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Crack Tip (crack + tip)
Terms modified by Crack Tip Selected AbstractsCrack Tip Morphology of Slowly Growing Cracks in GlassJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 2 2000Stéphane Hénaux We present atomic force microscopy (AFM) observations of crack tips in glass during subcritical propagation. These have been obtained by means of an AFM sample holder which has been specially designed to propagate indentation cracks in glass plates. Crack tips in soda,lime,silica glass are always preceded by a few nanometers deep deformation. In vitreous silica, no other surface deformation than the crack itself could be detected. For both materials, the crack opening is found to largely exceed the elastic solution. [source] Fatigue Crack Propagation and History Effects Induced by Plasticity,ADVANCED ENGINEERING MATERIALS, Issue 9 2009Sylvie Pommier Abstract For security-relevant components, a fracture mechanics assessment has to be carried out. When complex loading conditions are encountered, various problems arise. Among them the prediction of history effects induced by plasticity remains a difficult task and is the object of this paper. After an overload, for instance, plasticity-induced crack closure is known to decelerate the crack growth. This effect is known to be related to residual stresses ahead of and behind the crack tip. Since residual stresses are related to the material stress,strain behavior, the overload effect may vary significantly from one material to another. Finite-element (FE) methods are commonly employed to model plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modeled to predict the fatigue behavior of an industrial component, the method becomes computationally too expensive. By employing a multiscale approach, very precise analyses computed by FE methods can be brought to a global scale. The data generated using the FE method enables the identification of a global cyclic elastic-plastic model for the crack tip region. Once this model is identified, it can be employed directly with no need of additional FE computations, resulting in fast computations. This method was employed so as to predict fatigue crack growth under variable amplitude fatigue in steels at room temperatures and correlates well with experimental data. It was also extended so as to model fatigue crack growth in a nickel base superalloy under non-isothermal fatigue-dwell conditions. At present, the method is being extended to mixed-mode variable-amplitude loading conditions. [source] Examination of fatigue crack driving force parameterFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 9 2008Y. XIONG ABSTRACT Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter Kop in Elber's effective SIF range ,Keff(=Kmax,Kop). However, the parameters that replaced the traditional parameter Kop were based on different measurements or theoretical calculations, so it is difficult to distinguish their differences. This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip; the tests were carried out under different amplitude loading for structural steel. Based on these test results, differences of several parameter ,Keff in literature are analysed and an improved two-parameter driving force ,Kdrive(=(Kmax)n(,K,)1-n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the ,Kdrive parameter was equally effective or better than ,K(=Kmax,Kmin), ,Keff(=Kmax,Kop) and ,K*(= (Kmax),(,K+)1,,) in correlating and predicting the R -ratio effects on fatigue crack growth rate. [source] Fatigue behaviour of friction stir welded AA2024-T3 alloy: longitudinal and transverse crack growthFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2008M. T. MILAN ABSTRACT The fatigue crack growth properties of friction stir welded joints of 2024-T3 aluminium alloy have been studied under constant load amplitude (increasing -,K), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ,K values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to KC instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non-conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non-conservative crack growth rate predictions next to KC instability. At threshold ,K values non-conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered. [source] Analysis of temperature distribution near the crack tip under constant amplitude loadingFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2008K. N. PANDEY ABSTRACT An analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two-dimensional conduction heat transfer equation, in moving co-ordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power,law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor. [source] Molecular dynamics simulation of crack tip blunting in opposing directions along a symmetrical tilt grain boundary of copper bicrystalFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2007A. LUQUE ABSTRACT Mode I crack growth along some grain boundaries of copper embrittled by solute segregation shows strong anisotropy. For instance, growth along the direction on the symmetrical tilt boundary has been reported to occur by intergranular brittle fracture, whereas growth along the opposite sense occurs in a ductile manner. In this paper, we simulate such crack configurations using molecular