A finite-deformation-based phenomenological theory for shape-memory alloys

Thamburaja, T Prakash G.

doi:10.1016/j.ijplas.2009.12.004

Cited by 76 publications

(33 citation statements)

References 55 publications

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“…If fcc and bcc crystal plasticity continuum models have already been extensively studied (Cuitiño and Ortiz, 1993;Anand and Kothari, 1996;Anand, 2004;Houtte et al, 2006;Zhao et al, 2007;Kuchnicki et al, 2008;Jérusalem et al, 2008;Roters et al, 2010;Lee et al, 2010;Liu et al, 2011;Thamburaja, 2010;Rossiter et al, 2010;Zamiri and Pourboghrat, 2010;Watanabe et al, 2010;Sung et al, 2010), similar efforts have been much scarcer for HCP metals (Staroselsky, 1998;Staroselsky and Anand, 2003;Graff et al, 2007;Mayeur and McDowell, 2007;Tang et al, 2009;Mayama et al, 2009;Prakash et al, 2009;Choi et al, 2010b;Choi et al, 2010a;Lévesque et al, 2010). Despite the relatively ancient interests in HCP metals, the intrinsic mechanisms of HCP crystalline deformation, such as twinning (generally more present than in fcc and bcc metals), twin-slip interaction, or twin polarization among others, are still, as of now, not fully understood (Jérusalem et al, 2008;Wang et al, 2009a;Yue et al, 2010;Shen et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Fernández

Prado

Wei

et al. 2011

International Journal of Plasticity

101

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a b s t r a c tLightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843-1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip hc + ai versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.

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Section: Introductionmentioning

confidence: 99%

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Fernández

Prado

Wei

et al. 2011

International Journal of Plasticity

101

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“…Associated with the gradients, various internal length scales are included, which enable the description of the size-dependent yield strength and flow stress. There were a couple of attempts to combine gradient plasticity theories with superelasticity, however the purposes are for the regularization of numerical methods rather than size effects [114,112,22]. …”

Section: Previous Work On Sma Modelingmentioning

confidence: 99%

“…For this purpose, we follow the technique from Thamburaja [112], where the increment of martensitic volume fraction is decomposed into a forward part A + and a reverse part A -, i.e. where the direction Af will be the outcome of the variational principle, and the direction A = t (n) is prescribed.…”

Section: C4 Gradient Superelasticitymentioning

confidence: 99%

Computational modeling of size-dependent superelasticity of shape memory alloys

Qiao

Radovitzky

2016

Journal of the Mechanics and Physics of Solids

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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.

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“…The second fundamental assumption is that the response of the material is isotropic. Accordingly, it is assumed that it can be described in terms of a single scalar internal variable Z, which, as it is common within the literature (e.g., Boyd and Lagoudas, 1996;Lubliner and Auricchio, 1996;Panoskaltsis et al, 2004;Müller and Bruhns, 2006;Thamburaja, 2010), is identified by the fraction of a single (favorably oriented) martensite variant. In turn, and in view of Eq.…”

Section: A Constitutive Modelmentioning

confidence: 99%

Mechanics of Shape Memory Alloy Materials – Constitutive Modeling and Numerical Implications

Panoskaltsis¹

2013

Shape Memory Alloys - Processing, Characterization and Applications

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A finite-deformation-based phenomenological theory for shape-memory alloys

Cited by 76 publications

References 55 publications

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Computational modeling of size-dependent superelasticity of shape memory alloys

Mechanics of Shape Memory Alloy Materials – Constitutive Modeling and Numerical Implications

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