scholarly journals Scaling Laws in the Ductile Fracture of Metallic Crystals

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
M. I. Baskes ◽  
M. Ortiz
Keyword(s):  
Fracture Energy ◽  
Ductile Fracture ◽  
Cell Size ◽  
Power Law ◽  
Strain Gradient ◽  
Scaling Laws ◽  
Optimal Scaling ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
The Continuum

We explore whether the continuum scaling behavior of the fracture energy of metals extends down to the atomistic level. We use an embedded atom method (EAM) model of Ni, thus bypassing the need to model strain-gradient plasticity at the continuum level. The calculations are performed with a number of different 3D periodic size cells using standard molecular dynamics (MD) techniques. A void nucleus of a single vacancy is placed in each cell and the cell is then expanded through repeated NVT MD increments. For each displacement, we then determine which cell size has the lowest energy. The optimal cell size and energy bear a power-law relation to the opening displacement that is consistent with continuum estimates based on strain-gradient plasticity (Fokoua et al., 2014, “Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation,” Arch. Ration. Mech. Anal. (in press); Fokoua et al., 2014, “Optimal Scaling Laws for Ductile Fracture Derived From Strain-Gradient Microplasticity,” J. Mech. Phys. Solids, 62, pp. 295–311). The persistence of power-law scaling of the fracture energy down to the atomistic level is remarkable.

scholarly journals A strain gradient plasticity model of porous single crystal ductile fracture

2021 ◽  
pp. 104606
Author(s):  
Jean-Michel Scherer ◽  
Jacques Besson ◽  
Samuel Forest ◽  
Jérémy Hure ◽  
Benoît Tanguy
Keyword(s):  
Single Crystal ◽  
Ductile Fracture ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Plasticity Model ◽  
Gradient Plasticity

scholarly journals A Review on Strain Gradient Plasticity Approaches in Simulation of Manufacturing Processes

2020 ◽  
Vol 4 (3) ◽  
pp. 87
Author(s):  
Raffaele Russo ◽  
Franck Andrés Girot Mata ◽  
Samuel Forest ◽  
Dimitri Jacquin
Keyword(s):  
Strain Gradient ◽  
Classical Model ◽  
Strain Gradient Plasticity ◽  
Manufacturing Processes ◽  
Gradient Plasticity ◽  
Manufacturing Operations ◽  
High Level ◽  
Different Levels ◽  
Good Agreement ◽  
The Continuum

Predicting the performances of a manufactured part is extremely important, especially for industries in which there is almost no room for uncertainties, such as aeronautical or automotive. Simulations performed by means of numerical methods such as Finite Element Methods represent a powerful instrument in achieving high level of predictability. However, some particular combinations of manufactured materials and manufacturing processes might lead to unfavorable conditions in which the classical mathematical models used to predict the behavior of the continuum are not anymore able to deliver predictions that are in good agreement with experimental evidence. Since the first evidences of the shortcomings of the classical model were highlighted, many non-classical continuum mechanics theories have been developed, and most of them introduce dependencies at different levels with the Plastic Strain Gradient. This manuscript aims at gathering the milestone contributions among the Strain Gradient Plasticity Theories developed so far, with the object of exploring the way they interface with the requirements posed by the challenges in simulating manufacturing operations. Finally, the most relevant examples of the applications of Strain Gradient Plasticity Theories for manufacturing simulations have been reported from literature.

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.

A Study of Microindentation Hardness Tests by Mechanism-based Strain Gradient Plasticity

2000 ◽  
Vol 15 (8) ◽  
pp. 1786-1796 ◽  
Author(s):  
Y. Huang ◽  
Z. Xue ◽  
H. Gao ◽  
W. D. Nix ◽  
Z. C. Xia
Keyword(s):  
Strain Gradient ◽  
Size Dependence ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Hierarchical Framework ◽  
Microindentation Hardness ◽  
Dislocation Hardening ◽  
Hardness Tests ◽  
Micro Indentation

We recently proposed a theory of mechanism-based strain gradient (MSG) plasticity to account for the size dependence of plastic deformation at micron- and submicronlength scales. The MSG plasticity theory connects micron-scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. Here we show that the theory of MSG plasticity, when used to study micro-indentation, indeed reproduces the linear dependence observed in experiments, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model. In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformation in the hierarchical framework.

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