On the inelastic behavior of crystalline silicon at elevated temperatures

Rengarajan, G.; Reddy, J. N.

doi:10.1016/s0022-5096(01)00015-1

Cited by 3 publications

(5 citation statements)

References 40 publications

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“…This form is similar to that obtained in [17], though they consider partial transformations and thus allow rates of φ. In the development here, φ is a constant.…”

Section: Kinematics and Transformation Pathsmentioning

confidence: 54%

“…The constituent indices refer to variants of phases, so that m η represents the mass fraction of the particular variant, not the total mass fraction of the associated phase. Some simplification may be achieved by assuming kinematic decoupling of the transformation modes, as in [17]. However, assuming decoupled kinematics introduces errors for general large deformations, and we choose to retain the fully coupled kinematics for the transformation modes.…”

Section: Kinematics and Transformation Pathsmentioning

confidence: 99%

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Crystal level continuum modelling of phase transformations: the α ↔ epsi transformation in iron

Barton¹,

Benson²,

Becker³

2005

Modelling Simul. Mater. Sci. Eng.

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We present a crystal level model for thermo-mechanical deformation with phase transformation capabilities. The model is formulated to allow for large pressures (on the order of the elastic moduli) and makes use of a multiplicative decomposition of the deformation gradient. Elastic and thermal lattice distortions are combined into a single lattice stretch to allow the model to be used in conjunction with general equation of state relationships. Phase transformations change the mass fractions of the material constituents. The driving force for phase transformations includes terms arising from mechanical work, the temperature dependent chemical free energy change on transformation, and the interaction energy among the constituents. Deformation results from both these phase transformations and elasto-viscoplastic deformation of the constituents themselves. Simulation results are given for the α to ϵ phase transformation in iron. Results include simulations of shock-induced transformation in single crystals and of compression of polycrystals. Results are compared with available experimental data.

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“…This form is similar to that obtained in [17], though they consider partial transformations and thus allow rates of φ. In the development here, φ is a constant.…”

Section: Kinematics and Transformation Pathsmentioning

confidence: 54%

Section: Kinematics and Transformation Pathsmentioning

confidence: 99%

Crystal level continuum modelling of phase transformations: the α ↔ epsi transformation in iron

Barton¹,

Benson²,

Becker³

2005

Modelling Simul. Mater. Sci. Eng.

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show abstract

“…Many other perspectives and modeling approaches have been proposed, with a small sampling of these being [6,7,8,9,10,11,12,13,14,15]. The approach to phase transformation and twinning used here is somewhat unique in that it is a crystal mechanics based approach which includes elastic and plastic accommodation, is applicable to large strains including large volume changes and to complete transformation, and is formulated to work for either quasi-static loading or dynamic loading scenarios.…”

Section: Introductionmentioning

confidence: 99%

Bringing Together Computational and Experimental Capabilities at the Crystal Scale

Barton¹,

Edmiston²

2009

AIP Conference Proceedings

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Many phenomena of interest occur at the scale of crystals or are controlled be events happening at the crystalline scale. Examples include allotropic phase transformations in metals and pore collapse in energetic crystals. The research community is increasingly able to make detailed experimental observations at the crystalline scale and to inform crystal scale models using lower length scale computational tools. In situ diffraction techniques are pushing toward finer spatial and temporal resolution. Molecular and dislocation dynamics calculations are now able to directly inform mechanisms at the crystalline scale. Taken together, these factors give crystal based continuum models the ability to rationalize experimental observations, investigate competition among physical processes, and, when appropriately formulated and calibrated, predict behaviors. We will present an overview of current efforts, with emphasis on recent work investigating phase transformations and twinning in metals.

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“…From a micromechanics perspective, transformation systems in zirconia are non-orthogonal and this results in a non-Schmid effect during the transformation. In order to take into account the normal deformation in each transformation system which is responsible for the volume change, we adapted the formulation in [62] developed for crystalline silicon. A robust explicit algorithm is developed to update the constitutive law.…”

Section: Micromechanics-based Modelmentioning

confidence: 99%

“…From a micromechanics perspective, this is explained by the fact that transformation systems in zirconia are nonorthogonal which introduces a non-Schmid effect in the transformation response. In order to account for this non-Schmid effect, we adapted the formulation in [62] to include the normal deformation during transformation.…”

Section: Phase Transformation Flow Rulementioning

confidence: 99%

Phase transformation and incompatibility at grain boundaries in zirconia-based shape memory ceramics: a micromechanics-based simulation study

et al. 2022

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Zirconia-based shape memory ceramics (SMCs) exhibit anisotropic mechanical response when undergoing elastic deformations as well as during austenite–martensite phase transformation. This behavior results in different types of strain incompatibility at grain boundaries, which we study here using a micromechanical model. A single-crystal model is implemented to provide a full mechanistic three-dimensional description of the anisotropic elastic as well as martensitic transformation stress–strain response, including non-Schmid behavior caused by the significant volume change during martensitic transformation. This model was calibrated to and validated against compression tests of single-crystal zirconia micro-pillars conducted previously, and then used to model bi-crystals. Upon the introduction of a grain boundary, the simulation provides detailed information on the nucleation and evolution of martensite variants and stress distribution at grain boundaries. We identify bi-crystal configurations which result in very large stress concentrations at very low deformations due to elastic incompatibility, as well as others where the elastic incompatibility is relatively low and stress concentrations only occur at large transformation strains. We also show how this approach can be used to explore the misorientation space for quantifying the level of elastic and transformation incompatibility at SMCs grain boundaries. Graphical abstract Micromechanics models provide insights on grain boundary elastic and phase transformation strain incompatibility in shape memory zirconia

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On the inelastic behavior of crystalline silicon at elevated temperatures

Cited by 3 publications

References 40 publications

Crystal level continuum modelling of phase transformations: the α ↔ epsi transformation in iron

Crystal level continuum modelling of phase transformations: the α ↔ epsi transformation in iron

Bringing Together Computational and Experimental Capabilities at the Crystal Scale

Phase transformation and incompatibility at grain boundaries in zirconia-based shape memory ceramics: a micromechanics-based simulation study

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