Showing papers in "International Journal of Fracture in 2017"

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

Abstract: The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

Abstract: We address the simulation of dynamic crack propagation in brittle materials using a regularized phase-field description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the crack branching phenomenon as well as the existence of a limiting crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a crack accelerates , the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy Γ as an increasing function of the crack velocity. This Γ(v) relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the energy release rate associated with branching: a critical value of approximately 2Gc is observed i.e. the fracture energy contribution of two crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and branching mechanisms.

Experimental validation of a phase-field model for fracture

Abstract: Simulations from a numerical implementation of the phase-field model for brittle fracture are compared against analytical and experimental results in order to explore the verification and validation of the method. It is found that while the intrinsic length scale associated with the phase-field model can be set arbitrarily, the scale of the fracture process zone, and the scale at which the elastic field attains the corresponding analytical brittle fracture limit could be substantially larger than this intrinsic length. It is demonstrated that with a suitable choice of this length scale, phase-field simulations can provide valid predictions of the growth of cracks in quasi-static brittle fracture.

Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling

Abstract: A thermal–mechanical coupled phase field fracture model is developed to study the complex dynamic crack propagation path in brittle material under thermal shock loading. By introducing a global continuum phase-field variable to describe the diffusive crack, the coupling between heat transfer, deformation and fracture is conveniently realized. A novel elastic energy density function is proposed to drive the evolution of phase-field variable in a more realistic way. The three-field coupling equations are efficiently solved by adopting a staggered time integration scheme. The coupled phase field fracture model is verified by comparing with three classical examples and is then applied to study the fracture of disk specimens under central thermal shock. The simulations reproduce the three different types of crack paths observed in experiments. It is found that the crack grows through the heating area straightly at lower heating body flux, while branches into two at higher heating body flux loading. The crack branching prefers to occur in the heating area with larger heating radius and prefers to occur outside the heating area with smaller heating radius. Interestingly, the crack branches when propagation speed is at its lowest point, and it always occurs close to the compression region. It is shown that the heterogeneous stress field induced by temperature inhomogeneity may have a strong influence on the crack branching under the thermal shock loading.

Towards understanding the influence of porosity on mechanical and fracture behaviour of quasi-brittle materials: experiments and modelling

Abstract: In this work, porosity-property relationships of quasi-brittle materials are explored through a combined experimental and numerical approach. In the experimental part, hemihyrate gypsum plaster powder (CaSO 4 ⋅1/2H 2 O CaSO4⋅1/2H2O) and expanded spherical polystyrene beads (1.5–2.0 mm dia.) have been mixed to form a model material with controlled additions of porosity. The expanded polystyrene beads represent pores within the bulk due to their light weight and low strength compared with plaster. Varying the addition of infill allows the production of a material with different percentages of porosity: 0, 10, 20, 30 and 31 vol%. The size and location of these pores have been characterised by 3D X-ray computed tomography. Beams of the size of 20×20×150 20×20×150 mm were cast and loaded under four-point bending to obtain the mechanical characteristics of each porosity level. The elastic modulus and flexural strength are found to decrease with increased porosity. Fractography studies have been undertaken to identify the role of the pores on the fracture path. Based on the known porosity, a 3D model of each microstructure has been built and the deformation and fracture was computed using a lattice-based multi-scale finite element model. This model predicted similar trends as the experimental results and was able to quantify the fractured sites. The results from this model material experimental data and the lattice model predictions are discussed with respect to the role of porosity on the deformation and fracture of quasi-brittle materials.

Damage in elastomers: nucleation and growth of cavities, micro-cracks, and macro-cracks

