Computational modeling of size-dependent superelasticity of shape memory alloys

Abstract

The superelastic effect in shape memory alloys (SMAs) is attributed to the stressinduced reversible austenitic-martensitic phase transformations. It is characterized by the development of significant strains which are fully recoverable upon unloading, and also characterized by the stress-hysteresis in the loading and unloading cycle which corresponds to the energy dissipated during phase transformations. Recently, experiments have revealed size-dependent effects in the superelastic responses of SMAs at micro-and nanoscales. For instance, the CuAlNi microwires and submicron pillars show a substantially higher capacity for the energy dissipation than that of bulk samples, which offers a significant promise for the applications in protective materials.In this thesis, a continuum model is developed in order to improve our understanding of size effects in SMAs at small scales. The modeling approach combines classic superelastic models, which use the volume fraction as an internal variable to represent the martensitic phase transformation, with strain gradient plasticity theories. Size effects are incorporated through two internal length scales, an energetic length scale and a dissipative length scale, which correspond to the martensitic volume fraction gradient and its time rate of change, respectively. Introducing the gradient of the martensitic volume fraction leads to coupled macro-and microforce balance equations, where the displacements and the martensitic volume fraction are both independent fields. A variational formulation for the temporally-discretized coupled macro-and microforce balance equations is proposed, as well as a computational framework based on this formulation. A robust and scalable parallel algorithm is implemented within this computational framework, which enables the large-scale three-dimensional study of size effects in SMAs with unprecedented resolution. This modeling and computational framework furnishes, in effect, a versatile tool to analyze a broad range of problems involving size effects in superelasticity with the potential to guide microstructure design and optimization. In particular, the model captures the increase of the stress hysteresis and strain hardening in bulk polycrystalline SMAs for decreasing grain size, as well as the increase of the residual strain for decreasing pillar size in NiTi pillars. The model confirms that constraints like grain boundaries 3 and the surface Ti oxide layer are responsible for the size-dependent superelasticity in SMAs.

A micromechanics-based constitutive model for nanocrystalline shape memory alloys incorporating grain size effects

“…where subscripts A and M denote austenitic phase and martensitic phase, respectively. The hardening modulus P tr have been introduced by several authors (Qiao and Radovitzky, 2016;Tabesh et al, 2017;Yu et al, 2018b). Based on the observation of stress plateau in San Juan et al (2008), Qiao and Radovitzky (2016) ignored the influence of hardening modulus, that is, P tr is set to a value of zero.…”

“…The hardening modulus P tr have been introduced by several authors (Qiao and Radovitzky, 2016;Tabesh et al, 2017;Yu et al, 2018b). Based on the observation of stress plateau in San Juan et al (2008), Qiao and Radovitzky (2016) ignored the influence of hardening modulus, that is, P tr is set to a value of zero. Tabesh et al (2017) adopted a classic transformation hardening rule in the proposed gradient-based constitutive model.…”

“…Sun and He (2008) developed a multiscale continuum model to investigate the grainsize effects on the stress hysteresis of SMA polycrystals during the isothermal transformation. Inspired by the strain-gradient plasticity work of Lele and Anand (2009), Qiao and Radovitzky (2016) constructed a nonlocal continuum model incorporating the energetic length scale and the dissipative length scale as well as the spatial gradient of the martensite volume fraction. This isothermal model was intended to describe the grain-size dependent superelasticity of nanocrystalline SMAs.…”

Development of the method with enhanced accuracy for solving problems from the theory of thermo-pseudoelastic-plasticity

“…At points A, B, C, D, deformations are assigned as a percentage, stressin Gpa. Table 1 gives experimental data obtained in papers [3,4]. If we unload the sample at the stress that corresponds to point C in the diagram, part of deformation (an elastic component of the overall deformation of the model) will disappear.…”

On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

“…Afterwards, the nonlocal strain gradient theory has been extensively used to study the size-dependent behaviors of small scaled structures, such as the static and dynamic analyses of micro or nano rods (Li et al, 2016), beams (Barati et al, 2019;Esfahani et al, 2019;Zhang et al, 2019), tubes (Farajpour et al, 2019;Mohammadian et al, 2019), and plates (Babu and Patel, 2019;Lu et al, 2019). In addition to microscopic experimental research of SMA, Qiao and Radovitzky (2016), Qiao et al (2011) proposed a nonlocal continuum model, in which an energetic length scale and a dissipative length scale are introduced, to describe the size-dependent superelastic response in recent experiments of SMAs. And then, Qiao and Radovitzky (2013) proposed a numerical model supporting the previously proposed explanation that the external Ti oxide layer may be responsible for the loss of superelasticity in the small pillars.…”