Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

Abstract

The Bauschinger and size effects in the thinfilm plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the workconjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defectenergy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

Modeling dislocation absorption by surfaces within the framework of strain gradient crystal plasticity

“…The elastic constants and the magnitude of the Burgers vectors of aluminum are adopted here, i.e., l = 26.3 Gpa, m = 0.33 and b = 0.25 nm. According to many previous works (Bittencourt et al, 2003;Fredriksson and Gudmundson, 2005;Aifantis et al, 2006;Liu et al, 2011;Aghababaei and Joshi, 2012;Mayeur and McDowell, 2013), the bulk material length scale R varies from tens of nanometers to several microns, thus we take an intermediate value here, i.e., R = 0.5 lm. By fitting the numerical simulation results to the experiments data, Hurtado and Ortiz (2012) obtained a value of 90.0 N/m for C 1 of nickel greatly in excess of the corresponding known surface free energy density, which is attributed to the considerable surface damage of the samples in experiments during the manufacturing process.…”

Effect of Heterogeneous Ti Layers on Mechanical Properties of Cu/Ti Laminated Sheets Prepared by Accumulative Roll Bonding

“…A bigger hysteresis loop in the course of unloading–reloading reveals a more potent Bauschinger effect. As shown in Figure 11, the Bauschinger effect can be described by the inverse plastic strain (ε rp ) normalized by the yield strain (ε y ), [ 41,42 ] which increases as the plastic strain increases (Figure 11). The HDI stress is computed aswhere σ u denotes the yield stress in the course of loading (Figure 11c), and σ r is the yield stress in the course of unloading (Figure 11d).…”

“…A bigger hysteresis loop in the course of unloading-reloading reveals a more potent Bauschinger effect. As shown in Figure 11, the Bauschinger effect can be described by the inverse plastic strain (ε rp ) normalized by the yield strain (ε y ), [41,42] which increases as the plastic strain increases (Figure 11). The HDI stress is computed as…”