Length Scale Effects in Deformation of Polycrystalline Nickel
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The demand for compact, efficient and high performance electronic devices and sensor systems has become one of the primary driving force for rapid advancement in miniaturization of current technology. However, the attempt to push the limits of component length scales into the nano regime is being challenged by possibly unconventional laws of physics. One of the key design parameters for good performance of any system is its structural stability, defined by the strength of a material. The strength of a material is defined as its resistance to plastic (or permanent) deformation. In conventional metals plastic deformation is carried by the migration of lattice defects such as vacancies and dislocations. The barriers to the motion of these defects provide strength to metals, leading to an inverse power law scaling with inter barrier spacing, l = Bl q where represents the nominal strength, B is a measure for strengthening capability of barriers and q represents the order of strengthening. The well known Hall Petch relation (q=0.5) expresses this effect for grain boundary strengthening, where grain boundaries (GBs) obstruct motion of dislocations during plastic deformation. Extensive research over past few decades has shown that grain size strengthening may be limited by GB mediated deformation processes in nanocrsytalline (nc) metals with grain sizes of ≤ 20 nm. The strength of nanocrsytalline metals saturates, or in some cases decreases, with a reduction in grain size. Molecular dynamic simulations have provided some indication of atomic scale activities that dominate deformation in nc metals. Although it is difficult to experimentally monitor the atomistic processes, in situ mechanical tests in synchrotron facilities have captured some mesoscopic features of deformation in nanocrsytalline metals. For instance, experiments have shown that the typically extended elastic plastic transition during deformation of nanocrsytalline metals could be classified into two regimes. For initial stages of deformation, in the microplastic regime, the width of various diffracting peaks decreases suggesting the dominance of processes leading to structural relaxation. However, at later stages of deformation, in a manner similar to conventional metals, the diffraction peak widths increased signifying the increasing importance of deformation processes that involve an accumulation of defects. It is well known that thermal annealing also causes relaxation of materials and during high temperature deformation continuous relaxation of stress concentrations could retard premature failure of metals. As the ductility in nanocrsytalline metals is limited to 3-5%, with very limited strain hardening, the processes of structural relaxation are very important. Thus, there is a fundamental need to understand the nature of structural relaxation during microplastic deformation in nanocrystals. It is well known that character of grain boundaries plays an important role in material properties. As the grain boundary area per unit volume varies inversely with grain size, nanocrsytalline metals contain a significant amount of grain boundary area. Moreover, due to small grain sizes, conventional Frank Read sources cannot operate for nucleating dislocations. Dislocations in nc metals are nucleated from GBs, traverse grains and gets absorbed in other GBs. The small volume of grains further restricts dislocation interactions. Thus, dislocation nucleation, propagation and absorption become possible rate controlling mechanisms in nc metals. Molecular dynamic simulations of nanocrsytalline and bicrystalline samples have shown that grain boundary structure could significantly affect these mechanisms. Simulations have shown further that apart from dislocation plasticity other grain boundary mediated process like GB sliding and GB diffusion become important with decreasing grain size. These processes are also influenced by GB character. Thus, it is important to understand the role of GB character in deformation of nc metals. On one hand where the structural need for high strength has encouraged reduction of internal microstructural length scales, miniaturization has also encouraged reduction in external length scale of device components. In modern electronic and sensor devices a typical component size varies from a few hundred microns to few tens of nanometer. Several studies have shown that free surfaces could reduce the constraints on deforming grains. With decreasing sample dimensions, the free surface to volume ratio increases and the internal microstructural length scale may become comparable to the external sample size. An increasing contribution from these two geometrical parameters can introduce external size effects in mechanical properties of materials. In the past, most of the external size effects have been attributed to strain gradient plasticity and deformation source starvation. However, a different external size effect has been observed during uniaxial test of polycrystalline metals where the strength of materials was found to deviate from their bulk values at smaller sample sizes. While most studies have shown a weakening effect, there have also been a few observations of strengthening with a reduction in sample size. In most studies, the external sample size was kept constant and the internal grain size was varied by thermal annealing to produce samples with different external to internal size ratios. As the mechanical properties of metals are sensitive to the internal length scales it is difficult to explicitly follow the external size effect during these experiments. Moreover, compared to internal size effects mechanistic understanding of external size effect is limited, and systematic experimental efforts are required for proper characterization of these effects. The present investigation was undertaken to improve the scientific understanding of internal and external length effects on mechanical properties of nanocrystalline and coarse grained (~16 – 140 µm) polycrystalline nickel. For studying the internal size effects free standing nanocrystalline nickel samples with ~30 nm grain size and two different textures were synthesized using galvanostatic pulsed electrodeposition technique from Watts and Sulfamate baths. The nanocrsytalline deposits from a Watts bath showed a strong <100> fiber texture (NiS) while deposits from a Sulfamate bath were relatively weak textured (NiW), with s and w representing strong and weak texture, respectively. In situ mechanical tests at the PSI synchrotron facility in Switzerland were used to understand the nature of relaxation processes during thermal annealing and deformation of nc metals. The diffraction peak analysis showed that thermal annealing at 423 K of strong textured deposits caused a significant reduction in root mean square strain with limited grain growth. Furthermore, no residual strains developed, suggesting a homogenous distribution of relaxation processes during thermal annealing. In contrast, during deformation, structural relaxation was highly biased due to dislocation activities. The grains contributing to <200> diffraction peak transverse to loading axis showed early yielding and faster relaxation during deformation. The inhomogeneous nature of deformation was also reflected in development of transverse tensile residual stresses in the <200> grains. These experiments showed that relaxation processes during thermal annealing and deformation differ in their respective length scales. Nanocrsytalline deposits with two different textures were also deformed under synchrotron to access the role of GB character. As direct quantification of GB character distribution is difficult in nc metals, texture was taken as a qualitative representative for GB character. Previous studies have shown that the fraction of low angle boundaries increases with increasing sharpness of texture in fiber textured materials. Thus, the two textured deposits represented materials with two different low angle GB fractions. In situ tests showed that during the initial stages of microplastic deformation dislocation mechanisms were favored in strongly textured NiS. The transversely oriented <200> grains showed early yielding, which caused a redistribution of stress among other grain families. However, for weakly textured NiW deposits, smaller length scale atomic activities preceded dislocation activities. All the grains supported larger elastic strains at lower stresses suggesting significant plastic activity at GB regions. At higher stresses transversely oriented <220> grains yielded plastically and transferred elastic loads to <200> grains. Thus, the nature of plastic deformation was observed to depend on the distribution of GB character. For understanding the external size effects on mechanical properties polycrystalline nickel samples with grain sizes of 16, 51 and 140 µm were tested uniaxially at various sample thicknesses. Three different deformation regimes were identified based on the thickness of the samples. At higher thicknesses, in regime I, no significant variation of flow strength was observed. Flow strengths in regime II, at intermediate thicknesses, showed a strengthening effect with a reduction in thickness. However at lower thicknesses in regime III, a weakening trend was observed with decreasing thickness. The cross over from strengthening to weakening was observed to depend on grain size and applied strain. Detailed microstructural analysis with electron back scattered diffraction (EBSD) imaging showed that intragranular lattice rotation increases with a reduction in sample thickness. As lattice rotations may be considered to be accommodated by geometrically necessary dislocations, a semi empirical phenomenological model based on strain gradient plasticity was developed to understand the mechanics of external size effect during uniaxial test of polycrystalline samples. Further application of the model to the present experimental results showed that the characteristic length for strain gradient decreased with increasing grain size and applied strain.