Showing papers in "International Journal of Fracture in 2016"

Ductile failure modeling

Abstract: Ductile fracture of structural metals occurs mainly by the nucleation, growth and coalescence of voids. Here an overview of continuum models for this type of failure is given. The most widely used current framework is described and its limitations discussed. Much work has focused on extending void growth models to account for non-spherical initial void shapes and for shape changes during growth. This includes cases of very low stress triaxiality, where the voids can close up to micro-cracks during the failure process. The void growth models have also been extended to consider the effect of plastic anisotropy, or the influence of nonlocal effects that bring a material size scale into the models. Often the voids are not present in the material from the beginning, and realistic nucleation models are important. The final failure process by coalescence of neighboring voids is an issue that has been given much attention recently. At ductile fracture, localization of plastic flow is often important, leading to failure by a void-sheet mechanism. Various applications are presented to illustrate the models, including welded specimens, shear tests on butterfly specimens, and analyses of crack growth.

On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

Abstract: The phase field method is a versatile simulation framework for studying initiation and propagation of complex crack networks without dependence to the finite element mesh. In this paper, we discuss the influence of parameters in the method and provide experimental validations of crack initiation and propagation in plaster specimens. More specifically, we show by theoretical and experimental analyses that the regularization length should be interpreted as a material parameter, and identified experimentally as it. Qualitative and quantitative comparisons between numerical predictions and experimental data are provided. We show that the phase field method can predict accurately crack initiation and propagation in plaster specimens in compression with respect to experiments, when the material parameters, including the characteristic length are identified by other simple experimental tests.

20 Hz X-ray tomography during an in situ tensile test

Abstract: This paper describes an in-situ tensile test in synchrotron tomography achieved for the first time with a frequency of 20 tomograms per second (20 Hz acquisition frequency). This allows us to capture rapid material fracture processes, such as that of a metal matrix composite composed of 45 % of alumina particles embedded into 55 % of pure aluminium, which fractures by the sudden coalescence of internal damage. Qualitatively, the images show the nucleation and propagation of a crack during 9 s leading to total fracture of the sample. The images are then post-processed quantitatively to analyze the evolving shape of the crack and to derive the instantaneous speed of its tip. It is shown that the crack clearly propagates from one particle to the next, pausing briefly before propagating to the next particle, lending experimental support to a local load sharing analysis of the fracture of this class of composite.

An incremental stress state dependent damage model for ductile failure prediction

Abstract: The goal of this contribution is to formally present an incremental damage model conceived to predict failure of ductile materials in forming and crash applications. Denoted henceforth by the acronym Generalized Incremental Stress State Dependent Damage Model (GISSMO), the present model’s framework is based on an incremental damage accumulation which is dependent on a failure curve which, in turn, is a function of the current stress state. The damage variable is of scalar nature and inherently takes into account the effects of non-proportional loadings. Furthermore, GISSMO includes the evolution of an instability measure based on a critical strain. When this variable reaches unity, the coupling between the stress tensor and the damage variable is considered. This allows capturing the effects in post-critical regime macroscopically, from strain localization to final element erosion and crack formation. Since spurious mesh dependence is a concern when simulating material behavior up to fracture, a regularization strategy is proposed to compensate for the effects of mesh dependence in a global fashion. The aforementioned aspects of GISSMO are presented and discussed in detail in the present contribution as well as the calibration of the model based on experimental data of a dual-phase steel. It is shown that GISSMO is able to reproduce the fracture behavior of the calibrated material for several load paths.

Modeling the interaction between fluid-driven fracture and natural fault using an enriched-FEM technique

Abstract: In this paper, the interaction between the fluid-driven fracture and frictional natural fault is modeled using an enriched-FEM technique based on the partition of unity method. The intersection between two discontinuities is modeled by introducing a junction enrichment function. In order to model the fluid effect within the fracture, the fluid pressure is assumed to be constant throughout the propagation process. The frictional contact behavior along the fault faces is modeled using an X-FEM penalty method within the context of the plasticity theory of friction. Finally, several numerical examples are solved to illustrate the accuracy and robustness of proposed computational algorithm as well as to investigate the mechanism of interaction between the fluid-driven fracture and the natural fault.

