Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K_I and K_II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K_I and K_II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.     

An experimental investigation of mixed-mode fracture

In this paper, mixed-mode fracture is investigated experimentally. In the first part, critical conditions for initiation of crack growth are explored. The method of caustics was used in conjunction with a high speed video system to determine critical stress intensity factors at initiation of crack growth. It was found that the maximum tangential stress criterion originally proposed by Erdogan and Sih [1] was the best criterion in terms of predictive capability. Polymethylmethacrylate and Homalite-100 were used in the experiments and Homalite-100 was found to exhibit significant rate dependence. In the second part, crack growth initiated under mixed-mode loading is addressed. It is shown that subsequent slow crack growth in PMMA is under pure mode-I conditions.

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Résumé On étudie par voie expérimentale les ruptures selon un mode mixte. On explore, dans une première partie, les conditions d'amorçage de la croissance d'une fissure. En utilisant la méthode des caustiques en association avec un système vidéo à grande vitesse, on détermine les facteurs critiques d'intensité de contraintes correspondant à l'amorçage de la fissure. On trouve que le critère de contrainte maximum tangentielle, proposé à l'origine par Erdogan et Sih, est le meilleur en termes de capacité de prédiction. Pour les essais, on a utilisé du plyméthylméthacrylate et de l'Homalite-100, et on a trouvé que ce dernier matériau faisait état d'une sensibilité importante à la vitesse. La deuxième partie du travail est consacrée à la croissance d'une fissure sous un mode de sollicitations mixte. On montre que la propagation lente de la fissure dans le PMMA se produit sous des conditions de pur Mode I.

     

A static and dynamic finite element shell analysis with experimental verification

A system of finite element shell analysis codes, called SABOR/DRASTIC, is used to analyse a complex two-layered shell of revolution under static and dynamic asymmetric loads. The dynamic analysis is compared with experimentally measured response. In this linear elastic analysis, emphasis is placed on the inherent flexibility of the finite element method in modelling the complex structural geometry of a given test specimen. Static studies, which involve variations in important shell parameters, and dynamic studies, which provide a successful correlation with experiment, are used to illustrate both the detail and the generality with which shell analyses may now be performed with confidence.     

Adaptive finite element analysis of mixed-mode fracture problems containing multiple crack-tips with an automatic mesh generator

A fully automatic advancing front type mesh generator to take care of crack problems has been presented. It is coupled with the Zienkiewicz and Zhu error estimator and the refinement methodology depends on the concept of strain energy concentration for completely automatic adaptive analysis of mixed-mode crack problems. For the first time energy based path independent M₁-integral has been used to extract mixed-mode stress intensity factors in randomly changing quadratic triangular meshes. To fulfill the objective of automatic adaptive procedures, an approach has been suggested and validated for generation of integration paths automatically without user intervention. Stress intensity factors have been obtained within engineering accuracy.     

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

Characterization of mixed-mode fracture based on a complementary analysis by means of full-field optical and finite element approaches

This paper focuses on the characterization of mixed-mode fracture parameters through use of two formalisms based on Crack Relative Displacement Factors and Stress Intensity Factors, respectively. The evaluation of Crack Relative Displacement Factors is based on a kinematic approach that integrates the experimental displacement field measured by a digital image correlation method. In parallel with this step, the stress intensity factor is calculated from a finite element analysis. The coupling between these two approaches allows for the identification of fracture parameters in terms of an energy release rate without any prior knowledge of material elastic properties. Depending on the mixed-mode configuration, the proportion of the energy release rate corresponding to opening and shear modes can be calculated. Moreover, the proposed formalism allows determining, in addition to fracture parameters, the local elastic properties in terms of reduced elastic compliance directly from the test sample. Experimental protocols are carried out using a Single-Edge notched specimen made from a rigid Polyvinyl Chloride polymer loaded at various mixed-mode ratio values.     

An experimental verification of the finite element modelling of equal channel angular pressing

Strain hardening of pure copper and friction between the sample and die channels is considered for finite element modelling. To validate the FEM results, the FEM calculated effective strain variations were compared with the hardness measurements. Simulated load–stroke curve and peak load calculations were also compared with the experimentally recorded load–stroke curve and peak load. Different stages of the load–stroke curve of the ECAP process was explained in detail. In over all, good conformity is observed between the FEM calculations and experimental results.     

Combined stress hypothesis for mixed-mode fracture toughness criterion

A new hypothesis is presented for determining the mixed-mode fracture toughness criterion of brittle materials such as rocks, cement and ceramics. The obtained criterion gives a reasonable result, which is in good agreement with published data. The data, obtained here for mixed-mode fracture toughness of flyash eement paste, confirm also the use of the hypothesis for the problem of fracture toughness, including negative K_IC.     

A mixed-mode crack analysis of rotating disk using finite element method

This paper presents a rigorous elastodynamic hybrid-displacement finite element procedure for a safety analysis of fast rotating disks with mixed-mode cracks. Based on a modified Hamilton's principle, the finite element model is derived such that the proper crack-tip singularities are taken into consideration and the interelement displacement compatibility conditions are still satisfied. Thus, the specimen can be represented by a finite element assemblage in which “singular” elements are used around the crack-tip and high-order isoparametric “regular” elements are taken elsewhere.To determine the mixed-mode stress intensity factors, the modified $\text{J}\text{?}{}_{\mathrm{k}}$ integrals for rotating cracked disks have been established taking into account the effect of centrifugal force. Using the “strain-energy-density factor” concept, the direction of crack growth of a rotating disk with an arbitrary internal crack is predicted. To provide a method of non-destructive testing in evaluating the integrity of structures, natural vibrations of cracked disk are then studied. Lastly, the influence of inertia effects due to rotating speed changes in determining the dynamic stress intensity factors is examined.For verification purposes, the simple case of a rotating disk with radial cracks is first solved. Excellent correlations between the computed results and available referenced solutions are drawn. New solutions for the circular disk with circumferential or arbitrarily-oriented cracks are also presented.     

