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Viggo Tvergaard - One of the best experts on this subject based on the ideXlab platform.
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Discrete modelling of Ductile Crack Growth by void Growth to coalescence
International Journal of Fracture, 2007Co-Authors: Viggo TvergaardAbstract:Ductile Crack Growth is analyzed by discrete representation of the voids growing near a blunting Crack-tip. Coalescence of the nearest void with the Crack-tip is modeled, followed by the subsequent coalescence of other discretely represented voids with the newly formed Crack-tip. Necking of the ligaments between the Crack-tip and a void or between voids involves the development of very large strains, which are included in the model by using remeshing at several stages of the plastic deformation. The material is here described by standard isotropic hardening Mises theory. For a very small void volume fraction the Crack-tip tends to interact with one void at a time, while larger void volume fractions lead to simultaneous interaction of multiple voids on the plane ahead of the Crack-tip. In some cases a change from one of these mechanisms to the other is seen during Growth through the many voids represented here. First uniformly spaced voids of equal size are considered, but also a few computations for a random distribution of the void spacings or of the void sizes are carried out.
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three dimensional microstructural effects on plane strain Ductile Crack Growth
International Journal of Solids and Structures, 2006Co-Authors: A Needleman, Viggo TvergaardAbstract:Ductile Crack Growth under mode I, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model the material. Two populations of second-phase particles are represented, large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and the effects of different three dimensional distributions on the Crack path and on the overall Crack Growth rate are analyzed. For comparison purposes, a two dimensional distribution of cylindrical inclusions is analyzed. Crack Growth occurs off the initial Crack plane in all 3D computations, whereas straight ahead Crack Growth occurs with the two dimensional cylindrical inclusions. As a consequence, the three dimensional distributions of spherical inclusions exhibit an increased Crack Growth resistance as compared to the two dimensional distribution of cylindrical inclusions.
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three dimensional analysis of dynamic Ductile Crack Growth in a thin plate
Journal of The Mechanics and Physics of Solids, 1996Co-Authors: K K Mathur, A Needleman, Viggo TvergaardAbstract:Abstract A three dimensional analysis of dynamic Ductile Crack Growth in an edge Cracked plate is carried out, using a data parallel implementation in a transient three dimensional finite element program. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model Ductile fracture by the nucleation and subsequent Growth of voids to coalescence. Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating owing to plastic dissipation and the resulting thermal softening are accounted for in the analyses. The Crack speed and the Crack path are based on the Ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic Crack Growth criteria. A convected coordinate Lagrangian formulation is employed and the discretization is based on twenty-node brick elements with 2 × 2 × 2 Gauss points. The equations of motion are integrated numerically by an explicit integration procedure using a lumped mass matrix. Crack Growth occurs by tunneling in the central part of the plate and shear lip formation at the free surface. The effect of various material parameters and of plate thickness on this process is studied. For comparison purposes, a calculation with overall plane strain boundary conditions is carried out.
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mesh effects in the analysis of dynamic Ductile Crack Growth
Engineering Fracture Mechanics, 1994Co-Authors: A Needleman, Viggo TvergaardAbstract:Abstract For numerical studies of dynamic Crack Growth the mesh sensitivity of the Crack Growth predictions is investigated. The computed Crack Growth behavior is based on the Ductile fracture predictions of an elastic-viscoplastic constitutive relation for a porous plastic solid, which models the nucleation and Growth of voids to coalescence. Both initially sharp and initially blunt Cracks are analyzed. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. For the larger voids the size and spacing are directly specified in the analyses, whereas no length scale is specified for the small-scale voids. Crack Growth predictions in cases where the large-scale voids dominate show practically no mesh sensitivity, whereas cases dominated by the small-scale voids show a clear mesh sensitivity. For initially sharp Cracks the initiation of Crack Growth is quite sensitive to the mesh. However, for initially blunt Cracks the mesh sensitivity of the initiation time is removed.
