Locally enhanced Voronoi cell finite element model (LE‐VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions

Ductile heterogeneous materials such as cast aluminum alloys undergo catastrophic failure that initiates with particle fragmentation, which evolves with void growth and coalescence in localized bands of intense plastic deformation and strain softening. The Voronoi cell finite element model (VCFEM), based on the assumed stress hybrid formulation, is unable to account for plastic strain‐induced softening. To overcome this shortcoming of material softening due to plastic strain localization, this study introduces a locally enhanced VCFEM (LE‐VCFEM) for modeling the very complex phenomenon of ductile failure in heterogeneous metals and alloys. In LE‐VCFEM, finite deformation displacement elements are adaptively added to regions of localization in the otherwise assumed stress‐based hybrid Voronoi cell finite element to locally enhance modeling capabilities for ductile fracture. Adaptive h‐refinement is used for the displacement elements to improve accuracy. Damage initiation by particle cracking is triggered by a Weibull model. The nonlocal Gurson–Tvergaard–Needleman model of porous plasticity is implemented in LE‐VCFEM to model matrix cracking. An iterative strain update algorithm is used for the displacement elements. The LE‐VCFEM code is validated by comparing with results of conventional FE codes and experiments with real materials. The effect of various microstructural morphological characteristics is also investigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Fracture Criteria for Automobile Crashworthiness Simulation of Wrought Aluminium Alloy Components

In automobile crashworthiness simulation, the prediction of plastic deformation and fracture of each significant, single component is critical to correctly represent the transient energy absorption through the car structure. There is currently a need, in the commercial FEM community, for validated material fracture models which adequately represent this phenomenon. The aim of this paper is to compare and to validate existing numerical approaches to predict failure with test data. All studies presented in this paper were carried out on aluminium wrought alloys: AlMgSi1.F31 and AlMgSiCu‐T6. A viscoplastic material law, whose parameters are derived from uniaxial tensile and compression tests at various strain rates, is developed and presented herein. Fundamental ductile fracture mechanisms such as void nucleation, void growth, and void coalescence as well as shear band fracture are present in the tested samples and taken into consideration in the development of the fracture model. Two approaches to the prediction of fracture initiation are compared. The first is based on failure curves expressed by instantaneous macroscopic stresses and strains (i. e. maximum equivalent plastic strain vs. stress triaxiality). The second approach is based on the modified Gurson model and uses state variables at the mesoscopic scale (i. e. critical void volume fraction). Notched tensile specimens with varying notch radii and axisymmetric shear specimens were used to produce ductile fractures and shear band fractures at different stress states. The critical macroscopic and mesoscopic damage values at the fracture initiation locations were evaluated using FEM simulations of the different specimens. The derived fracture criteria (macroscopic and mesoscopic) were applied to crashworthiness experiments with real components. The quality of the prediction on component level is discussed for both types of criteria.     

Three‐dimensional mixed‐mode (I and II) crack‐front fields in ductile thin plates — effects of T‐stress

It has been well‐established that the non‐singular T‐stress provides a first‐order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic–plastic crack‐front field under mode I loading conditions. The objective of this paper is to exam the T‐stress effect on three‐dimensional (3D) crack‐front fields under mixed‐mode (modes I and II) loading. To this end, detailed 3D small strain, elastic–plastic simulations are carried out using a 3D boundary layer (small‐scale yielding) formulation. Characteristics of near crack‐front fields are investigated for a wide range of T‐stresses (T/σ₀ = ?0.8, ?0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters M_e = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T‐stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T‐stress. It is important to include these effects when investigating the mixed‐mode ductile fracture failure process in thin‐walled structural components.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Stress triaxiality effect on void nucleation in ductile metals

The stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.     

Correlation of material constraint with fracture toughness of interface regions in a dissimilar metal welded joint

In this work, the constraint parameter A_p based on crack‐tip equivalent plastic strain was calculated by finite element analyses for the cracks located at different locations in two interface regions in a dissimilar metal weld joint (DMWJ). The capabilities of the parameter A_p for characterizing material constraint and establishing correlation of material constraint with fracture toughness of the interface region cracks have been examined. The results show that the parameter A_p can characterize material constraint effect caused by material mismatch and initial crack positions in the interface regions. Based on the A_p, the correlation lines and formulae of material constraint with fracture toughness of the interface region cracks in the DMWJ can be established, and they may be used for obtaining material constraint‐dependent fracture toughness for the interface region cracks. The results in this work combining with those in the previous studies indicate that the parameter A_p may be a unified constraint parameter that can characterize both geometry constraint (including in‐plane and out‐of‐plane constraints) and material constraint, and it may be used in accurate fracture assessments of welded components with different geometry and material constraints.     

A high-cycle fatigue life model for variable amplitude multiaxial loading

A high‐cycle fatigue life model for structures subjected to variable amplitude multiaxial loading is presented in this paper. It treats any kind of repeated blocks of variable amplitude multiaxial loading without using a cycle counting method. This model based on a mesoscopic approach is characterized by the following features: (i) the choice of a damage factor related to the accumulated mesoscopic plastic strain per stabilised cycle; (ii) the use of a mesoscopic mechanical behaviour taking into account the fatigue mechanisms such as plasticity and void growth. This behaviour is a von Mises elastoplastic model with linear kinematic hardening and hydrostatic stress dependent yield stress. The fatigue life model has six parameters identified with one SN curve and two fatigue limits. In‐phase and out‐of‐phase experimental tests from the literature are simulated. The predicted fatigue lives are compared to experimental ones.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 2. Ductile fracture

