Many-Scale Investigations of Deformation Behavior of Polycrystalline Composites: II-Micro-Macro Simultaneous FE and Discrete Dislocation Dynamics Simulation

Abstract

The current work numerically investigates commercial polycrystalline Ag/17vol.%SnO2 composite tensile deformation behavior with available experimental data. Such composites are useful for electric contacts and have a highly textured initial material status after hot extrusion. Experimentally, the initial sharp fiber texture and the number of Σ3-twins were reduced due to tensile loading. The local inhomogeneous distribution of hardness and Young's modulus gradually decreased from nanoindentation tests, approaching global homogeneity. Many-scale simulations, including micro-macro simultaneous finite element (FE) and discrete dislocation dynamics (DDD) simulations, were performed. Deformation mechanisms on the microscale are fundamental since they link those on the macro- and nanoscale. This work emphasizes micromechanical deformation behavior. Such FE calculations applied with crystal plasticity can predict local feature evolutions in detail, such as texture, morphology, and stress flow in individual grains. To avoid the negative influence of boundary conditions (BCs) on the result accuracy, BCs are given on the macrostructure, i.e., the microstructure is free of BCs. The particular type of 3D simulation, axisymmetry, is preferred, in which a 2D real microstructural cutout with 513 Ag grains is applied. From FE results, Σ3-twins strongly rotated to the loading direction (twins disappear), which, possibly, caused other grains to rotate away from the loading direction. The DDD simulation treats the dislocations as discrete lines and can predict the resolved shear stress (RSS) inside one grain with dependence on various features as dislocation density and lattice orientation. The RSS can act as the link between the FE and DDD predictions.

Keywords: crystal plasticity; discrete dislocation dynamics; dislocation mechanisms; local yield stress; many-scale simulation; texture; Σ3-twins effect.

Figure 1

Global true stress–strain flow curves of the PM12-3 MMC [14] and the pure Ag (Table 1) under tension.

Figure 2

The $\mathrm{\Sigma }$3-twins in PM12-3 composite from EBSD measurements: (a–d) after extrusion before tenion; (a) in the longitudinal direction with the arrow presenting the extrusion direction [13]; (b) $\mathrm{\Sigma }$3-twin boundaries in (a); (c) in the transverse direction [13]; (d) $\mathrm{\Sigma }$3-twin boundaries in (c); (e–h) analogous to (a–d), but at the material status after tension.

Figure 3

The nanoindentation measurement (HV0.3) of PM 12-2 MMC in the longitudinal section (100 measured points): (a) averaged values with 50 $\mathsf{\mu }$m distance between two neighboring points and the arrow presenting the extrusion direction; (b) averaged values with 10 $\mathsf{\mu }$m distance between two neighbor points and the arrow presenting the extrusion direction; (c) hardness value evolution according to indentation depth for some selected points in (b); (d) same as (c), but for applied forces.

Figure 4

Applied force and Young’s modulus v.s. penetration depth and the recalculated mean values of Young’s moduli from the nanoindentation test (HV0.3) for PM 12-2 MMC in the longitudinal section: (a–c) and Figure 3a from the same test; (d–f) according to Figure 3b.

Figure 5

A sketch to show the work hardening rates ${\mathrm{\Theta }}_0$ and ${\mathrm{\Theta }}_{\infty }$.

Figure 6

The real microstructure of Figure 2a with 513 Ag grains (upper); after pixel selection (middle); selected-region meshing (lower).

Figure 7

(a) Dimensions of micro, macrostructures, and the transition zone in the two-scale simultaneous FE simulation; (b) the meshing of the whole structure; (c) the meshing in the transition zone; (d) part of the meshing in the transition zone and the real microstructure with 513 Ag grains and about 222 SnO${}_2$ particles.

Figure 8

The experimental global flow curve and the numerical one predicted by the Taylor model for the parameter identification.

Figure 9

Comparison of the experimental [14] and homogenized $\sigma -\epsilon$ curves from FE prediction for PM12-3 Ag/SnO${}_2$ composite.

Figure 10

Micro-macro two-scale simultaneous FE simulation: (a) the von Mises stress distribution of the Ag phase and the deformed edges of the microstructure at 25% global strain; (b) the stress flow behavior according to the global strain: Ag phase mean value and two Ag grains possessing the maximum and the minimum stress at a given strain; (c) positions of the two grains in (b) together with black-colored particles.

Figure 11

Standard inverse pole figures for the AgSnO${}_2$ PM12-3 composite: (a) EBSD measured initial texture after hot extrusion and before tension; (b) measured texture after tension; (c) initial texture for FE simulation (for experiment Figure 7a); (d) FE predicted textures after tension.

Figure 12

(a) Measured grain boundaries of $\mathrm{\Sigma }$3-twins and selected 50 pairs of twins; (b) corresponding grains of the marked 50 pairs of $\mathrm{\Sigma }$3-twins in (a).

Figure 13

The stress flow behavior according to the global strain among the 50 pairs of $\mathrm{\Sigma }$3-twins in Figure 12.

Figure 14

Standard inverse pole figures for the selected 50 pairs of $\mathrm{\Sigma }$3-twins in Figure 12: (a) Measured initial texture after hot extrusion and before tension; (b) FE predicted textures after tension.

Figure 15

The dislocation morphology evolution predicted by a DDD simulation: (a) at the initial status; (b) after yielding.

Figure 16

Eight DDD simulations: (a) the initial eight orientations projected to the loading axis (24 poles according to the symmetry); (b) zoom-in view for (a); (c) RSS-strain curves showing the inhomogeneous CRSS values (without multiplying the Taylor factor) and the variation of local Young’s moduli.

Figure 17

Predicted RSS and $\mathrm{\Delta }$RSS: (a) RSS flow behavior from DDD simulation; (b) the same as (a) multiplied by a Taylor factor to compare with FE results; (c) at 12% strain, $\mathrm{\Delta }$RSS ($\mathrm{\Delta }\tau =\tau -{\tau }_0$) in 513 Ag grains and the Ag phase mean values from FE and DDD simulation (multiplied by a Taylor factor of 2.71); (d) analogous to (c), but at 20% strain.