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Somnath Ghosh - One of the best experts on this subject based on the ideXlab platform.
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homogenized constitutive and fatigue nucleation models from crystal plasticity fe simulations of ti alloys part 2 macroscopic probabilistic crack nucleation model
International Journal of Plasticity, 2013Co-Authors: M Anahid, Somnath GhoshAbstract:Abstract This is the second of a two-part paper aimed at the developing macroscopic models of fatigue deformation and failure in polycrystalline Ti alloys. In this part, a probabilistic crack nucleation model is developed for predicting damage nucleation in macroscopic computations of the structural components from rigorous microscopic analyzes. Inputs to this model include morphological characteristics of the microstructure at any material point along with the local stress/strain state. This stress-state, needed to trigger this model, can be obtained from finite element analysis using the homogenized, anisotropic plasticity constitutive (HAPC) model developed in part 1 ( Ghosh et al., in press ). A deterministic functional form, relating time for macroscopic crack nucleation to the macroscopic stress state and microstructural characteristic parameters, is derived from rigorous crystal plasticity FE simulations of representative volume element of a bi-crystal system that implements a physics-based Grain Level crack nucleation model. Subsequently, a probabilistic model for expected crack nucleation in the macroscopic (structural) scale is generated from this functional form. The probabilistic model has a direct connection to the mechanisms of microstructural crack nucleation and can be obtained from macroscopic FE analysis with knowledge of statistics of the local microstructure.
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a cold dwell fatigue crack nucleation criterion for polycrystalline ti 6242 using Grain Level crystal plasticity fe model
International Journal of Fatigue, 2008Co-Authors: Kedar Kirane, Somnath GhoshAbstract:A Grain-Level fatigue crack nucleation criterion for cold dwell in Ti-6242 alloy is developed in this paper using a rate and size dependent anisotropic elasto-crystal plasticity constitutive model, and validated with experiments. Early crack initiation in Ti-6242 under cold dwell fatigue has been identified to be caused by stress concentrations in a hard Grain, induced by load shedding from creep in adjacent soft Grains. Accurate prediction of local stress and strain evolution during loading requires a robust representation of morphological and crystallographic features of the microstructure. These are accounted for in the FE model in a statistically equivalent sense. The proposed crack nucleation model is based on the observed similarities between crack evolution at the tip of a crack and a dislocation pileup. The nucleation model is calibrated and validated using data available from acoustic microscopy though real time monitoring of crack evolution in dwell fatigue experiments.
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a framework for automated analysis and simulation of 3d polycrystalline microstructures part 1 statistical characterization
Acta Materialia, 2008Co-Authors: M Groeber, Somnath Ghosh, Michael D Uchic, D M DimidukAbstract:This is the first of a two-part paper aimed at developing a robust framework for the collection, quantification and simulation of 3D polycrystalline microstructures. Serial-sectioning methods are used to generate data that characterize the microstructural morphology and crystallography of Grains. The microstructure simulation model and codes take as input a series of electron backscatter diffraction (EBSD) patterns from the serial-sectioning experiments. Robust statistical analysis of the Grain-Level microstructures in 3D is conducted in this part of this paper. This analysis can provide necessary information for modeling and simulation efforts in the form of a highly refined and unbiased description of specific features, such as the distribution of Grain size, shape and orientation.
Pablo D Zavattieri - One of the best experts on this subject based on the ideXlab platform.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part ii numerical examples
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract Numerical aspects of the Grain Level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of Grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of Grain Level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part i theory and numerical implementation
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of Grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to Grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or Grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating Grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo Grain Level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part i theory and numerical implementation
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of Grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to Grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or Grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating Grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo Grain Level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.