The second Sandia Fracture Challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading

Abstract: Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in $$\sim $$ 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

Numerical simulation of initiation, propagation and coalescence of cracks using the non-ordinary state-based peridynamics

Abstract: The stress-based failure criterion is implemented into the non-ordinary state-based peridynamic model. The non-ordinary state-based peridynamic model is developed to simulate the initiation, propagation and coalescence process of cracks subjected to quasi-static and dynamic loads. Three-point-bending tests with a notch offset from the center of the beam are numerically conducted under quasi-static loads. The mode I fracture toughness of Kimachi sandstone has also been evaluated using the non-ordinary state-based peridynamic model by semi-circular bend. Moreover, the proposed method is applied to investigate the effects of arrays of cracks on propagation and coalescence process of multiple cracks subjected to dynamic loads. The numerical results are in good agreement with the previous experimental and numerical results. It is concluded that the non-ordinary state-based peridynamic model is able to analyze fracture problems.

Experimental study on the mechanical properties of AZ31B-H24 magnesium alloy sheets under various loading conditions

Abstract: In order to fully characterize the plasticity and fracture of magnesium AZ31B-H24 sheets, a set of mechanical experiments (105 in total) were performed under different loading conditions, including monotonic uniaxial tension, notch tension, in-plane uniaxial compression, wide compression (or called biaxial compression), plane strain compression, through-thickness compression, in-plane shear, punch test, and uniaxial compression–tension reverse loading. Both the plastic strain histories and stress responses were obtained under the above loading conditions, which give a comprehensive picture of mechanical behaviors of this material. An orthotropic yield criterion involving two linear anisotropic transformation tensors, CPB06ex2, in conjunction with its associated flow rule, and a modified semi-analytical Sachs isotropic hardening model was fully calibrated to describe both the anisotropy in plastic flow and tension–compression asymmetry in stress–strain behaviors. An all-strain based modified-Mohr–Coulomb fracture model, transformed from a stress triaxiality based model, was applied to describe the calibrated fracture locus. Applying a linear transformation to the plastic strain tensor, a non-conjugated anisotropic equivalent strain was proposed to characterize anisotropic fracture behaviors. Good correlations were achieved between experimental results and model predictions in terms of material yield strengths, strain hardening curves, plastic flow directions and ductile fracture strains.

On determining mixed-mode traction–separation relations for interfaces

Abstract: Traction–separation relations can be used to represent the adhesive interactions of a bimaterial interface during fracture. In this paper, a direct method is proposed to determine mixed-mode traction–separation relations based on a combination of global and local measurements including load-displacement, crack extension, crack tip opening displacement, and fracture resistance curves. Mixed-mode interfacial fracture experiments were conducted using the end loaded split (ELS) configuration for a silicon-epoxy interface, where the epoxy thickness was used to control the phase angle of the fracture mode-mix. Infra-red crack opening interferometry was used to measure the normal crack opening displacements, while both normal and shear components of the crack-tip opening displacements were obtained by digital image correlation. For the resistance curves, an approximate value of the J-integral was calculated based on a beam-on-elastic-foundation model that referenced the measured load-displacement data. A damage-based cohesive zone model with mixed-mode traction–separation relations was then adopted in finite element analyses, with the interfacial properties determined directly from the experiments. With the mode-I fracture toughness from a previous study, the model was used to predict mixed-mode fracture of the silicon/epoxy interfaces for phase angles ranging from $$-42^{\circ }$$ to $$0^{\circ }$$ . Results from experiments using ELS specimens with phase angles that differed from those employed in parameter extraction were used to validate the model. Additional measurements would be necessary to further extend the reach of the model to mode-II dominant conditions.

