Modeling and simulation of architectured iron-based SMA materials

ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS 2017), Snowbird, UT, SEP 18-20, 2017International audienceThe paper presents results of finite element analysis of architectured iron-based shape memory alloy (SMA) samples consisting of bulk SMA and void combined to different proportions and according to different geometric patterns. The finite element simulation uses a constitutive model for iron-based SMAs that was recently developed by the authors in order to account for the behavior of the bulk material. The simulation of the architectured SMA is then carried out using a unit cell method to simplify calculations and reduce computation time. For each unit cell, periodic boundary conditions are assumed and enforced. The validity of this assumption is demonstrated by comparing the average behavior of one unit cell to that of a considerably larger sample comprising multiple such cells. The averaging procedure used is implemented numerically, by calculating volume averages of mechanical fields such as stress and strain over each finite element model considered as a combination of mesh elements

Strain localization analysis using a multiscale model

In order to analyze the formability of steels in sheet metal forming, a ductility loss criterion is coupled with a multiscale model. The behavior at the mesoscopic (grain) scale is modeled by a large strain micromechanical constitutive law, which is then used in a self-consistent scale transition scheme. Hardening at the slip system level is taken into account through mean dislocation densities considered as internal variables. The determination of active slip systems and the calculation of plastic slip activity are achieved with help of a regularization technique drawn from viscoplastic formulations. The model is shown to be able to correctly simulate the macroscopic behavior for single-phase steels during both monotonic and sequential loading paths. Finally, Rice's localization criterion, based on the ellipticity loss of the elastic-plastic tangent modulus, is introduced and applied to determine forming limit diagrams (FLDs). The model allows us to obtain correct FLDs for monotonic as well as sequential loading paths. Pre-strain impact on FLDs is qualitatively reproduced as well.ArcelorMittal CNR

Modélisation micromécanique de l'effet de précipités sur le comportement d'un polycristal en alliage à mémoire de forme

Le processus de fabrication des AMF conduit à la formation de précipités. Des études expérimentales montrent leur influence sur les propriétés de la transformation martensitique. Le développement d'un modèle micro-mécanique utilisant une transition d'échelle de type Mori-Tanaka permet de prendre en compte l'effet des précipités à l'échelle intra-granulaire. Une seconde transition d'échelle de type auto-cohérente permet le passage de l'échelle du grain à celle du polycristal

Modeling of niobium precipitates effect on the Ni 47Ti 44Nb 9 Shape Memory Alloy behavior

Commercial Ni 47Ti 44Nb9 Shape Memory Alloy (SMA) is generally adopted for tightening applications thanks to its wide transformation hysteresis, compared with classical NiTi. Its sensibility to thermo-mechanical treatments allows it to be either martensitic or austenitic in a wide range of temperature, between -60 °C and 80 °C. A modeling of niobium precipitates effects on Ni 47Ti 44Nb9 SMA behavior is proposed. For this object, a two phase thermo-mechanical model is developed. It describes the global effective behavior of an elastoplastic inclusion (niobium precipitates) embedded within an SMA matrix. The constitutive law developed by Peultier et al. (2006) and improved by Chemisky et al. (2011) is adopted to model the matrix shape memory behavior. The elastoplastic constitutive law for inclusion is the one proposed by Wilkins with Simo and Hughes's radial return algorithm. The Mori-Tanaka scale transition scheme is considered for the determination of the effective constitutive equations. Obtained results highlight the effect of niobium precipitates on the thermomechanical behavior of Ni47Ti 44Nb9, and particularly on the corresponding hysteresis size. It appears that the niobium plasticity increases this hysteresis size. The developed constitutive law has been implemented in the ABAQUS Finite Element code and considered for the numerical prediction of the tightening pressure in a connection applicatio

A finite-element based numerical tool for Ni47Ti44Nb9 SMA structures design application to tightening rings

This paper deals with the design of Ni47Ti44Nb9 Shape Memory Alloy (SMA) tightening components. The tightening of an SMA ring on an elastic pipe is analyzed using the finite element code ABAQUS® and a UMAT subroutine developed in our group to model the specific behavior of Ni47Ti44Nb9 SMA. Main features of the thermomechanical model implemented in this UMAT routine are briefly recalled. Numerical predictions are validated using experimental tightening pressures obtained on a test bed developed in this work. The validation strategy is documented and the results for different ring thicknesses are presented. This finite element tool is then applied to a parametric study of the influence of ridges on the tightening pressure. Eventually, geometrical defects like out of roundness are considered

Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent hardening, dislocation storage and annihilation, mean free path, etc.) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice’s criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional “fitting” parameter, is used to build Ellipticity Limit Diagrams (ELDs).ArcelorMittal Researc

Modélisation du comportement thermomécanique des films minces en AMF par une approche non locale

La recherche de la miniaturisation des applications dans les secteurs industriels multiplie la conception de microcomposants ou de microsytèmes taillés dans des couches minces d'alliage à mémoire de forme (AMF). Ces structures minces sont souvent le siège de phénomènes d'instabilité tels que la localisation de la déformation et sa propagation à contrainte constante, observés durant la transformation de phase directe ou inverse. Afin de décrire ces phénomènes particuliers, un modèle phénoménologique non local basé sur l'extension d'un modèle local existant est proposé dans ce travail. Ce modèle initialement, développé dans le cadre de la thèse d'Arnaud Duval (2009) est enrichi par la description de deux types de comportements : le comportement hystérétique lors de la décharge superélastique et le comportement thermique à contrainte constante. Implanté dans le code de calculs par éléments finis Abaqus, le modèle proposé est utilisé pour étudier l'influence de paramètres matériau et géométriques sur le phénomène de localisation

Modélisation de l'effet de l'hydrogène sur le comportement superélastique des AMF à base de NiTi

En raison de leur biocompatibilité, les fils superélastiques en Ni-Ti sont utilisés avec succès dans les traitements orthodontiques. Des résultats expérimentaux montrent une dégradation des propriétés mécaniques fonctionnelles en présence d'hydrogène. Nous proposons, dans cette étude, de prendre en compte cette fragilisation par hydrogène dans la modélisation du comportement des alliages Ni-Ti. Pour cela, des résultats expérimentaux obtenus pour différents temps de chargement par hydrogène à température ambiante sont utilisés. Les fils orthodontiques sont chargés, par voie cathodique en hydrogène, en utilisant une densité de courant constante 20A/m² de 6 à 72 heures dans une solution aqueuse de NaCl 0,9% à la température ambiante. Les courbes contrainte-déformation obtenues permettent en particulier d’étudier l’influence de l’hydrogène sur les contraintes critiques de transformation martensitique directe et inverse. A l’aide de la deuxième loi de Fick, les évolutions des températures de transformation directe et inverse en fonction de la concentration moyenne d’hydrogène absorbé sont alors déduites et intégrées dans une loi de comportement dédiée aux alliages Ni-Ti. Celle-ci est ensuite implémentée dans le code éléments finis Abaqus et permet alors une comparaison avec les observations expérimentales

Impact of microstructural mechanisms on ductility limits

In order to investigate the effects of microstructure and deformation mechanisms on the ductility of multiphase steels, a formability criterion based on loss of ellipticity of the boundary value problem is coupled with an advanced multiscale model accounting for intragranular microstructure development and evolution. The resulting large strain elastic–plastic single crystal constitutive law (based on crystal plasticity) is incorporated into a self-consistent scale-transition scheme. The present contribution focuses on the relationship between the intragranular microstructure of B.C.C. steels and their ductility. The model allows interesting comparisons in terms of formability limits for different dislocation networks, during monotonic loading tests applied to polycrystalline aggregates.ArcelorMittal & CNR

Impact of intragranular microstructure development on ductility limits of multiphase steels

In this paper, the effects of microstructure and deformation mechanisms on the ductility of multiphase steels are investigated. To this end, a formability criterion based on loss of ellipticity of the boundary value problem is coupled with an advanced multiscale model accounting for intragranular microstructure development and evolution. The spatially heterogeneous distribution of dislocations inside the grain is represented by three types of local dislocation densities. The resulting large strain elastic-plastic single crystal constitutive law (based on crystal plasticity) is incorporated into a self-consistent scale-transition scheme. The present contribution focuses on the relationship between the intragranular microstructure of B.C.C. steels and their ductility. The model allows interesting comparisons in terms of formability limits for different dislocation networks, during monotonic loading tests applied to polycrystalline aggregates.ArcelorMitta