dynamics (embedded atom method [EAM]) in 3-dimensional perfect bicrystalline samples of pure copper of the aforementioned orientation at room temperature. In both cases the response is ductile, crack opening taking place by dislocation emission from the crack tip. The critical stress intensity factors (SIFs) for dislocation emission have been calculated by matching the displacement fields of the atoms in the tip neighbourhood with the continuum elastic fields. They are of the same order of magnitude for both growth senses despite the different morphology of their respective blunted crack tips and of the patterns of dislocations constituting their plastic zones. Thus, it seems that, in agreement with published results of continuum crystalline plasticity for the same problem, the plastic anisotropy associated with the different orientation of the slip systems with respect to the crack cannot in this case explain the experimental behaviour observed with solute embrittled bicrystals. [source] Sphere contact fatigue of a coarse-grained Al2O3 ceramicFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2006T. FETT ABSTRACT The opposite sphere test is an appropriate tool to determine crack-growth exponents for fatigue under repeated contact loading. Lifetime measurements for a coarse-grained Al2O3 are reported. To explain the fatigue exponents that strongly deviated from those obtained in cyclic bending tests, a fracture mechanics analysis was carried out. It was aimed at determining the correct stress intensity factor solution for the tests, including limited dimensions of test specimens deviating from the case of a cone crack in a half space. Cone crack development was observed microscopically and the related stress intensity factors were computed for the observed crack shape. For modelling the fatigue behaviour, it is assumed that the fatigue effect is influenced by a reduction of the shielding term of crack growth resistance due to periodical friction between the grain-interlock bridges in coarse-grained alumina. This results in a loss of traction at the junctions, crack tip shielding is reduced, and the effective load at the crack tip is increased. [source] Crack initiation in the brittle fracture of ferritic steelsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 9-10 2006M. COATES ABSTRACT Fracture in many steels is thought to initiate from fractured carbides. It is often supposed that in pre-cracked specimens, many carbides fracture in the plastic zone of the pre-crack, and that eventually fracture propagates from one of these to cause fracture of the whole specimen. Sources of fracture initiation in steels were investigated using a modified A533B steel as a model material. Specimens were annealed to produce a distribution of micron-sized carbides in a ferrite matrix. Four-point bend tests were carried out in the temperature range 77,373K to determine the material's ductile brittle transition. Pre-cracked samples were loaded up to 90% of the fracture strength at temperatures on the lower shelf (163K) and at the mid point of the transition region (243K). The samples were then sectioned and polished to produce SEM and TEM samples containing the crack tip. Other samples were made of areas some distance from the crack tip and out of the plastic zone. An extensive search for fracture initiation sites found no evidence for fracture initiation originating from fractured carbides. [source] Nanoscopic fatigue and stress corrosion crack growth behaviour in a high-strength stainless steel visualized in situ by atomic force microscopyFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2005K. MINOSHIMA ABSTRACT In situ atomic force microscope (AFM) imaging of the fatigue and stress corrosion (SC) crack in a high-strength stainless steel was performed, under both static and dynamic loading. The AFM systems used were (1) a newly developed AFM-based system for analysing the nanoscopic topographies of environmentally induced damage under dynamic loads in a controlled environment and (2) an AFM system having a large sample stage together with a static in-plane loading device. By using these systems, in situ serial clear AFM images of an environmentally induced crack under loading could be obtained in a controlled environment, such as in dry air for the fatigue and in an aqueous solution for the stress corrosion cracking (SCC). The intergranular static SC crack at the free corrosion had a sharp crack tip when it grew straight along a grain boundary. The in situ AFM observations showed that the fatigue crack grew in a steady manner on the order of sub-micrometre. The same result was obtained for the static SC crack under the free corrosion, growing straight along a grain boundary. In these cases, the crack tip opening displacement (CTOD) remained constant. However, as the static SC crack was approaching a triple grain junction, the growth rate became smaller, the CTOD value increased and the hollow ahead of the crack tip became larger. After the crack passed through the triple grain junction, it grew faster with a lower CTOD value; the changes in the CTOD value agreed with those of the crack growth rate. At the cathodic potential, the static SC crack grew in a zigzag path and in an unsteady manner, showing crack growth acceleration and retardation. This