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An analysis of the brittle-Ductile transition in dynamic Crack Growth
International Journal of Fracture, 1993Co-Authors: Viggo Tvergaard, A NeedlemanAbstract:The brittle-Ductile transition in dynamic Crack Growth is investigated through the numerical analysis of a plane strain edge Cracked specimen, subject to impulsive loading at one end. The material is characterized as an elastic-viscoplastic solid, with a temperature dependent flow strength. Thermal softening due to adiabatic heating and a model for Ductile failure by void nucleation, Growth and coalescence are incorporated into the constitutive relation. The Ductile void Growth mechanism involves two populations of void nucleating particles; discretely modelled low strength inclusions that give large voids near the Crack tip at an early stage and homogeneously distributed small second phase particles that require large strains for void nucleation. Cleavage is modelled in terms of a spatially non-uniform, but temperature and strain rate independent, critical value of the maximum principal normal stress. The numerical results show a clear transition from cleavage dominated Crack Growth at low temperatures to purely Ductile Crack Growth at higher temperatures. There is an accompanying large increase in the material's resistance to dynamic Crack initiation and Growth. The computed Crack Growth behaviour is a direct outcome of the material description; no ad hoc dynamic fracture criterion is employed. Effects of variations in the material model on the brittle-Ductile transition are explored.
Mitsuru Ohata - One of the best experts on this subject based on the ideXlab platform.
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application of damage model based on void Growth analysis to Ductile Crack Growth simulation
Welding International, 2019Co-Authors: Takehisa Yamada, Mitsuru OhataAbstract:The aim of this study is to confirm that Ductile Crack Growth resistance of Cracked components can be predicted by simulation model with the proposed damage model, which is derived by unit cell anal...
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Simulation-based method for hierarchal material design to improve Ductile Crack Growth resistance of structural component
International Journal of Fracture, 2015Co-Authors: Hiroto Shoji, Mitsuru Ohata, Fumiyoshi MinamiAbstract:The purpose of this study is to propose a method to correlate micro-structural characteristics of two-phase steel with structural performance in terms of Ductile Crack Growth resistance (R-curve). For this purpose, a meso-scopic simulation method is proposed to predict two types of Ductile properties of two-phase steel that control the R-curve from micro-structural characteristics. The R-curve of three-point bend specimen with fatigue pre-Crack predicted by a macro-scopic simulation method that we have proposed, in which these two types of Ductile properties obtained by the proposed meso-scopic methods are implemented, is in good agreement with experimental result.
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simulation model to correlate micro structural characteristics of two phase steel with Ductile Crack Growth resistance
Procedia Materials Science, 2014Co-Authors: Hiroto Shoji, Mitsuru Ohata, Fumiyoshi MinamiAbstract:The purpose of this study is to propose a numerical simulation method for estimating the effect of micro-structural characteristics of two-phase steel on Ductile Crack Growth resistance (R-curve) of structural components. For this purpose, a hierarchical approach is proposed to correlate the micro-structural characteristics with the R-curve, which consists of a meso-scopic approach and a macro-scopic approach. A meso-scopic approach correlates the micro-structural characteristics with the two types of Ductile properties of steel that controls R-curve. Then, a macro-scopic approach predicts R-curve from the two types of Ductile properties obtained by the proposed meso-scopic approach. It is demonstrated that the proposed hierarchical approach can predict R-curve of a 3-point bend specimen with a Crack from micro-structural characteristics of two-phase steel.
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hierarchical damage simulation to correlate micro structural characteristics of steel with Ductile Crack Growth resistance of component
ICF13, 2013Co-Authors: Mitsuru Ohata, Hiroto Shoji, Fumiyoshi MinamiAbstract:The final goal of this study is to develop a method for estimating the effect of micro-structural characteristics of steel (especially two-phase steel) on Ductile Crack Growth resistance of a structural component. For this purpose, hierarchical approach to link the micro-structural characteristics of steel and Ductile Crack Growth resistance curve of a component is proposed. First attention is paid to reveal mechanical properties that control Ductile Crack Growth resistance curve (CTOD-R curve), so that the R-curve could be numerically predicted only from those properties. It is shown from the observation of a mechanism for Ductile Crack Growth that two types of “Ductile properties” of steel associated with Ductile damage can mainly influence CTOD-R curve; one is a resistance of Ductile Crack initiation estimated with critical local strain for Ductile Cracking from the surface of notch root, and the other one is a stress triaxiality dependent ductility obtained with circumferentially notched round-bar specimens. The damage model for numerically simulating the R-curve is proposed taking these two “Ductile properties” into account, where Ductile Crack initiation from Crack-tip is in accordance with local strain criterion, and subsequent Crack Growth triaxiality dependent damage criterion. This macroscopic simulation can correlate the mechanical properties of steel with CTOD-R curve of a component. The second approach is to develop a simulation method to predict the effect of micro-structural characteristics of two-phase steel on the two types of Ductile properties that were found to be Ductile Crack Growth controlling mechanical properties. To simulate meso-scale Ductile damage behaviors, 3D micro-structural FE-model is developed for analyzing the stress/strain localization behaviors by micro-structural strength mismatch and Ductile damage model for reproducing damage evolution up to micro-void/micro-Crack formation. This meso-scopic simulation can correlate micro-structural characteristics with mechanical properties of two-phase steel. Through the proposed hierarchical approaches, micro-structural morphology of two-phase steel to improve Ductile Crack Growth resistance of a component can be discussed.
