A. Eberhardt

Constitutive equations for polycrystalline thermoelastic shape memory alloys.: Part I. Intragranular interactions and behavior of the grain

A micromacro thermomechanical modelization of grain behavior of a polycrystalline shape memory alloy is presented. This model, based on thermodynamical approach and identification of stress sources, takes into account experimental observations of the transformation microstructure. Because plates of martensite are usually observed to appear in domains, similar to subgrains, we show that determination of average global fraction of martensite is not sufficient to describe grain behavior. A better approximation is done by taking an average fraction of martensite in each domain as internal variables. With these parameters a full description of evolution of material can be made. We point out that free energy of the material depends on an interaction matrix between martensites. Moreover the calculation of this matrix for CuAlBe alloys allows one to determine the interface between domains. The results of this study are used to model the whole behavior of the polycrystalline material with a self-consistent method.

Mechanical properties of low modulus ββ titanium alloys designed from the electronic approach

Titanium alloys dedicated to biomedical applications may display both clinical and mechanical biocompatibility. Based on nontoxic elements such as Ti, Zr, Nb, Ta, they should combine high mechanical resistance with a low elastic modulus close to the bone elasticity (E=20 GPa) to significantly improve bone remodelling and osseointegration processes. These elastic properties can be reached using both lowering of the intrinsic modulus by specific chemical alloying and superelasticity effects associated with a stress-induced phase transformation from the BCC metastable beta phase to the orthorhombic alpha(″) martensite. It is shown that the stability of the beta phase can be triggered using a chemical formulation strategy based on the electronic design method initially developed by Morinaga. This method is based on the calculation of two electronic parameters respectively called the bond order (B(o)) and the d orbital level (M(d)) for each alloy. By this method, two titanium alloys with various tantalum contents, Ti-29Nb-11Ta-5Zr and Ti-29Nb-6Ta-5Zr (wt%) were prepared. In this paper, the effect of the tantalum content on the elastic modulus/yield strength balance has been investigated and discussed regarding the deformation modes. The martensitic transformation beta-->alpha(″) has been observed on Ti-29Nb-6Ta-5Zr in contrast to Ti-29Nb-11Ta-5Zr highlighting the chemical influence of the Ta element on the initial beta phase stability. A formulation strategy is discussed regarding the as-mentioned electronic parameters. Respective influence of cold rolling and flash thermal treatments (in the isothermal omega phase precipitation domain) on the tensile properties has been investigated.

Strain rate sensitivity in superelasticity

This paper deals with the influence of martensitic transformation latent heat on the superelastic behaviour modelling. Exothermic and endothermic effects are responsible for a strong evolution on the temperature field inside the material that modifies its mechanical response. This is responsible for a strain rate effect that is taken into account by introducing a coupling equation between the production rate of martensite and the temperature change, into a micro–macro modelling of the superthermoelastic behaviour with the assumption that the temperature field remains uniform but different to the test temperature imposed. Numerical simulations so obtained show a good agreement with experimental results performed on Cu-based superelastic alloys.

Interphase boundary sliding at high temperature in two-phase (α/β)-brass bicrystals

Abstract High-temperature phase-boundary sliding has been studied by simple shear creep tests in two-phase (α/β)-brass bicrystals obtained by diffusion in the solid state. The constitutive law obtained is of the form σ∼ τn in which the exponent n is equal to 1 for low stresses and to 2 for stresses greater than a limiting value. To account for the experimental results, two mechanisms for sliding accommodation were considered, i.e., diffusion in the neighbourhood of phase-boundary asperities for low stresses and dislocation movement during deformation for higher stresses. The asperities, which develop in the phase boundary during the sliding, arise from the interaction between the interface and the dislocations of the β phase correlated with a phase transformation.

Interaction of bone-dental implant with new ultra low modulus alloy using a numerical approach

Although mechanical stress is known as being a significant factor in bone remodeling, most implants are still made using materials that have a higher elastic stiffness than that of bones. Load transfer between the implant and the surrounding bones is much detrimental, and osteoporosis is often a consequence of such mechanical mismatch. The concept of mechanical biocompatibility has now been considered for more than a decade. However, it is limited by the choice of materials, mainly Ti-based alloys whose elastic properties are still too far from cortical bone. We have suggested using a bulk material in relation with the development of a new beta titanium-based alloy. Titanium is a much suitable biocompatible metal, and beta-titanium alloys such as metastable TiNb exhibit a very low apparent elastic modulus related to the presence of an orthorhombic martensite. The purpose of the present work has been to investigate the interaction that occurs between the dental implants and the cortical bone. 3D finite element models have been adopted to analyze the behavior of the bone-implant system depending on the elastic properties of the implant, different types of implant geometry, friction force, and loading condition. The geometry of the bone has been adopted from a mandibular incisor and the surrounding bone. Occlusal static forces have been applied to the implants, and their effects on the bone-metal implant interface region have been assessed and compared with a cortical bone/bone implant configuration. This work has shown that the low modulus implant induces a stress distribution closer to the actual physiological phenomenon, together with a better stress jump along the bone implant interface, regardless of the implant design.

Fatigue behavior of Cu-Al-Be shape memory single crystals

Abstract The fatigue behavior of Cu-Al-Be shape memory single crystals is studied in cyclic loading mechanical tests. Based on literature and on tensile tests performed at various temperatures, a model is proposed to explain the mechanism of fatigue. This model is based on the idea that during cyclings, the different zones of the samples spend various lengths of time in the martensitic state. During that time, martensite evolves because of the occurrence of some reordering or other diffusional phenomena inside, and consequently, the value of the martensite start temperature for each zone changes. The kinetics of the change in mechanical behavior along with the cycles, as a function of the test temperature, are accurately described by a Johnson–Mehl relation. Relaxation tests suggest that the mechanism described not only depends on time and temperature but is also re-enforced by the movement of the martensite-matrix interface. From the kinetics of this fatigue behavior, an empirical activation energy related to the mechanism is inferred for this Cu-Al-Be alloy.

Texture Evolution in Commercially Pure Al during Equal Channel Angular Extrusion (ECAE) as a Function of Processing Routes

FCC metals with different stacking fault energy (SFE), namely Al, Cu and Ag have been investigated for the evolution of crystallographic texture during ECAE deformation using Route A. Different materials with different SFE result in their characteristic textures. The results have been analysed on the basis of microstructural features and related established concepts on texture evolution in FCC metals during other deformation modes.

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 by the authors 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.

Experiments and Modelling of ECAE Textures of f.c.c. Polycrystals

FCC metals with different stacking fault energy (SFE), namely Al, Ag and Cu have been investigated for the evolution of crystallographic texture during ECAE deformation using Route A. Different materials with different SFE result in their characteristic textures. The results have been analysed on the basis of microstructural features and related established concepts on texture evolution in FCC metals.

Orthorhombic lattice deformation of CuAlBe shape-memory single crystals under cyclic strain

X-ray diffraction experiments were carried out to prove that X-ray methods can be used to assess strain-induced fatigue in CuAlBe shape-memory alloys. The pseudoelastic fatigue behaviour of CuAlBe single crystals presents a strong decrease of the critical stress of the martensitic transformation. During the fatigue test, the austenitic lattice exhibits a lattice distortion. This lattice distortion evolves during the fatigue test: the austenitic cubic lattice (β1) tends to transform gradually towards an orthorhombic one. Various hypotheses concerning this lattice distortion are proposed.