Large Deformation Constitutive Theory for a Two-Phase Shape Memory Alloy (original) (raw)
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Continuum Mechanics and Thermodynamics, 2014
A new version of rate-independent generalized plasticity, suitable for the derivation of general thermomechanical constitutive laws for materials undergoing phase transformations, is proposed within a finite deformation framework. More specifically, by assuming an additive decomposition of the finite strain tensor into elastic and inelastic (transformation induced) parts and by considering the fractions of the various material phases as internal variables, a multi-phase formulation of the theory is developed. The concepts presented are applied for the derivation of a three-dimensional thermomechanical model for shape memory alloy materials. The ability of the model in simulating several patterns of the extremely complex behavior of these materials, under both monotonic and cyclic loadings, is assessed by representative numerical examples. Keywords Shape memory alloys • Phase transformations • Pseudoelasticity • Shape memory effect • Multi-phase generalized plasticity Communicated by Andreas Öchsner.
A finite-strain finite element model for the pseudoelastic behavior of shape memory alloys
Computer Methods in Applied Mechanics and Engineering, 1997
This paper presents a finite deformation finite element model for the pseudoelastic response of shape memory alloys under stress loading-unloading conditions at constant temperature. A local multiplicative decomposition of the deformation gradient into volumetricelastic and isochori-inelastic components is assumed, where the inelastic component is associated with phase transformation and defines an additional intermediate configuration. Strain measure defined on the intermediate configuration is the Hencky strain. The constitutive equations are cast in the framework of generalized plasticity and the two-way phase transformation is modeled via a Kuhn-Tucker type transformation criteria for the rate-independent shape memory behavior. These equations are able to predict the stress-induced phase transformations during complete loading-unloading cycles, and can also predict the correct material behavior when incomplete transformations take place. The resulting nonlinear system of equations is solved for updated stress variables via the radial return algorithm embedded in the Newton-Raphson iteration scheme. Numerical results are presented to show the performance of the model.
2021
This paper presents a unified modelling effort to describe partial phase transformation during cyclic thermo-mechanical loading in Shape Memory Alloys (SMA). To this purpose, a three-dimensional (3D) finite strain constitutive model considering TRansformation-Induced Plasticity (TRIP) is combined with a modified hardening function to enable the accurate and efficient prediction of partial transformations during cyclic thermo-mechanical loading. The capabilities of the proposed model are demonstrated by predicting the behavior of the material under pseudoelastic and actuation operation using finite element analysis. Numerical results of the modified model are presented and compared with the original model without considering the partial transformation feature as well as with uniaxial actuation experimental data. Various aspects of cyclic material behavior under partial transformation are analyzed and discussed for different SMA systems.
A macroscopic constitutive model of shape memory alloy considering plasticity
This paper presents a macroscopic constitutive model which is able to reproduce the thermo-mechanical behaviors of the super-elastic SMA undergoing plastic strain. A mechanical constitutive equation, which predicts the stress-strain response of the SMA undergoing plastic strain, is developed based on the expression of Gibbs free energy with plastic strain. A linear plastic constraint equation is supposed to describe the effect of plasticity on the phase transformation behaviors of SMA. A sine-type phase transformation equation is established to describe the phase transformation behaviors of the SMA undergoing plastic strain. The mechanical constitutive equation, plastic constraint equation, and phase transformation equation together compose the presented macroscopic constitutive model which reproduces the thermo-mechanical behaviors of the SMA undergoing plastic strain. Especially all material constants related to the presented macroscopic constitutive model can be determined through macroscopic experiments. Therefore it is easy to use this presented model for the practical applications of SMA. The mechanical behaviors of the supper-elastic SMA undergoing plastic strain and the effect of plasticity are numerically simulated by the presented macroscopic constitutive model. Results show that the presented macroscopic constitutive model can effectively reproduce the thermo-mechanical behaviors of the super-elastic SMA and express the effect of plasticity.