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buckling and tensile strain capacity of girth welded 48 x80 pipeline
ASME 2013 32nd International Conference on Ocean Offshore and Arctic Engineering, 2013Co-Authors: Mitsuru Ohata, Takahiro Sakimoto, Junji Shimamura, Kenji OiAbstract:This paper presents the experimental and analytical results focused on the compressive and tensile strain capacity of X80 linepipe. A full-scale bending test of girth welded 48″ OD X80 linepipes was conducted to investigate the compressive strain limit regarding to the local buckling and tensile strain limit regarding to the girth weld fracture. As for the compressive buckling behavior, one large developing wrinkle and some small wrinkles on the pipe surface were captured relatively well from observation and strain distribution measurement after pipe reaches its endurable maximum bending moment. The tensile strain limit is discussed from the viewpoint of competition of two fracture phenomena: Ductile Crack initiation / propagation from an artificial notch at the HAZ of the girth weld, and strain concentration and necking / rupture in the base material.The Ductile Crack Growth behavior from the girth weld notch is simulated by FE-analysis based on the proposed damage model, and compared with the experimental results. In this report, it is also demonstrated that the simulation model can be applicable to predicting Ductile Crack Growth behaviors from a circumferentially notched girth welded pipe with internal high pressure subjected to post-buckling loading.Copyright © 2013 by ASME
A Needleman - One of the best experts on this subject based on the ideXlab platform.
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three dimensional microstructural effects on plane strain Ductile Crack Growth
International Journal of Solids and Structures, 2006Co-Authors: A Needleman, Viggo TvergaardAbstract:Ductile Crack Growth under mode I, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model the material. Two populations of second-phase particles are represented, large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and the effects of different three dimensional distributions on the Crack path and on the overall Crack Growth rate are analyzed. For comparison purposes, a two dimensional distribution of cylindrical inclusions is analyzed. Crack Growth occurs off the initial Crack plane in all 3D computations, whereas straight ahead Crack Growth occurs with the two dimensional cylindrical inclusions. As a consequence, the three dimensional distributions of spherical inclusions exhibit an increased Crack Growth resistance as compared to the two dimensional distribution of cylindrical inclusions.
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three dimensional analysis of dynamic Ductile Crack Growth in a thin plate
Journal of The Mechanics and Physics of Solids, 1996Co-Authors: K K Mathur, A Needleman, Viggo TvergaardAbstract:Abstract A three dimensional analysis of dynamic Ductile Crack Growth in an edge Cracked plate is carried out, using a data parallel implementation in a transient three dimensional finite element program. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model Ductile fracture by the nucleation and subsequent Growth of voids to coalescence. Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating owing to plastic dissipation and the resulting thermal softening are accounted for in the analyses. The Crack speed and the Crack path are based on the Ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic Crack Growth criteria. A convected coordinate Lagrangian formulation is employed and the discretization is based on twenty-node brick elements with 2 × 2 × 2 Gauss points. The equations of motion are integrated numerically by an explicit integration procedure using a lumped mass matrix. Crack Growth occurs by tunneling in the central part of the plate and shear lip formation at the free surface. The effect of various material parameters and of plate thickness on this process is studied. For comparison purposes, a calculation with overall plane strain boundary conditions is carried out.
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mesh effects in the analysis of dynamic Ductile Crack Growth
Engineering Fracture Mechanics, 1994Co-Authors: A Needleman, Viggo TvergaardAbstract:Abstract For numerical studies of dynamic Crack Growth the mesh sensitivity of the Crack Growth predictions is investigated. The computed Crack Growth behavior is based on the Ductile fracture predictions of an elastic-viscoplastic constitutive relation for a porous plastic solid, which models the nucleation and Growth of voids to coalescence. Both initially sharp and initially blunt Cracks are analyzed. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the Crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. For the larger voids the size and spacing are directly specified in the analyses, whereas no length scale is specified for the small-scale voids. Crack Growth predictions in cases where the large-scale voids dominate show practically no mesh sensitivity, whereas cases dominated by the small-scale voids show a clear mesh sensitivity. For initially sharp Cracks the initiation of Crack Growth is quite sensitive to the mesh. However, for initially blunt Cracks the mesh sensitivity of the initiation time is removed.
