钛及钛合金在超低温下弹性常数与各向异性第一性原理分析

The Study of Ultra-Low Temperature Influence on the Elastic Constants and Anisotropy for Titanium and Titanium Alloys

摘要:

钛合金具有高比强度、良好的耐腐蚀性及优异的高低温性能。尤其在超低温环境下，钛合金展现出的优秀力学性能，使其成为深空探测、液氢燃料容器等极端工况下的关键材料。一般情况下，钛及其合金的强度随使用温度的降低逐渐提高，同时保持良好的塑性。然而，某些钛合金(如Ti-6Al-4V合金)在变形温度低于70 K时塑性显著降低。针对这一问题，基于第一性原理计算，构建了2×2×2的Ti超晶胞(16个Ti原子)和Ti15-Al体系(15个Ti原子、1个Al原子)模型，结合声子谱计算，研究了基态及有限温度下纯钛和Ti15-Al体系的弹性常数。通过对比分析，量化了Al元素对密排六方晶体结构钛的弹性常数及弹性各向异性的影响，揭示了超低温度环境对Ti及Ti15-Al合金弹性各向异性与弹性常数的影响规律。结果表明，HCP钛晶体在弹性性能上具有显著的各向异性，Al元素的添加可有效降低其弹性各向异性。在2—300 K温度范围内，纯钛的弹性各向异性基本不受温度变化影响，而Ti15-Al体系的弹性各向异性随温度降低发生显著变化：参数Δs₁逐渐降低，Δs₂逐渐升高，并与Ti的对应变化曲线相交，交点对应的温度为分别为72和77 K。此外，随着温度降低，纯钛的弹性模量数值随温度降低逐渐增加，变化率基本保持不变，而Ti15-Al合金的弹性模量却表现出先增加后降低的趋势，在约70 K处出现转折，与Ti15-Al合金韧-脆转变温度相吻合。(专精特新·特殊环境材料服役行为专辑十五之九)

Abstract:

Titanium alloys are widely used in the aerospace industry due to their high specific strength and excellent mechanical properties at both high and low temperatures. As the deformation temperature decreases， the strength of pure titanium increases， and it maintains excellent plasticity. However， titanium alloys， such as Ti-6Al-4V， exhibit a significant reduction in plasticity when the deformation temperature drops below 70 K. To address this issue， the present study constructs computational models of a 2×2×2 Ti supercell （16 Ti atoms） and a Ti15-Al system （15 Ti atoms and 1 Al atom）. First-principles calculations combined with phonon analysis are employed to study the elastic constants of titanium alloys at ultra-low temperatures. The elastic constants of both pure titanium and Ti15-Al systems at the ground state and at finite temperatures are calculated separately. The impact of the addition of Al element on the elastic constants and elastic anisotropy of the hexagonal close-packed titanium structure is analyzed and compared. The elastic anisotropy of titanium alloys at various ultra-low temperatures is quantitatively characterized， and the influence of temperature on the elastic anisotropy and constants of both Ti and Ti15-Al alloys is thoroughly discussed. The results show that HCP titanium exhibits significant elastic anisotropy， and the addition of Al reduces the elastic anisotropy of the Ti15-Al alloy compared to pure titanium. In the temperature range of 2 K to 300 K， the elastic anisotropy of pure Ti remains relatively constant， while that of Ti15-Al undergoes significant changes with decreasing temperature： the Δs₁ parameter gradually decreases， while Δs₂ increases. These two curves eventually intersect at temperatures of 72 K and 77 K， respectively. As the temperature decreases， the elastic modulus of pure titanium remains nearly constant， while the elastic modulus of Ti15-Al alloy shows a continuous increasing trend， with a notable turning point around 70 K， which closely coincides with the ductile-to-brittle transition temperature of the Ti15-Al alloy.