Numerical analysis of the effect of microstructures of particle-reinforced metallic materials on the crack growth and fracture resistance

This paper presents a systematical computational study of the effect of microstructures of materials reinforced with brittle hard particles on their fracture behavior and toughness. Crack growth in particle-reinforced materials (here, in high speed steels) with various artificially designed arrangements of brittle inclusions is simulated using microstructure-based finite element meshes and an element elimination method. The following types of brittle inclusions arrangements are considered: (simple microstructures) net-like continuous, band-like, random with different inclusion sizes, and (complex microstructures) layered and clustered arrangements, with different inclusion sizes and orientations. Crack paths, force-displacement curves, fracture toughness and fractal dimension of fracture surfaces are determined numerically for each microstructure of the materials. It is demonstrated that extensive crack deviations from the initial cracking directions and an increase in the fracture toughness can most efficiently be achieved by using complex microstructures, such as alternated layers of fine and coarse inclusions.     

A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials

A probabilistic damage model is developed to study crack initiation and growth in quasi‐brittle materials. Two different thresholds are considered to describe these mechanisms. A Weibull model is used to account for the randomness of crack initiation(s) and then a fracture mechanics based threshold is considered to model crack propagation. The model is integrated in a finite element code via a nonlocal damage approach. A regularization operator based on a stress regularization is introduced. Both damage thresholds are checked using the ‘regularized’ stress field to avoid mesh dependence. The interaction between propagating cracks and potential initiation sites is accounted for. Copyright © 2012 John Wiley & Sons, Ltd.     

Statistical investigation of the fracture behaviour of inhomogeneous materials in tension and three-point bending

Development of damage in heterogeneous materials submitted to tensile tests and flexural tests is analysed using finite element analysis and considering statistical distribution of material strength. Materials are assumed to have a brittle local behaviour and fracture stresses are distributed randomly through test specimens. Also, the analysis considers that it exists a dimension which is characteristic of damage growing, depending on the fracture processes induced. A simulation procedure for evaluating damage development through test specimens is next implemented and the influence of the scattering width of the fracture stress distributions is analysed.     

CDM based modelling of damage and fracture mechanisms in concrete under tension and compression

Anisotropic damage evolution and crack propagation in the elastic–brittle materials is analysed by the concepts of continuum damage mechanics (CDM) and finite element method (FEM). The modified Murakami–Kamiya (MMK) model of elastic-damage material is used to describe damage anisotropy in concrete. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The incremental form of the stress–strain equations is developed. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The local approach to fracture (LAF) by FEM is applied to the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modelled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress–strain curves are reached. A concrete specimen with the pre-load, inclined crack is analysed in order to simulate different fracture mechanisms in tension or compression. The constitutive model is capable of predicting the kinked-type crack under tension and the wing-type crack under compression.     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

A comparative investigation of micro-flaw models for the simulation of brittle fracture in rock

The search for a numerical method to model fracture formation around deep level gold mine excavations had led to the development of the DIGS (Discontinuity Interaction and Growth Simulation) boundary element code to simulate the incremental growth of fractures. However, the need to develop constitutive models of basic failure processes resulted in the adoption of a tessellation approach to simulate grain interaction and breakage. Linear variation displacement discontinuity elements are arranged in structures which simulate the microstructure of the rock by applying either a Voronoi (polygonal) or Delaunay (triangular) tessellation procedure. The tessellation approach has been applied to investigate the role of micromechanical mechanisms such as pre-existing pores and sliding flaws on the macroscopic failure patterns at a scale that is representative of realistic rock microstructures. Procedures for calculating the crack density tensors and the average stress and strain in a sample permit comparison of the results with alternative models of brittle fracture such as continuum damage mechanics. Simulations of laboratory tests have revealed that the tessellation approach can represent experimentally observed macroscopic failure modes such as splitting in uniaxial compression and shear band formation in biaxial compression, as well as the dependence of strength and inelastic deformation on the flaw density.     

Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials

In this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi‐brittle failure phenomena. The model is capable of describing the rate‐dependent behavior in dynamics and the three phases in failure of quasi‐brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture‐process zone creation, represented with rate‐dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate‐dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time‐stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed-Mode Delamination – Experimental and Numerical Studies

Abstract: A fracture energy approach for modelling mixed-mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post-failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E-glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included.     

