Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method

The newly-developed scaled boundary finite element method (SBFEM) is able to calculate stress intensity factors directly because the singularity in stress solutions at crack tips is analytically represented. By taking this advantage, a mixed-mode crack propagation model based on linear elastic fracture mechanics (LEFM) was developed in this study. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised in the SBFEM, a remeshing procedure as simple as in boundary element methods was developed with minimum mesh changes whereas the generality and flexibility of the FEM is well maintained. Fully-automatic modelling of mixed-mode crack propagation is then achieved by combining the remeshing procedure with a propagation criterion. Three mixed-mode examples were modelled. Comparisons of the numerical results with those from available publications show that the developed model is capable of predicting crack trajectories and load-displacement relations accurately and efficiently.     

Analysis of mixed-mode dynamic crack propagation by interface element based on virtual crack closure technique

An interface element tailored for the virtual crack closure technique (VCCT) was used to study an example of dynamic crack propagation under mixed mode loading. Through this interfacial element approach, VCCT can be implemented into a commercial finite element analysis (FEA) code having user subroutines without interrupting the main code. Further, with the implementation of relevant fracture criteria, this interface element can be used to simulate a wide range of fracture problems by utilizing the enhanced capabilities available by the commercial FEA codes. For illustration, this element has been implemented with the commercial FEA software ABAQUS^® through the user defined element (UEL). One example of fast crack propagation at constant speed and under mixed-mode loading was examined by comparison to the other’s numerical results using singular moving elements. No convergence difficulty was encountered for all the cases with different values of crack velocity. Neither singular element, nor the collapsed element was required. Therefore, due to its simplicity, the VCCT interface element as demonstrated could be a potential tool for engineers to practice dynamic fracture analysis in conjunction with commercial FEA codes.     

Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method

This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for fully-automatic modelling of cohesive crack growth in quasi-brittle materials. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. The constitutive law of these elements is modelled by the cohesive/fictitious crack model to simulate the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K_I vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating K_I using a “shadow subdomain”, are also described. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the new method. The results show that this SBFEM-FEM coupled method is capable of fully-automatically predicting both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for problems with strong snap-back. Parametric studies were carried out on the crack incremental length, the concrete tensile strength, and the mode-I and mode-II fracture energies. It is found that the K_I ? 0 criterion is objective with respect to the crack incremental length.     

On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth

Predicting mixed-mode fatigue crack propagation is an important and troublesome issue in structure assessment for decades. In the present paper an extended finite element method (XFEM) combined with a new cyclic cohesive zone model (CCZM) is introduced for simulating fatigue crack propagation under mixed-mode loading conditions, which has been implemented in the commercial general purpose software ABAQUS. The algorithm allows introducing a new crack surface at arbitrary locations and directions in a finite element mesh, without re-meshing. The cyclic cohesive zone model is based on the known S–N curves and Goodman diagram for metallic materials and validated by uniaxial tension results. Furthermore, the sensitivity of the model parameter is investigated for mixed-mode fatigue. The virtual crack closure technique has been extended to the cohesive zone model and proposed to calculate the energy release rate for the generalized Paris’ law. Finally, the crack propagation rate and direction under mixed-mode fatigue loading conditions are studied.     

Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method

In this paper, automated simulation of multiple crack fatigue propagation for two-dimensional (2D) linear elastic fracture mechanics (LEFM) problems is developed by using boundary element method (BEM). The boundary element method is the displacement discontinuity method with crack-tip elements proposed by the author. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Local discretization on the incremental crack extension is performed easily. Further the new adding elements and the existing elements on the existing boundaries are employed to construct easily the total structural mesh representation. Here, the mixed-mode stress intensity factors are calculated by using the formulas based on the displacement fields around crack tip. The maximum circumferential stress theory is used to predict crack stability and direction of propagation at each step. The well-known Paris’ equation is extended to multiple crack case under mixed-mode loadings. Also, the user does not need to provide a desired crack length increment at the beginning of each simulation. The numerical examples are included to illustrate the validation of the numerical approach for fatigue growth simulation of multiple cracks for 2D LEFM problems.     

An embedded cohesive crack model for finite element analysis of brickwork masonry fracture

This paper presents a numerical procedure for fracture of brickwork masonry based on the strong discontinuity approach. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. A simple central-force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need of performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent procedure for the selection of the separated nodes. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed-mode fracture records for different orientations of the brick layers on masonry panels.     

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.     

Determination of double-Determination of double-K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kⁱⁿⁱ, which can be directly evaluated by the initial cracking load, P_ini, and the precast crack length, a₀, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with K^un, which can be obtained inserting the maximum load, P_max, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, K _Ic ⁱⁿⁱ and K _Ic ^un , obtained from the small size three-point bending notched beams and the large size compact tension specimens show that K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.