Size-dependent crystal plasticity: From micro-pillar compression to bending

TLDR: In this paper, size-dependent crystal plasticity of metal single crystals is investigated using finite element method based on a phenomenological crystal-plasticity model, incorporating both first-order and second-order effects.

About: This article is published in Mechanics of Materials.The article was published on 2016-09-01 and is currently open access. It has received 13 citations till now. The article focuses on the topics: Plasticity & Bending.

Figures

Table 1 Model parameters of single crystal copper

Fig. 1 Schematic of FE models for micro-pillar compression (a) and cantilever beam (b)

Fig. 6 Effect of GNDs on load-displacement curves of cantilever beam with dimensions of 5.0 μm × 5.0 μm × 20.0 μm

Fig. 4 First-order effect shown by compressive stress-strain curves of single crystal copper with loading direction along [111] ( D is the side length of the square cross-section)

Fig. 1 Schematic of FE models for micro-pillar compression (a) and cantilever beam (b)

Fig. 9 Sample size effect of Cu single crystal obtained with cantilever beam: experimental data and simulation results. The table lists the effective geometrical parameters of cantilever beams used in the experiments of Motz et al. (Motz et al., 2005).

Frequently asked questions

Q1. What are the contributions in "Size-dependent crystal plasticity: from micro-pillar compression to bending" ?

A modelling study demonstrates the subtleness and importance of accounting for first-order and second-order effects in modelling crystalline materials in small length-scales. 

Q2. What is the effect of /L H on the effective flow stress?

Without loss of the generality, two types of cantilever beams with different cross-sectional geometry are employed to investigate the influence of /L H on the effective flow stress for the specific cross-sectional beams. 

Q3. What is the underlying mechanism driving the size effect in polycrystalline metals?

(Geers et al., 2006) categorized the size effect in polycrystalline metals into (i) intrinsically first-order effect, which was considered to cover all effects resulting from the nature of microstructure and (ii) second-order effect † , which was considered to result from gradients of deformation (strain gradient, slip gradient, etc.). 

Q4. What is the widely adopted relationship for the simulation results?

the widely adopted relationship,0n f Kd , is used to fit the simulation results obtained for both variable and constantvalues of /L H , respectively. 

Q5. What is the annihilation coefficient of dislocations?

In other words, the parameter 2k , representing the annihilation of dislocation, should be size-dependent to reflect dislocations loss from the free surface. 

Q6. What is the drawback of the power-law relationship approach?

To overcome the drawback of the power-law relationship approach, crystal-plasticity (CP) modelling was employed to help extract the nature of size effect in single-crystal metal (Gong and Wilkinson, 2011; Raabe et al., 2007). 

Q7. What is the initial slip resistance of a single crystal sample?

Equation (13) implies that for a fixed magnitude of dislocation density the generation and multiplication of dislocations requirehigher stress level for a smaller sized single crystal sample. 

Q8. What is the radius of the indenter?

The indenter’s radius was 2.0μm for all simulations (our simulations show that the perceived indenter/reaction load is independent of the indenter radius). 

Q9. What is the effect of the first-order effect on the sample size?

These experimental data indicates that the sample size effect in bending, due to the coexistence of first-order and second-order effects (i.e. externally imposed stress/strain gradients), is more pronounced than that in uniaxial compression where first-order effect dominate. 

Q10. What is the maximum load in bending of the cantilever beam?

To facilitate a quantitative estimation of sample size effect in bending, the effective flow stress ofcantilever beam ,B f was calculated following the definition as in the experiment (Gong andWilkinson, 2011; Motz et al., 2005),max, 2 4 B f F LWH , (25)where maxF represents the maximum load in bending of the cantilever beam.