unsteady crack growth was considered to be due to the changes in the local hydrogen content near the crack tip. The changes in the CTOD value also agreed with those of the crack growth rate. The CTOD value in the corrosive environment was influenced by the microstructure of the material and the local hydrogen content, showing a larger scatter band, whereas the CTOD value of the fatigue crack in dry air was determined by the applied stress intensity factor, with a smaller scatter band. In addition, the CTOD value in the corrosive environment under both static and dynamic loading was smaller than that of the fatigue crack; the environmentally induced crack had a sharper crack tip than the fatigue crack in dry air. [source] The evolution of the stress,strain fields near a fatigue crack tip and plasticity-induced crack closure revisitedFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1 2004L. G. ZHAO ABSTRACT The evolution of the stress,strain fields near a stationary crack tip under cyclic loading at selected R -ratios has been studied in a detailed elastic,plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R -ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic,plastic finite element simulations of advancing fatigue cracks were carried out under plane-stress, plane-strain and generalized plane-strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane-strain and generalized plane-strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane-stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack-closure measurement, and indeed on the role of plasticity-induced crack closure in the reduction of the applied stress intensity factor range. [source] Fracture behaviour of PC/ABS resin under mixed-mode loadingFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 12 2001Husaini Fracture behaviour of polycarbonate (PC)/acrylonitrile-butadiene-styrene (ABS) under mixed-mode loading conditions was studied for several weight fractions of PC and ABS. Mode I and mixed-mode fracture tests were carried out by using compact,tension,shear specimens. At a certain value of mixed-mode loading ratio KII,/KI, a crack of the shear type will initiates at the initial crack tip. Fracture toughness increases under mixed-mode loading with an increase in the mode II component, whereas it reduces with the appearance of a shear-type fracture. Fracture toughness and the appearance of a shear-type fracture depends on the blending ratio of PC and ABS. The transition to shear-type fracture occurs at lower value of KII,/KI for resins with higher fracture toughness. [source] Study of crack growth in solid propellantsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2001E. E. Gdoutos The stress and displacement fields in an edge-cracked sheet specimen made of a solid propellant and subjected to a uniform displacement along its upper and lower faces was studied. The solid propellant was simulated as a hyperelastic material with constitutive behaviour described by the Ogden strain energy potential. A non-linear finite deformation analysis was performed based on the finite element code ABAQUS. A detailed analysis of the stress field in the vicinity of the crack tip was undertaken. The deformed profiles of the crack faces near the crack tip were determined. The results of stress analysis were coupled with the strain energy density theory to predict the crack growth behaviour including crack initiation, stable crack growth and final termination for two specimens with different dimensions. Crack growth resistance curves representing the variation of crack growth increment versus applied displacement were drawn. [source] Effect of microcracking on the micromechanics of fatigue crack growth in austempered ductile ironFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 9 2001J. Ortiz The effect of microcracking on the mechanics of fatigue crack growth in austempered ductile iron is studied in this paper. The mechanism of fatigue crack growth is modelled using the boundary element method, customized for the accurate evaluation of the interaction effects between cracks and microcracks emanating from graphite nodules. The effects of nodule size and distribution and crack closure are considered, with deviation bounds of computed results estimated through weight-function analyses. A continuum approach is employed as a means of quantifying the shielding effect of microcracking on the dominant propagating crack, due to the reduction of stiffness of the material in the neighbourhood of the crack tip. Although the results obtained may not yield actual numbers for real cases, they are in accordance with experimental observations and demonstrate how the main factors affect the crack growth of the macrocrack. [source] The analysis of thermoelastic isopachic data from crack tip stress fieldsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 4 2000Dulieu-Barton A computer program,FACTUS (fracture analysis of crack tips using SPATE),has been developed for the efficient analysis of thermoelastic data obtained from around a crack tip. The program is based on earlier work for the determination of stress intensity factors (SIFs), and also includes a novel solution procedure for the derivation of the non-singular stress term ,0x,. The program has been used in the analysis of a series