Anisotropic ductile failure of a high-strength line pipe steel

Abstract: Fracture properties of a mother plate for API grade X100 line pipe were investigated using tensile notched bars, CT and SENB pre-cracked specimens. The material had an anisotropic plastic behaviour due to the thermo-mechanical control rolling process. In addition, anisotropic rupture properties were also observed. Specimens tested along the rolling direction were more ductile and more crack growth resistant than those tested along the long transverse direction. Unit cell calculations were used to show that this fracture behaviour is not related to plastic anisotropy. Assuming that fracture is controlled by internal necking between anisotropically spaced voids, a model combining GTN and Thomason models is proposed which enables describing rupture anisotropy. A modified phenomenological model is also proposed so as to reduce the computational cost.

On the growth of cracks under mixed-mode I + III loading

Abstract: We examine the growth of cracks under mixed-mode I + III loading conditions. Specially designed specimen configurations are used to identify that crack front fragmentation occurs through nucleation of nearly regularly spaced daughter cracks, and that coarsening of this spacing during growth increases through an elastic shielding mechanism. It is shown further that linkage of the daughter cracks does not occur concurrently with the formation of the primary system of daughter cracks, but at a later stage of the growth of the daughter cracks. A mechanism of the combined growth of the parent and daughter cracks under mixed-mode I + III loading is suggested for capturing the pattern formation of the echelon crack patterns observed in laboratory experiments and field observations.

Initiation of edge debonding: coupled criterion versus cohesive zone model

Abstract: Cohesive zone models and criteria based on finite fracture mechanics are two alternatives to analyze edge debonding. A comparison between the two approaches is presented in this paper. The coupled criterion which combines a stress and an energy conditions to estimate crack initiation is used and compared with a bilinear cohesive law. Predictions of the debonding onset are in good agreement provided the characteristic fracture length of the interface remains smaller than the characteristic dimension of the specimen.

A comparative study of the r-adaptive material force approach and the phase-field method in dynamic fracture

Abstract: This contribution presents a comparison between a discrete and a smeared approach to approximate a crack in finite element simulations including the contribution of inertia to the behavior of brittle material under transient loading in the case of fracture. The discrete approximation of a crack is based in this case on a node duplication technique triggered by the evaluation of the so-called “material force” at the crack tip. The smeared approximation of a crack bases on the diffuse description of the crack by a phase-field approach. The governing equations under consideration of transient contributions are shown and the procedure for the finite element implementation is outlined. Numerical simulations investigate the capabilities and limitations of both methods. Firstly, the procedure to introduce initial cracks in a structure and the setup necessary to make them interact with stress waves properly, are under investigation. Moreover, this study deals with the evaluation of the velocity of the crack propagation and its comparison to experimental data. Finally, the phenomenon of crack branching is studied. The presentation and discussion of the results of the simulations provide an overview on the potential of both approaches with respect to an efficient and a realistic simulation of fracture processes in dynamic problems.

Biaxial experiments and phenomenological modeling of stress-state-dependent ductile damage and fracture

Abstract: The paper discusses an anisotropic continuum damage and fracture model for ductile metals. The phenomenological approach takes into account the effect of stress state on damage and failure criteria. Different branches of the criteria are considered corresponding to various microscopic mechanisms depending on stress intensity, stress triaxiality and the Lode parameter. To validate the proposed framework different experiments with biaxially loaded specimens and corresponding numerical simulations have been performed. Digital image correlation technique has been used to analyze current strain states in critical regions of the specimens.

Simulation and experimental investigation of the spall fracture of 304L stainless steel irradiated by a nanosecond relativistic high-current electron beam

