scholarly journals A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190258 ◽  
Author(s):  
Andrea Panteghini ◽  
Lorenzo Bardella ◽  
Christian F. Niordson
Keyword(s):  
Strain Gradient ◽  
Free Energy Density ◽  
Higher Order ◽  
Strain Gradient Plasticity ◽  
Threshold Values ◽  
Gradient Plasticity ◽  
Proportional Loading ◽  
Size Dependent ◽  
Plastic Potential ◽  
Dislocation Density Tensor

We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004 J. Mech. Phys. Solids 52 , 2545–2568, doi:10.1016/j.jmps.2003.11.002 ) distortion gradient plasticity, adopting Nye's dislocation density tensor as primal HO variable, we expect our results to hold qualitatively for any HO SGP theory, including crystal plasticity.

scholarly journals Strain gradient plasticity under non-proportional loading

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140267 ◽  
Author(s):  
N. A. Fleck ◽  
J. W. Hutchinson ◽  
J. R. Willis
Keyword(s):  
Plastic Flow ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
The Other ◽  
Critical Examination ◽  
Plastic Range ◽  
Gradient Plasticity ◽  
Proportional Loading

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and the increments of strains and their gradients. The specific versions of the theories examined coincide for proportional straining. Implications stemming from the differences in formulation of the two classes of theories are explored for two basic examples having non-proportional loading: (i) a layer deformed into the plastic range by tensile stretch with no constraint on plastic flow at the surfaces followed by further stretch with plastic flow constrained at the surfaces and (ii) a layer deformed into the plastic range by tensile stretch followed by bending. The marked difference in predictions by the two theories suggests that critical experiments will be able to distinguish between them.

scholarly journals On a mixed energetic–dissipative constitutive law for non-proportional loading, with focus on small-scale plasticity

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Lorenzo Bardella
Keyword(s):  
Kinematic Hardening ◽  
Threshold Value ◽  
Constitutive Law ◽  
Small Scale ◽  
Threshold Values ◽  
Gradient Plasticity ◽  
Proportional Loading ◽  
Material Parameters ◽  
Size Dependent

We analyse the mixed energetic–dissipative potential (MP) recently proposed by our group to predict, within higher-order strain gradient plasticity (SGP), reliable size-dependent responses under general loading histories. Such an MP follows former proposals by Chaboche, Ohno and co-workers for nonlinear kinematic hardening in the context of size-independent metal plasticity. The MP is given by M quadratic addends that each transitions, at a different threshold value, into a linear dissipative contribution. Hence, the MP involves 2 M positive material parameters, given by the M threshold values and the M moduli weighing each quadratic recoverable term. We analytically demonstrate that, under proportional loading, the MP limit for M  → ∞ converges to a less-than-quadratic potential with well-defined properties. This result is of crucial importance for identifying the material parameters of any model adopting the MP. Moreover, our analysis provides a formula for the characterization of the energetic and dissipative parts of any possible MP limit, showing that, regarding the capability to describe the effect of diminishing size within SGP, the MP can be selected such that its contribution to the strengthening (i.e. an increase in yield point) is mostly dissipative, whereas its contribution to the increase in strain hardening is mostly recoverable.

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