Modeling of Size-Dependent Strengthening in Particle-Reinforced Aluminum Composites with Strain Gradient Plasticity

2011 ◽  
Vol 35 (7) ◽  
pp. 745-751 ◽  
Author(s):  
Yeong-Sung Suh ◽  
Moon-Shik Park ◽  
Seung Song
Keyword(s):  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Aluminum Composites ◽  
Size Dependent

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.

Length Scale in Solder Joints Materials

2006 ◽  
Author(s):  
Juan Gomez ◽  
Cemal Basaran
Keyword(s):  
Strain Gradient ◽  
Constitutive Models ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Additional Material ◽  
Size Dependent ◽  
Dependent Behavior ◽  
Material Length Scale ◽  
Material Length

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on Pb/Sn solder alloys the material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in the literature for different materials like copper, nickel and aluminum.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

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