of large plate specimens with central or edge slots/cracks. The derived SIFs are compared with independent values. Issues, e.g. crack closure and the extent and effect of the plastic zone, are discussed. [source] Bonded aircraft repairs under variable amplitude fatigue loading and at low temperaturesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1 2000Vlot Bonded repairs can replace mechanically fastened repairs for aircraft structures. Compared to mechanical fastening, adhesive bonding provides a more uniform and efficient load transfer into the patch, and can reduce the risk of high stress concentrations caused by additional fastener holes necessary for riveted repairs. Previous fatigue tests on bonded Glare (glass-reinforced aluminium laminate) repairs were performed at room temperature and under constant amplitude fatigue loading. However, the realistic operating temperature of ,40 °C may degrade the material and will cause unfavourable thermal stresses. Bonded repair specimens were tested at ,40 °C and other specimens were tested at room temperature after subjecting them to temperature cycles. Also, tests were performed with a realistic C-5A Galaxy fuselage fatigue spectrum at room temperature. The behaviour of Glare repair patches was compared with boron/epoxy ones with equal extensional stiffness. The thermal cycles before fatigue cycling did not degrade the repair. A constant temperature of ,40 °C during the mechanical fatigue load had a favourable effect on the fatigue crack growth rate. Glare repair patches showed lower crack growth rates than boron/epoxy repairs. Finite element analyses revealed that the higher crack growth rates for boron/epoxy repairs are caused by the higher thermal stresses induced by the curing of the adhesive. The fatigue crack growth rate under spectrum loading could be accurately predicted with stress intensity factors calculated by finite element modelling and cycle-by-cycle integration that neglected interaction effects of the different stress amplitudes, which is possible because stress intensities at the crack tip under the repair patch remain small. For an accurate prediction it was necessary to use an effective stress intensity factor that is a function of the stress ratio at the crack tip Rcrack tip including the thermal stress under the bonded patch. [source] The role of friction and secondary flaws on deflection and re-initiation of hydraulic fractures at orthogonal pre-existing fracturesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Xi Zhang SUMMARY In this study, we explore the nature of plane-strain hydraulic fracture growth in the presence of pre-existing fractures such as joints without or with secondary flaws. The 2-D plane-strain fracture studied can be taken as a cross-section through the short dimensions of an elongated 3-D fracture or as an approximate representation of the leading edge of a 3-D fracture where the edge curvature is negligible. The fluid-driven fracture intersects a pre-existing fracture to which it is initially perpendicular and is assumed not to immediately cross, but is rather deflected into the pre-existing fracture. The intersection results in branching of the fracture and associated fluid flow into the pre-existing fracture. Further growth results in opening and frictional sliding along the pre-existing fracture. Fracture propagation in an impermeable homogeneous elastic medium and fluid invasion into a pre-existing fracture are both driven by an incompressible, Newtonian fluid injected at a constant rate. The frictional stress on the surfaces of pre-existing fractures is assumed to obey the Coulomb law. The governing equations for quasi-static fluid-driven fracture growth are given and a scaling is introduced to help identify important parameters. The displacement discontinuity method and the finite difference method are employed to deal with this coupling mechanism of rock fracture and fluid flow. In order to account for fluid lag, a method for separately tracking the crack tip and the fluid front is included in the numerical model. Numerical results are obtained for internal pressure, frictional contact stresses, opening and shear displacements, and fluid lag size, as well as for fracture re-initiation from secondary flaws. After fracture intersection, the hydraulic fracture growth mode changes from tensile to shearing. This contributes to increased injection pressure and to a reduction in fracture width. In the presence of pre-existing fractures, the fluid-driven cracks can be arrested or retarded in growth rate as a result of diversion of fluid flow into and frictional sliding along the pre-existing fractures. Frictional behaviour significantly affects the ability of the fluid to enter or penetrate the pre-existing fracture only for those situations where the fluid front is within a certain distance from the intersecting point. Importantly, fluid penetration requires higher injection pressure for frictionally weak pre-existing fractures. Fracture re-initiation from secondary flaws can reduce the injection pressure, but re-initiation is suppressed by large sliding on pre-existing fractures that are frictionally weak. [source] On strike-slip faulting in layered mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2002Maurizio Bonafede Summary