Influences of granular constraints and surface effects on the heterogeneity of elastic, superelastic, and plastic responses of polycrystalline shape memory alloys

Abstract

Deformation heterogeneities at the microstructural length-scale developed in polycrystalline shape memory alloys (SMAs) during superelastic loading are studied using both experiments and simulations. In situ X-ray diffraction, specifically the far-field high energy diffraction microscopy (ff-HEDM) technique, was used to non-destructively measure the grain-averaged statistics of position, crystal orientation, elastic strain tensor, and volume for hundreds of austenite grains in a superelastically loaded nickel-titanium (NiTi) SMA. These experimental data were also used to create a synthetic microstructure within a finite element model. The development of intragranular stresses were then simulated during tensile loading of the model using anisotropic elasticity. Driving forces for phase transformation and slip were calculated from these stresses. The grain-average responses of individual austenite crystals examined before and after multiple stress-induced transformation events showed that grains in the specimen interior carry more axial stress than the surface grains as the superelastic response “shakes down”. Examination of the heterogeneity within individual grains showed that regions near grain boundaries exhibit larger stress variation compared to the grain interiors. This intragranular heterogeneity is more strongly driven by the constraints of neighboring grains than the initial stress state and orientation of the individual grains.

Introduction

Shape memory alloys (SMAs) are a class of materials that may exhibit superelasticity, or the ability to fully recover large inelastic deformations induced by mechanical loading. The large inelastic strain during these events arises from a diffusionless solid-solid phase transformation between phases with high and low crystallographic symmetry. Equiatomic, polycrystalline nickel-titanium (NiTi) SMAs in particular can recover strains of up to 6% in transforming between a cubic austenite (B2) and a monoclinic martensite (B19′) phase. Because of this remarkable behavior, they are used for a variety of commercial applications (Duerig, Pelton, Stöckel, 1999, Mohd Jani, Leary, Subic, Gibson, 2014, Otsuka, Wayman, 1999). Due to the unique properties exhibited by SMAs and the resultant commercial interest, SMAs have received persistent interest from the scientific community. Empirical and theoretical studies have investigated a variety of phenomena related to the stress-induced phase transformation including the crystallography (Abeyaratne, Knowles, 1991, Ball, James, 1987, Bhattacharya, 2003, Bowles, Mackenzie, 1954, Wechsler, Lieberman, Read, 1953), the influence of microstructure and processing on performance (Bhattacharya, Kohn, 1995, Bhattacharya, Kohn, 1996, Cai, Schaffer, Daymond, Yu, Ren, 2014, Gall, Sehitoglu, Chumlyakov, Kireeva, 1999, Kimiecik, Jones, Daly, 2016, Kimiecik, Wayne Jones, Daly, 2015, Pelton, Clausen, Stebner, 2015, Schaffer, Plumley, 2009, Stebner, Paranjape, Clausen, Brinson, Pelton, 2015), the inelastic nature of deformation, and the inevitable coupling between phase transformation and plastic deformation (Bowers, Chen, De Graef, Anderson, Mills, 2014, Cai, Schaffer, Yu, Daymond, Ren, 2015, Chowdhury, Sehitoglu, 2016, Delville, Malard, Pilch, Sittner, Schryvers, 2011, Norfleet, Sarosi, Manchiraju, Wagner, Uchic, Anderson, Mills, 2009, Simon, Kroger, Somsen, Dlouhy, Eggeler, 2010). These studies show that, like any deformation process, phase transformation is strongly influenced by microstructural constraint (grain structure, texture) and structural constraint (pores, voids, specimen size, geometry). However, one theme to emerge from these studies is that the constraint can reduce transformation strain magnitude, introduce residual (non-reversible) deformation and can lead to material damage and failure — all deleterious effects from the perspective of applications (Eggeler et al., 2004).

Microstructural constraint can arise from a variety of compatibility requirements. In polycrystals, grains must maintain compatibility across the grain boundaries. At the interfaces between austenite and martensite phases in SMAs an additional constraint exists due to the necessity to form a low-distortion, low elastic energy interface (Ball, James, 1987, Wechsler, Lieberman, Read, 1953). Such constraint is well-documented to result in localized slip and contribute to poor mechanical behavior — specifically structural and functional fatigue (Bowers, Chen, De Graef, Anderson, Mills, 2014, Norfleet, Sarosi, Manchiraju, Wagner, Uchic, Anderson, Mills, 2009, Perkins, Muesing, 1983, Simon, Kroger, Somsen, Dlouhy, Eggeler, 2010). Phase transformation at precipitate-matrix boundaries could be constrained due to coherent or semi-coherent nature of the interface and resultant local stress fields (Tirry, Schryvers, 2009, Wang, Kustov, Li, Schryvers, Verlinden, Van Humbeeck, 2015, Xie, Zhao, Lei, 1990). Structural constraint on the other hand refers to the effect of very small specimen sizes (Chen, Schuh, 2011, Manchiraju, Kroeger, Somsen, Dlouhy, Eggeler, Sarosi, Anderson, Mills, 2012) and other structural features such as porosity (Paul, Paranjape, Stebner, Dunand, Brinson, 2016, Zhao, Taya, Kang, Kawasaki, 2005). Among these constraint effects, the influence of grain boundaries on phase transformation as well as the behavior of grains in the specimen interior vs. free surface have received relatively less attention.

