为研究合金化对沉淀强化行为的影响，采用第一性原理方法计算了二元Ti-xM (M = Al、V、Cr、Mn、Fe、Co、Ni、Zr、Nb、Mo、Ta、W)合金弹性模量随成分的变化，提出了弹性模量Mo当量概念，以高效计算复杂成分钛合金(如Ti-Al-V合金以及Ti55521)的弹性模量；结合弹性模量及Russell-Brown沉淀强化模型，研究了二元Ti-xM (M = V、Cr、Mn、Fe、Co、Ni、Nb、Mo、Ta、W)合金以及Ti55521合金中的沉淀强化。结果显示，在体积分数及沉淀相颗粒尺寸相同的情况下，Co、Fe、W、Mo、Ni、Mn沉淀强化作用较强，Cr、Nb、Ta强化作用居中，V强化作用最弱。随合金元素含量x增加，沉淀强化作用均有所增强。热机械处理Ti55521合金经短时时效后，沉淀强化作用有所减弱，但长时时效后，沉淀强化效果增强。

Titanium alloys have shown wide application potential in the areas such as aerospace and marine because of their comprehensive properties, including high specific strength, ductility, corrosion resistance, and damage tolerance. Given the rapid development of new-generation advanced military hardware toward large scale, high-speed, light-weight, and structure-complicated titanium alloys experience increasingly harsh application environments. Thus, developing novel high-strength and high-toughness titanium alloys is an important direction in the field of titanium research. To date, the compositional design of titanium alloys is performed within the framework of some empirical rules without involving strengthening and toughening mechanisms. This kind of approach can hardly achieve an accurate and efficient material design. Based on the abovementioned background, the effect of alloying on the precipitation strengthening of the α + β dual-phase titanium alloy was studied by using the first-principles exact muffin-tin orbital method in combination with a coherent potential approximation. High-strength and high-toughness titanium alloys obtain its high strength through precipitation strengthening in the β-phase matrix with α-phase precipitates. The influence of alloying on the precipitation strengthening is crucial to the understanding and prediction of alloy strength and rational alloy design. In the present work, the elastic moduli and lattice constants of a serial binary titanium alloy Ti-xM (M = Al, V, Cr, Mn, Fe, Co, Ni, Nb, Mo, Ta, W) against the composition x were calculated using the first-principles method. Based on which, the elastic moduli of the titanium alloy with a complex composition (such as Ti-Al-V and Ti55521) were evaluated using the concept of elastic Mo equivalency. Subsequently, the precipitation strengthening of binary titanium alloys and the Ti55521 alloy was evaluated by using the elastic modulus within the framework of the modulus strengthening model. Result shows that alloying elements, such as Co, Fe, W, Mo, Ni, and Mn, have the strongest precipitation strengthening effect for the same particle size and volume fraction of α precipitates, followed by Cr, Nb, and Ta, whereas V is the weakest. The strengthening effect increases with the content of alloying element. For the Ti55521 alloy prepared by using a thermal mechanical process, subsequent short-time aging weakens the precipitation strengthening effect compared with long-time aging.