Abstract: The nucleation of internal cavities and their transition to cracks are examined at high spatial and temporal resolutions within polydimethylsiloxane (PDMS) elastomers of various cross-link densities under externally applied quasi-static mechanical loads. The focus here is on experiments where the initiation and propagation of internal damage are designed to occur in between two spherical glass beads that are firmly embedded within a matrix of the PDMS elastomer and are placed close to each other in order to generate a high triaxial stress state. An optical microscope is used to monitor the various processes of nucleation and growth of cavities and cracks at a spatial resolution of about $$1\,\upmu \hbox {m}$$ and a temporal resolution of about 66.7 ms. In combination with corresponding full-field simulations, the experiments show that the nucleation of cavities—that is, the onset of cavitation—is an extremely fast process (involving stretch rates in excess of $$100\,\hbox {s}^{-1})$$ that is controlled primarily by the stiffening at large deformations of the underlying elastomer and, more critically, by its fracture properties. The experiments and simulations also show that cavitation is followed by two distinct events upon further macroscopic loading: the transition of the nucleated cavities to micro-cracks, and the further transition of some micro-cracks to macro-cracks. These two distinct events are also controlled primarily by the fracture properties of the underlying elastomer.

Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

Abstract: We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The M integral and JkJk integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.

An approximate solution for a plane strain hydraulic fracture that accounts for fracture toughness, fluid viscosity, and leak-off

Abstract: The goal of this paper is to develop an approximate solution for a propagating plane strain hydraulic fracture, whose behavior is determined by a combined interplay of fluid viscosity, fracture toughness, and fluid leak-off. The approximation is constructed by assuming that the fracture behavior is primarily determined by the three-process (viscosity, toughness, and leak-off) multiscale tip asymptotics and the global fluid volume balance. First, the limiting regimes of propagation of the solution are considered, that can be reduced to an explicit form. Thereafter, applicability regions of the limiting solutions are investigated and transitions from one limiting solution to another are analyzed. To quantify the error of the constructed approximate solution, its predictions are compared to a reference numerical solution. Results indicate that the approximation is able to predict hydraulic fracture parameters for all limiting and transition regimes with an error of under one percent. Consequently, this development can be used to obtain a rapid solution for a plane strain hydraulic fracture with leak-off, which can be used for quick estimations of fracture geometry or as a reference solution to evaluate accuracy of more advanced hydraulic fracture simulators.

Microstructural statistics for fatigue crack initiation in polycrystalline nickel-base superalloys

Abstract: In advanced engineering alloys where inclusions and pores are minimized during processing, the initiation of cracks due to cyclic loading shifts to intrinsic microstructural features. Criteria for the identification of crack initiation sites, defined using elastic-plastic loading parameters and twin boundary length, have been developed and applied to experimental datasets following cyclic loading. The criteria successfully quantify the incidence of experimentally observed cracks. Statistical microstructural volume elements are defined using a convergence approach for two nickel-base superalloys, IN100 and Rene 88DT. The material element that captures the fatigue crack-initiating features in Rene 88DT is smaller than IN100 due to a combination of smaller grain size and higher twin density.

A nonlocal damage model for plain concrete consistent with cohesive fracture

Abstract: A rate-independent damage constitutive law is proposed to describe the fracture of plain concrete under tensile loading. Here, the target scale is the individual crack. In order to deal with localised damage, the model is inherently nonlocal: the gradient of the damage field is explicitly involved in the constitutive equations; it is parameterised by a nonlocal length scale which is interpreted as the width of the process zone. The model is defined so that its predictions are close to those of a cohesive law for vanishing nonlocal length scales. Therefore, the current model is plainly consistent with cohesive zone model analyses: the nonlocal length scale appears as a small parameter which does not need any specific identification. And four parameters—among which the tensile strength and the fracture energy—enable to adjust the softening cohesive response. Besides, a special attention has been paid to the shape of the initial damage surface and to the relation between damage and stiffness. The damage surface takes into account not only the contrast between tensile and compressive strengths but also experimental evidences regarding its shape in multiaxial tension. And the damage–stiffness relation is defined so as to describe important phenomena such as the stiffness recovery with crack closure and the sustainability of compressive loads by damaged structures. Finally, several comparisons with experimental data (global force/opening responses, size dependency, curved crack paths, crack opening profiles) enable to validate qualitatively and quantitatively the pertinence of the constitutive law in 2D and 3D.