We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress). [source] On the Fracture Toughness of Advanced MaterialsADVANCED MATERIALS, Issue 20 2009Maximilien E. Launey Abstract Few engineering materials are limited by their strength; rather they are limited by their resistance to fracture or fracture toughness. It is not by accident that most critical structures, such as bridges, ships, nuclear pressure vessels and so forth, are manufactured from materials that are comparatively low in strength but high in toughness. Indeed, in many classes of materials, strength and toughness are almost mutually exclusive. From a fracture-mechanics perspective, the ability of a microstructure to develop toughening mechanisms acting either ahead or behind the crack tip can result in resistance-curve (R-curve) behavior where the fracture resistance actually increases with crack extension; the implication here is that toughness is often developed primarily during crack growth and not for crack initiation. Biological materials are perfect examples of this; moreover, they offer microstructural design strategies for the development of new materials for structural applications demanding combinations of both strength and toughness. [source] Self-similar solution of a plane-strain fracture driven by a power-law fluidINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2002J. I. Adachi Abstract This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n,0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd. [source] Computation of the J -integral for large strainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Ágnes Horváth Abstract The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J -integral can also be applied to characterize the cracks in elastic or elastic,plastic bodies. This paper describes the computation of the two-dimensional J -integral for large strains to elastic and elastic,plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] BEM-analysis of interaction of elastic waves with unilateral interface crackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Gai Bing-Zheng Abstract In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating,correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. Copyright © 2001 John Wiley & Sons, Ltd. [source] An optimally convergent discontinuous Galerkin-based extended finite element method for fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010Yongxing Shen Abstract The extended finite element method (XFEM) enables the representation of cracks in arbitrary locations of a mesh. We introduce here a variant of the XFEM rendering an optimally convergent scheme. Its distinguishing features are as follows: (a) the introduction of singular asymptotic crack tip fields with support on only a small region around the crack tip (the enrichment region), (b) only one and two enrichment functions are added for anti-plane shear and planar problems, respectively and (c) the relaxation of the continuity between the enrichment region and the rest of the domain, and the adoption of a discontinuous Galerkin (DG) method therein. The method is provably stable for any positive value of a stabilization parameter, and by weakly enforcing the continuity between the two regions it eliminates ,blending elements' partly responsible for the suboptimal convergence of some early XFEMs. Moreover, the particular choice of enrichment functions results in a surprisingly sparse stiffness matrix that remains reasonably conditioned as the mesh is refined. More importantly, the stress intensity factors can be extracted with a satisfactory accuracy as primary unknowns. Quadrature strategies required for the optimal convergence are also discussed. Finally, the DG method was modified to retain stability based on an inf-sup condition. Copyright © 2009 John Wiley & Sons, Ltd. [source] An extended finite element method with analytical enrichment for cohesive crack modelingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009James V. CoxArticle first published online: 28 NOV 200 Abstract A recent approach to fracture modeling has combined the extended finite element method (XFEM) with cohesive zone models. Most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation and enrichment functions are discussed. A parameter study for a simple mode I model problem is presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. The effects of mesh refinement and mesh orientation are considered. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined. The analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode I crack independent of mesh orientation. A mixed mode example further demonstrates the potential of the formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007C. Miehe Abstract The paper considers a variational formulation of brittle fracture in elastic solids and proposes a numerical implementation by a finite element method. On the theoretical side, we outline a consistent thermodynamic framework for crack propagation in an elastic solid. