Crack propagation due to brittle and ductile failures in microporous thermoelastoviscoplastic functionally graded materials

Plane strain transient finite thermomechanical deformations of heat-conducting functionally gradient materials comprised of tungsten and nickel-iron matrix are analyzed to delineate brittle/ductile failures by the nodal release technique. Each material is modeled as strain-hardening, strain-rate-hardening and thermally-softening. Effective properties are derived by the rule of mixtures. At nominal strain-rate of 2000 s⁻¹ brittle crack speed approaches Rayleigh’s wave speed in the tungsten-plate, the nickel-iron-plate shatters at strain-rates above 1130 s⁻¹, and the composite plate does not shatter. The maximum speed of a ductile crack in tungsten and nickel-iron is about 1.5 km/s, and that in the composite is about 0.14 km/s.     

On fast fracture in an elastic-(plastic)-viscoplastic solid – 1. Stress and velocity fields with loading and unloading processes

An asymptotic analysis of the near-tip field is given for fast crack propagation in an elastic-plastic-viscoplastic solid. The plasticity of the material is characterised by power law hardening, and the visco-plasticity covers primary, secondary and tertiary creep depending on a parameter q being smaller, equal to and larger than zero, respectively. The yield condition used is Von Mises criterion. Explicit results are given for the order of the crack-tip singularity, the angular position at which unloading occurs, and the angular variations of stresses and velocities in the near crack-tip fields. In particular, it is shown that the eigenvalue, which determines the order of stress singularity, relates only to the viscoplastic parameters but is independent of the crack-tip speed, boundary and loading conditions. Also, it is found that the plasticity effect cannot explicitly enter the asymptotic stress field. Otherwise, additional assumptions would be required.     

Simulation of crack growth in composite material shell structures

This paper implements a domain integral energy method for modelling crack growth in composite material shell structures using the finite element method. Volume integral expressions to evaluate the dynamic energy release rate in a through‐thickness three‐dimensional crack are derived. Using the domain integral, the energy release rate computation is implemented in the DYNA3D explicit non‐linear dynamic finite element analysis program wherein crack propagation is modelled by releasing the constraints between initially constrained node pairs. The implementation enables the program to either determine the energy resistance response for the material (provided experimental data is available) or predict the rate of crack propagation in shell structures. The numerical implementation was verified by simulating mode I and mode III slow crack growth problems in semi‐infinite transversely isotropic media, for which analytic solutions are available. Oscillations of energy following the release of nodal constraints as the crack propagates in discrete increments were suppressed using light mass proportional damping and a moving averaging scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Prediction of initiation and growth of single level delaminations in a transversely loaded composite specimen using fracture mechanics

The behaviour of a composite test specimen with an embedded delamination subjected to transverse tension has been investigated through experimental testing and finite element (FE) analyses. The testing program consisted of specimens in two geometrical configurations; square and rectangular delamination. The initiation and growth of the delamination was numerically predicted by fracture mechanics. FE models were analysed with both MSC.Nastran and Abaqus FE codes. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. Both approaches accurately predicted failure initiation locations as observed in the test specimens. Failure loads were also well predicted. The mode mix at the crack tip in the proposed specimen was found to be similar to the mode mix expected in a conventional in-plane compression specimen.     

Comparison of a phase‐field model and of a thick level set model for brittle and quasi‐brittle fracture

This paper provides a comparison between one particular phase‐field damage model and a thick level set (TLS) damage model for the simulation of brittle and quasi‐brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase‐field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase‐field model and of the TLS model are quite different. TLS potential enforces a priori a bound on damage gradient whereas the phase‐field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase‐field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental and numerical assessment of fracture toughness of dual-phase austempered ductile iron

The effects of the microstructure topology on the fracture toughness of dual-phase austempered ductile iron are studied in this paper by means of finite element modelling and experimental testing. To this end, specimens with matrix microstructures ranging from fully ferrite to fully ausferrite were studied and the preferential zones and phases for crack propagation were identified in every case. The effectiveness of the ausferrite phase as a reinforcement of the ferritic matrix via the encapsulation of the brittle and weak last-to-freeze (LTF) zones was confirmed. The toughening mechanism is consequence of the increment in the crack path longitude as it avoids the encapsulated LTF zones. Besides, the presence of small pools of allotriomorphic ferrite increase the crack propagation resistance of the ausferrite-ferrite matrices.     

