Gradient plasticity used for modeling extrinsic and intrinsic size effects in the torsion of Au microwires

2016 ◽  
Vol 25 (1-2) ◽  
pp. 53-56
Author(s):  
Xiaokun Wei ◽  
Avraam Konstantinidis ◽  
Chengzhi Qi ◽  
Elias Aifantis
Keyword(s):  
Grain Size ◽  
Sample Size ◽  
Plasticity Theory ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Internal Length ◽  
Size Dependent ◽  
Internal Length Scale ◽  
Model Size ◽  
Phenomenological Coefficients

AbstractThe gradient plasticity theory proposed by Aifantis and coworkers has been successfully used to model size effect phenomena at the microscale and nanoscale, by introducing into the formulation an internal length scale associated with the phenomenological coefficients of the gradient plasticity model. In this paper, Aifantis’ gradient plasticity theory is applied to model the sample size-dependent torsion of thin wires, with a strain-dependent internal length scale as well as grain size dependence based on the Hall-Petch relationship. This study reveals that internal length scale is related with sample size and grain size, with such a connection determined by the ductility of the material.

A micromechanics-based constitutive model for nanocrystalline shape memory alloys incorporating grain size effects

2021 ◽  
pp. 1045389X2110282
Author(s):  
Xiang Zhu ◽  
Guansuo Dui ◽  
Yicong Zheng
Keyword(s):  
Grain Size ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Size Effects ◽  
Boundary Phase ◽  
Length Scale ◽  
Internal Length ◽  
Length Scales ◽  
Size Dependent ◽  
Grain Size Effects

A micromechanics-based model is developed to capture the grain-size dependent superelasticity of nanocrystalline shape memory alloys (SMAs). Grain-size effects are incorporated in the proposed model through definition of dissipative length scale and energetic length scale parameters. In this paper, nanocrystalline SMAs are considered as two-phase composites consisting of the grain-core phase and the grain-boundary phase. Based on the Gibbs free energy including the spatial gradient of the martensite volume fraction, a new transformation function determining the evolution law for transformation strain is derived. Using micromechanical averaging techniques, the grain-size-dependent superelastic behavior of nanocrystalline SMAs can be described. The internal length scales are calibrated using experimental results from published literature. In addition, model validation is performed by comparing the model predictions with the corresponding experimental data on nanostructured NiTi polycrystalline SMA. Finally, effects of the internal length scales on the critical stresses for forward and reverse transformations, the hysteresis loop area (transformation dissipation energy), and the strain hardening are investigated.

Stress–elastic strain relation for a two-phase isotropic strain gradient plastic composite

2009 ◽  
Vol 20 (4) ◽  
pp. 319-342
Author(s):  
VIET HA HOANG
Keyword(s):  
Strain Gradient ◽  
Elastic Strain ◽  
Constitutive Law ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Two Phase ◽  
Internal Length ◽  
Plastic Composite ◽  
Strain Relationship ◽  
Internal Length Scale

The stress–elastic strain relationship is studied for a composite under a plastic deformation. The constitutive law of each component is described by a deformation theory of strain gradient plasticity which introduces an internal length scale. The conventional deformation plastic theory is obtained when the internal length scale tends to 0. The Hashin–Shtrikman upper bound for a two-phase composite governed by a power law is derived. It is predicted, by differentiating the bounds, that in most cases, the stress and the elastic strain follow a non-linear relation immediately after the elastic range. However, for some particular values of the ratio of the internal length scale and the micro-scale of the composite, this relation is linear. The prediction is illustrated by various numerical examples.

A regularized continuum model for fault zones with rate and state friction

2021 ◽  
Author(s):  
Mohsen Goudarzi ◽  
René de Borst ◽  
Taras Gerya ◽  
Meng Li ◽  
van Dinther Ylona
Keyword(s):  
Numerical Model ◽  
Fault Zone ◽  
Induced Seismicity ◽  
Subduction Zones ◽  
Bulk Material ◽  
Fault Zones ◽  
Length Scale ◽  
Internal Length ◽  
Internal Length Scale ◽  
Earthquake Sequences

<p>Accurate representation of fault zones is important in many applications in Earth sciences, including natural and induced seismicity. The framework developed here can efficiently model fault zone localization, evolution, and spontaneous fully dynamic earthquake sequences in a continuum plasticity framework. The geometrical features of the faults are incorporated into a regularized continuum framework, while the response of the fault zone is governed by a rate and state-dependent friction. Although a continuum plasticity model is advantageous to discrete approaches in representing evolving, unknown, or arbitrarily positioned faults, it is known that either non-associated plasticity or strain-softening can lead to mesh sensitivity of the numerical results in absence of an internal length scale. A common way to regularize the numerical model and introduce an internal length scale is by the adoption of a Kelvin-type visco-plasticity element. The visco-plastic rheological behavior for the bulk material is implemented along with a return-mapping algorithm for accurate stress and strain evolution. High slip rates (in the order of 1 m/s) are captured through numerical examples of a predefined strike-slip fault zone, where a detailed comparison with a reference discrete fault model is presented. Additionally, the regularization effect of the Kelvin viscosity parameter is studied on the fault slip velocity for a growing fault zone due to an initial material imperfection.  The model is consistently linearized leading to quadratic convergence of the Newton solver. Although the proposed framework is a step towards the modeling of earthquake sequences for induced seismicity applications, the numerical model is general and can be applied to all tectonic settings including subduction zones.</p><div> <div> <div> </div> <div> <div> <div> </div> <div> <p> </p> <p> </p> </div> </div> </div> </div> </div>

Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide

2000 ◽  
Vol 653 ◽  
Author(s):  
J. Gil Sevillano
Keyword(s):  
Size Effects ◽  
Mixed Effects ◽  
Length Scale ◽  
Internal Length ◽  
Strain Gradients ◽  
Dislocation Glide ◽  
Spatial Gradients ◽  
Internal Length Scale ◽  
Plastic Process

AbstractA classification of size effects (SE) in plasticity is attempted. ”Intrinsic” SE are perceived when any internal length scale directly influencing some process or property interferes with the size of the material region where the process is going on or when two internal length scales directly affecting the same process or property interfere. ”Extrinsic” SE arise from the external imposition of spatial gradients in the plastic process or by the building up of internal gradients by the (externally induced) process itself. In dislocation-mediated plasticity plastic strain gradients are resolved by the storage of geometrically necessary dislocations (GND) leading to prominent size effects. Of course, mixed effects with intrinsic and extrinsic contributions can be found as well as superposed effects involving more than two characteristic lengths (i.e., size effects on size effects).The inclusion of both types of SE in continuum or crystallographic theories is commented.

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

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