Abstract: The results of numerical and experimental investigations of the shock-wave induced spall fracture of bulk samples with thickness up to 10 mm made of 304L stainless steel irradiated by a nanosecond relativistic high-current electron beam with duration of $${\sim }$$ 45 ns, electron energy of 1.35 MeV, and peak power density of $$\hbox {34 GW/cm}^{2}$$ are presented. By a mathematical model developed for numerical simulation of the shock-wave dynamics, it was found that a quasi-planar shock wave with duration of $${\sim }0.2\,\upmu \hbox {s}$$ , and initial amplitude of 17 GPa was formed in the irradiated samples. The effects of orientation of $$\updelta $$ -ferrite interlayers in the austenitic matrix relative to the shock wave direction on the spall fracture were experimentally investigated. It was found that spallation was carried out by mixed ductile–brittle fracture. For the transversal orientation of $$\updelta $$ -ferrite, the contribution of a brittle fracture mode in the spallation is higher than that for the longitudinal orientation. In both cases, the spalled layer thickness increased almost linearly with the increase of the target thickness, which was in good agreement with literature data. By the comparison of experimental data with simulation results, it was revealed that the spall strength can be estimated as 6.1 GPa at strain rate $$0.48\,\upmu \hbox {s}^{-1}$$ and 3.4 GPa at strain rate 0.18 $$\upmu \hbox {s}^{-1}$$ , for samples with the longitudinal and transversal orientation of $$\updelta $$ -ferrites, respectively. The comparison of the obtained spall strength values with literature data is considered.

A three dimensional augmented finite element for modeling arbitrary cracking in solids

Abstract: This paper presents a new three dimensional (3D) augmented finite element method (A-FEM) that can account for arbitrary crack initiation and propagation in 3D solids without the need of additional DoF or phantom nodes. The method permits the derivation of explicit, fully condensed elemental equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node tetrahedron element and a simple local tracking algorithm has been employed for calculating and recording the evolving planar or non-planar crack surface. It has been demonstrated through ample numerical examples that the new 3D A-FEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 3D solids with planar or non-planar crack surfaces.

An analysis of the influence of grain boundary strength on microstructure dependent fracture in polycrystalline tungsten

Abstract: This work examines the influence of changes in grain boundary (GB) strength on microstructure dependent crack propagation in polycrystalline tungsten (W). The property of focus is brittleness index (BI) originally introduced by Evans and Marshall in 1976 and 1979, respectively, used in order to quantify the extent of brittleness of a material. In an earlier work, GBs of Ni-doped polycrystalline W have been characterized for embrittlement using ab-initio quantum mechanical simulations as a function of Ni atomic volume fraction and GB thickness. This work focuses on quantifying the influence of GB strength on microstructure dependent crack propagation. Continuum mechanical GB strength properties and effective W grain properties are derived from ab-initio simulation based stress–strain curves. The crack propagation simulations when GBs are considered of finite width are based on an extended finite element (XFEM) framework. Simulations that consider GBs of infinitesimal width due to mesh resolution issues are based on a combined XFEM-cohesive finite element model that employs cohesive elements at GBs. Analyses of crack propagation through finite width GBs focus on understanding the role of square root of length scale dimension in the original BI formulation. Based on analyses of crack propagation through finite width GBs oriented at angles varying from $$0^{\circ }\,\hbox {to}\,90^{\circ }$$ with respect to advancing crack, a quantitative criterion based on a failure index which predicts crack propagation path in polycrystalline W is proposed and examined.

Time-dependent crack propagation in a poroelastic medium using a fully coupled hydromechanical displacement discontinuity method

Abstract: Many problems in subsurface rocks which are naturally filled with saturated cracks and pores (with one or more fluid phases) are better understood in a poroelastic framework. Displacement discontinuity method (DDM) is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic problems. The paper derives fundamental solutions of a poroelastic DDM. Then introduces a numerical formulation and implementation for the poroelastic DDM in a code named constant element poroelastic DDM (CEP-DDM). The accuracy and validity of the proposed solution and the newly developed code is verified by an analytical solution at short-time and long-time. Numerical results showed good agreement with analytical results at short time (undrained response) and long time ( $$t=8000$$ s) (drained response). A crack propagation scheme for crack propagation problems is introduced and demonstrated in an example which enables the code to follow crack propagation in time and space.