Scaling of the fracture process zone in rock

Abstract: The zone of microcracks surrounding a notch tip—the process zone—is a phenomenon observed in fracture of quasi-brittle materials, and the characterization of the process zone is the topic of the paper. Specimens of different sizes with a center notch fabricated from a granite of large grain (Rockville granite, average grain size of 10 mm), were tested in three-point bending. Acoustic emissions were recorded and locations of microcracks were determined up to peak load. The results show that both the length and width of the process zone increase with the increase of the specimen size. Furthermore, the suitability of a proposed theoretical relationship between the length and width of the process zone and specimen size was studied experimentally and numerically. The discrete element method with a tension softening contact bond model was used to investigate the development of the process zone with the specimen size. A synthetic rock composed of rigid circular particles that interact through normal and shear springs was tested in the numerical simulations. It was shown that the limiting specimen size, beyond which no further noticeable increase in the length of the process zone is observed, is significantly larger than the limiting specimen size beyond which the width of the process zone shows no size effect.

Crack coalescence morphology in rock-like material under compression

Abstract: This paper uses peridynamic simulations to determine the extent of coalescing damage and identify the underlying causes. The basic crack types and crack coalescence patterns in specimens with a flaw pair under uniaxial compression are systematically investigated. Various crack types including horsetail cracks, anti-wing cracks, and tensile wing cracks are successfully observed and the coalescence sequences are identified. By varying angles, six crack coalescence categories with respect to the overlapping ratios provide insightful information of different crack growths and indicate various cracking modes underlying various coalescence patterns. The arrangement of the flaw pair strongly influences the crack initiation position and trajectories, allowing for different coalescence morphologies. Coalescence formed by two internal tensile wing cracks, or transfixion, shows unbroken crack segments with a further loading, along with growing shear cracks until failure. In contrast, after the coalescence is formed through two horsetail cracks, the interior of the rhombic shape gets deformed with further loading. The peridynamic code adopted in this research can provide realistic simulation results and help researchers to conduct expanded tests as well as to enhance understanding the fracture of rock-like material.

Experimentally-validated mesoscale modeling of the coupled mechanical–thermal response of AP–HTPB energetic material under dynamic loading

Abstract: This manuscript presents a combined computational–experimental study of the mesoscale thermo-mechanical behavior of the Hydroxyl-terminated polybutadiene (HTPB) bonded ammonium perchlorate (AP) composite energetic material subjected to dynamic loading conditions. The computational model considers the AP–HTPB interface debonding, post-debonding interface friction and temperature rise due to viscoelastic dissipation as well as dissipative interfacial processes. The interface is modeled using a cohesive zone model combined with a contact algorithm to account for the interface separation, particle/binder contact and heat generation. The HTPB binder is modeled as viscoelastic with adiabatic temperature rise. Three experiments are conducted to calibrate and validate the model. Raman spectroscopy and indentation experiment are employed to determine the interface properties, whereas Kolsky bar tension test along with in-situ synchrotron X-ray diffraction measurements are used to validate the model and understand the interface separation characteristics under dynamic loading.

Parallel programming of a peridynamics code coupled with finite element method

Abstract: Using OpenMP (the Open Multi- Processing application programming interface), dynamic peridynamics code coupled with a finite element method is parallelized. The parallel implementation improves run-time efficiency and makes the realistic simulation of crack coalescence possible. To assess the accuracy and efficiency of the parallel code, we investigate its speedup and scalability. In addition, to validate the parallel code, experimental results for crack coalescence development sequences are compared. It is noted that this parallelized code markedly reduces computation time along with the coupling scheme. Moreover, the coupling approach used in this parallel code enables a more realistic and feasible numerical prediction of coalescing fractures. With the parallel implementation, two main types of crack coalescences between two flaws, formed by two short shear cracks and by a short central tensile segment and subsequent shear cracks are in detail discussed in terms of their development sequences. Consequently, this proposed coupled peridynamics code can be used to efficiently solve actual coalescence development sequences, thereby providing a numerical solution for fracture mechanics.

