Indentation in shape memory alloys

Abstract

Research on shape memory alloys (SMAs) has been broadly active since the discovery of shape memory in the compound NiTi in 1963, a decade after first reports of the effect in Au-Cd. For general reviews, see [1-4]. Early work on NiTi-based SMAs (primarily NiTi, and NiTiX, where X =Pt, Pd, Au, Cu, Hf, Zr, or Nb, and others) led to applications such as the NiTi hydraulic tube couplings developed by the Raychem Corporation. Today, a wide variety of new ideas have emerged [1-5] for applications such as sensors, actuators, damping materials, MEMS, biomedical devices, and hydro/aerodynamic control at surfaces. A noticeable resurgence of interest in SMAs has occurred, largely in response to recent advances in alloy preparation techniques (including physical vapor deposition routes), machining and joining technologies, and modeling capabilities. It is well known that NiTi alloys can exhibit either the shape memory effect (SME) or the superelastic effect (SE, often called pseudoelasticity). These are, respectively, isobaric and isothermal forms of shape memory, and a single alloy may exhibit either, depending on stress and temperature. Real behavior often combines aspects of each effect in a complex hysteretic fashion. Both shape memory and superelasticity depend on martensitic transformations, which, for NiTi, involve athermal first-order displacive transformations from a CsCl parent to a monoclinic, orthorhombic, or rhombohedral low-temperature allotrope, sometimes in succession. The heats of transformation may exceed 20J g-1 and the reactions may have large temperature and stress hysteresis. The maximum practical strain energy storage density in NiTi (>106 MJ m-3) [6] is extremely high. Displacive transformations are found in many metals and ceramics, but robust shape memory can usually only be obtained when: (a) The parent phase is a high-symmetry ordered compound. (b) The transformational volume change is negligible. (c) Twin boundaries in the martensite are glissile (i.e., mobile under the influence of shear stresses). Practical SMAs must usually also possess classical metallic toughness, and good strength against conventional slip plasticity. Furthermore, the martensite phase must be thermally stable below Mf. It is not surprising then that only a select few alloy systems have found wide application. With regard to the above criteria, the NiTi system is exceptionally robust. Figure 3.1a schematically illustrates the nature of the martensite microstructure that forms on cooling the austenite, "A," below the Ms temperature. The austenite-to-martensite transformation-in the absence of stress-produces no macroscopic shape change, because the large transformational shear strain is locally accommodated by formation of multiple crystal orientation variants of the martensite (Figure presented). This is possible because of the symmetry change: any one of 12 differently oriented monoclinic martensite domains ("lattice correspondence variants," L) can displacively arise from a given orientation of the cubic austenite grain. It is observed that, at the nano-and microscales, transformation proceeds by the formation of twin-related pairs of these orientation variants (labeled L 1 and L2 in the top sketch Fig. 3.1a), which nucleate cooperatively to produce a single, coherent habit-plane variant (labeled H). It is further observed that multiples of distinct habit-plane variants (labeled H1, H2, and H3)-of which there are 24 possibilities-evolve cooperatively, such that the net shear strain is near zero. The resulting microstructure is generally complex and heavily twinned at a very fine scale, and can frequently contain martensite-austenite phase mixtures. Shape memory is possible because of the mobility of twin boundaries in the martensite. When shear stresses favor one martensite variant orientation over another, twinning reactions (sometimes called "detwinning") can produce a large (but not unlimited) macroscopic plastic strain (see Fig. 3.1b). Under stress, some variants shrink as others grow; but since each must later revert to the same original austenite orientation (if heated), the apparent plastic deformation of the martensite can be reversed as the austenite is "recovered." The "remembered shape" is that which is "set" in the austenite. The cubic phase defines the reference condition and it is only deformation of the martensite that can be thermally reversed, at least against nontrivial reaction stresses. A second form of shape memory occurs under isothermal conditions at temperatures above the austenite finish (Af). When the austenite is stressed at temperatures just above Af, martensite can form spontaneously because shear stress effectively increases the martensite start (Ms) temperature. When martensite variants form under