Study On Elastic Properties Of Magnesium Alloys By Ultrasonic Resonance Spectroscopy And First Principle Calculation

The bone trauma caused by the rapid development of transportation,construction and other industries,as well as the rapid aging of the population,has been the main health problems of Chinese residents.Therefore,the development of magnesium alloy degradable orthopedic implant materials with good biocompatibility is becoming more and more urgent.The high elastic modulus,poor room temperature plasticity of the existing clinically approved Mg based biomedical bone implant materials,which origins from the hexagonal structure,leads to high processing difficulty and low yield.In order to obtain magnesium alloy materials with excellent comprehensive properties,the elastic properties of Mg-Al-Zn alloy with hexagonal close packed crystal structure,Mg-Sc alloy with body centered cubic structure and Mg-Li alloy with body centered cubic structure were studied by micromechanical mechanism,ultrasonic resonance spectrum method and first principal calculation method.The high strength and high toughness magnesium alloys with elastic modulus perfectly matching with human bones were obtained by composition and crystal orientation design.Based on the elastic constitutive relation of anisotropic polycrystals with hexagonal close packed single crystals,a micromechanical method（inverse Voigt-Reuss-Hill approximation）for extracting the elastic constants of hexagonal close packed single crystals from the elastic parameters of anisotropic polycrystals is proposed in this paper.The full set of elastic constants of the polycrystal can be measured by resonance ultrasonic spectrum and electromagnetic acoustic resonance method.The elastic constants of pure Mg and Ti₃SiC₂ single crystals obtained by the inverse Voigt-Reuss-Hill approximation are in good agreement with the literature values,indicating that the inverse Voigt-Reuss-Hill approximation has high reliability in obtaining elastic constants with hexagonal close packed crystal.Based on the inverse Voigt-Reuss-Hill approximation,the influence of composition and crystal orientation on the Young’s modulus in Mg-Al-Zn alloys were studied by extracting the elastic constants from the elastic constants of Mg-Al-Zn polycrystals withα-Mg single phase and Mg-Al-Zn polycrystals withα-Mg and Mg₁₇Al₁₂ two phases.The results showed that all the Mg-Al-Zn alloys were almost isotropic,and Al would slightly reduce the Young’s modulus and elastic anisotropy of Mg-Al-Zn single crystals,and the Young’s modulus of Mg-3Al-1Zn and Mg-9Al-1Zn with different orientations ranges from about 42 GPa to 50 GPa.Besides,Mg₁₇Al₁₂single crystal,as a common intermetallic compound in Mg-Al-Zn alloys,has obvious elastic anisotropy,and its elastic constants are:c_{1 1}=88.3 GPa,c_{1 2}=31.8 GPa,c₄₄=19.1 GPa,Zener anisotropy parameter is 0.68.Furthermore,the insignificant elastic mismatch betweenα-Mg matrix and Mg₁₇Al₁₂ precipitations within Mg-Al-Zn biphasic will lead to a small elastic interaction between the two phases.Therefore,the formation of would slightly increase the Young’s modulus of Mg-Al-Zn alloy,but further reduce its elastic anisotropy,and the Young’s modulus of biphasic Mg-9Al-1Zn with different orientations ranges from about 42 GPa to 48 GPa.The elastic properties of body centered cubic Mg-Sc with high strength and good plasticity were studied by resonance ultrasonic spectrum,electromagnetic acoustic resonance and first-principle calculations.The results showed that the elastic constants of Mg-20.5 at.%Sc polycrystalline with high strength（YS～270 MPa）and good plasticity（δ～30%）were:c_{1 1}=64.1 GPa,c_{1 2}=27.4 GPa,c₄₄=18.4 GPa.And the elastic constants,c_{1 1},c_{1 2},c₄₄,Young’s modulus E and shear modulus G gradually increases while the temperature decreases from 300 K to 0 K.In addition,the 0 K test results are in good agreement with the first-principle calculation results.According to the first-principle calculations,the elastic constants c₁₁,c₁₂,c₄₄ increase with Sc content.In addition,all the Mg-Sc single crystals own high elastic anisotropy,with highest Young’s modulus along<111>crystal direction(E₁₁₁),and lowest Young’s modulus along<100>crystal direction(E_{10 0}).The E₁₁₁ of Mg-Sc single crystal increases with the increasing of Sc content However,the Sc content had little effect on the value of E₁₀₀,with value range from 31 GPa to 34 GPa.Therefore,Mg-Sc single crystal with<100>crystal direction,or Mg-Sc polycrystals with a texture in which the crystallographic direction with<100>crystal direction is oriented along one direction,are promising candidates for obtaining effective biodegradable orthopedic implants.The comprehensive mechanical properties of Mg-Li alloys with body centered cubic structure could be significantly improve by addition of Al element.The elastic constants of Mg-40 at.%Li-5 at.%Al single crystal with high strength（YS～400MPa）and good plasticity（δ～20%）were:=36.2 GPa,=20.4 GPa,=33.2GPa.Based on the transformation of elastic constant tensor,the lowest Young’s modulus of Mg-40Li-5Al single crystal along<100>crystal direction is about 21.4GPa,which perfectly matches with those of human bone’s.Different from the room temperature softening phenomenon of traditional Mg-Li-Al alloy,the Mg-40Li-5Al alloy shows a unique aging enhancement phenomenon during room temperature aging.After aging at room temperature for 1000 h,its Vickers hardness,elongation rate and compressive yield strength are 168.5±3.5 HV,～20%and～435 MPa respectively.Moreover,the Young’s modulus of Mg-40Li-5Al single crystal along<100>crystal direction decreases during room temperature,which could be attributed to the precipitation or dissolution of Al-richθphase.Therefore,Mg-Li-Al single crystal with<100>crystal direction,or Mg-Li-Al polycrystals with a texture in which the crystallographic direction with<100>crystal direction is oriented along one direction,are promising candidates for obtaining effective biodegradable orthopedic implants.