A model of ductile failure of a body with a crack has been developed which enables predicting fracture toughness on the upper shelf of the fracture toughness temperature dependence taking into account the influence of the stress state. The model is based on the physical-mechanical model of ductile failure which is controlled by the critical value εf reached by plastic strain at the crack tip ε _i ^ρ . In this case it is assumed that both the ε _i ^ρ value, which precedes the crack growth onset by the mechanism of pore coalescence, and the critical strain εf are functions of specific stress state parameters, namely: the critical strain is a function of the stress state triaxiality σ _m /σ _n (σ _m is the hydrostatic stress, σ _i is the stress intensity), and ε _i ^ρ is a function of the parameter χ introduced, which is an explicit function of all three principal local stresses in the process zone at the crack tip and which defines the degree to which the stress state approaches the plane strain conditions for a body of specified thickness. The model developed has two modifications one of which enables predicting fracture toughness of large-size bodies from the results of testing only small cylindrical specimens without cracks (smooth and with a circular recess) and the other from the results of testing small cylindrical specimens and small specimens with a crack. Translated from Problemy Prochnosti, No. 2, pp. 5–19, March–April, 1997.     

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.     

A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel

Fracture initiation in ductile metal plates occurs due to substantial tunneling of the crack in the interior of the specimen followed by final failure of side ligaments by shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. This phenomenon is clearly exhibited in a recent experimental investigation [8] performed on pre-notched plates of a ductile heat treatment of 4340 carbon steel. Experimental evidence obtained in [8] suggests that tunneling begins at an average value of J which is significantly lower than the J value at which gross initiation is observed on the free surface. In the present work, fracture initiation in the 4340 steel specimens used in [8] is analyzed by performing a 3-dimensional numerical simulation. A damage accumulation model that accounts for the ductile failure mechanisms of void nucleation, growth, and void coalescence is employed. Results indicate that incipient Cmaterial failure at the center-plane of the 3-dimensional specimen is predicted quite accurately by this computation. Also, good agreement between results obtained at the center-plane of the 3-dimensional specimen and a plane strain analysis, suggests that a local definition of J can be used to characterize fracture initiation in the center-plane of the specimen. Finally, radial and thickness variations of the stress and porosity fields are examined with view of understanding the subsequent propagation of the failure zone.     

On the influence of state of stress on ductile failure initiation in high strength steels

The effect of stress state on the effective plastic strain to initiate ductile failure in three high strength steels is investigated. Circumferentially notched tension specimens were used, and failure initiation strains were correlated with a parameter which is a measure of the “triaxiality” of the stress state. Results are given for both in-plane and through-thickness directions in rolled plate.The failure initiation data, together with appropriate stress-strain fields, and estimates of characteristic lengths over which failure initiates, have been used to predict failure initiation at notches and at crack tips; conventional fracture mechanics parameters, such as K_I at crack extension in small scale yielding are estimated for one of the high strength steels.     

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic–perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near‐tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T ‐stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T ‐stress becomes more negative irrespective of lattice orientation. Also, the near‐tip field for a range of constraint levels can be characterized by two‐parameters such as K–T or J–Q as in isotropic plastic solids.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

Simulation of brittle and ductile fracture in an impact loaded prenotched plate

We analyze the initiation and propagation of a crack from a point on the surface of a circular notch-tip in an impact loaded prenotched plate. The material of the plate is assumed to exhibit strain hardening, strain-rate hardening, and softening due to the rise in temperature and porosity. The degradation of material parameters due to the evolution of damage in the form of porosity is considered. Brittle failure is assumed to initiate when the maximum tensile principal stress at a point reaches a critical level. Ductile failure is assumed to ensue when the effective plastic strain reaches a critical value. A crack initiating from the node where a failure first occurs is taken to propagate to the adjacent node that has the highest value of the failure parameter (the maximum tensile principal stress or the effective plastic strain). The opening and propagation of a crack are modeled by the node release technique. Surface tractions and the normal component of the heat flux are taken to be null on the newly created crack surfaces. For the brittle failure, the stress field around the crack tip resembles that in mode-I deformations of a prenotched plate loaded in tension. The distribution of the effective plastic strain in a small region around the surface of the notch-tip is not affected much by the initiation of a ductile fracture there except for a shift in the location of the point where the effective plastic strain is maximum. The initiation of the ductile failure is delayed when a crack is opened at the point where the brittle failure ensues.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.     

Continuum and atomistic modeling of electromechanically-induced failure of ductile metallic thin films

A multiscale modeling approach is presented for the analysis of electromechanically-induced void morphological evolution and failure in ductile metallic thin films, which are used for device interconnections in integrated circuits. Self-consistent mesoscopic simulations of surface morphological evolution are combined with atomistic calculations of surface properties and molecular-dynamics (MD) simulations of plastic deformation mechanisms in the vicinity of void surfaces. Results are presented that demonstrate a coupled mode of surface instability that leads to formation of electromigration-induced slit-like features and stress-induced crack-like features on void surfaces. In addition, MD results are presented for the dislocation-mediated mechanism and the kinetics of void growth in ductile metallic systems subject to hydrostatic and biaxial tensile strains. The incorporation of MD-derived constitutive information for plastic deformation into the mesoscopic analysis and simulation framework also is discussed.     

Stress distribution ahead of an interface crack tip in a ductile adhesive layer

ABSTRACT In an adhesive layer sandwiched by stiff substrates, if the plastic zone size r_p reaches several layer thicknesses ahead of the crack tip, the maximum stress develops around the region of x₁=r_p, and the stress level is even higher than the one predicted by the remote K‐field. The unusual high stress is due to the restraint of the plastic flow by adhesion with the substrates, which is similar to the ‘friction hill’ occurring in plane strain compression or tension. As a theoretical approach, a slip line field model is proposed, which provides a fairly good approximation of the stress distribution σ₂₂ ? x₁ within the plastic zone. Using the slip line field approach, a new model is proposed to estimate the plastic zone size.