Effect of random defects on dynamic fracture in quasi-brittle materials

Abstract: We propose an asynchronous spacetime discontinuous Galerkin (aSDG) method combined with a novel rate-dependent interfacial damage model as a means to simulate crack nucleation and propagation in quasi-brittle materials. Damage acts in the new model to smoothly transition the aSDG jump conditions on fracture surfaces between Riemann solutions for bonded and debonded conditions. We use the aSDG method’s powerful adaptive meshing capabilities to ensure solution accuracy without resorting to crack-tip enrichment functions and extend those capabilities to support fracture nucleation, extension and intersection. Precise alignment of inter-element boundaries with flaw orientations and crack-propagation directions ensures mesh-independent crack-path predictions. We demonstrate these capabilities in a study of crack-path convergence as adaptive error tolerances tend to zero. The fracture response of quasi-brittle materials is highly sensitive to the presence and properties of microstructural defects. We propose two approaches to model these inhomogeneities. In the first, we represent defects explicitly as crack-like features in the analysis domain’s geometry with random distributions of size, location, and orientation. In the second, we model microscopic flaws implicitly, with probabilistic distributions of strength and orientation, to drive nucleation of macroscopic fractures. Crack-path oscillation, microcracking, and crack branching make numerical simulation of dynamic fracture particularly challenging. We present numerical examples that explore the influence of model parameters and inhomogeneities on fracture patterns and the aSDG model’s ability to capture complex fracture patterns and interactions.

Lattice orientation and crack size effect on the mechanical properties of Graphene

Abstract: The effect of lattice orientation and crack length on the mechanical properties of Graphene are studied based on molecular dynamics simulations. Bond breaking and crack initiation in an initial edge crack model with 13 different crack lengths, in 10 different lattice orientations of Graphene are examined. In all the lattice orientations, three recurrent fracture patterns are reported. The influence of the lattice orientation and crack length on yield stress and yield strain of Graphene is also investigated. The arm-chair fracture pattern is observed to possess the lowest yield properties. A sudden decrease in yield stress and yield strain can be noticed for crack sizes < 10 nm. However, for larger crack sizes, a linear decrease in yield stress is observed, whereas a constant yield strain of 0.05 is noticed. Therefore, the yield strain of 0.05 can be considered as a critical strain value below which Graphene does not show failure. This information can be utilized as a lower bound for the design of nano-devices for various strain sensor applications. Furthermore, the yield data will be useful while developing the Graphene coating on Silicon surface in order to enhance the mechanical and electrical characteristics of solar cells and to arrest the growth of micro-cracks in Silicon cells.

Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials

Abstract: A multiscale computational homogenization method for the modeling of hydro-mechanical coupling problem for quasi-brittle materials is developed. The present method is based on an asymptotic expansion homogenization combined with the semi-concurrent finite element modelling approach. Modified periodic boundary conditions and a molecular dynamics (MD) based inclusion or filler generation procedure are devised for the hydro-mechanical coupling problem. A modified elastic damage constitutive model and a damage induced permeability law have been developed for the hydraulic fracturing. The statistical convergence of the microscale representative volume element (RVE) model regarding the RVE characteristic size is studied. It was found that the RVE characteristic size is determined by both the mechanical and hydraulic properties of the RVE simultaneously. The present method is validated by the experimental results for brittle material. The damage zone and crack propagation path captured by the present method is compared with the experimental results (Chitrala et al. in J Pet Sci Eng 108:151–161, 2013). The results show that the present method is an effective for the modelling of hydro-mechanical coupling for brittle materials.

The formation and growth of echelon cracks in brittle materials

Abstract: Cracks subjected to mode III shear loading fragment into numerous daughter cracks. The formation of such patterns—called echelon cracks—is explored in this work through a phase-field model of fracture. It is shown that the phase field method predicts that a crack subjected to mixed-mode I $$+$$ III grows along the extension of the parent crack plane, contrary to experimental observations. In order to replicate the experimentally observed fragmentation of crack fronts, defects are introduced in the vicinity of the crack front to trigger fragmentation of the front; examples of successful formation and growth of these echelon cracks is demonstrated in this paper. It is also shown that the intrinsic scale parameter in the phase field model must be very small in comparison to the scale of formation of the echelon cracks.

