The indentation size effect of single-crystalline tungsten revisited

In this study, we have investigated the indentation size effect (ISE) of single crystalline tungsten with low defect density. As expected, the hardness shows a pronounced increase with decreasing indentation depth as well as a strong strain rate dependence. For penetration depths greater than about 300 nm, the ISE is well captured by the Nix–Gao model in the context of geometrically necessary dislocations. However, clear deviations from the model are observed in the low depth regime resulting in a bilinear effect. The hardness behavior in the low depth regime can be modeled assuming a non-uniform spacing of the geometrically necessary dislocations. We propose that the bilinear indentation size effect observed reflects the evolution of the geometrically necessary dislocation density. With increasing strain rate, the bilinear effect becomes less pronounced. This observation can be rationalized by the activation of different slip systems

Indentation behavior of single‐crystalline tungsten

Tungsten has great potential for high temperature applications due to its very high melting point. Its brittleness far above room temperature, though, limits its application. Previous investigations have shown that plastic deformation and fracture toughness of polycrystalline tungsten strongly depend on the microstructural characteristics, such as grain size, grain shape, and texture. In this work, we aim at understanding the deformation behavior of tungsten at the microscale and in particular the influence of the strain gradients by combining nanoindentation and finite element modelling. First, in order to compare our experimental results with finite element modelling, different approaches to determine the projected contact area in the computational experiment were evaluated. Then, we quantitatively characterized the indentation size effect in tungsten single-crystals of different crystal orientations, which has frequently been described by the Nix-Gao model. While the model works well for large indentation depths, the application of the classic Nix-Gao model needs to be re-evaluated in the depth regime less than 200nm,which we will show by studying the material length scale h*

Size-dependent geometrically necessary dislocation structures in single-crystalline tungsten

Wedge indentation experiments were conducted to study the depth dependence of geometrically necessary dislocation (GND) structures in single-crystalline tungsten. Single-crystalline tungsten exhibits a pronounced indentation size effect (ISE), which can be rationalized based on GNDs. The dislocation mechanisms, however, are still under debate. Due to the plane strain condition during the wedge indentation, the dislocations in the cross sections underneath indents could be analyzed based on the Nye tensor and the lattice rotations determined using transmission Kikuchi diffraction. The dislocation structures depend on the size of the indent confirming the different hardness regimes and the bilinear ISE reported recently. For shallow indents, the dislocations are rather localized at the tip of the indent, while with increasing depth the dislocation volume expands; subgrains and distinct rays of increased dislocation density form. At larger depths, the indentation-induced deformation fields exhibit characteristics similar to the kink-type shear at a stationary crack tip

Finite element simulation of stretch forming of aluminium-polymer laminate foils used for pharmaceutical packaging

Pharmaceutical high barrier blister packages are manufactured from aluminium-polymer laminate foils (e.g. consisting of PA-Al-PVC layers). By a cold stretch forming process cavities are formed. The aim of this work is to determine a homogenized elastic-plastic description of the laminate by micromechanics. Therefore, a microstructural model is developed where the layers are mapped in a representative volume element. The obtained homogenized material model is applied to simulate the stretch forming to gain more insight into the forming process

Finite element simulation of stretch forming of aluminium-polymer laminate foils used for pharmaceutical packaging

Pharmaceutical high barrier blister packages are manufactured from aluminium-polymer laminate foils (e.g. consisting of PA-Al-PVC layers). By a cold stretch forming process cavities are formed. The aim of this work is to determine a homogenized elastic-plastic description of the laminate by micromechanics. Therefore, a microstructural model is developed where the layers are mapped in a representative volume element. The obtained homogenized material model is applied to simulate the stretch forming to gain more insight into the forming process

The indentation size effect of single-crystalline tungsten revisited

In this study, we have investigated the indentation size effect (ISE) of single crystalline tungsten with low defect density. As expected, the hardness shows a pronounced increase with decreasing indentation depth as well as a strong strain rate dependence. For penetration depths greater than about 300 nm, the ISE is well captured by the Nix–Gao model in the context of geometrically necessary dislocations. However, clear deviations from the model are observed in the low depth regime resulting in a bilinear effect. The hardness behavior in the low depth regime can be modeled assuming a non-uniform spacing of the geometrically necessary dislocations. We propose that the bilinear indentation size effect observed reflects the evolution of the geometrically necessary dislocation density. With increasing strain rate, the bilinear effect becomes less pronounced. This observation can be rationalized by the activation of different slip systems

Dislocation structure analysis in the strain gradient of torsion loading

Complex stress states due to torsion lead to dislocation structures characteristic for the chosen torsion axis. The formation mechanism of these structures and the link to the overall plastic deformation are unclear. Experiments allow the analysis of cross sections only ex situ or are limited in spacial resolution which prohibits the identification of the substructures which form within the volume. Discrete dislocation dynamics simulations give full access to the dislocation structure and their evolution in time. By combining both approaches and comparing similar measures the dislocation structure formation in torsion loading of micro wires is explained. For the ⟨100⟩ torsion axis, slip traces spanning the entire sample in both simulation and experiment are observed. They are caused by collective motion of dislocations on adjacent slip planes. Thus these slip traces are not atomically sharp. Torsion loading around a ⟨111⟩ axis favors plasticity on the primary slip planes perpendicular to the torsion axis and dislocation storage through cross-slip and subsequent collinear junction formation. Resulting hexagonal dislocation networks patches are small angle grain boundaries. Both, experiments and discrete dislocation simulations show that dislocations cross the neutral fiber. This feature is discussed in light of the limits of continuum descriptions of plasticity