蔗渣-淀粉发泡缓冲材料的本构方程及有限元仿真

目的研究蔗渣-淀粉发泡缓冲材料的缓冲性能,建立此类缓冲材料的本构方程,方便此类材料的应用。方法对不同密度的蔗渣-淀粉复合材料,在不同湿度和应变率条件下对其进行静态压缩试验,并在Sherwood-Frost本构模型的基础上加以扩展,加入湿度对应变的影响项,建立该复合材料的静态压缩本构方程。根据实验数据,采用Origin拟合的数学方法确定相关系数。以该静态压缩本构方程拟合出的应力-应变曲线作为材料特性载入Abaqus软件中,模拟淀粉-蔗渣纤维发泡缓冲材料并进行静态压缩试验仿真,得到仿真曲线,并与实际试验曲线进行对比。结果仿真实验与实际实验的数据误差较小,整体误差在10%以内。结论建立的静态压缩本构方程可以很好地表征该复合材料的缓冲性能,避免了设计缓冲衬垫时需要大量试验才能得到材料曲线的问题。     

Determination of energy release rate and mode mix in three-dimensional layered structures using plate theory

A plate theory-based method for determining energy release rates is presented for general loadings of three dimensional layered structures. Mode decomposition is performed for cases that exhibit an inverse square root singularity and for which certain other restrictions apply. Predictions for energy release rate and mode mix for typical problems are presented and verified by comparison with results obtained by three dimensional finite element analyses.     

A material model to reproduce mixed‐mode fracture in concrete

This paper presents a material model to reproduce crack propagation in cement‐based material specimens under mixed‐mode loading. Its numerical formulation is based on the cohesive crack model, proposed by Hillerborg, and extended for the mixed‐mode case. This model is inspired by former works by Gálvez et al but implemented for its use in a finite element code at a material level, that is to say, at an integration point level. Among its main features, the model is able to predict the crack orientation and can reproduce the fracture behaviour under mixed‐mode fracture loading. In addition, several experimental results found in the literature are properly reproduced by the model.     

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.     

板料成形中韧性断裂准则应用研究进展

对板料成形中的成形极限应力图、最大变薄率、成形极限图以及韧性断裂准则等预测成形极限的方法,进行了综述和分析。指出利用韧性断裂准则,不但能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化。利用有限元方法模拟时,韧性断裂准则既可以应用到完全耦合的弹塑性损伤模型的增量方法中,也可以应用到一步有限元逆算法中。为了准确地预测成形极限,除了提高有限元模拟精度外,应找到一种本质地反映材料性能的韧性断裂准则。     

特殊板壳式换热器封板的有限元模拟及强度研究

 对于板壳式换热器中的特殊开口封板,利用APDL语言（ANSYS parametric design language）实现全参数化驱动的三维有限元模型,通过三维有限元模拟,并对关键区域作路径分析,获得封板的应力分布规律．实验结果验证了数值模拟的有效性．经过分析,归纳出封板中的应力影响因素,提出工程关联式模型．以不开口区环板上的最大综合应力为研究对象,对封板进行参数化数值分析,并对数值模拟结果进行数据处理与拟合,得到封板强度计算工程算式．拟合公式所得数据与原模拟数据相比,平均绝对误差为0.238 MPa,平均相对误差为1.8%,这对于工程应用已经足够精确,可为新产品的工程应用提供参考．     

Approximate Green's functions for singular and higher order terms of an edge crack in a finite plate