An automated finite element analysis of the initiation and growth of damage in carbonfibre composite materials

The analysis and prediction of the development of damage in composite materials up to the point of final failure is important in the assessment of whether composite structures and components are fit for their purpose. Progressive damage modelling, using finite element analysis, has demonstrable potential as a tool for this.

If this approach is to be of real value, it needs to be automated so that the application of specialist knowledge is minimized. The ABAQUS finite element (FE) code has been used to develop fully-automated, threedimensional modelling of damage development in carbon fibre composites under tensile loading.

This paper describes the approach used in the development of these models. It covers work on the development of suitable FE meshes, the identification of suitable criteria to control the onset and effects of local damage, and the extension of the methodology to real component geometries.     

基于显式动力学的焊点冲击失效分析

组件级高速剪切测试是用来研究芯片封装中Sn-Ag-Cu焊点冲击可靠性问题的一个重要手段。实验研究表明：随着冲击速度的增加,焊点封装结构的失效会由焊锡母材的韧性破坏向界面金属间化合物(IMC)的脆性断裂过渡;同时,其荷载-位移响应曲线形态也会发生显著的改变。为了能够更详细地了解封装结构的冲击失效行为,并进一步改进其结构设计,该文提出结合焊锡材料应变率相关的动态硬化特性,利用渐进损伤模型来模拟其动态损伤过程;同时,引进一种能够有效表征复合型裂纹扩展的内聚力模型来模拟IMC的脆性动态断裂。与实验结果的对比表明：该文提出的方法能够较为有效地表征焊点封装结构在不同冲击速度下的失效行为。     

Pore–crack orientation effects on fracture behavior of brittle porous materials

Mechanical behavior of two-dimensional microstructures containing circular pores were simulated under uniaxial and biaxial loading using the finite element method. Resulting stress distributions were combined with classical fracture mechanics to investigate fracture behavior of brittle porous materials assuming that randomly oriented cracks are present along pore surfaces. Multiple crack orientations were found to introduce a variability in Weibull modulus even for the same set of microstructures containing equal number and size of cracks. Also, the variability increases with increasing crack size to pore size ratio. Under uniaxial loading, angular distribution of fracture origin widens with increasing porosity.     

Microstructural effects on ductile fracture in heterogeneous materials. Part II: Applications to cast aluminum microstructures

This is the second of a two part paper aimed at investigating the effects of microstructural morphology, material properties and loading on rate-dependent ductile fracture of heterogeneous materials. The locally enhanced Voronoi cell finite element method (LE-VCFEM) is used for micromechanical analyses of deformation and failure in complex microstructural volume elements. The first part of this paper sequence evaluates the sensitivity of strain to failure of computer simulated microstructures to loading rate, microstructural morphology and material properties. In this second part, LE-VCFEM simulations of actual microstructures of a cast aluminum alloy micrograph are used to validate a strain to failure model developed in the first part. A method for identification of critical regions within a heterogeneous microstructure is also developed and validated using in-situ observations of a two-point bending test. The influence of applied strain rates on ductile fracture of micrograph-based complex microstructures is also investigated.     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

Statistical three-dimensional investigation of the damage evolution in heterogeneous materials

A simulation procedure is implemented for evaluating the damage development though structures or test specimens constituted of heterogeneous materials. Stress and strain fields are obtained using a three-dimensional finite element analysis. Materials are assumed to have a brittle local behaviour and statistical distributions of fracture stresses are considered and distributed randomly through the structure or the test specimen. The influence of the scattering width of the stress distributions is analysed in the case of tensile tests and three-point bending tests. Experimental investigation of the fracture development is carried out in the case of polymer concrete using holography and the results obtained are compared with the results derived from the simulation procedure.     

Computational mesomechanics of particle-reinforced composites

Numerical models of deformation, damage and fracture in particle-reinforced composite materials, based on the method of multiphase finite elements (MPFE) and element elimination technique (EET), are presented in this paper. The applicability of these techniques for different materials and different levels of simulation was studied. The simulation of damage and crack growth was conducted for several groups of composites: WC/Co hard metal alloys, Al/Si and Al/SiC composites on macro- and mesolevel. It is shown that the used modern techniques of numerical simulation (MPFE and EET) are very efficient in understanding deformation and damage evolution in heterogeneous brittle/ductile materials with inclusions.     

