E. Patoor

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.

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

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.

Optimisation of mechanical properties of Ti–Nb binary alloys for biomedical applications

b-Ti alloys consisting of non-cytotoxic elements have been extensively studied for biomedical applications with regard to their mechanical properties as shape memory effect and superelasticity. The success of implants is directly related to the principle of osseointegration, a process of implant–bone interaction. This process depends on the loading conditions at the surrounding bone, which are affected by the geometrical and material properties of the prosthesis (Girod et al. 2010). To reach mechanical compatibility, the ‘stress shielding’ effect should be avoided. This effect is due to the absence of mechanical stress and the large difference in stiffness dependent on elastic modulus between the host bone and the implant material, which can induce bone atrophy and loss of implant (Niinomi 2008; Sumitomo et al. 2008). This Young’s modulus should be as close as possible to that of the host bone (20 GPa) to achieve a homogeneous load transfer between implant and bone (Laheurte et al. 2010). In addition to low Young’s modulus, high strength is also required for such applications to endure stresses. However, it is not easy to achieve low Young’s modulus and high strength simultaneously. The aim of our study was to find adequate strategies for combining superelasticity, relatively high strength while keeping a low elastic modulus. Severe cold-rolling deformation followed by a short heat treatment resulting in nanostructure is shown to be effective in improving strength and superelasticity without sacrificing low Young’s modulus values.

Application to Shape Memory Devices

Shape memory alloys play a large role in the development of intelligent systems. Design of these systems needs to know the global relationship between the applied forces and the conjugated kinematical variables for shape memory elements. Such a relation is strongly non linear and temperature dependent. Aim of this work is to derive these relations starting from the definition of a macroscopic criterion for stress induced transformation. This transformation criterion is deduced from micromechanical modelling and takes into account the dissymmetry observed between tensile and compressive tests in these materials. Structure calculations aspects are taken into account using the framework of beam theory. To illustrate these problems two loading cases are solved. First example deals with the analytical solution for pure torsion of a cylindrical beam. Second example deals with more complex loading conditions applying the Bresse integrals technique to superelastic structures. Numerical results obtained in that way well agree with experimental determination performed on superelastic beam in bending and on a helical spring.

Phenomenological Model for Phase Transformation Characteristics of Textured Shape Memory Alloys

In the present study, a new transformation criterion that includes the effect of tensioncompression 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 a SMA polycrystal, using a self-consistent micromechanical model previously developed by Patoor et al. (Patoor, E., Eberhardt, A., Berveiller, M., 1996. Micromechanical Modelling of Superelasticity in Shape Memory Alloys. Journal de Physique IV 6, C1 277) 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.