TY - JOUR

T1 - Reversible stress-induced martensitic phase transformations in a bi-atomic crystal

AU - Elliott, Ryan S.

AU - Triantafyllidis, Nicolas

AU - Shaw, John A.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - In an earlier work, Elliott et al. [2006a, Stability of crystalline solids-II: application to temperature-induced martensitic phase transformations in bi-atomic crystals. Journal of the Mechanics and Physics of Solids 54(1), 193232], the authors used temperature-dependent atomic potentials and path-following bifurcation techniques to solve the nonlinear equilibrium equations and find the temperature-induced martensitic phase transformations in stress-free, perfect, equi-atomic binary B2 crystals. Using the same theoretical framework, the current work adds the influence of stress to study the model's stress-induced martensitic phase transformations. The imposition of a uniaxial Biot stress on the austenite (B2) crystal, lowers the symmetry of the problem, compared to the stress-free case, and leads to a large number of stable equilibrium paths. To determine which ones are possible reversible martensitic transformations, we use the (kinematic) concept of the maximal EricksenPitteri neighborhood (max EPN) to select those equilibrium paths with lattice deformations that are closest, with respect to lattice-invariant shear, to the austenite phase and thus capable of a reversible transformation. It turns out that for our chosen parameters only one stable structure (distorted αIrV) is found within the max EPN of the austenite in an appropriate stress window. The energy density of the corresponding configurations shows features of a stress-induced phase transformation between the higher symmetry austenite and lower symmetry martensite paths and suggests the existence of hysteretic stressstrain loops under isothermal loadunload conditions. Although the perfect crystal model developed in this work over-predicts many key material properties, such as the transformation stress and the ClausiousClapeyron slope, when compared to real experimental values (based on actual polycrystalline specimens with defects), it isto the authors knowledgethe first atomistic model that has been demonstrated to capture all essential trends and behavior observed in shape memory alloys.

AB - In an earlier work, Elliott et al. [2006a, Stability of crystalline solids-II: application to temperature-induced martensitic phase transformations in bi-atomic crystals. Journal of the Mechanics and Physics of Solids 54(1), 193232], the authors used temperature-dependent atomic potentials and path-following bifurcation techniques to solve the nonlinear equilibrium equations and find the temperature-induced martensitic phase transformations in stress-free, perfect, equi-atomic binary B2 crystals. Using the same theoretical framework, the current work adds the influence of stress to study the model's stress-induced martensitic phase transformations. The imposition of a uniaxial Biot stress on the austenite (B2) crystal, lowers the symmetry of the problem, compared to the stress-free case, and leads to a large number of stable equilibrium paths. To determine which ones are possible reversible martensitic transformations, we use the (kinematic) concept of the maximal EricksenPitteri neighborhood (max EPN) to select those equilibrium paths with lattice deformations that are closest, with respect to lattice-invariant shear, to the austenite phase and thus capable of a reversible transformation. It turns out that for our chosen parameters only one stable structure (distorted αIrV) is found within the max EPN of the austenite in an appropriate stress window. The energy density of the corresponding configurations shows features of a stress-induced phase transformation between the higher symmetry austenite and lower symmetry martensite paths and suggests the existence of hysteretic stressstrain loops under isothermal loadunload conditions. Although the perfect crystal model developed in this work over-predicts many key material properties, such as the transformation stress and the ClausiousClapeyron slope, when compared to real experimental values (based on actual polycrystalline specimens with defects), it isto the authors knowledgethe first atomistic model that has been demonstrated to capture all essential trends and behavior observed in shape memory alloys.

KW - Buckling

KW - Finite strain

KW - Phase transformation

KW - Stability and bifurcation

KW - Thermoelastic material

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U2 - 10.1016/j.jmps.2010.10.011

DO - 10.1016/j.jmps.2010.10.011

M3 - Article

AN - SCOPUS:78651292186

VL - 59

SP - 216

EP - 236

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 2

ER -