Equivalent plastic strain gradient crystal plasticity - Enhanced power law subroutine

2013 ◽  
Vol 36 (2) ◽  
pp. 134-148 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Thomas Böhlke
Keyword(s):  
Plastic Strain ◽  
Power Law ◽  
Crystal Plasticity ◽  
Strain Gradient ◽  
Equivalent Plastic Strain ◽  
Plastic Strain Gradient

scholarly journals Equivalent plastic strain gradient enhancement of single crystal plasticity: theory and numerics

2012 ◽  
Vol 468 (2145) ◽  
pp. 2682-2703 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Thomas Böhlke
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Equivalent Plastic Strain ◽  
Plasticity Theory ◽  
Strain Gradient Theory ◽  
Local Algorithm ◽  
Alternative Formulation ◽  
Element Discretization ◽  
Gradient Enhancement ◽  
Plastic Strain Gradient

We propose a visco-plastic strain gradient plasticity theory for single crystals. The gradient enhancement is based on an equivalent plastic strain measure. Two physically equivalent variational settings for the problem are discussed: a direct formulation and an alternative version with an additional micromorphic-like field variable, which is coupled to the equivalent plastic strain by a Lagrange multiplier. The alternative formulation implies a significant reduction of nodal degrees of freedom. The local algorithm and element stiffness matrices of the finite-element discretization are discussed. Numerical examples illustrate the advantages of the alternative formulation in three-dimensional simulations of oligo-crystals. By means of the suggested formulation, complex boundary value problems of the proposed plastic strain gradient theory can be solved numerically very efficiently.

Gradient of Soil Constitutive Model

2010 ◽  
Vol 168-170 ◽  
pp. 1126-1129
Author(s):  
Wen Xu Ma ◽  
Ying Guang Fang
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Soil Analysis ◽  
Natural Material ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Gradient Effect ◽  
Non Local ◽  
Associated Flow Rule ◽  
Plastic Strain Gradient

For the soil is a very complex natural material, significant strain gradient effect exist in soil analysis. Based on the "gradient" phenomenon, we add the plastic strain gradient hardening item into the traditional Cambridge yield surface. By using the consistency conditions and associated flow rule, we get the explicit expression of plastic strain gradient stiffness matrix. And the finite element method of plastic strain gradient is also shown in this article. Plastic strain gradient is actually a phenomenological non-local model containing microstructure information of the material. It may overcome the difficulties in simulating the gradient phenomenon by traditional mechanical model.

Microscopy and microindentation mechanics of single crystal Fe−3 wt. % Si: Part II. TEM of the indentation plastic zone

1993 ◽  
Vol 8 (6) ◽  
pp. 1300-1310 ◽  
Author(s):  
W. Zielinski ◽  
H. Huang ◽  
W.W. Gerberich
Keyword(s):  
Plastic Strain ◽  
Plastic Zone ◽  
Single Crystal ◽  
Strain Gradient ◽  
Continuum Models ◽  
Large Loop ◽  
Direct Observations ◽  
Small Loop ◽  
Secondary Reactions ◽  
Plastic Strain Gradient

Direct observations of dislocation arrangements about a range of microindentations into the [100] face of an Fe−3 wt. % Si single crystal have been accomplished. Dislocations of both large loop character initiated from the indenter and small loop character initiated as secondary reactions are found. Analysis of these allows the various contributions to the plastic strain gradient around the indentation to be assessed, with the experimental observations being reasonably consistent with continuum models.

scholarly journals The combined effect of size, inertia and porosity on the indentation response of ductile materials

2020 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
Tiago dos Santos ◽  
Ankit Srivastava
Keyword(s):  
Plastic Strain ◽  
Size Effect ◽  
Porous Materials ◽  
Strain Gradient ◽  
Cavity Expansion ◽  
Material Hardness ◽  
Parametric Analyses ◽  
Expansion Model ◽  
Indentation Response ◽  
Plastic Strain Gradient

Herein, we present a self-similar cavity expansion model that follows from the work of Cohen and Durban (2013b) to analyze the dynamic indentation response of elasto-plastic porous materials while accounting for the plastic strain gradient induced size effect. The incorporation of the plastic strain gradient induced size effect in the dynamic cavity expansion model for elasto-plastic porous materials is the key novelty of our model. The predictions of the cavity expansion model for the material hardness, for different indentation depths and speeds, are compared against the available experimental results for OFHC copper, for strain rates varying from 10−4 s−1 to 108 s−1. We note that despite several simplifying assumptions, the predictions of our cavity expansion model show a reasonable agreement with the experimentally measured material hardness over a wide range of indentation depths and speeds. In addition, we have also carried out parametric analyses to elucidate the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process. In particular, our parametric analyses show that there exists a critical value of the indentation speed beyond which the contribution of inertial effect becomes extremely important and the material hardness increases rapidly. While the influence of the initial porosity on the material hardness is found to increase with increasing indentation speed and decrease with increasing size effect.

Material Intrinsic Length in Plastic Strain Gradient Theory and Microbending Process of Metal Foils

2011 ◽  
Vol 403-408 ◽  
pp. 685-690
Author(s):  
He Zong Li ◽  
Xiang Huai Dong ◽  
Su Xia Huang ◽  
Alexander Diehl ◽  
Hinnerk Hagenah
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Size Effects ◽  
Bending Moment ◽  
Strain Gradient Theory ◽  
Foil Thickness ◽  
Gradient Theory ◽  
Metal Foils ◽  
Intrinsic Length ◽  
Plastic Strain Gradient

In microbending experiments of metal foils an increase of non-dimensional bending moment with decreasing foil thickness has been observed, which indicates the obvious presence of size effects. It is attributed to plastic strain gradient. So a constitutive model taking into account plastic strain gradient together with conventional plastic strain hardening is proposed to analyze the non-dimensional bending moment in microbending process. It is confirmed that the predictions by using the proposed hardening model agree well with the experimental data, while those determined by using conventional elastoplastic model cannot capture such size effects. A semi-empirical expression is reasonable to determine the material intrinsic length as a function of shear modulus, initial yield strength, length of Burger’s vector, grain size, and macro geometrical characteristic scale of the specimen.

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