We employ a free energy density for Mg–Al alloys that is dependent on concentration, strain, and temperature, and derived from quantum mechanical calculations by Ghosh & Bhattacharya (Acta Mater 193:28–39, 2020) , to model the dynamic precipitation of the Mg\(_{17}\)Al\(_{12}\) phase during creep experiments in Mg–Al alloys. Our calculations show that the overall volume fraction of the dynamically formed precipitates is influenced by stress, and furthermore, this influence is anisotropic and asymmetric. Specifically, when the stress is volumetric or along the c-axis direction, the volume fraction of the precipitate phase is greater in compression and lower in tension. Surprisingly, stress along the a- or b-axis directions does not alter the volume fraction of the precipitates. The resistance to creep is improved by the presence of finely dispersed precipitates with a small aspect ratio, closer to spherical or ellipsoidal in shape and high number density. A greater volume fraction of these fine particles are produced during compressive creep tests than tensile creep experiments and thereby explaining the higher creep rate observed in tension than in compression in these alloys. Overall, our calculations explain the tension–compression asymmetry of the creep rate observed in creep experiments in Mg–Al alloys (Agnew et al. in Magn Technol 2000:285–290, 2000; Agnew et al. in Magn. Alloys Appl. 685–692, 2000).

我们采用依赖于浓度、应变和温度的 Mg-Al 合金自由能密度，并从 Ghosh & Bhattacharya (Acta Mater 193:28–39, 2020) 的量子力学计算得出，以模拟镁\(_{17}\)铝\(_{12}\)Mg-Al 合金蠕变实验中的相。我们的计算表明，动态形成的析出物的总体积分数受应力的影响，而且这种影响是各向异性和不对称的。具体而言，当应力为体积应力或沿 c 轴方向时，析出相的体积分数在压缩时较大，在拉伸时较小。令人惊讶的是，沿 a 轴或 b 轴方向的应力不会改变沉淀物的体积分数。通过存在具有小纵横比、形状更接近球形或椭圆体且数量密度高的细分散沉淀物，提高了抗蠕变性。与拉伸蠕变实验相比，压缩蠕变试验期间产生的这些细颗粒的体积分数更大，从而解释了在这些合金中观察到的拉伸蠕变速率高于压缩蠕变速率。总的来说，我们的计算解释了在 Mg-Al 合金蠕变实验中观察到的蠕变速率的拉伸 - 压缩不对称性（Agnew 等人在 Magn Technol 2000:285-290, 2000 中；Agnew 等人在 Magn. Alloys Appl. 685 –692, 2000)。