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An analysis of the brittle-Ductile transition in dynamic Crack Growth
International Journal of Fracture, 1993Co-Authors: Viggo Tvergaard, A NeedlemanAbstract:The brittle-Ductile transition in dynamic Crack Growth is investigated through the numerical analysis of a plane strain edge Cracked specimen, subject to impulsive loading at one end. The material is characterized as an elastic-viscoplastic solid, with a temperature dependent flow strength. Thermal softening due to adiabatic heating and a model for Ductile failure by void nucleation, Growth and coalescence are incorporated into the constitutive relation. The Ductile void Growth mechanism involves two populations of void nucleating particles; discretely modelled low strength inclusions that give large voids near the Crack tip at an early stage and homogeneously distributed small second phase particles that require large strains for void nucleation. Cleavage is modelled in terms of a spatially non-uniform, but temperature and strain rate independent, critical value of the maximum principal normal stress. The numerical results show a clear transition from cleavage dominated Crack Growth at low temperatures to purely Ductile Crack Growth at higher temperatures. There is an accompanying large increase in the material's resistance to dynamic Crack initiation and Growth. The computed Crack Growth behaviour is a direct outcome of the material description; no ad hoc dynamic fracture criterion is employed. Effects of variations in the material model on the brittle-Ductile transition are explored.
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an analysis of dynamic Ductile Crack Growth in a double edge Cracked specimen
International Journal of Fracture, 1991Co-Authors: A Needleman, Viggo TvergaardAbstract:Dynamic Crack Growth is analysed numerically for a plane strain double edge Cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for Ductile fracture by the nucleation and subsequent Growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the Crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The Crack Growth velocities determined here are entirely based on the Ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic Crack Growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic Crack Growth behavior and for the time variation of Crack tip characterizing parameters are obtained for each case analyzed.
Lin Xia - One of the best experts on this subject based on the ideXlab platform.
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Ductile Crack Growth iii transition to cleavage fracture incorporating statistics
Journal of The Mechanics and Physics of Solids, 1996Co-Authors: Lin Xia, Fong C ShihAbstract:Abstract The fracture resistance of ferritic steels in the Ductile/brittle transition regime is controlled by the competition between Ductile tearing and cleavage fracture. Under typical conditions, a Crack initiates and grows by Ductile tearing but ultimate failure occurs by catastrophic cleavage fracture. In this study the tearing process is simulated using void-containing cell elements embedded within a conventional elastic-plastic continuum; details of the cell model are discussed in Parts I and II of this article. Weakest link statistics is incorporated into the cell element model and this new model is employed to predict the onset of unstable cleavage fracture. Our approach differs from previous analyses in several important ways. The elastic-plastic field computed for Crack Growth by Ductile tearing is fully integrated with a weakest link cleavage fracture model. The model also accounts for the competition between the nucleation of voids from carbide inclusions and the unstable Cracking of inclusions precipitating catastrophic cleavage fracture. This model leads immediately to a natural definition of the Weibull stress measure pertinent to cleavage fracture. The model is not restricted by the extent of plastic deformation and Ductile tearing. Two effects are associated with Ductile Crack Growth: the cumulative sampling volume is increased and the Crack tip constraint is altered. Both effects have important roles which are treated within the present cleavage fracture model. Load-displacement behavior, Ductile tearing resistance and transition to cleavage fracture are investigated for several different test geometries and a range of microstructural parameters. It is found that certain variations in microstructure can result in pronounced effects on the cleavage fracture toughness though they have no effect on the Ductile tearing resistance preceding cleavage. Rate effects on Ductile tearing and transition to cleavage fracture are also discussed. The model predicts trends in Ductile/brittle transition that are consistent with available experimental data.
