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Robert H. Dodds - One of the best experts on this subject based on the ideXlab platform.
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T-stress effects on steady crack growth in a thin, ductile plate under Small-Scale Yielding conditions: Three-dimensional modeling
Engineering Fracture Mechanics, 2011Co-Authors: J.c. Sobotka, Robert H. DoddsAbstract:Abstract The non-singular T-stress provides a first-order estimate of geometry and loading mode, e.g. tension vs. bending, effects on elastic–plastic, crack-front fields under mode I conditions. The T-stress has a pronounced effect on measured crack growth resistance curves for ductile metals – trends most computational models confirm using a two-dimensional setting. This work examines T-stress effects on three-dimensional (3D), elastic–plastic fields surrounding a steadily advancing crack for a moderately hardening material in the framework of a 3D, Small-Scale Yielding boundary-layer model. A flat, straight crack front advances at a constant quasi-static rate under near invariant local and global mode I loading. The boundary-layer model has thickness B that defines the only geometric length-Scale. The material flow properties and (local) toughness combine to limit the in-plane plastic-zone size during steady growth to at most a few multiples of the thickness (conditions obtainable, for example, in large, thin aluminum components). The computational model requires no crack growth criterion; rather, the crack front extends steadily at constant values of the plane-stress displacements imposed on the remote boundary for the specified far-field stress intensity factor and T-stress. The specific numerical results presented demonstrate similarity scaling of the 3D near-front stresses in terms of two non-dimensional loading parameters. The analyses reveal a strong effect of T-stress on key stress and strain quantities for low loading levels and less effect for higher loading levels, where much of the plastic zone experiences plane-stress conditions. To understand the combined effects of T-stress on stresses and plastic strain levels, normalized values from a simple void-growth model, computed over the crack plane for low loading, clearly reveal the tendency for crack-front tunneling, shear-lip formation near the outside surfaces, and a minimum steady-state fracture toughness for T = 0 loading.
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Steady crack growth in a thin, ductile plate under Small-Scale Yielding conditions: Three-dimensional modeling
Engineering Fracture Mechanics, 2011Co-Authors: J.c. Sobotka, Robert H. DoddsAbstract:Abstract This work employs high resolution, finite element computations to investigate key features of the elastic–plastic fields near a steadily advancing crack at quasi-static rates under three-dimensional, Small-Scale Yielding conditions. The model represents a structurally thin component constructed of a material (e.g., Al and Ti alloys) with flow stress and fracture toughness properties that together limit the size of the in-plane plastic zone during steady-growth to no more than several multiples of the plate thickness. The computational approach generalizes the streamline integration procedure used previously for two-dimensional studies into three dimensions to represent steady-state growth on a fixed mesh in a boundary-layer framework. The plate thickness provides the only geometrical length Scale. Crack extension occurs at the remotely applied, fixed loading without the need for a local growth criterion. In the first computations of this type, the present work considers a straight crack front advancing under local and global mode I loading with zero T-stress in a moderately hardening material. Applied remote loads at steady growth generate plastic zone sizes ahead of the advancing crack front ranging from 0.25 to 6.4 times the thickness. Key results include: (1) the crack-front fields exhibit a self-similar scaling characterized by a non-dimensional loading parameter; (2) three-dimensional effects extend to distances of approximately 1.5–2.5 times the thickness ahead of the advancing crack front for key values of this loading parameter, beyond which the fields (elastic–plastic then linear-elastic at greater distances) become uniform over the thickness; and (3) crack opening profiles on the outside surface reveal a “wedge-like”, opening shape which simplifies the definition of a crack-tip opening angle.
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effect of t stress on fatigue crack closure in 3 d Small Scale Yielding
International Journal of Solids and Structures, 2004Co-Authors: S Roychowdhury, Robert H. DoddsAbstract:Abstract This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure in the Small-Scale Yielding regime. The finite element analyses grow a sharp, straight-through crack in a modified boundary layer model under mode I, constant amplitude cyclic loading with prescribed but independent peak values of stress intensity factor, Kmax, and the T-stress, Tmax. A purely kinematic hardening law with constant modulus represents the material constitutive behavior. The computational results demonstrate that a two parameter characterization of crack tip fields in terms of K max /σ 0 B and Tmax/σ0, where σ0 denotes the yield stress of the material, correlates successfully the normalized opening load Kop/Kmax across variations of thickness (B), constraint level and material flow properties. Both negative and positive T-stress reduce the through-thickness variation in local opening load levels along the crack front. A negative T-stress increases Kop/Kmax values, particularly at low peak loads where the plastic zone size remains a fraction of the thickness; a positive T-stress has limited effect on Kop/Kmax values. The fringe plots of individual plastic strain components reveal (a) in the absence of T-stress (Tmax/σ0=0), plastic contraction in the thickness direction compensates primarily for permanent stretching in the direction normal to the crack plane required for closure, (b) for negative T-stress (Tmax/σ0 0), both in-plane directions experience permanent stretching and the thickness direction alone undergoes plastic contraction.