stress, macroscopic shear occurs because the (shear) stress favors certain variants over others, and the resulting microstructure can be envisioned as being similar to that of mechanically deformed martensite suggested in Fig. 3.1b (right). But when the stress is removed, the phase equilibrium temperatures drop back down and the martensite isothermally reverts to austenite. Shape recovery occurs much as in the case of thermal shape memory, except that the process occurs on falling stress at constant temperature. Very large amounts of strain energy can be stored and released via this mechanism and superelastic objects are highly robust against damage and distortion. It should be noted that, if the martensite is strained further than can be accommodated by the detwinning process illustrated in Fig. 3.1b (or if stress on an austenitic superelastic alloy is high enough), conventional slip plasticity-and consequent dislocation production-may occur that will inhibit complete return to an original shape. The maximum recoverable strain for practical NiTi is 4-8% in tension. Returning to the first form of shape memory, thermal SME, our description so far describes a "one-way" shape recovery on heating. If the return to set shape is mechanically restrained, very large forces can be developed, as is done in the case of the Raychem tube connector (Figure presented). As shown schematically in Fig. 3.2, when SMAs are to be used as cyclic actuators, however, some kind of force-producing element, such as a spring or pendant mass, must be mechanically linked so as to deform the martensite phase during the cooling part of the actuation cycle. When the actuator is warm, the austenite appears "hard" to the biasing force and responds as a stiff elastic element that remains contracted along the bias axis. When cooling occurs in the presence of the bias force (think of the pendant mass), the resultant martensite looks plastically soft to the bias stress, and plasticity occurs up to the strain limit for transformational shear (i.e., 4-8%). In the pendant mass example, cyclic heating and cooling alternately raises and lowers the hanging weight, whereas the spring shown in the sketch stretches and contracts. To reiterate, in the absence of the bias forces, no shape change is expected on cooling-there is no strong memory of previous martensite shapes. SMAs may, however, be specially processed to possess some degree of memory of both the shapes of the parent and martensitic phases, which gives a two-way SME or TWSME (see Fig. 3.2, right-hand sketch). TWSME is usually obtained via thermomechanical "training" that involves heating and cooling under controlled load, displacement, and temperature conditions, often using stresses that will cause generation of dislocations. Two-way SME is believed to depend on nucleation of preferred martensite variants under the influence of stress fields around dislocations introduced during the training process. Though two-way alloys provide an internalized "reset" mechanism for actuators, significant work can only be extracted during the heating part of the cycle. Also, tighter limits on strain recovery and thermal stability apply when TWSME is required. Although there have been extensive studies of bulk SME and SE behavior using macroscopic tensile, shear, and compression loading, until recently, few studies have been devoted to the microscopic behavior of these alloys under contact loading conditions. To help better understand shape memory and superelastic effects at small scales and under complex loading conditions, we and several other groups have studied SMAs using micro-and nanoindentation techniques [7-32]. Unlike in simple tension, compression, or shear experiments, the stress distribution under an indenter is highly nonuniform and strains can easily exceed the maximum that can be recovered by SMEs. The shape of the indenter has a strong effect on both the magnitude and distribution of these stresses [33-35]. If one ignores natural tip imperfection, sharp pyramids (i.e., Vickers and Berkovich indenters) do not possess a characteristic length scale, so the indentation response in SMAs should be independent of indentation depth. Spherical indenters do have a natural length scale, the ball radius R, and indentation response is thus expected to have some form of depth dependence. Pyramids do too if the displacements are on the order of the (imperfect) tip radius. Below, we provide a brief overview of recent work on indentation in SMAs. Together, they demonstrate the robust operation of shape memory and superelastic mechanisms at both small length scales and under complex (highly anisotropic and nonuniform) loading conditions. Some of these results are suggestive of several new kinds of applications for SMAs. © Springer Science+Business Media, LLC, 2008.