Statistical aspects in crack growth phenomena: how the fluctuations reveal the failure mechanisms

Abstract: Material failure often gives rise to strong fluctuations that reflect on the rough trajectory followed by cracks and on their intermittent dynamics. Understanding the origin of these fluctuations is a major challenge in fracture mechanics since they emerge from the interaction of the cracks with the material microstructure that it still poorly understood. Here, we illustrate through recent studies how the statistical properties of these fluctuations can reveal elementary failure mechanisms taking place at the microstructure scale. The implications of these findings in terms of material characterization and failure analysis is discussed and some promising directions for future investigations are presented.

The second Sandia Fracture Challenge: blind prediction of dynamic shear localization and full fracture characterization

Abstract: In the context of the second Sandia Fracture Challenge, dynamic tensile experiments performed on a Ti–6Al–4V alloy with a complex fracture specimen geometry are modeled numerically. Sandia National Laboratories provided the participants with limited experimental data, comprising of uniaxial tensile test and V-notched rail shear test results. To model the material behavior up to large plastic strains, the flow stress is described with a linear combination of Swift and Voce strain hardening laws in conjunction with the inverse method. The effect of the strain rate and temperature is incorporated through the Johnson–Cook strain rate hardening and temperature softening functions. A strain rate dependent weighting function is used to compute the fraction of incremental plastic work converted to heat. The Hill’48 anisotropic yield function is adopted to capture weak deformation resistance under in-plane pure shear stress. Fracture initiation is predicted by the recently developed strain rate dependent Hosford–Coulomb fracture criterion. The calibration procedure is described in detail, and a good agreement between the blind prediction and the experiments at two different speeds is obtained for both the crack path and the force–crack opening displacement (COD) curve. A comprehensive experimental and numerical follow-up study on leftover material is conducted, and plasticity and fracture parameters are carefully re-calibrated. A more elaborate modeling approach using a non-associated flow rule is pursued, and the fracture locus of the Ti–6Al–4V is clearly identified by means of four different fracture specimens covering a wide range of stress states and strain rates. With the full characterization, a noticeable improvement in the force–COD curve is obtained. In addition, the effect of friction is studied numerically.

Simulating fully 3D non-planar evolution of hydraulic fractures

Abstract: Three-dimensional model of fracture propagation is proposed. The model simultaneously accounts rock deformation in the vicinity of a fracture and a cavity, fluid flow inside the fracture and its propagation in the direction that is selected by a growth criterion. The results of the sensitivity analysis of model solution to the variation of model parameters are presented.

Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations

Abstract: We develop an approach to studying the influence of stresses and strains on the kinetics of chemical reaction fronts based on the expression of the chemical affinity tensor that determines the configurational force acting at the transformation front For a chemical reaction between diffusive gaseous and deformable solid constituents we formulate a kinetic equation in a form of the dependence of the reaction front velocity on the normal component of the chemical affinity tensor that in turn depends on stresses We describe a locking effect—blocking the reaction by stresses at the reaction front and define the forbidden stresses or strains at which the chemical reaction cannot go We develop a finite-element model to describe how stresses affect a chemical reaction front propagation To demonstrate how the model works we consider a chemical front propagation in a plate with a groove assuming that the solid constituents are linear elastic Comparing the front propagation in the vicinity of the groove top and at the bottom of the plate far from the groove we study how the stress concentrations, internal stresses and external loading, material and reaction parameters affect the reaction

Influences of hydrogen on deformation and fracture behaviors of high Zn 7XXX aluminum alloys

Abstract: Hydrogen degrades the mechanical properties of high strength 7XXX aluminum alloys in two ways: (i) degrades the mechanical properties by hydrogen embrittlement, and (ii) partitioned into micropores as molecular hydrogen and make contributions to ordinary ductile fracture. The multifaceted effects of hydrogen on the mechanical properties of high Zn content 7XXX aluminum alloys during deformation and fracture is studied by using synchrotron X-ray microtomography. Our results have revealed that the hydrogen susceptibility has increased with increasing the Zn amount. High concentration of hydrogen was induced by the EDM wire eroder. This high concentrated hydrogen induces quasi-cleavage fracture and restricts the growth of micropores during ductile deformation. The threshold concentration of hydrogen ahead of the crack tip for the nucleation of quasi-cleavage feature was estimated to be $$13~\hbox {cm}^{3}/100~\hbox {g Al}$$ .

