Digital image correlation and finite element analysis of inter- and intra-granular deformation

Abstract

Deformation in individual grains within a polycrystal depends on their orientation with respect to the direction of external loading (e.g. uniaxial tension), and also on mis-orientation with respect to neighbouring grains. Thus, strain inhomogeneity at the grain level is strongly dependent on the local microstructure, and not simply of the grain’s own orientation, as implied in selfconsistent modelling schemes [J.W. Hutchinson, Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. London, A 348 (1976) 101–127, A.M. Korsunsky, K.E. Jarnes, M.R. Daymond, Intergranular stresses in polycrystalline fatigue: diffraction measurement and self-consistent modelling, Eng Fracture Mech. 71 (2004) 805–812].Digital image correlation (DIC) is an excellent tool for probing deformation behaviour at different resolutions, since it is independent of the precise physical length scale, and can be applied to any digital image, e.g. obtained from optical or scanning electron microscopy, or AFM.In this study large-grained polycrystalline samples of commercial purity nickel were used. The surface of a dogbone specimen was etched prior to the experiment to create a pattern suitable for DIC interpretation. A custom-made loading stage for small samples was placed in the Alicona InfiniteFocus microscope, and uniaxial tensile force was applied to cause the specimen to elongate. Small steps for crosshead displacement between 7 μm and 34 μm were used to generate elastic deformation, followed by plastic stretching. At every loading step an image was taken with the digital camera attached to the microscope, up to the total strain within the specimen of 35%.The Alicona InfiniteFocus instrument could be used for two purposes: (i) to obtain high resolution images (1624×1232 pixels) of the sample surface during deformation, so that in-plane displacement and strain fields could be extracted; and (ii) to collect the data about surface profile evolution (roughening) caused by plastic slip during deformation. Digital image correlation analysis was carried out using LaVision DaVis software. Results show significant inter-granular and intra-granular strain inhomogeneity. When a plot of strain along a line crossing a particular grain is considered, areas of high and low strain can be readily identified that persist at different strain levels throughout the deformation history. As discussed by Zhang and Tong [N. Zhang, W. Tong, An experimental study on grain deformation and interactions in Al-0.5%Mg multicrystal, Intl. J. Plasticity 20 (2004) 523–542], this indicates the stability of the mechanisms responsible for the slip activity. The presence of neighbouring grains orientated so as to resist plastic deformation by crystal slip (i.e. possessing high Schmid factors) causes a softer adjacent grain to undergo more severe deformation. These observations were borne out by crystal plasticity finite element simulations.