional stability of the crack trajectory. In this manner, it is possible to obtain mechanical information of interest for application purposes, even in the presence of such singular points.

A cohesive crack propagation model: Mathematical theory and numerical solution

Communications on Pure and Applied Analysis, 2012

We investigate the propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. As we take cohesive effects along the crack path into account and impose a non-penetration condition, inequalities appear in the constitutive equations describing the elastic behavior of a domain with crack. In contrast to existing approaches, we consider cohesive effects arising from crack opening in normal as well as in tangential direction. We establish a constrained energy minimization problem and show that the solution of this problem satisfies the set of constitutive equations. In order to solve the energy minimization problem numerically, we apply a finite element discretization using a combination of standard continuous finite elements with so-called cohesive elements. A particular strength of our method is that the crack path is a result of the minimization process. We conclude the article by numerical experiments and compare our results to results given in the literature.

A fracture evolution procedure for cohesive materials

International Journal of Fracture, 2001

The present paper deals with the problem of the evaluation of the softening mechanical response of cohesive materials under tensile loading. A nonlinear fracture mechanics approach is adopted. A new numerical procedure is developed to study the evolution of the crack processes for 2D solids. The proposed algorithm is based on the derivation and use of the fracture resistance curve, i.e., the R-curve, and it takes into account the presence of the process zone at the crack tip. In fact, assuming a nonlinear constitutive law for the cohesive interface, the procedure is able to determine the R-curve, the process zone length and hence the mechanical response of any material and structure. Numerical applications are developed for studying the damage behavior of a infinite solid with a periodic crack distribution. Size effects are investigated and the ductile-brittle transition behavior for materials characterized by the same crack density is studied. The results obtained adopting the proposed procedure are in good accordance with the results recovered through nonlinear step by step finite element analyses. Moreover, the developed computations demonstrate that the procedure is simple and efficient.

The simulation of dynamic crack propagation using the cohesive segments method

Journal of the Mechanics and Physics of Solids, 2008

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

Cohesive cracks versus nonlocal models: Closing the gap

International Journal of Fracture, 1993

Fracture of quasi-brittle materials, particularly concrete and cement-based material, has been treated in the past using a number of mildly related models. Hillerborg's fictitious crack model (also called cohesive crack model and Dugdale-Barenblatt model), Bažant's crack band model, and nonlocal models, are three of the most used for theoretical as well as for applied analysis. Using a uniaxial formulation and a Rankine-type model, the present work shows that the cohesive crack may be obtained as a particular case of a fully nonlocal formulation. The discussion of the generalization of the uniaxial formulation to triaxial behavior suggests that a directional averaging, rather than an isotropic one, may be necessary.

A cohesive zone model for cracks terminating at a bimaterial interface

International Journal of Solids and Structures, 1997

Linear elastic fracture mechanics (LEFM) does not provide a realistic propagation criterion for a crack tip touching a bimaterial interface. In fact, LEFM predicts that the crack penetrates the interface at either zero or infinite value of the characteristic applied load, depending on the relative stiffness of the bonded materials. This paper presents a cohesive zone model that provides a propagation criterion for such cracks in terms of the parameters that define the relation between the crack opening displacement and the traction acting along the crack surfaces. Extensive numerical results are presented for the case of constant cohesive traction, 6, associated with a critical crack tip opening displacement, q<. A quantitative evaluation of the effective toughening resulting from the presence of the interface is presented, for both small scale and large scale bridging, in terms of the Dundurs parameters (9 and /I), and pn/L, where pZ is proportional to the small scale critical cohesive zone length and L is a characteristic length of the crack problem. In particular, universal results for small scale bridging are presented as where k,. and 6, are, respectively the critical stress intensity factor and critical cohesive zone length, i is the power of the stress singularity associated with the elastic crack touching the interface, and A and B* are universal functions. These equations generalize those derived from the Dugdale model for a homogeneous medium. It is shown through the analysis of a finite length crack that for a relatively wide range of LX$ and pz/L values, the presence of the interface has a rather insignificant effect on the critical stress, and the elastic singularity associated with a crack terminating at the interface between two dissimilar elastic materials dominates the stress field within an extremely small near-tip region,

Asymptotic analysis of a cohesive crack: 1. Theoretical background

International Journal of Fracture, 1992

A method to analyze the evolution of a cohesive crack, particularly appropriate for asymptotic analysis, is presented. Detailed descriptions of the zeroth order and first order asymptotic approaches are given and from these results the far field equivalent elastic crack theorem is derived. An analytically soluble example, the Griffith crack, and a simple model, the Dugdale model, are used to exemplify the results.