A nonlinear cohesive/friction coupled model for shear induced delamination of adhesive composite joint

Abstract: This paper originally proposes a nonlinear cohesive/frictional contact coupled model for the mode-II shear delamination of adhesive composite joint based on a modified Xu and Needleman’s exponential cohesive model. First, the friction is assumed to increase nonlinearly at the delamination interface when the tangential cohesive softening appears. Second, a non-associative plasticity model based on the Mohr–Coulomb frictional contact law is proposed, which includes a frictional slip criterion and a slip potential function. Third, a return mapping algorithm based on the non-associative plasticity theory is proposed to solve the updated normal and tangential tractions and stiffnesses. It is shown the tangential cohesive traction and stiffness depend on the friction and dilatancy of the delamination interface. Finally, the proposed theoretical model is implemented using three-dimensional finite element analysis by ABAQUS-UEL (user element subroutine) and demonstrated by comparing the finite element results with the analytical results for the $$[0^{\circ }]_{6}$$ , $$[\pm 30^{\circ }]_{5}$$ , $$[\pm 45^{\circ }]_{5}$$ end-notched flexure adhesive composite joints with the mode-II shear delamination. The effects of the friction coefficient, cohesive strength, normal contact stiffness and mesh size on the load–displacement curves and delamination mechanisms of composites are studied. Numerical results show the shear delamination growth is governed by the transition from the decreased tangential cohesive traction to the increased tangential friction, and the frictional effect becomes distinct after unstable delamination for angle-ply laminates.

Slant strained band development during flat to slant crack transition in AA 2198 T8 sheet: in situ 3D measurements

Abstract: In this work 3D strain and damage analyses are performed in the immediate vicinity of the notch root of a flat CT-like specimen made of aluminum alloy. Experimental data, partially exploited by Morgeneyer et al. (Acta Mat 69:78–91, 2014b), were obtained by using synchrotron laminography and the 3D reconstructed volumes are subsequently analyzed via Digital volume correlation. These data enable for in situ assessments of strain fields and ductile damage in the zone where the stress triaxiality evolves from elevated to lower levels, which is accompanied by flat-to-slant crack transition. The measured strain field patterns in this area are analyzed herein in a systematic manner by studying the incremental strain activity during several loading steps. It is shown that from the very beginning of the loading history multiple slant strained bands appear in front of the notch root while the corresponding damage growth sets in at later loading stages and higher strains. The activity of the different strained bands at the notch root is alternating between different locations over the loading history. However, the band leading to final rupture is always active. The region where slant fracture occurs is identified to be in plane strain condition with respect to the crack propagation direction.

Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation

Abstract: A non-local formulation of the classical continuum mechanics theory called peridynamics is used to study initiation and propagation of dynamic fractures. The purpose of this study is twofold. First, we introduce a new post-processing technique to estimate stress intensity factors using peridynamic data. Second, the peridynamic stress intensity factors are used to study the influence of loading rate on key aspects of dynamic fracture. In particular attention is focused on examining the influence of loading rate and material properties on time to fracture and the local stress state at the fracture tip during initiation and propagation. In the first part of the paper emphasis is placed on using stress intensity factors to verify the numerical method. Simulations are performed on simplified test cases and the results are compared to relevant experimental and numerical studies found in the literature. Peridynamic stress intensity factors are then used to demonstrate the influence of loading rate on fracture initiation and propagation. To this end simulations are performed by partially loading the internal surfaces of a notch at various loading rates and monitoring the stress intensity at the tip of the notch. For each loading rate, the stress intensity factor increases smoothly to a value above the input fracture toughness at which point initiation occurs. After initiation, the stress intensity factor remains nearly constant in time. It is shown that the stress intensity factor at initiation and the time to fracture depend on the loading rate. Predictions show that the critical stress intensity is insensitive to loading rate when the fracture initiation time is below a material-dependent characteristic time scale. As loading rate increases, the time to fracture decreases and stress intensity at initiation increases markedly. The characteristic time-scale is shown to be only dependent on the material stiffness and independent of the strength of the singularity at the fracture tip. In our simulations, increasing the loading rate resulted in fracture branching. Also, the fracture speed increases with loading rate. However, the dynamic stress intensity factor of a propagating fracture is shown to be independent of loading conditions for a linear peridynamic solid with rate-independent input fracture toughness.