Computational modeling of crack propagation in real microstructures of steels and virtual testing of artificially designed materials

A computational approach to the optimization of service properties of two-phase materials (in this case, fracture resistance of tool steels) by varying their microstructure is developed. The main points of the optimization of steels are as follows: (1) numerical simulation of crack initiation and growth in real microstructures of materials with the use of the multiphase finite elements (MPFE) and the element elimination technique (EET), (2) simulation of crack growth in idealized quasi-real microstructures (net-like, band-like and random distributions of the primary carbides in the steels) and (3) the comparison of fracture resistances of different microstructures and (4) the development of recommendations to the improvement of the fracture toughness of steels. The fracture toughness and the fractal dimension of a fracture surface are determined numerically for each microstructure. It is shown that the fracture resistance of the steels with finer microstructures is sufficiently higher than that for coarse microstructures. Three main mechanisms of increasing fracture toughness of steels by varying the carbide distribution are identified: crack deflection by carbide layers perpendicular to the initial crack direction, crack growth along the network of carbides and crack branching caused by damage initiation at random sites.     

Simulating Initial and Progressive Failure of Open-Hole Composite Laminates under Tension

A finite element (FE) model is developed for the progressive failure analysis of fiber reinforced polymer laminates. The failure criterion for fiber and matrix failure is implemented in the FE code Abaqus using user-defined material subroutine UMAT. The gradual degradation of the material properties is controlled by the individual fracture energies of fiber and matrix. The failure and damage in composite laminates containing a central hole subjected to uniaxial tension are simulated. The numerical results show that the damage model can be used to accurately predicte the progressive failure behaviour both qualitatively and quantitatively.     

Simulation of high speed impact into ceramic composite systems using cohesive-law fracture model

A numerical study for the analysis of oblique metal/ceramic/metal three layer composite systems against a long-rod has been performed. The study was done using a three-dimensional dynamic program NET3D, which uses the finite element Lagrangian method with explicit time integration. To model the discrete nature for fracture and damage of brittle materials, we implemented cohesive-law fracture model with a node separation algorithm for the tensile failure and Mohr–Coulomb model for the compressive loading. A tetrahedral element implemented in the code provides more potential fracture surfaces than a hexahedral element. As a verification of the scheme, an oblique impact into the composite system was conducted and the calculated penetration depth and propagating crack paths were found to be in good agreement with experiment. Next a series of three-dimensional numerical simulations have been conduced to examine the ballistic performance of three layer composite systems. The residual velocity and residual length of the rod were computed for different plate thickness ratios of equal areal density. The impact velocities considered are 1.5, 1.8 and 2.2 km/s. The oblique angle of the plate is 0° and 45°. The optimum thickness ratios of ceramic to metal are very similar to those obtained from the previous experiment.     

Level-set topology optimization for maximizing fracture resistance of brittle materials using phase-field fracture model

Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level-set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase-field fracture model is formulated herein to simulate crack initiation and propagation, in which a staggered algorithm is developed to solve such time-dependent crack propagation problems. In line with diffusive damage of the phase-field approach for fracture; topological derivatives, which provide gradient information for the topology optimization in a LS framework, are derived for fracture mechanics problems. A reaction-diffusion equation is adopted to update the LS function within a finite element framework. This avoids the reinitialization by overcoming the limitation to time step with the Courant-Friedrichs-Lewy condition. In this article, three numerical examples, namely, a L-shaped section, a rectangular slab with predefined cracks, and an all-ceramic onlay dental bridge (namely, fixed partial denture), are presented to demonstrate the effectiveness of the proposed LS based topology optimization for enhancing fracture resistance of multimaterial composite structures in a phase-field fracture context.     

Adaptive combined DE/FE algorithm for brittle fracture of plane stress problems

A novel adaptive combined DE/FE algorithm is proposed to simulate the fracture procedure of brittle materials of plane stress problems. The main concept of the approach is that a model is composed of the finite element completely at the initial stage without any discrete element generated until portion of the model grid becoming severely deformed; and then the model is fragmented into two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The interface force between the two subdomains is calculated by using the penalty method. An extrinsic cohesive fracture model is employed to simulate the brittle fracture procedure only in the DE subdomain. The adaptive algorithm may allow for the use of the accurate and efficient FEs in the lower distorted region and the DEs which are automatically generated in the severely deformed FE region . The feasibility of the adaptive algorithm is validated by the impact fracture simulation of a glass beam. The comparison of calculation time consumption shows that the adaptive algorithm has a higher efficiency than the DEM. At last, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with the experimental results showing that the adaptive algorithm can be implemented to capture some fracture characteristics of brittle materials.