Determination and transport of phase transformation yield surfaces for shape memory alloys

Gibeau, Elie; Laydi, Mohamed Rachid; Lexcellent, Christian

doi:10.1002/zamm.200900364

Cited by 4 publications

(7 citation statements)

References 16 publications

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“…As for the shape of the transformation surface itself, it appears that quadratic anisotropic yield criteria which are commonly used for a wide variety of materials in numerical computations, such as Hill [19] or its more general form, Tsai-Wu [20] do not fit well the data obtained by experiments. In the mentioned models [7,18,20], the particular pear shape of the Prager equation introduced for SMAs by Patoor et al [3] seems to fit better the experimental observations.…”

Section: Phase Transformation Of Anisotropic Shape Memory Alloys: Thementioning

confidence: 92%

“…They rely on a transformation criterion that depends on the invariants of the stress tensor. Following the normality rule for the transformation strains, associativity to such criterion is characterized by the invariance of transformation power with respect to loading direction [18]. At the point of saturation, an analytical expression of the transformation strains can thus be expressed.…”

Section: Phase Transformation Of Anisotropic Shape Memory Alloys: Thementioning

confidence: 99%

“…In several models [7,18,38], e t eq is considered to be in direct relation with the martensitic volume fraction (MVF) n:…”

Section: Evolution Equations Of Transformation Strainmentioning

confidence: 99%

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Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Chatziathanasiou

Chemisky

Meraghni

et al. 2015

Shap. Mem. Superelasticity

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract In the present study, a new transformation criterion that includes the effect of tension-compression asymmetry and texture-induced anisotropy is proposed and combined with a thermodynamical model to describe the thermomechanical behavior of polycrystalline shape memory alloys. An altered Prager criterion has been developed, introducing a general transformation of the axes in the stress space. A convexity analysis of such criterion is included along with an identification strategy aimed at extracting the model parameters related to tension-compression asymmetry and anisotropy. These are identified from a numerical simulation of an SMA polycrystal, using a self-consistent micromechanical model previously developed by Patoor et al. (J Phys IV 6(C1):277-292, 1996) for several loading cases on isotropic, rolled, and drawn textures. Transformation surfaces in the stress and transformation strain spaces are obtained and compared with those predicted by the micromechanical model. The good agreement obtained between the macroscopic and the microscopic polycrystalline simulations states that the proposed criterion and transformation strain evolution equation can capture phenomenologically the effects of texture on anisotropy and asymmetry in SMAs.

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Section: Phase Transformation Of Anisotropic Shape Memory Alloys: Thementioning

confidence: 92%

Section: Phase Transformation Of Anisotropic Shape Memory Alloys: Thementioning

confidence: 99%

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Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Chatziathanasiou

Chemisky

Meraghni

et al. 2015

Shap. Mem. Superelasticity

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“…If there is any, the originality of this investigation comes from the fact that the three-dimensional behavior of SMAs integrates the intrinsic asymmetry between tension and compression in the fracture analysis. However, it is well known that, the SMAs behaviour is strongly non linear (Gibeau et al 2010) and this observation must be integrated into the model because a stress redistribution occurs around the crack tip. Moreover, the different elastic properties (for instance, the Young modulus) of the mother phase and the product phases can also be included.…”

Section: Comments and Conclusionmentioning

confidence: 98%

Analytical prediction of the phase transformation onset zone at a crack tip of a shape memory alloy exhibiting asymmetry between tension and compression

2010

Self Cite

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Shape Memory Alloys (SMAs) such as NiTi exhibit stress induced martensitic phase transformation. The purpose of this paper is to provide a better understanding of SMA (such as NiTi) fracture behavior, by considering the vicinity of the crack tip where the transformation occurs. This analysis integrates the asymmetry between tension and compression in an analytical prediction of the surface of phase transformation around the crack tip for loading modes 1, 2, 3 and mixed 1+2. The influence of the asymmetry between tension-compression is more important in plane stress conditions than in plane strain conditions, particularly for mode 1 loading. In order to validate this model, we are currently setting up an experimental investigation to observe strain localization during crack propagation (transformation and martensitic saturation regions) on NiTi thin sheets.

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“…It has been found that the "yield" (transformation start stress in stress induced phase transformation) surface does neither really match the Huber-von Mises yield criterion nor the Tresca yield criterion. Determination and transport of phase transformation yield surfaces for shape memory alloys are also given by Gibeau, Laydi and Lexcellent (2010). "Yield" surfaces of shape memory alloys and their applications were studied by Huang (1999), Lim and McDowell (1999), Gall et al (1998), Novák and Šittner (2004) The "yield" surfaces of four polycrystalline SMAs (NiTi, NiAl, CuZnGa, and CuAlNi) are investigated by Lexcellent et al (2002;2007;.…”

Section: Phase Transformation Yield Criterion Of Shape-memory Alloysmentioning

confidence: 99%

Computational Plasticity

2012

Advanced Topics in Science and Technology in China

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PrefaceComputational plasticity is a new and important branch of computational mechanics. Computational Plasticity: With Emphasis on the Application of the Unified Strength Theory and Associated Flow Rule is the third title in the series on plasticity published by Springer and by Springer or by the collabration of Springer and ZJU Press. The other two files are: Generalized Plasticity (Springer, Berlin, 2006) and Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses of Structures (Springer and ZJU Press, Hangzhou, 2009). The founding work in this series on plasticity is Unified Strength Theory and its Applications that was published by Springer in Berlin in 2004, in which the unified strength theory (UST) and its 30 years developments history are described in detail.Generalized Plasticity, the first monograph in this series on plasticity, is a combination of traditional plasticity for metallic materials (non-SD materials) and plasticity for geomaterials (SD materials, i.e. strength difference in tension and in compression, sometimes referred to as tension-compression asymmetry). It was published by Springer in 2006, in which the unified slip line theory for plane strain problems and unified characteristics theory for plane stress and spatial axisymmetric problems, as well as the unified fracture criterion for mixed mode cracks and plastic zones at the tip of a crack using the unified strength theory are described. Generalized Plasticity can be used for both non-SD materials and SD materials. The time effect, however, is not taken into account in Generalized Plasticity. The time independent UST can be extended to time dependent UST.The second title in this series on plasticity is Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses of Structures, which was published by ZJU Press and Springer in 2009. Structural Plasticity deals with limit analysis, shakedown analysis and dynamic plastic analyses of structures using the analytical method. The straight line segments on the series yield surfaces of the unified strength theory make these surfaces convenient for analytical treatment of plasticity problems. A series of results of the unified solutions for elastic and plastic limit analysis, shakedown analysis and dynamic plastic analysis for structures are given by using the unified strength theory. These unified solutions can provide a very useful tool for the design of engineering structures. Most solutions in textbooks regarding the plastic analysis of structures are special cases of the unified solution, using the unified strength theory. The third title in this series on plasticity is Computational Plasticity: With Emphasis on the Application of the Unified Strength Theory and Associated FlowRule, in which numerical methods are applied. The unified strength theory and associated flow rule are implemented in several computational plasticity codes and applied to many engineering problems.A series of results can be obtained in Generalized Plasticity (slip line theory), Structural Plast...

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Determination and transport of phase transformation yield surfaces for shape memory alloys

Cited by 4 publications

References 16 publications

Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Analytical prediction of the phase transformation onset zone at a crack tip of a shape memory alloy exhibiting asymmetry between tension and compression

Computational Plasticity

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