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Ductile Crack Growth ii void nucleation and geometry effects on macroscopic fracture behavior
Journal of The Mechanics and Physics of Solids, 1995Co-Authors: Lin Xia, Fong C ShihAbstract:Many metals that fail by void Growth and coalescence display a macroscopically planar fracture process zone of one or two void spacings in thickness; outside this region, the voids exhibit little or no Growth. A finite element model of this mode of failure was described in Part I of this paper [J. Mech. Phys. Solids, 43, 233–259 (1995)]. A row of void-containing cell elements is placed on the symmetry plane ahead of the initial Crack. The cells incorporate the softening characteristics of hole Growth and dependence on stress triaxiality. These cells are embedded within a conventional elastic-plastic continuum. Under increasing strain, the voids grow and coalesce to form new Crack surfaces, thereby advancing the Crack. Parametric studies reveal that the important microstructural parameters in the model are D and f0, characterizing the spacing and the initial volume fraction of voids on the fracture plane. Using this model, Xia et al. [J. Mech. Phys. Solids, 43, 389–413 (1995)] have successfully predicted details of the load, displacement and Crack Growth histories—collectively referred to as the macroscopic fracture behavior—of four specimen geometries, which give rise to significantly different Crack tip constraints under fully plastic conditions. Here we study the quantitative effects of void nucleation by a stress and strain criterion on the macroscopic fracture behavior. This behavior is compared with predictions using a similar volume of voids present from the very beginning. Geometry effects on macroscopic fracture behavior under contained and fully yielded conditions are discussed for the three-point-bend specimen and the center-Crack-panel loaded in tension. Here the objective is to show the connection between the Crack Growth resistance and the fracture environment, namely, the constraint ahead of the Crack tip and the tensile stress on the fracture plane.
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A computational approach to Ductile Crack Growth under large scale yielding conditions
Journal of the Mechanics and Physics of Solids, 1995Co-Authors: Lin Xia, C.fong Shih, John W. HutchinsonAbstract:Mode I Crack initiation and Growth under plane strain conditions in tough metals is computed using an elastic-plastic continuum model which accounts for void Growth and coalescence ahead of the Crack tip. The material parameters are the Young’s modulus, yield stress and strain hardening exponent of the metal, along with the parameters characterizing the spacing and volume fraction of voids in material elements lying in the plane of the Crack. For a given set of these parameters and a specific specimen, or component, subject to a specific loading, relationships among load, load-line displacement and Crack advance can be computed with no restrictions on the extent of plastic deformation. Similarly, there is no limit on Crack advance, except that it must take place on the symmetry plane ahead of the initial Crack. Suitably defined measures of Crack tip loading intensity, such as those based on the J-integral, can also be computed, thereby directly generating Crack Growth resistance curves. In this paper, the model is applied to five specimen geometries which are known to give rise to significantly different Crack tip constraints and Crack Growth resistance behaviors. Computed results are compared with sets of experimental data for two tough steels for four of the specimen types. Details of the load, displacement and Crack Growth histories are accurately reproduced, even when extensive Crack Growth takes place under conditions of fully plastic yielding.
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Ductile Crack Growth-I. A numerical study using computational cells with microstructurally-based length scales
Journal of the Mechanics and Physics of Solids, 1995Co-Authors: Lin Xia, C.fong ShihAbstract:Many metals which fail by a void Growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no Growth. To model this process a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, D, can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension D. Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole Growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity. The collection of cells softened by hole Growth constitutes the fracture process zone of length l1. Two fracture mechanism regimes can be identified corresponding to l1 ≈ D and l1 ⪢ D. The connection between these mechanisms and fracture resistance is discussed. Finite element calculations have been carried out to determine Crack Growth resistance curves for plane strain, mode I Crack Growth under small scale yielding. A row of voided cells is placed on the symmetry plane ahead of the initial Crack. These cell elements are embedded within a conventional elastic-plastic continuum. Under increasing load, the voids in the cells grow and coalesce to form a new Crack surface thereby advancing the Crack. Resistance curves are calculated for Crack Growth exceeding many multiples of D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. The effect of Crack tip constraint on fracture resistance is examined under small scale yielding by way of the T-stress. As a final application, resistance curves for a deep and a shallow Crack bend bar are computed. These are compared with experimental data.
Fong C Shih - One of the best experts on this subject based on the ideXlab platform.