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Grain Level analysis of crack initiation and propagation in brittle materials
Acta Materialia, 2001Co-Authors: Pablo D Zavattieri, Horacio D EspinosaAbstract:A study on the accuracy of cohesive models for capturing dynamic fragmentation of ceramic microstructures is presented. The investigation consists of a combined experimental/numerical approach in which microcracking and damage kinetics are examined by means of plate impact recovery experiments. The numerical analysis is based on a 2-D micromechanical stochastic finite element analysis. The model incorporates a cohesive law to capture microcrack initiation, propagation and coalescence, as well as crack interaction and branching, as a natural outcome of the calculated material response. The stochasticity of the microfracture process is modeled by introducing a Weibull distribution of interfacial strength at Grain boundaries. This model accounts for randomness in Grain orientation, and the existence of chemical impurities and glassy phase at Grain boundaries. Representative volume elements (RVE) of ceramic microstructure with different Grain size and shape distributions are considered to account for features observed in real microstructures. Normal plate impact velocity histories are used not only to identify model parameters, but also to determine under what conditions the model captures failure mechanisms experimentally observed. The analyses show that in order to capture damage kinetics a particular distribution of Grain boundary strength and detailed modeling of Grain morphology are required. Simulated microcrack patterns and velocity histories have been found to be in a good agreement with the experimental observations only when the right Grain morphology and model parameters are chosen. It has been found that the addition of rate effects to the cohesive model results in microcrack diffusion not observed experimentally.
Horacio D Espinosa - One of the best experts on this subject based on the ideXlab platform.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part ii numerical examples
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract Numerical aspects of the Grain Level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of Grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of Grain Level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part i theory and numerical implementation
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of Grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to Grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or Grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating Grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo Grain Level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.
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a Grain Level model for the study of failure initiation and evolution in polycrystalline brittle materials part i theory and numerical implementation
Mechanics of Materials, 2003Co-Authors: Horacio D Espinosa, Pablo D ZavattieriAbstract:Abstract A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of Grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to Grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or Grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating Grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo Grain Level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.
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Grain Level analysis of crack initiation and propagation in brittle materials
Acta Materialia, 2001Co-Authors: Pablo D Zavattieri, Horacio D EspinosaAbstract:A study on the accuracy of cohesive models for capturing dynamic fragmentation of ceramic microstructures is presented. The investigation consists of a combined experimental/numerical approach in which microcracking and damage kinetics are examined by means of plate impact recovery experiments. The numerical analysis is based on a 2-D micromechanical stochastic finite element analysis. The model incorporates a cohesive law to capture microcrack initiation, propagation and coalescence, as well as crack interaction and branching, as a natural outcome of the calculated material response. The stochasticity of the microfracture process is modeled by introducing a Weibull distribution of interfacial strength at Grain boundaries. This model accounts for randomness in Grain orientation, and the existence of chemical impurities and glassy phase at Grain boundaries. Representative volume elements (RVE) of ceramic microstructure with different Grain size and shape distributions are considered to account for features observed in real microstructures. Normal plate impact velocity histories are used not only to identify model parameters, but also to determine under what conditions the model captures failure mechanisms experimentally observed. The analyses show that in order to capture damage kinetics a particular distribution of Grain boundary strength and detailed modeling of Grain morphology are required. Simulated microcrack patterns and velocity histories have been found to be in a good agreement with the experimental observations only when the right Grain morphology and model parameters are chosen. It has been found that the addition of rate effects to the cohesive model results in microcrack diffusion not observed experimentally.
S Liu - One of the best experts on this subject based on the ideXlab platform.
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multiscale constraint based model to predict uniaxial multiaxial creep damage and crack growth in 316 h steels
International Journal of Mechanical Sciences, 2019Co-Authors: Kamran Nikbin, S LiuAbstract:Abstract A new failure ductility/multiscale constraint strain-based model to predict creep damage, rupture and crack growth under uniaxial and multiaxial conditions is developed for 316H Type stainless steels by linking globally uniform failure strains with a multiaxial constraint factor. The model identifies a geometric constraint and a time-dependent local constraint at the sub-Grain Level. Uniaxial and notched 316H steel as-received and pre-compressed data at various load Levels and temperatures with substantial scatter were used to derive the appropriate constitutive equations by using the proposed empirical/mechanistic approach. Constrained hydrostatic development of creep damage at the sub-Grain Level is assumed to directly relate to the uniform lower-bound creep steady state region of damage development measured at the global Level. Uniaxial and notched bar rupture at long terms is predicted based on the initial short-term creep or a representative tensile strength and a multiaxial constraint factor. The model is consistent with the well-known NSW remaining multiaxial ductility creep crack growth model which predicts crack growth bounds over the plane strain/stress states. This model, therefore, unifies the creep process response over the whole range of uniaxial, notched and crack growth processes which is extremely consequential to simple long term failure predictions of components at elevated temperatures.
