Discrete Dislocation Dynamics Modeling of Nanotwinned Materials: Orientation Effects in a Multilayer Twinned Structure of Copper

TL;DR

This work develops a three-dimensional discrete dislocation dynamics framework that incorporates dislocation–twin boundary interactions in a multilayer nanotwinned copper structure with lamella thickness $\lambda=160~\mathrm{nm}$. By mapping slip systems into hard/soft modes and calibrating a mobility law with MD data, the study reveals pronounced orientation-dependent plasticity driven by TBs, including confined slip, twinning, and TB-assisted transmission. An anisotropic Schmid-law-like approach using mode-specific CRSS values quantifies the yield-stress dependence on loading direction, predicting a peak near $\theta \approx 79^{\circ}$ and highlighting soft-mode dominance over a broad orientation range. These insights advance understanding of TB-induced anisotropy in nanotwinned metals and point to TB-defect effects and size considerations as important avenues for future work, with implications for designing high-strength, ductile nanostructured copper.

Abstract

The impact of twin boundaries (TBs) on the microstructure evolution and plastic deformation mechanisms of face-centered cubic (FCC) metals has been extensively studied since the discovery that nanotwinned materials exhibit a favorable combination of high strength and ductility. In this work, a dislocation-twin boundary interaction model for copper is incorporated into a three-dimensional discrete dislocation dynamics (DDD) framework. This approach is applied to systematically investigate the orientation effects on the deformation of nanotwinned copper, utilizing a multilayer twinned structure (MTS) with a twin thickness of 160 nm. The simulation results show that the stress-strain response of MTSs under uniaxial loading depends significant on the orientation of the loading axis. Dislocations inclined to TBs are confined to slip in single- or multi-layer twin lamellae; when the loading axis is oriented perpendicular or parallel to TBs, such whereas when loading axis inclined to TBs, the dislocations with glide plane parallel to TBs are easily activated (mainly twinning dislocations) and the TBs do not hinder the dislocations and behave in soft modes. If the hard mode dominates the deformation mechanism, microstructures with single-layer confined slip lead to significant hardening behavior, while microstructures with multilayer confined slip maintain stable plastic flow and do not lead to hardening. Finally, through the introduction of critical resolved shear stresses (CRSSs) specific to various deformation modes and the adaptation of Schmid's law, we have effectively projected the additional anisotropic characteristics induced by TBs in MTSs.

Figures (10)

• Figure 1: Computational model and polar plots of active slip systems. (a) Geometric model and loading schematics where the Thompson tetrahedra indicate the crystal orientation; the superscripts M and T indicate the matrix and twin, respectively. The polar angle $\theta$ and azimuthal angle $\omega$ define the loading direction $\bm{\xi}$. (b-d) Polar plots of the active slip systems: (b) slip system index (see Table \ref{['ch5:tab:modes']}), (c) Schmid factor, and (d) activated slip mode. The green circular symbols in (d) indicate the investigated loading directions.
• Figure 2: (a) stress, (b) total dislocation density, (c) twinning strain and (d) TD density versus loading strain for various loading orientations. The color scheme is the same as in Fig. \ref{['ch5:OE-computation-model']}(d). The curves of $\theta=0^{\circ}$ and $90^{\circ}$ in (c) overlap, in both cases the twinning strains are zero.
• Figure 3: Dependence on loading axis orientation of (a) yield stress $\sigma_{\rm y}$, (b) CRSS $\tau_{\rm c}$ and (c) ratio $\varepsilon_{\rm t}/\varepsilon_{\rm p}$ between twinning strain and total plastic strain; all quantities are determined at $\varepsilon_{\rm p}=0.2\%$; left: polar plots, (right) dependency on pole angle. The embedded polar plots and error bars indicate sample standard deviations (STDEV).
• Figure 4: Strain distribution and dislocation microstructure at $\varepsilon=0.53\%$, $\bm{\xi} = \left[111\right]$: (a) slip band nephograms ($\varepsilon_{\rm p}^{\rm l}/\varepsilon_{\rm p}$) and (b) dislocation microstructures; (a1) and (b1) present overall views of the multilayer twin structure, (a2) and (b2) present section views along the TB marked by the red dashed line in the overall view where (b2) represents a layer of thickness 100nm around the TB; the bidirectional arrow in (a1) indicates the tension axis (TA), the numbered arrows in (b1) point to typical dislocation interactions, a legend of the numbers is given in Table \ref{['ch5:tab:dislocation-interactions']}.
• Figure 5: Strain distribution and dislocation microstructures at $\varepsilon=1\%$, $\theta=45^{\circ}$: (a) $\omega=95^{\circ}$, (b) $\omega=65^{\circ}$; the numbered arrows refer to typical dislocation intereactions, a legend of the numbers is given in Table 2; the insets show slip band nephograms illustrating the strain distribution.