There is a general understanding that similarly oriented grains are theoretically expected to produce similar superelastic transformation strain, but instead they produce a range of strains in real polycrystals, potentially due to the microstructural constraints discussed above (Kimiecik, Wayne Jones, Daly, 2015, Mao, Han, Tian, Luo, Zhang, Ji, Wu, 2008, Merzouki, Collard, Bourgeois, Ben Zineb, Meraghni, 2010). However, studies of the heterogeneous behavior of similarly oriented grains have been limited to 2D or surface observations, hence the grain deformations have been unconstrained in at least one direction and observations of fully confined grains have been lacking. 3D analyses have typically relied on a modeling component to provide statistics about stress-induced martensite formation in SMA polycrystals (Gall, Lim, McDowell, Sehitoglu, Chumlyakov, 2000, Paranjape, Anderson, 2014). While the conclusions from these modeling efforts are general, they rely on idealized, synthetic microstructures and it is challenging to validate those findings empirically. Other efforts have utilized oligocrystalline SMAs to analyze some specific phenomena related to microstructural and structural constraint — e.g., nucleation of multiple martensite variants at grain triple junctions due to complex stress state vs. single variant at grain boundaries (Ueland and Schuh, 2013a). The effect of grain constraint on other inelastic deformation mechanisms e.g., plasticity has been explored both experimentally (Sachtleber, Zhao, Raabe, 2002, Thorning, Somers, Wert, 2005) and analytically (Mika and Dawson, 1998). Accumulated plastic strain and lattice rotations near grain boundaries were observed to deviate from the relatively homogenous deformation states about grain centroids. However, similar to phase transformation, those efforts are either limited to 2D or have investigated idealized microstructures.

Efforts documenting the effect of free surfaces on phase transformation in SMAs at the micron length scale are limited and are primarily based on microwire and micropillar experiments. As a consequence, these results are confined to < 500 µm specimens with a limited number of grains. Findings include a higher fatigue life for oligocrystalline microwires compared to polycrystals (Ueland and Schuh, 2012) and a transition from multi-domain martensite microstructure to single domain with a reduction in wire size (Ueland and Schuh, 2013b). At an even smaller length scale, transmission electron microscopy (TEM) based studies have documented the occurrence of phase transformation in NiTi nano-pillars (Ye et al., 2010), while suppression of transformation is reported in NiTi thin films with grain size less than 50  nm (Waitz et al., 2008). While a combination of techniques have been used in these studies of phenomena related to granular interaction and relaxation at free surfaces of laboratory-produced materials, a desire for a 3D experimental investigation of these phenomena within bulk samples taken from commercially-produced alloys still exists.

The advent of new techniques for non-destructive, in situ 3D characterization has enabled such a study. High energy diffraction microscopy (HEDM), or 3D X-ray diffraction (3DXRD) techniques, can non-destructively provide spatially resolved microstructure (grain morphologies, phase, crystal orientation) and deformation (lattice strain tensor) information in bulk specimens during thermo-mechanical loading (Bernier, Barton, Lienert, Miller, 2011, Lienert, Li, Hefferan, Lind, Suter, Bernier, Barton, Brandes, Mills, Miller, Jakobsen, Pantleon, 2011, Poulsen, Nielsen, Lauridsen, Schmidt, Suter, Lienert, Margulies, Lorentzen, Jensen, 2001, Suter, Hennessy, Xiao, Lienert, 2006). These techniques have been utilized to study grain-scale phenomena, e.g., intragranular orientation spread and stress spread developed during elastic and plastic deformation in steel (Juul, Winther, Dale, Koker, Shade, Oddershede, 2016, Oddershede, Wright, Beaudoin, Winther, 2015, Winther, Wright, Schmidt, Oddershede, 2017), grain rotation and intragranular misorientation evolution in Cu (Pokharel et al., 2015), change in the volume fractions of the domains in ferroelectric materials (Oddershede et al., 2015a), twin nucleation in Ti (Bieler et al., 2013), and stress evolution in Ti grains (Schuren et al., 2015). Specific to SMAs, 3DXRD technique has been used to probe the grain rotation and grain fragmentation in a CuAlBe SMA during superelastic loading (Berveiller et al., 2011) and most recently to image the 3D morphology of a stress-induced transformation interface and the austenite stress field in front of the transformation front in a fine-grained (1 to 5µm), thin (100µm) NiTi wire (Sedmák et al., 2016).

Here, we use this non-destructive, 3D technique to simultaneously characterize grain-resolved deformation and microstructure during mechanical loading, including the evolution in residual stresses in the grains during cyclic loading, trends in the residual stresses in terms of grain position and orientation, and effect of the residual stresses on subsequent phase transformation. We also use the microstructure information from HEDM to construct a realistic synthetic microstructure for anisotropic, elastic simulations to elucidate two specific phenomena. First, we quantify the deformation heterogeneity in surface vs. interior grains in a superelastically cycled SMA. We propose that the origin of this heterogeneity is from the interaction between grain neighborhoods. Second, we quantify the disparity in intragranular stress state in similarly orientated grains with different neighborhoods. We show that this disparity influences the phase transformation characteristics of the grains. The role of HEDM in our study is to furnish grain-averaged characterization of deformation and orientations. The simulations augment the information at sub-grain scale. An understanding of these phenomena is crucial in designing SMAs that are less prone to structural and functional fatigue. The results from this work advance the general understanding of granular interactions in phase transforming materials.