Nanoindentation of Micrograins in Polycrystals under Multiaxial Stress: Control of Abrupt & Stochastic Plastic Events
Deforming objects in the world of the small has proven a much more complex task than just bending a common-sized object like a spoon. Over the last decade, it has become clear that the application of stress on micron-sized objects, such as micropillars, leads to abrupt and stochastic plastic strain jumps that do not satisfy Weibull statistics (as expected for uncorrelated defect yielding) but instead seem to follow highly wide, power-law distributions, pointing towards cooperative dislocation plasticity. Are power-law distributed plastic events the rule or the exception in crystals? If the rule, can we design protocols to control and suppress them in order to achieve deterministic and smooth microforming processes? We propose to combine experiments and theory to unravel the mysteries of abrupt microplastic deformation in a natural dislocation environment: micron-sized grains (\micrograins") of polycrystals. We propose a novel experimental design that utilizes nanoindentation and 4-point bending techniques on the substrate of polycrystalline thin films of two typical FCC metals (Al and Cu), and make concrete theoretical conjectures, based on intuition built from previous theoretical and experimental efforts in micropillar compression and nanoindentation. Based on a wide set of observations over the last decade, we put forward two distinct hypotheses that we propose to investigate in both theory and experiments: Our first conjecture is that crystal plasticity in the central region of micron-sized grains has micropillar-like stochastic features: power-law plastic strain jumps at stresses above the macroscale yield strength, displaying strong size and rate effects. We will demonstrate this similarity in spherical nanoindentation experiments in the central-region of multi-orientation grains of Al and Cu thin films. Al and Cu are selected for their disparity in stacking fault energy and consequently, their different propensity for cross-slip relaxation; however, our protocol may be applied to any crystalline material of technological interest. We will test our hypothesis by performing two-dimensional extended discrete dislocation plasticity (2.5D-DDP) simulations, inspired by comparable successful studies of micropillar plasticity, and extended to model nanoindentation with two slip systems and on a surface of a bicrystal with microhard grain-boundaries (GB), ie. not allowing dislocation absorption (116). Our model will include effective three dimensional dislocation mechanisms such as dislocation multiplication and double-cross-slip assisted glide. Second, we hypothesize that the application of uniform in-plane stress on our thin films below the yield point can smoothen the micrograin plastic response during nanoindentation. On a technological level, we propose that indentation-induced localization (sink-in) may be diminished by the application of concurrent in-plane stress that activates slow, viscoplastic relaxations near GBs. We aim to demonstrate our hypothesis through a 4-point bending apparatus that introduces a homogeneous in-plane stress state before indentation. We will perform simulations of a coarse-grained mesoscale theory of plasticity in a system with microhard GBs, benchmarked through 2.5D-DDP simulations, which will capture the effects of slow viscoplastic relaxations. Our nanoindentation abrupt event statistics studies, either in the micrograin interior or near GBs, will be correlated to direct observations of induced surface dislocation microstructures. For we will use TEM-based methods (PACOM/TKD) in combination with EBSD. Indents placed in the center of grains will be analyzed based on the orientation of the grain, while those near to GBs will be analyzed based on the orientation of each grain, the distance from the GB and the 5 degrees of freedom of the GB.