Mechanism for Low Modulusin β-Type Titanium or Zirconium Alloys with Body-Centered Cubic Structure
Recently,β-type titanium and zirconium alloys with body-centered cubic(bcc)structure for biomedical applications,have been attracted considerable attention due to their relatively low moduli,which are essential to avoid the bone degradation and the absorption originating from the difference in the elastic modulus between human bone and implant.Nonetheless,the mechanism for low elastic modulus,especially in the ternary and quaternary β-type titanium and zirconium alloys(such as Ti-Nb-Sn,Zr-Nb-Mo,Zr-Si-Nb,Zr-Mo-Sn,Ti-Nb-Ta-Zr and Ti-Nb-Zr-Sn alloys),has not yet been elucidated in detail,although a deeper under standing on this issue could pave the way for further decreasing the elastic modulus of biomedical β-type alloys.It is well known that the elastic modulus of β-type alloys with bcc structure is closely associated with their single-crystal elastic constants(SECs).In general,these elastic parameters(i.e.,C11,C12 and C44)can be obtained directly in β-type single crystal alloys by conventional resonant ultrasound spectroscopy.However,in most ternary β-type titanium or zirconium alloys with low elastic modulus,it is quite hard to fabricate the corresponding single crystals for obtaining their SECs directly because of the low bcc-structural(β phase)stability.In this study,four types of representative ternary β-type polycrystalline titanium and zirconium alloys with low elastic modulus(including the cold rolled plus annealed Ti-33Nb-4Sn and Ti-35Nb-4Sn alloys,together with the solution treated Zr-12Nb-4Sn and Zr-4Mo-4Sn alloys)had been selected,and the in situ synchrotron X-ray diffraction(SXRD)technique was carried out to obtain the experimental values of diffrac-tion elastic constants(DECs)for their corresponding {110} β,{200} β,{211} β and {310} β crystallographic planes.Meanwhile,through running repeatedly Eshelby-Kroner-Kneer elastoplastic self-consistent model with different hypothetical SECs and evaluating the minimum weighted sum of squared residuals between the calculated DECs output values and the experimental DECs values,the SECs of these ternary β-type polycrystalline titanium and zirconium alloys were successfully extracted even without fabricating their corresponding single crystals,with the aim to reveal the relationship between the elastic parameters and the average number of valence electrons(e/a)and further clarify the mechanism for low modulus in β-type Tior Zr alloys.It was found that in comparison to binary β-type TiCr,TiV and TiNb single crystal alloys,the cold rolled plus annealed Ti-33Nb-4Sn and Ti-35Nb-4Sn alloys,as well as the solu-tion treated Zr-12Nb-4Sn and Zr-4Mo-4Sn alloys exhibited slightly lower shear modulus C'regarding to {110}＜1(1-)0＞shear and much lower shear modulus C 4with respect to {001}＜100＞shear.A further analysis of Hill approximation revealed that in ternary β-type Ti-33Nb-4Sn,Ti-35Nb-4Sn,Zr-12Nb-4Sn and Zr-4Mo-4Sn alloys,the relatively low elastic modulus EH was closely related to their low shear moduli C'and C44,which was obviously different from the case of the binary β-type TiCr,TiV and TiNb single crystal alloys where the elastic moduli EH were dominantly controlled by shear modulus C'and decreased monotonically with the decrease of e/a.To be specific,referring to the cold rolled plus annealed Ti-33Nb-4Sn and Ti-35Nb-4Sn alloys,due to the effect of a large number of dis-location tangles and grain boundaries introduced by the thermo-mechanical treatment on the suppression of α"martensitic transforma-tion accomplished by the atomic shear and shuffle processes,β phase with less β-stabilizing elements could survive at room tempera-ture against the martensitic transformation from β to α",and still remained the low β phase stability in regards to the resistance to the{ 110}＜1(1-)0＞shear(i.e.,shear modulus C')and especially to the {001}＜100＞shear(i.e.,shear modulus C44).Similarly,in the case of the solution treated Zr-12Nb-4Sn and Zr-4Mo-4Sn alloys,the composition design ensured less content of β stabilizers,and thus the low β phase stability represented by the slightly lower shear modulus C'regarding to the { 110}＜1(1-)0＞shear and much lower shear modulus C44 with respect to the {001}＜100＞shear than those of binary β-type Ti-based alloys,could lead to the remarkable decrease in the elastic moduli EH.The above results showed that in addition to the shear modulus C'with respect to the {110}＜1(1-)0＞shear,the decrease in the shear modulus C44 in regards to the {001}＜100＞shear could also exert potential influence on decreasing the elastic modulus EH in the present β-type polycrystalline alloys.Consequently,with the combination of the appropriate compositional design(adjusting β-stabilizing elements)and thermo-mechanical treatment(cold rolling and low-temperature annealing),both of the shear moduli C'and C44 could be concurrently reduced purposefully with the aim to achieve the ultralow Young's modulus EH close to that of human bone in β-type Ti or Zr polycrystalline alloys.These experimental results challenged the criterion for fabricating the biomedical low modulus alloys through only reducing shear modulus C'by adjusting alloy composition,and it might open a new avenue for further decreasing the elastic modulus of β-type alloys for the biomedical applications in a broader context.
β-type Ti or Zr alloyslow elastic modulussynchrotron radiation X-ray diffraction(SXRD)elastic constants
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