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three dimensional effects on fatigue crack closure in the Small Scale Yielding regime a finite element study
Fatigue & Fracture of Engineering Materials & Structures, 2003Co-Authors: S Roychowdhury, Robert H. DoddsAbstract:Plasticity induced closure often strongly influences the behaviour of fatigue cracks at engineering Scales in metallic materials. Current predictive models generally adopt the effective stress-intensity tractor (ΔK eff =K max -K oP ) in a Paris law type relationship to quantify crack growth rates. This work describes a 3D finite element study of mode I fatigue crack growth in the Small-Scale Yielding (SSY) regime under a constant amplitude cyclic loading with zero T-stress and a ratio K min /K max = 0. The material behaviour follows a purely kinematic hardening constitutive model with constant hardening modulus. Dimensional analysis suggests, and the computational results confirm, that the normalized remote opening load value, K op /K max at each location along the crack front remains unchanged when the peak load (K max ), thickness (B) and material flow stress (σ 0 ) all vary to maintain a fixed value of K = K max/σ0 √B. Through parametric computations at various K levels, the results illustrate the effects of normalized peak loads on the through-thickness opening-closing behaviour and the effects of σ 0 /E, where E denotes material elastic modulus. The examination of defamation fields along the fatigue crack front provides additional insight into the 3D closure process.
J W Hutchinson - One of the best experts on this subject based on the ideXlab platform.
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effect of strain dependent cohesive zone model on predictions of interface crack growth
Journal De Physique Iv, 1996Co-Authors: Viggo Tvergaard, J W HutchinsonAbstract:Crack growth along an interface joining an elastic-plastic solid to a solid that does not yield plastically is studied numerically, accounting for mixed mode loading under conditions of Small Scale Yielding. The fracture process is represented in terms of a cohesive zone model, for which the work of separation per unit area and the peak stress required for separation are basic parameters; but where also a plastic strain effect on the fracture process is incorporated. This additional effect is included to model accelerated void nucleation and growth at the interface, resulting from intense plastic straining just in front of the crack tip.
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effect of strain dependent cohesive zone model on predictions of crack growth resistance
International Journal of Solids and Structures, 1996Co-Authors: Viggo Tvergaard, J W HutchinsonAbstract:Crack growth in an elastic-plastic solid is studied by a computational model, in which a cohesive zone model is used to characterize the fracture process. The separation work per unit area and the peak stress required for separation are the basic parameters in the cohesive zone model, but also an effect of plastic straining, reducing the peak stress for separation, is incorporated here. This additional effect represents acceleration of the void growth process and nucleation of more voids, resulting from intense plastic straining in the immediate vicinity of the crack tip. The analyses are carried out for conditions of Small-Scale Yielding under plane strain, with the mode I stress intensity factors specified at the loading parameter. Also the effect of a T-stress on crack growth resistance is investigated.
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effect of t stress on mode i crack growth resistance in a ductile solid
International Journal of Solids and Structures, 1994Co-Authors: J W HutchinsonAbstract:Abstract An elastic-plastic crack growth model, with a traction-separation law specified on the crack plane to characterize the fracture process, is used to study the effect of the non-singular T -stress, acting parallel to the crack plane. The work of separation per unit area and the peak normal stress are the two main parameters used to characterize the fracture process, and crack growth resistance curves are calculated numerically for a number of values of the peak stress to initial yield stress ratio, and for different levels of strain hardening. Small-Scale Yielding in plane strain is considered with the remote field specified by a constant value of the T -stress, applied initially, and an increasing magnitude of the mode I stress intensity factor. It is shown that the predicted T -stress dependence of the fracture toughness during crack growth is qualitatively similar to experimental observations, even though the experiments go beyond Small-Scale Yielding.
Huang Yuan - One of the best experts on this subject based on the ideXlab platform.
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assessment of low cycle fatigue crack growth under mixed mode loading conditions by using a cohesive zone model
International Journal of Fatigue, 2015Co-Authors: Huang YuanAbstract:Abstract Most cohesive zone models were used to reproduce fatigue crack growth under Small Scale Yielding and failed to predict elastic–plastic fatigue crack growth. In the present work a new cohesive zone model is introduced to give a uniform description of both fatigue crack growth and elastoplastic rupture. Damage accumulation of the cohesive model contains both monotonic damage as well as cyclic damage and validated by corresponding mixed-mode fracture and fatigue experiments of an austenitic stainless steel. Computations confirm that the present cohesive zone model may provide a uniform description for the whole fatigue crack growth regimes.
Viggo Tvergaard - One of the best experts on this subject based on the ideXlab platform.
