Abstract
Experiments have shown that a gradient design, in which grain size spans over four orders of magnitude, can make strong nanomaterials ductile. The enhanced ductility is attributed to the considerable strain hardening capability obtained in the gradient metals. A non-uniform deformation on the lateral sample surface is also observed. This might inject geometrically necessary dislocations (GNDs) into the sample. However, no direct evidence has been provided. Therefore the issues remain: why can the gradient structure generate high strain hardening, and how does it reconcile the strength-ductility synergy of gradient nanostructures? Here for the first time we quantitatively investigate the strain hardening of a gradient interstitial-free steel by developing a dislocation density-based continuum plasticity model, in which the interaction of the component layers in the gradient structure is represented by incorporating GNDs and back stress. It is demonstrated that both the surface non-uniform deformation and the strain-hardening rate up-turn can be quantitatively well predicted. The results also show that the strain hardening rate of the gradient sample can reach as high as that of the coarse-grained counterpart. A strength-ductility map is then plotted, which clearly show that the gradient samples perform much more superior to their homogeneous counterparts in strength-ductility synergy. The predicted map has been verified by a series of experimental data. A detailed analysis on GNDs distribution and back stress evolution at the end further substantiates our view that the good strain hardening capability results from the generation of abundant GNDs by the surface non-uniform deformation into the nano-grained layers of the gradient sample.
Highlights
Refining grains down to nanoscale renders metals ultra-high strength but low ductility (Beyerlein et al, 2015; Farrokh and Khan, 2009; Gleiter, 1989; Khan et al, 2000; Khan and Liu, 2016; Li et al, 2014; Meyers et al, 2006; Ovid'ko, 2002; RodríguezGalan et al, 2015; Rupert, 2016; Weng, 2011; Zhu and Li, 2010)
Since the focus of the present study is on uniaxial tensioning of gradient structure in which the sample is subjected to uniaxial uniform strain εaz through its thickness in experiments, the overall stress-strain response sGz in the gradient sample can be approximately obtained through volume averaging over all the component layers as: sGz where sGziND denotes the z-component stress of layer i in the gradient sample considering both geometrically necessary dislocations (GNDs) and back stress; hi and ht are the thickness of layer i and that the half thickness of the entire gradient sample, respectively; and n* is the layer number of the whole sample adopted in the finite element model
Since the MC model is proposed for homogeneous interstitial free (IF) steels with grain size ranging from submicrometer to tens of micrometers, while the NC model is for those with grain size varying from tens of nanometers to submicrometer, and considering that (i) the existing modified versions of KME models for coarse- and fine-grained metals can be applied down to 1 mm (Delince et al, 2007) and those for nano- and ultrafine-grained metals can be applied up to 583 nm (Liu and Mishnaevsky Jr., 2014); and (ii) the enhanced dynamic recovery usually occurs in submicrometers, e.g., 700 nm for copper (Duhamel et al, 2010), the boundary should lie in the range of submicrometers
Summary
Refining grains down to nanoscale renders metals ultra-high strength but low ductility (Beyerlein et al, 2015; Farrokh and Khan, 2009; Gleiter, 1989; Khan et al, 2000; Khan and Liu, 2016; Li et al, 2014; Meyers et al, 2006; Ovid'ko, 2002; RodríguezGalan et al, 2015; Rupert, 2016; Weng, 2011; Zhu and Li, 2010). The up-turn, found in copper (Yang et al, 2015), is believed to be responsible for the high strength and ductility in the gradient IF steel sample, i.e., 2.5 times higher yield strength at a loss of only 3.3% uniform elongation as compared with the CG counterpart. They observed a non-uniform deformation on the lateral surface of the gradient sample with a height profile up to 30 mm that is absent in ordinary homogeneous structures (Fig. 2).
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