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius,Planck inequality in the sense of Coleman's method. Here, the canonical direction of the crack propagation associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip and minimizes the incremental energy release. On the numerical side, we exploit this variational structure in terms of crack-driving configurational forces. First, a standard finite element discretization in space yields a discrete formulation of the global dissipation in terms configurational nodal forces. As a consequence, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface segments of the mesh. Critical for the success of this procedure is its embedding into an r-adaptive crack-segment reorientation procedure with configurational-force-based directional indicator. Here, successive crack releases appear in discrete steps associated with the given space discretization. These are performed by a staggered loading,release algorithm of energy minimization at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive-definite discrete subproblems with successively decreasing overall stiffness, providing an extremely robust algorithmic setting in the postcritical range. We demonstrate the performance of the formulation by means of representative numerical simulations. Copyright © 2007 John Wiley & Sons, Ltd. [source] A framework for fracture modelling based on the material forces concept with XFEM kinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005Ragnar Larsson Abstract A theoretical and computational framework which covers both linear and non-linear fracture behaviour is presented. As a basis for the formulation, we use the material forces concept due to the close relation between on one hand the Eshelby energy,momentum tensor and on the other hand material defects like cracks and material inhomogeneities. By separating the discontinuous displacement from the continuous counterpart in line with the eXtended finite element method (XFEM), we are able to formulate the weak equilibrium in two coupled problems representing the total deformation. However, in contrast to standard XFEM, where the direct motion discontinuity is used to model the crack, we rather formulate an inverse motion discontinuity to model crack development. The resulting formulation thus couples the continuous direct motion to the inverse discontinuous motion, which may be used to simulate linear as well as non-linear fracture in one and the same formulation. In fact, the linear fracture formulation can be retrieved from the non-linear cohesive zone formulation simply by confining the cohesive zone to the crack tip. These features are clarified in the two numerical examples which conclude the paper. Copyright © 2005 John Wiley & Sons, Ltd. [source] An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Jeong-Ho Kim Abstract The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori,Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxiliary fields and their implications on the solution procedure are discussed in detail. The computational implementation is done using the finite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a finite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally efficient. Copyright © 2003 John Wiley & Sons, Ltd. [source] Study of epoxy toughened by in situ formed rubber nanoparticlesJOURNAL OF APPLIED POLYMER SCIENCE, Issue 1 2008Jun Ma Abstract The effect of rubber nanoparticles on mechanical properties and fracture toughness was investigated. Rubber nanoparticles of 2,3 nm were in situ synthesized in epoxy taking advantage of the reaction of an oligomer diamine with epoxy. The chemical reaction was verified by gel permeation chromatography (GPC) and 1HNMR, and the microstructure was characterized by transmission electron microscope. The rubber nanoparticles caused much less Young's modulus deterioration but toughened epoxy to a similar degree in comparison with their peer liquid rubber that formed microscale particles during curing. Fifteen wt % of rubber nanoparticles increased fracture energy from 140 to 840 J/m2 with Young's modulus loss from 2.85 to 2.49 GPa. The toughening mechanism might be the stress relaxation of the matrix epoxy leading to larger plastic work absorbed at the crack tip; there is no particle cavitation or deformation; neither crack deflection nor particle bridging were observed. The compound containing rubber nanoparticles demonstrates Newtonian liquid behavior with increasing shear rate; it shows lower initial viscosity at low shear rate than neat epoxy; this provides supplementary evidence to NMR and GPC result. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] Cyclic Fatigue-Crack Growth and Fracture Properties in Ti3SiC2 Ceramics at Elevated TemperaturesJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 12 2001Da Chen The cyclic fatigue and fracture toughness behavior of reactive hot-pressed Ti3SiC2 ceramics was examined at temperatures from ambient to 1200°C with the objective of characterizing the high-temperature mechanisms controlling crack growth. Comparisons were made of two monolithic Ti3SiC2 materials with fine- (3,10 ,m) and coarse-grained (70,300 ,m) microstructures. Results indicate that fracture toughness values, derived from rising resistance-curve behavior, were significantly higher in the coarser-grained microstructure at both low and high temperatures; comparative behavior was seen under cyclic fatigue loading. In each microstructure, ,Kth fatigue thresholds were found to be essentially unchanged between 25° and 1100°C; however, there was a sharp decrease