Investigation of viscoelastic fracture fields in asphalt mixtures using digital image correlation

Abstract: In this work we have studied the fracture behavior of asphalt mixtures, a heterogeneous mix of hard aggregates (usually in the form of crushed quarried rock) with a petroleum based asphalt binder, used in paving applications. Specifically, we studied the dependence of asphalt mixes’ fracture response on loading rate, temperature, and recycled content—the latter used primarily to replace virgin materials like aggregates and binder. Fracture tests were conducted on semi-circular bend edge cracked specimens obtained from mixes with different compositions, and the fracture event was recorded with a camera to allow for digital image correlation (DIC) measurements. DIC, with a spatial resolution of about 40 $$\upmu $$ m/pixel, measured the far-field strain and displacement fields developing around a preexisting notch tip. Our focus here is on characterizing the material behavior by quantifying its viscoelastic response and fracture properties. The elastic–viscoelastic correspondence principle was used to extract viscous and elastic components from the full-field DIC-measured strain and displacement fields. Various energy dissipation mechanisms other than the fracture itself were evaluated. Stress–strain response and energy dissipated in the far-field regions were quantified. The pseudo-elastic stress intensity factor was then used to study the fracture properties, and quantify the effects on fracture properties of loading rate, temperature, and recycled content in the binder. It was seen that the viscoelastic characteristics of the material were a dominant factor in the material behavior obtained at room temperature. In general, the elastic component of the displacement was only up to about 30% of the total displacement, indicating a strong influence of viscoelasticity in this state. Loading rate, temperature and recycled asphalt shingles (RAS) content all affected the viscous response by introducing more elastic response when loading rate or recycled content increased or when temperature decreased. It became clear from these macroscopic measurements that the increase of RAS content considerably embrittles the material producing less viscous effects and less energy dissipated in the far-field, almost comparable to reductions associated with the loading rate increase (from 6.25 to 50 mm/min) or the temperature change ( $$-12$$ to $$25\,{^{\circ }}$$ C).

Fracture of monolayer boronitrene and its interface with graphene

Abstract: We investigate through molecular dynamics simulations the fracture properties of boronitrene (BN), graphene, and their interfaces. Four types of interfaces between boronitrene and graphene are considered. It is found that the fracture toughness of graphene is highest among the examined models and is 3.61 and 4.24 $$\hbox {MPa}\sqrt{\hbox {m}}$$ in the armchair and zigzag directions, respectively. Compared to graphene, boronitrene exhibits approximately 12 and 21% smaller values of the fracture toughness in the armchair and zigzag directions, respectively. In the armchair direction, the fracture toughness of the interface between boronitrene and graphene with B–C bonds in the interface is weakest and is about 2.49 $$\hbox {MPa}\sqrt{\hbox {m}}$$ , while the interfacial fracture toughness with C–N bonds in the interface is very close to that of graphene. In the zigzag direction, the interfacial fracture toughness is close to that of BN sheet. Under tension in the zigzag direction, a centered crack, which is initially perpendicular to the tensile direction, kinks at both tips in graphene and boronitrene regions. Since graphene has larger fracture toughness than that of boronitrene, an initial crack in their interface is forbidden to penetrate the graphene region; i.e., the crack can only propagate in the boronitrene region or along their interface of the hybrid BN/graphene sheets. The crack shape in the hybrid BN/graphene sheets depends on the arrangement of B–C–N atoms around the interface and the initial crack tip region.

Transition from energy dissipation to crack openings during continuum–discontinuum fracture of concrete

Abstract: Fracture in quasi-brittle materials like concrete is mainly governed by two processes: energy dissipation and discontinuous displacement fields or discrete cracks. In this study we discuss the simultaneous development of both types of fracture. Energy dissipation and crack openings are analyzed during the fracture development by acoustic emission and digital image correlation (DIC) respectively. DIC results are processed using nonlinear damage modelling and lattice element modelling to reveal the microcracking zone. It is observed that overall failure mechanism is governed by three processes (1) high energy dissipation phase during which energy release rate increases (2) continuum–discontinuum transitional phase where energy dissipation rate attains its maximum value, and (3) discontinuum phase where energy dissipation rate drops and crack openings start increasing.

Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon–quadtree meshes

Abstract: This manuscript presents an extension of the recently-developed hybrid polygon–quadtree-based scaled boundary finite element method to model crack propagation in concrete. This hybrid approach combines the use of quadtree cells with arbitrary sided polygons for domain discretization. The scaled boundary finite element formulation does not distinguish between quadtree cells and arbitrary sided polygons in the mesh. A single formulation is applicable to all types of cells and polygons in the mesh. This eliminates the need to develop transitional elements to bridge the cells belonging to different levels in the quadtree hierarchy. Further to this, the use of arbitrary sided polygons facilitate the accurate discretization of curved boundaries that may result during crack propagation. The fracture process zone that is characteristic in concrete fracture is modelled using zero-thickness interface elements that are coupled to the scaled boundary finite element method using a shadow domain procedure. The scaled boundary finite element method can accurately model the asymptotic stress field in the vicinity of the crack tip with cohesive tractions. This leads to the accurate computation of the stress intensity factors, which is used to determine the condition for crack propagation and the resulting direction. Crack growth can be efficiently resolved using an efficient remeshing algorithm that employs a combination of quadtree decomposition functions and simple Booleans operations. The flexibility of the scaled boundary finite element method to be formulated on arbitrary sided polygons also result in a flexible remeshing algorithm for modelling crack propagation. The developed method is validated using three laboratory experiments of notched concrete beams subjected to different loading conditions.

In-situ measurement of the large strain response of the fibrillar debonding region during the steady peeling of pressure sensitive adhesives

Abstract: The debonding of pressure sensitive adhesives (PSA) is a classical example of the difficult and unsolved issue of fracture in soft viscoelastic confined materials. The presence of a complex debonding region where the adhesive undergoes cavitation and the very large strain of a spontaneously formed fibrillar network has defied many modeling attempts over the past 70 years. We present here a novel technique to provide an accurate measurement of the local large strain response of the fibrillar debonding region during the steady-state peeling of a well known commercial adhesive over a wide range of peeling velocity and angle. The technique is based on high resolution imaging of the debonding region during peeling and is coupled to a cohesive zone modeling of the adhesive interaction between the flexible tape backing and the rigid substrate. The resulting database provides a strong ground for validating and further developing models (Villey et al. in Soft Matter 11:3480–3491, 2015) aiming to capture the effects of both geometry and non-linear adhesive rheology on the exceptional adherence energy of PSAs.

Fracture surface topography analysis of the hydrogen-related fracture propagation process in martensitic steel

Abstract: The hydrogen-related fracture propagation process in martensitic steel was investigated through crystallographic orientation and fracture surface topography analyses. The hydrogen-related fracture surface consisted of three typical surfaces, namely smooth surfaces, surfaces with serrated markings, and surfaces with dimples. Crystallographic orientation analysis suggested that the smooth surface was generated by intergranular fracture at prior austenite grain boundaries, and the surface with serrated markings originated from quasi-cleavage fracture propagated along $$\{011\}$$ planes. According to the reconstructed fracture propagation process by fracture surface topography analysis, the intergranular fracture at prior austenite grain boundaries initiated and propagated suddenly at the early stages of fracture. The quasi-cleavage fracture along $$\{011\}$$ planes then gradually propagated within the prior austenite grains. At the final stages of fracture, ductile fracture accompanied by dimples occurred around the edge of the specimen. The results clearly indicated that the fracture propagation path changed with the proceeding fracture from the prior austenite grain boundaries to along $$\{011\}$$ planes within the prior austenite grains.

Directionality of electromagnetic radiation from fractures

Abstract: The directionality of electromagnetic radiation from tensile fracturing is calculated within our previously proposed model and shown to agree with experimental observations in the field. The best locations and orientations of measuring antennas are presented.

Effective simulation of the mechanics of longitudinal tensile failure of unidirectional polymer composites

Abstract: An efficient computational model to simulate tensile failure of both hybrid and non-hybrid composite materials is proposed. This model is based on the spring element model, which is extended to a random 2D fibre packing. The proposed model is used to study the local stress fields around a broken fibre as well as the failure process in composite materials. The influence of fibre strength distributions and matrix properties on this process is also analysed. A detailed analysis of the fracture process and cluster development is performed and the results are compared with experimental results from the literature.