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Statistics of ductile fracture surfaces: the effect of material parameters
International Journal of Fracture, 2013Co-Authors: Laurent Ponson, Elisabeth Bouchaud, Viggo Tvergaard, Alan NeedlemanAbstract:The effect of material parameters on the statistics of fracture surfaces is analyzed under Small Scale Yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, Small Scale Yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid with two populations of void nucleating second phase particles represented. Large particles that result in void nucleation at an early stage are modeled discretely while Small particles that require large strains to nucleate are homogeneously distributed. The three dimensional analysis permits modeling of a three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. Material parameters characterizing void nucleation are varied and the statistics of the resulting fracture surfaces is investigated. All the fracture surfaces are found to be self-affine over a size range of about two orders of magnitude with a very similar roughness exponent of $$0.56\,\pm \,0.03$$ . In contrast, the full statistics of the fracture surfaces is found to be more sensitive to the material microscopic fracture properties: height fluctuations are shown to crossover from a Student’s distribution with power law tails at Small Scales to a Gaussian behavior at large Scales, but this transition occurs at a material dependent length Scale. Using the family of Student’s distributions, this transition can be described introducing an additional exponent $$\mu = 0.15\,\pm \,0.02$$ , the value of which compares well with recent experimental findings. The description of the roughness distribution used here gives a more complete quantitative characterization of the fracture surface morphology which allows a better comparison with experimental data and an easier interpretation of the roughness properties in terms of microscopic failure mechanisms.
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theoretical investigation of the effect of plasticity on crack growth along a functionally graded region between dissimilar elastic plastic solids
Engineering Fracture Mechanics, 2002Co-Authors: Viggo TvergaardAbstract:Abstract The influence of a functionally graded layer joining dissimilar elastic–plastic solids is studied in relation to interface crack growth. Conditions of Small Scale Yielding are considered, and the boundary conditions applied on the outer edge of the region analysed are displacements for the elastic oscillating stress singularity fields corresponding to a sharp interface. A cohesive zone model is used to represent the fracture process, where the work of separation per unit area and the peak stress are basic parameters. Only crack growth on the initial crack plane parallel to the graded layer is analysed, but different locations of the crack plane relative to the layer are considered to obtain a parametric understanding. Crack growth resistance curves are illustrated, and the dependence of the steady-state fracture toughness on mode mixity is presented for several combinations of material parameters.
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effect of strain dependent cohesive zone model on predictions of interface crack growth
Journal De Physique Iv, 1996Co-Authors: Viggo Tvergaard, J W HutchinsonAbstract:Crack growth along an interface joining an elastic-plastic solid to a solid that does not yield plastically is studied numerically, accounting for mixed mode loading under conditions of Small Scale Yielding. The fracture process is represented in terms of a cohesive zone model, for which the work of separation per unit area and the peak stress required for separation are basic parameters; but where also a plastic strain effect on the fracture process is incorporated. This additional effect is included to model accelerated void nucleation and growth at the interface, resulting from intense plastic straining just in front of the crack tip.
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effect of strain dependent cohesive zone model on predictions of crack growth resistance
International Journal of Solids and Structures, 1996Co-Authors: Viggo Tvergaard, J W HutchinsonAbstract:Crack growth in an elastic-plastic solid is studied by a computational model, in which a cohesive zone model is used to characterize the fracture process. The separation work per unit area and the peak stress required for separation are the basic parameters in the cohesive zone model, but also an effect of plastic straining, reducing the peak stress for separation, is incorporated here. This additional effect represents acceleration of the void growth process and nucleation of more voids, resulting from intense plastic straining in the immediate vicinity of the crack tip. The analyses are carried out for conditions of Small-Scale Yielding under plane strain, with the mode I stress intensity factors specified at the loading parameter. Also the effect of a T-stress on crack growth resistance is investigated.
Andrei Kotousov - One of the best experts on this subject based on the ideXlab platform.
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a crack closure model of fatigue crack growth in plates of finite thickness under Small Scale Yielding conditions
Mechanics of Materials, 2009Co-Authors: John Codrington, Andrei KotousovAbstract:Abstract Crack growth rates are significantly affected by the thickness of the specimen when all other parameters are kept constant. A quantitative estimation of the thickness effect is thus necessary to make predictions of crack growth rates more accurate and reliable. For this purpose a theoretical model was developed based on the strip-yield assumption and first-order plate theory. No empirical or fitting parameters were used in this work unlike some previous studies. The theoretical values obtained for the normalised load ratio parameter, U , were employed to describe experimental data, obtained under Small-Scale Yielding conditions, at various load ratios and plate thicknesses. Such a representation considerably narrowed the scatter in the crack growth rates versus the effective stress intensity factor range, Δ K eff , demonstrating the potential of the theoretical model.