A boundary element alternating method for two-dimensional mixed-mode fracture problems

A boundary element alternating method (BEAM) is presented for two dimensional fracture problems. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. For the numerical part of the method the boundary element method is used. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally the BEAM is applied to a variety of two-dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gave accurate stress-intensity factors with minimal computing effort.     

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load-crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.     

Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods

In conventional cohesive zone models the traction-separation law starts from zero load, so that the model cannot be applied to predict mixed-mode cracking. In the present work the cohesive zone model with a threshold is introduced and applied for simulating different mixed-mode cracks in combining with the extended finite element method. Computational results of cracked specimens show that the crack initiation and propagation under mixed-mode loading conditions can be characterized by the cohesive zone model for normal stress failure. The contribution of the shear stress is negligible. The maximum principal stress predicts crack direction accurately. Computations based on XFEM agree with known experiments very well. The shear stress becomes, however, important for uncracked specimens to catch the correct crack initiation angle. To study mixed-mode cracks one has to introduce a threshold into the cohesive law and to implement the new cohesive zone based on the fracture criterion. In monotonic loading cases it can be easily realized in the extended finite element formulation. For cyclic loading cases convergence of the inelastic computations can be critical.     

三维四向编织复合材料宏观有限元模型冲击损伤仿真及试验验证

三维编织复合材料作为整体编织材料,能够克服层合复合材料层间强度低、易分层的缺陷,相对于金属材料,还具有质量轻、高比刚、高比强度以及良好的抗冲击性能、较高的损伤容限,在汽车、高铁、航海、航空及航天领域中具有广泛应用前景。使用空气炮发射系统开展了钢珠以约210 m/s速度冲击三维四向编织复合材料平板的不同位置试验,基于宏观观察和细观观测,分析了三维编织复合材料在受到钢珠高速冲击下的破坏模式和破坏机制。此外,本文建立了三维四向编织复合材料宏观连续介质损伤（CDM）有限元模型,其中模型计算剩余速度和试验测得剩余速度误差在5%以内,试验和数值模拟的破坏形貌也高度一致,验证了所建立的宏观CDM有限元模型的有效性。     

Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a rubber mount was predicted by combining test of material properties and finite element analysis (FEA). The natural rubber material material’s fatigue life equation was acquired based on uniaxial tensile test and fatigue life tests of the natural rubber. The strain distribution contours and the maximum total principal strains of the rubber mount at different loads in the x and y directions were obtained using finite element analysis method. The critical region cracks prone to arise were obtained and analyzed. Then the maximum total principal strain was used as the fatigue parameter, which was substituted into the natural rubber’s fatigue life equation, to predict the fatigue life of the rubber mount. Finally, fatigue lives of the rubber mount at different loads were measured on a fatigue test rig to validate the accuracy of the fatigue life prediction method. The test results imply that the fatigue lives predicted agree well with the test results.     

An experimental verification of nonlocal fracture criterion

By using a nonlocal field theory, Eringer et al. [6] obtained a finite solution for the stress at the tip of a sharp crack. This solution permitted the development of a nonlocal fracture criterion for crystalline materials that is given in terms of atomic distance and theoretical cohesive strength.

The nonlocal fracture criterion is generalized for application to real materials by the introduction of a characteristic dimension (a measure of the size of the internal structures). Particleboard, a wood-based composite with controllable internal characteristics (particle dimensions and amount of resin), is used to substantiate the nonlocal fracture criterion.     

Computational modeling of mixed-mode fatigue crack growth using extended finite element methods

The extended finite element method (XFEM) combined with a cyclic cohesive zone model (CCZM) is discussed and implemented for analysis of fatigue crack propagation under mixed-mode loading conditions. Fatigue damage in elastic-plastic materials is described by a damage evolution equation in the cohesive zone model. Both the computational implementation and the CCZM are investigated based on the modified boundary layer formulation under mixed-mode loading conditions. Computational results confirm that the maximum principal stress criterion gives accurate predictions of crack direction in comparison with known experiments. Further popular multi-axial fatigue criteria are compared and discussed. Computations show that the Findley criterion agrees with tensile stress dominant failure and deviates from experiments for shear failure. Furthermore, the crack propagation rate under mixed mode loading has been investigated systematically. It is confirmed that the CCZM can agree with experiments.     

Elastic-plastic finite element analysis of dynamic fracture

Recent evidence has pointed to the possible inadequacy of elastodynamic treatments of rapid crack propagation and crack arrest. This paper describes the development of a dynamic elastic-plastic finite element capability designed to address this concern by taking direct account of crack tip plasticity. Comparisons with known dynamic fracture mechanics solutions and with experimental data are made to demonstrate the fidelity of the approach. A comparison with an elastodynamic solution in an impact loaded 4340 steel bend specimen is also made. This result reveals that a significant effect of crack tip plasticity may exist even for high strength materials.