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a parametric study of mixed mode i iii Ductile fracture in tough materials under small scale yielding
Engineering Fracture Mechanics, 1998Co-Authors: Xiaosheng Gao, Fong C ShihAbstract:Abstract Mixed-mode I/III Crack Growth in high purity, tough materials under small-scale yielding conditions are studied using an elastic–plastic continuum model. The fracture process is controlled by the interaction of two mechanisms, the Growth of the existing voids and the nucleation of new voids under increased plastic strain. Crack Growth is constrained to occur only along the initial Crack plane because of the symmetry conditions of load and geometry. The effects of mode mixity on mixed-mode fracture toughness are studied under different circumstances, and the effects of other factors, such as microstructural parameters, continuum properties of the solid and the Crack-tip constraint, are also examined. The study indicates that mixed mode I/III fracture resistance, followed by some amount of Ductile Crack Growth, displays a minimum at a critical phase angle [φ=tan−1(KIII/KI)] between 45° and 55°. This indicates a direction at which an initially flat mode I Crack may reorient to cause slant fracture or formation of shear lips.
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Ductile Crack Growth iii transition to cleavage fracture incorporating statistics
Journal of The Mechanics and Physics of Solids, 1996Co-Authors: Lin Xia, Fong C ShihAbstract:Abstract The fracture resistance of ferritic steels in the Ductile/brittle transition regime is controlled by the competition between Ductile tearing and cleavage fracture. Under typical conditions, a Crack initiates and grows by Ductile tearing but ultimate failure occurs by catastrophic cleavage fracture. In this study the tearing process is simulated using void-containing cell elements embedded within a conventional elastic-plastic continuum; details of the cell model are discussed in Parts I and II of this article. Weakest link statistics is incorporated into the cell element model and this new model is employed to predict the onset of unstable cleavage fracture. Our approach differs from previous analyses in several important ways. The elastic-plastic field computed for Crack Growth by Ductile tearing is fully integrated with a weakest link cleavage fracture model. The model also accounts for the competition between the nucleation of voids from carbide inclusions and the unstable Cracking of inclusions precipitating catastrophic cleavage fracture. This model leads immediately to a natural definition of the Weibull stress measure pertinent to cleavage fracture. The model is not restricted by the extent of plastic deformation and Ductile tearing. Two effects are associated with Ductile Crack Growth: the cumulative sampling volume is increased and the Crack tip constraint is altered. Both effects have important roles which are treated within the present cleavage fracture model. Load-displacement behavior, Ductile tearing resistance and transition to cleavage fracture are investigated for several different test geometries and a range of microstructural parameters. It is found that certain variations in microstructure can result in pronounced effects on the cleavage fracture toughness though they have no effect on the Ductile tearing resistance preceding cleavage. Rate effects on Ductile tearing and transition to cleavage fracture are also discussed. The model predicts trends in Ductile/brittle transition that are consistent with available experimental data.
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Ductile Crack Growth ii void nucleation and geometry effects on macroscopic fracture behavior
Journal of The Mechanics and Physics of Solids, 1995Co-Authors: Lin Xia, Fong C ShihAbstract:Many metals that fail by void Growth and coalescence display a macroscopically planar fracture process zone of one or two void spacings in thickness; outside this region, the voids exhibit little or no Growth. A finite element model of this mode of failure was described in Part I of this paper [J. Mech. Phys. Solids, 43, 233–259 (1995)]. A row of void-containing cell elements is placed on the symmetry plane ahead of the initial Crack. The cells incorporate the softening characteristics of hole Growth and dependence on stress triaxiality. These cells are embedded within a conventional elastic-plastic continuum. Under increasing strain, the voids grow and coalesce to form new Crack surfaces, thereby advancing the Crack. Parametric studies reveal that the important microstructural parameters in the model are D and f0, characterizing the spacing and the initial volume fraction of voids on the fracture plane. Using this model, Xia et al. [J. Mech. Phys. Solids, 43, 389–413 (1995)] have successfully predicted details of the load, displacement and Crack Growth histories—collectively referred to as the macroscopic fracture behavior—of four specimen geometries, which give rise to significantly different Crack tip constraints under fully plastic conditions. Here we study the quantitative effects of void nucleation by a stress and strain criterion on the macroscopic fracture behavior. This behavior is compared with predictions using a similar volume of voids present from the very beginning. Geometry effects on macroscopic fracture behavior under contained and fully yielded conditions are discussed for the three-point-bend specimen and the center-Crack-panel loaded in tension. Here the objective is to show the connection between the Crack Growth resistance and the fracture environment, namely, the constraint ahead of the Crack tip and the tensile stress on the fracture plane.