An improved numerical manifold method incorporating hybrid crack element for crack propagation simulation

Abstract: The numerical manifold method (NMM) simulates continuous and discontinuous problems in a unified framework; thus NMM has advantages in analysing crack propagation. However, calculation of the stress intensity factors (SIFs) when adopting the NMM requires additional procedures, such as the J-integral and the interaction integral. In this study, a hybrid crack element (HCE) method is incorporated into the NMM to directly obtain the SIFs; the new algorithm combines the merits of both the NMM and HCE method. In the proposed algorithm, the HCE is used in the crack-tip region while the NMM is applied in the remaining region. The SIFs at the crack-tip are calculated directly from the solution of the governing equation with less computational complexity relative to existing methods. The proposed algorithm does not require any changes to the initial mesh during crack propagation. It is verified by a few examples and the results show that the simulated crack propagation paths are in good agreement with the results from existing studies while the computational efficiency is improved due to the direct calculation of the SIFs and the consistency of the mesh system in the crack propagation process.

Energy release rate and criticality of multiscale defects kinetics

Abstract: Configuration mechanics of solid with defects (microcracks, microshears) was used for statistical description of multiscale defect interaction, presentation of out-of-equilibrium free energy release rate and defects kinetics, which reveals specific type of criticality—structural-scaling transition According to this transition defects kinetics occurs as generation of collective modes of defects that have the nature of self-similar solutions for defects kinetic equations It is showm using original “in-situ” experiments that spatial-temporal scenario of collective modes leads to specific fractographic pattern on fracture surface and self-similar material responses in wide range of load intensity

Impact of microstructure on void growth and linkage in pure magnesium

Abstract: The role of the microstructure on void growth and linkage in magnesium has been investigated. 2D model materials have been fabricated using pico-second laser technology whereby holes were drilled into the gage section of tensile samples composed of thin Mg sheet. These were pulled in uniaxial tension inside the chamber of an SEM which allowed for a quantitative assessment of the void growth and linkage processes. In contrast to the recent studies of void growth and linkage in fcc metals (copper and aluminum), the local microstructure plays a significant role on the deformation and fracture behavior of magnesium. Void growth was observed to occur non-uniformly due to interactions between the holes and microstructural features such as grain and twin boundaries. In addition, the main fracture mechanisms responsible for void linkage include failure associated with these boundaries. Twin and grain boundaries introduce microstructural features on a length scale comparable to the holes which are not present in models based on continuum mechanics. In order to model the deformation and fracture of magnesium, the initial microstructure as well as microstructural evolution must be taken into account.

A note on the Virtual Crack Closure Technique for a bimaterial interface crack

Abstract: The Virtual Crack Closure Technique was first presented in 1977 for cracks in linear elastic, homogeneous and isotropic material. It makes use of the Irwin crack closure integral to obtain values of the modes I, II and III energy release rates from finite element data. It can easily be extended to anisotropic material. In addition, it was extended to cracks along an interface between two dissimilar linear elastic, homogeneous and isotropic materials. In that case, the energy release rates were seen to depend upon the size of the virtual crack extension usually taken as the size of the element adjacent to the crack tip. Some attempts have been made to remove this dependence. Nevertheless, in most cases, the accuracy of both the energy release rates and stress intensity factors was not consistently good. In this note, the dependence of the energy release rates on the size of the virtual crack extension for interface cracks is analytically accounted for so that the stress intensity factors may be accurately obtained when fine finite element meshes are used, together with a virtual crack extension consisting of more than one element.