in ,Kth at 1200°C (above the plastic-to-brittle transition temperature), where significant high-temperature deformation and damage are first apparent. The substantially higher cyclic-crack growth resistance of the coarse-grained Ti3SiC2 microstructure was associated with extensive crack bridging behind the crack tip and a consequent tortuous crack path. The crack-tip shielding was found to result from both the bridging of entire grains and from deformation kinking and bridging of microlamellae within grains, the latter forming by delamination along the basal planes. [source] Origins and Applications of London Dispersion Forces and Hamaker Constants in CeramicsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 9 2000Roger H. French The London dispersion forces, along with the Debye and Keesom forces, constitute the long-range van der Waals forces. London's and Hamaker's work on the point-to-point dispersion interaction and Lifshitz's development of the continuum theory of dispersion are the foundations of our understanding of dispersion forces. Dispersion forces are present for all materials and are intrinsically related to the optical properties and the underlying interband electronic structures of materials. The force law scaling constant of the dispersion force, known as the Hamaker constant, can be determined from spectral or parametric optical properties of materials, combined with knowledge of the configuration of the materials. With recent access to new experimental and ab initio tools for determination of optical properties of materials, dispersion force research has new opportunities for detailed studies. Opportunities include development of improved index approximations and parametric representations of the optical properties for estimation of Hamaker constants. Expanded databases of London dispersion spectra of materials will permit accurate estimation of both nonretarded and retarded dispersion forces in complex configurations. Development of solutions for generalized multilayer configurations of materials are needed for the treatment of more-complex problems, such as graded interfaces. Dispersion forces can play a critical role in materials applications. Typically, they are a component with other forces in a force balance, and it is this balance that dictates the resulting behavior. The ubiquitous nature of the London dispersion forces makes them a factor in a wide spectrum of problems; they have been in evidence since the pioneering work of Young and Laplace on wetting, contact angles, and surface energies. Additional applications include the interparticle forces that can be measured by direct techniques, such as atomic force microscopy. London dispersion forces are important in both adhesion and in sintering, where the detailed shape at the crack tip and at the sintering neck can be controlled by the dispersion forces. Dispersion forces have an important role in the properties of numerous ceramics that contain intergranular films, and here the opportunity exists for the development of an integrated understanding of intergranular films that encompasses dispersion forces, segregation, multilayer adsorption, and structure. The intrinsic length scale at which there is a transition from the continuum perspective (dispersion forces) to the atomistic perspective (encompassing interatomic bonds) is critical in many materials problems, and the relationship of dispersion forces and intergranular films may represent an important opportunity to probe this topic. The London dispersion force is retarded at large separations, where the transit time of the electromagnetic interaction must be considered explicitly. Novel phenomena, such as equilibrium surficial films and bimodal wetting/dewetting, can result in materials systems when the characteristic wavelengths of the interatomic bonds and the physical interlayer thicknesses lead to a change in the sign of the dispersion force. Use of these novel phenomena in future materials applications provides interesting opportunities in materials design. [source] On a numerical scheme for curved crack propagation based on configurational forces and maximum dissipationPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Henning Schütte A numerical scheme is presented to predict crack trajectories in two dimensional components. First a relation between the curvature in mixed,mode crack propagation and the corresponding configurational forces is derived, based on the principle of maximum dissipation. With the help of this, a numerical scheme is presented which is based on a predictor,corrector method using the configurational forces acting on the crack together with their derivatives along real and test paths. With the help of this scheme it is possible to take bigger than usual propagation steps, represented by splines. Essential for this approach is the correct numerical determination of the configurational forces acting on the crack tip. The methods used by other authors are shortly reviewed and an approach valid for arbitrary non,homogenous and non,linear materials with mixed,mode cracks is presented. Numerical examples show, that the method is a able to predict the crack paths in components with holes, stiffeners etc. with good accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||||||||