Michael D Sangid - One of the best experts on this subject based on the ideXlab platform.
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a complete Grain Level assessment of the stress strain evolution and associated deformation response in polycrystalline alloys
Acta Materialia, 2020Co-Authors: Michael D Sangid, John Rotella, Peter Kenesei, Junsang Park, Diwakar Naragani, Paul A ShadeAbstract:Abstract Polycrystalline alloys are used pervasively across structural applications contingent upon extensive experimental testing. A statistically representative number of tests are necessary to expose the variability in the material's performance, as a result of non-uniform microstructures and associated micromechanical fields. In a more direct means of capturing this pertinent information, multi-modal experimental techniques are presented to measure and track the complete micromechanical state, evolving during loading, of each and every Grain within the regions of interest. Specifically, a combination of high-energy X-ray diffraction microscopy and digital image correlation coupled with electron backscatter diffraction are conducted on a specimen for each of the alloys, Haynes 282 and Ti7Al. The results of the multi-modal analysis definitively demonstrate that the degree of heterogeneity increases with deformation Level and is used to assess the number of Grains necessary for a representative volume element description of the stress state for each of these materials. Moreover, higher resolution imaging is used for identification of the slip system activity and subsequently used to study slip transmission events. An accurate knowledge of the resolved shear stress in adjacent Grains (Grain interactions) is demonstrated to be a key descriptor of the slip transmission events.
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incorporating Grain Level residual stresses and validating a crystal plasticity model of a two phase ti 6al 4 v alloy produced via additive manufacturing
Journal of The Mechanics and Physics of Solids, 2018Co-Authors: Kartik Kapoor, Yung Suk Jeremy Yoo, Todd A Book, Josh Kacher, Michael D SangidAbstract:Abstract Titanium alloys, produced via additive manufacturing techniques, offer tremendous benefits over conventional manufacturing processes. However, there is inherent uncertainty associated with their properties, often stemming from the variability in the manufacturing process itself along with the presence of residual stresses in the material, which prevents their use as critical components. This work investigates Ti-6Al-4 V produced via selective laser melting by carrying out crystal plasticity finite element (CPFE) simulations and high-resolution digital image correlation (HR-DIC) on samples subject to cyclic loading. This is preceded by detailed material characterization using electron backscatter diffraction, back-scattered electron imaging and transmission electron microscopy, whose results are utilized to inform the CPFE model. A method to incorporate the effect of Grain-Level residual stresses via geometrically necessary dislocations is developed and implemented within the CPFE framework. Using this approach, Grain Level information about residual stresses obtained spatially over the region of interest, directly from the experimental material characterization, is utilized as an input to the model. Simulation results match well with HR-DIC and indicate that prior β boundaries play an important role in strain localization. In addition, possible sites for damage nucleation are identified, which correspond to regions of high plastic strain accumulation.
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study of Grain Level deformation and residual stresses in ti 7al under combined bending and tension using high energy diffraction microscopy hedm
International Journal of Solids and Structures, 2016Co-Authors: Kamalika Chatterjee, Michael D Sangid, Ajey Venkataraman, T Garbaciak, John Rotella, Armand Joseph Beaudoin, Peter Kenesei, Junsang Park, A L PilchakAbstract:Abstract In-situ high energy diffraction microscopy (HEDM) experiments are carried out to analyze the state of combined bending and tension in a Ti-7Al alloy under room temperature creep. Grain-Level elastic strain tensors are evaluated from HEDM data. Atomistic calculations are used to predict elastic constants of Ti-7Al, to be used in determination of stress from strain. The stress gradient and residual stresses are successfully determined, which allows the demarcation between macro-/micro-Level residual stresses. A cluster of three neighboring Grains are identified that highlight the variation of mean and effective stress between Grains. Crystallographic orientations and slip characteristics are analyzed for the selected Grains. It is inferred that the interfaces between loaded Grains with markedly different stress triaxiality and slip tendency are potential spots for material damage.
