Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture

Adaptive mesh refinement and coarsening schemes are proposed for efficient computational simulation of dynamic cohesive fracture. The adaptive mesh refinement consists of a sequence of edge‐split operators, whereas the adaptive mesh coarsening is based on a sequence of vertex‐removal (or edge‐collapse) operators. Nodal perturbation and edge‐swap operators are also employed around the crack tip region to improve crack geometry representation, and cohesive surface elements are adaptively inserted whenever and wherever they are needed by means of an extrinsic cohesive zone model approach. Such adaptive mesh modification events are maintained in conjunction with a topological data structure (TopS). The so‐called PPR potential‐based cohesive model (J. Mech. Phys. Solids 2009; 57 :891–908) is utilized for the constitutive relationship of the cohesive zone model. The examples investigated include mode I fracture, mixed‐mode fracture and crack branching problems. The computational results using mesh adaptivity (refinement and coarsening) are consistent with the results using uniform mesh refinement. The present approach significantly reduces computational cost while exhibiting a multiscale effect that captures both global macro‐crack and local micro‐cracks. Copyright © 2012 John Wiley & Sons, Ltd.     

Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials

Dynamic crack microbranching processes in brittle materials are investigated by means of a computational fracture mechanics approach using the finite element method with special interface elements and a topological data structure representation. Experiments indicate presence of a limiting crack speed for dynamic crack in brittle materials as well as increasing fracture resistance with crack speed. These phenomena are numerically investigated by means of a cohesive zone model (CZM) to characterize the fracture process. A critical evaluation of intrinsic versus extrinsic CZMs is briefly presented, which highlights the necessity of adopting an extrinsic approach in the current analysis. A novel topology‐based data structure is employed to enable fast and robust manipulation of evolving mesh information when extrinsic cohesive elements are inserted adaptively. Compared to intrinsic CZMs, which include an initial hardening segment in the traction–separation curve, extrinsic CZMs involve additional issues both in implementing the procedure and in interpreting simulation results. These include time discontinuity in stress history, fracture pattern dependence on time step control, and numerical energy balance. These issues are investigated in detail through a ‘quasi‐steady‐state’ crack propagation problem in polymethylmethacrylate. The simulation results compare reasonably well with experimental observations both globally and locally, and demonstrate certain advantageous features of the extrinsic CZM with respect to the intrinsic CZM. Copyright © 2007 John Wiley & Sons, Ltd.     

Removing mesh bias in mixed-mode cohesive fracture simulation with stress recovery and domain integral

To remove mesh bias and provide an accurate crack path representation in mixed-mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode-I and mixed-mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower-quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed-mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.     

A modified cohesive zone model for a high‐speed expanding crack

The present work studies a self‐similar high‐speed expanding crack of mode‐I in a ductile material with a modified cohesive zone model. Compared with existing Dugdale models for moving crack, the new features of the present model are that the normal stress parallel to crack faces is included in the yielding condition in the cohesive zone and traction force in the cohesive zone can be non‐uniform. For a ductile material defined by von Mises criterion without hardening, the present model confirms that the normal stress parallel to crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. In addition, strain hardening effect is examined based on a non‐uniform traction distribution in the cohesive zone.     

Fracture assessment of graphite V‐notched and U‐notched specimens by using the cohesive crack model

This article explores the capability of the Cohesive Zone Model in predicting the critical load of blunt notched specimens made of coarse‐grained polycrystalline graphite, a brittle material that has gained the attention of researchers because of its favourable properties for protection against thermal loads. To that aim, 39 different tests on U‐notched and V‐notched specimens made of this material, with loading modes raging from mode I to mixed mode I/II, have been modelled by using the Cohesive Zone Model. The model has been implemented through the embedded crack approach, avoiding thus the necessity of defining the crack trajectory prior to the simulation because it is automatically generated once the maximum principal stress overcomes the tensile strength of the material. The numerical predictions obtained show good agreement with the experimental results.     

Analysis of automotive mixed‐adhesive joints weakened by moist conditions: Experimental characterization and numerical simulation using cohesive zone model

This paper is mostly concerned with an experimental and numerical study to clarify the behaviour and failure in the mono‐adhesive joints and mixed‐adhesive joints under different environmental conditions (dry [E₀], 75.3% relative humidity [E₁], 84.2% relative humidity [E₂], and submerged in tap water [E₃] at 25°C) and different strain rates (1 and 100 mm/min). Experimental investigations are compared with the numerical analysis, which is carried out by bilinear cohesive zone model (CZM). Through this work, degradations of cohesive parameters are calculated by using open‐faced double cantilever beam (DCB) and end notch flexure (ENF) specimens. The experimental data show that the cohesive parameters of Araldite 2015 have negative correlation to moisture content. Although Araldite AV138 parameters experience a decrease in mode I, in mode II, its cohesive parameter increases. First, it is found that the decrease in experimental failure load of mixed‐adhesive joints with regard to the dry condition is recorded as 32.6%, 54%, and 59.1% for E₁, E₂, and E₃ conditions, respectively. Following this further, single lap joint (SLJ) that has non‐uniform moisture content distribution is modelled by engaging specific CZM parameters related to the specific moisture content. The results show a good agreement between experimental and numerical data.     

Stable crack propagation in steel at 1173 K: Experimental investigation and simulation using 3D cohesive elements in large-displacements

This paper deals with the numerical simulation of a stable crack propagation experiment at in a 16MND5 steel. At this temperature, the material is viscoplastic. A cohesive zone model is formulated in order to simulate the rupture of a CT specimen. A large displacement 3D cohesive element with eight nodes is implemented in the finite element code ABAQUS. The associated traction-separation law is of Tvergaard and Hutchinson type, in which an hardening slope has been added. This hardening simulates the material strengthening associated to the increasing strain rate in front of the crack tip when crack tip starts to propagate.We show that in this case the form of the cohesive law has great impact on the simulated propagation velocity.