Ductile failure modeling and simulations using coupled FE–EFG approach

Abstract: In the present work, a ductile fracture model has been employed to predict the failure of tensile specimen using coupled finite element–element free Galerkin (FE–EFG) approach. The fracture strain as a function of stress triaxiality has been evaluated by analyzing the notched tensile specimens. In the coupled approach, a small portion of the domain, where severe plastic deformation is expected, is modeled by EFG method whereas the rest of the domain is modeled by FEM to exploit the advantages of both the methods. A ramp function has been used in the interface region to maintain the continuity between FE and EFG domains. The nonlinear material behavior is modeled by von-Mises yield criterion and Hollomon’s power law. An implicit return mapping algorithm is employed for stress equilibrium in the plasticity model. The effect of geometric nonlinearity as a result of large deformation is captured by updated Lagrangian approach. The coupled approach is used to study the fracture behavior of two different cracked specimens in order to highlight its capabilities.

Enhanced XFEM for crack deflection in multi-material joints.

Abstract: In this work, an enhanced eXtended finite element method (XFEM) implementation is outlined. It allows for modeling two-dimensional crack growth including potential crack deflection at significantly tougher constitutents of multi-material continua. At such material interfaces a user-defined crack deflection criterion is utilized that allows for crack deflection parallel to the interface but is also able to model crack growth that again diverges from the interface. The enhanced XFEM implementation is illustrated analyzing crack growth in a plate with two interacting inclusions showing a distinct toughening effect. Moreover, several different adhesive joint design studies are used to validate the model. The results show that the present XFEM implementation allows for an accurate strength and realistic crack pattern prediction in joint designs of complex shape, e.g. with fillets or rounded adherend corners. The given framework is general and could also be applied to the study of fracture processes including crack deflection as e.g. micro-mechanical fracture in fibre-reinforced composites or cracks around inclusions.

Direct numerical simulation of ductile spall failure

Abstract: Large-scale direct numerical simulations of void growth and coalescence from 3-dimensional distributions of void nucleating particles are used to investigate the effect of material strain hardening and strain rate sensitivity on spall response. The computational model spans multiple particle spacings in the in-plane directions, and several finite elements span the initial particle diameters in the mixed-zone Arbitrary Lagrange–Eulerian (ALE) simulations. The matrix material is represented by traditional plasticity models in which material failure is not permitted. The 1000 $$+$$ particles are represented by the same material model as the surrounding matrix except the particles have low tensile strength to permit fracture, which is used to simulate particle cracking or decohesion. Voids grow and coalesce naturally in the ALE framework, and the simulations produce dimpled failure surfaces similar to those observed experimentally in spalled samples. The strain hardening and strain rate sensitivity of the matrix material are altered to explore their influence on the void growth and coalescence processes and on the simulated free surface velocity. The details available from the computational model permit association of the longitudinal stress evolution with features on the free surface velocity profile.

Virtual crack closure technique for an interface crack between two transversely isotropic materials

Abstract: The virtual crack closure technique makes use of the forces ahead of the crack tip and the displacement jumps on the crack faces directly behind the crack tip to obtain the energy release rates $${{\mathcal {G}}}_I$$ and $${\mathcal {G}}_{II}$$ . The method was initially developed for cracks in linear elastic, homogeneous and isotropic material and for four noded elements. The method was extended to eight noded and quarter-point elements, as well as bimaterial cracks. For bimaterial cracks, it was shown that $${\mathcal {G}}_I$$ and $${\mathcal {G}}_{II}$$ depend upon the virtual crack extension $$\varDelta a$$ . Recently, equations were redeveloped for a crack along an interface between two dissimilar linear elastic, homogeneous and isotropic materials. The stress intensity factors were shown to be independent of $$\varDelta a$$ . For a better approximation of the Irwin crack closure integral, use of many small elements as part of the virtual crack extension was suggested. In this investigation, the equations for an interface crack between two dissimilar linear elastic, homogeneous and transversely isotropic materials are derived. Auxiliary parameters are used to prescribe an optimal number of elements to be included in the virtual crack extension. In addition, in previous papers, use of elements smaller than the interpenetration zone were rejected. In this study, it is shown that these elements may, indeed, be used.