An edge crack in a finite plate (FSECP) subjected to wedge forces is solved by the superposition of the analytical solution of a semi-infinite crack, and the numerical solution of a FSECP with free crack faces, which is solved by the Williams expansion. The unknown coefficients in the expansion are determined by a continuous least squares method after comparing it with the direct boundary collocation and the point or discrete least squares methods. The results are then used to validate the stress intensity factor (SIF) formula provided by Tada et al. that interpolates the numerical results of Kaya and Erdogan, and an approximate crack face opening displacement formula obtained in this paper by Castigliano's theorem and the SIF formula of Tada et al. These approximate formulae are accurate except for point forces very close to the outer edge, and can be used as Green's functions in the crack-closure based crack growth analysis, as well as in interpreting the size effect of quasi-brittle materials. Green's functions for coefficients relevant to the second to the fifth terms in the crack tip asymptotic field are also provided. Finally, a FSECP with a uniform pressure over a part of the crack faces is solved to illustrate the application of the obtained Green's functions and to further assess their accuracy by comparing with a finite element analysis.     

Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in multiple cracked bodies. The Zienkiewicz–Zhu error estimator is employed in conjunction with the modified superconvergent patch recovery (SPR) technique to obtain more accurate estimation of error. A stability analysis is performed to determine active cracks from a set of competitive cracks. Various crack growth criteria together with the respective crack trajectory prediction are compared. Several numerical examples are illustrated to demonstrate the efficiency, robustness and accuracy of computational algorithm in the simulation of multiple crack growth. Copyright © 2010 John Wiley & Sons, Ltd.     

韧性断裂准则在高强钢板料成形中的应用

 针对板料成形中的韧性断裂准则预测成形极限的方法,进行了综述和分析,提出了利用韧性断裂准则能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化．将Cockroft和Latham准则应用到高强度钢板DP590的成形预测中．对高强钢DP590进行了单向拉伸试验,获得了相应的物性参数．同时对该高强钢进行了方盒件成形试验,并进行了相应的有限元模拟．通过对高强钢的极限试验,利用有限元模拟获得了该材料的Cockroft和Latham准则常数．最后利用该常数对方盒件的拉深过程进行了缺陷的预测,模拟结果和试验结果完全吻合．表明韧性断裂准则是可以应用到高强度钢板的成形中的．     

Stochastic XFEM fracture and crack propagation behavior of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings

In this article, the statistics of fracture response in terms of the mean and coefficient of variation of mixed mode stress intensity factor (SIF) of an isotropic plate with hole emanating radial cracks and crack growth subjected to in-plane mechanical tensile, shear, and combined loading is evaluated. The random system parameters, such as normalized crack length, crack angle, and normalized radius of hole, are assumed as uncorrelated random variables. The basic formulation is based on the extended finite-element method with level set method combined with second-order perturbation method. The effects of the normalized radius of the hole, normalized crack length, crack angles, different positions of the hole with cracks, and in-plane loadings on the statistics of mixed mode SIF with input random system parameters are analyzed.     

Phase-field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric-meshfree approach

Phase-field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric-meshfree approach is developed for the phase-field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric-meshfree approach uses moving least-squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase-field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach.     

Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials

This work investigates elastic-plastic crack growth in ceramic/metal functionally graded materials (FGMs). The study employs a phenomenological, cohesive zone model proposed by the authors and simulates crack growth by the gradual degradation of cohesive surfaces ahead of the crack front. The cohesive zone model uses six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) to describe the constitutive response of the material in the cohesive zone. A volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model) describes the elastic-plastic response of the bulk background material. The numerical analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive zone model and the computational scheme to analyze crack growth in a single-edge notch bend, SE(B), specimen made of a TiB/Ti FGM. Cohesive parameters are calibrated using the experimentally measured load versus average crack extension (across the thickness) responses of both Ti metal and TiB/Ti FGM SE(B) specimens. The numerical results show that with the calibrated cohesive gradation parameters for the TiB/Ti system, the load to cause crack extension in the FGM is much smaller than that for the metal. However, the crack initiation load for the TiB/Ti FGM with reduced cohesive gradation parameters (which may be achieved under different manufacturing conditions) could compare to that for the metal. Crack growth responses vary strongly with values of the exponent describing the volume fraction profile for the metal. The investigation also shows significant crack tunneling in the Ti metal SE(B) specimen. For the TiB/Ti FGM system, however, crack tunneling is pronounced only for a metal-rich specimen with relatively smaller cohesive gradation parameter for the metal.