A New Three-Dimensional Constitutive Model For Shape Memory Alloys
Pseudoelasticicy and shape memory effect due to martensitic transformation of polycrystalline shape memory alloy materials are modeled in the setting of threedimensional media. In the present work, description of rate-independent pseudoelastic behavior and shape memory effect is presented within the context of Generalized Standard Materials, using an internal variable named transformation strain tensor. Nondifferentiable but convex potentials of free energy and dissipation are defined and a special form for inelastic potential, based on the Drucker-Prager type, is proposed. The numerical integration of the resulting set of nonlinear ordinary differential equations involves the implementation of a radial projection scheme so as to satisfy the existing inequality constraints. The numerical results for proportional and nonproportional load show good agreement between the mechanical model and the behavior of polycrystalline materials presenting shape memory behavior.
Journal of Aerospace Engineering, 2009
Despite significant work over many years, using either one of the micromechanics based or phenomenological approaches, there are still prospects of much improvement to be made in constitutive modeling of shape memory alloys ͑SMAs͒. This is especially true if we sufficiently target the general scope in the modeling, i.e., including such important attributes as ͑1͒ multiaxiality; ͑2͒ possible asymmetry in tension and compression; ͑3͒ accounting for pseudoelasticity and pseudoplasticity; ͑4͒ rate dependence; and ͑5͒ effects of shape memory training under cyclic loading. The desire for comprehensive modeling of SMA materials provides the primary motivation for the inelastic model described here. Its theoretical formulation employs two main ingredients: ͑1͒ multiplicity of hardening mechanisms and ͑2͒ the partition of the energy storage/dissipation that is so vital in capturing the extremes of pseudoelasticity and pseudoplasticity in SMAs. For the purpose of validation and assessment part of the model capabilities, we report the results of a large number of simulations that were inspired by recent experimental test results under both monotonic and cyclic as well as uniaxial and multiaxial stress conditions.
A three-dimensional constitutive model for shape memory alloys
Archive of Applied Mechanics, 2010
Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile-shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.
Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior
Computer Methods in Applied Mechanics and Engineering, 1997
Shape-memory alloys show features not present in materials traditionally used in engineering; as a consequence. they are the basis for innovative applications. A review of the available literature shows a dearth of computational tools to support the design process of shape-memory-alloy devices. A major reason is that conventional inelastic models do not provide an adequate framework for representing the unusual macrobehavior of shape-memory materials. The present work focuses on a new family of inelastic models. based on an internal-variable formalism and known as generalized plasticity. Generalized plasticity is adopted herein as framework for the development of one-and three-dimensional constitutive models for shape-memory materials. The proposed constitutive models reproduce some of the basic features of shape-memory alloys, such as superelasticity. different material behavior in tension and compression, and the single-variant-martensite reorientation process. For isothermal conditions the implementation of the model in a finite-element scheme and the form of the algorithmically consistent tangent are discussed in detail. Numerical simulations of typical tests performed on shape-memory materials (e.g. uniaxial loading, four-point bending and three-point bending tests) are presented and compared with available experimental data. Based on the overall developments, it appears that the proposed approach is a viable basis for the development of an effective computational tool to be used in the simulation of shape-memory-alloy devices.
International Journal of Plasticity, 2008
In this paper we suggest a new phenomenological material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motivated by the requirement, also expressed by regulatory agencies, to carry out finite element simulations of NiTi stents. Depending on the quality of the numerical results it is possible to circumvent, at least partially, expensive experimental investigations. Stent structures are usually designed to significantly reduce their diameter during the insertion into a catheter. Thereby large rotations combined with moderate and large strains occur. In this process an agreement of numerical and experimental results is often hard to achieve. One of the reasons for this discrepancy is the use of unrealistic material models which mostly rely on the assumption of small strains. In the present paper we derive a new constitutive model which is no longer limited in this way. Further its efficient implementation into a finite element formulation is shown. One of the key issues in this regard is to fulfil ''inelastic" incompressibility in each time increment. Here we suggest a new kind of exponential map where the exponential function is suitably computed by means of the spectral decomposition. A series expansion is completely avoided. Finite element simulations of stent structures show that the new concept is well appropriate to demanding finite element analyses as they occur in practically relevant problems.