A fast-acting, mean-field method for simulating precipitation of the γ′′ and γ′ phases during aging of superalloy 718 following super-delta-solvus solution treatment was formulated and validated using observations in the literature. The approach assumed classical (homogeneous) nucleation and diffusion-controlled growth (N&G) of disk/ellipsoidal-shaped-γ′′ and spherical-γ′ particles. For the γ′′ precipitates in particular, the evolution equations for both nucleation and growth incorporated corrections for the non-spherical shape, assuming a fixed aspect ratio. In addition, special attention was paid to the choice of input material properties for simulations. These parameters included the bulk free energies of transformation, particle-matrix (misfit) elastic strain energy (for γ′′), effective diffusivities, and the γ′′–γ and γ′–γ interface energies. The applicability of the diffusivities and interface energies chosen for the N&G simulations was established by their consistency in replicating previously measured rate constants for the diffusion-controlled coarsening of both γ′′ and γ′. The N&G formulation was discretized to obtain numerical (spreadsheet) solutions via the Kampmann–Wagner approach. Simulation results for the temporal evolution of volume fraction and average size of the precipitates showed good agreement with experimental measurements. The sensitivity of model predictions to various input parameters was also quantified.

速效，用于模拟所述的沉淀平均场法γ '和γ超合金718的老化以下超Δ-固溶线固溶处理时'相配制和使用文献中观测进行验证。该方法假定盘/椭圆形γ ′和球形γ ′粒子具有经典（均质）成核和扩散控制的生长（N＆G）。对于γ尤其是''析出，假定固定纵横比，则成核和生长的演化方程都包含了对非球形形状的校正。此外，还特别注意了模拟输入材料属性的选择。这些参数包括转换的体自由能，粒子矩阵（失配）弹性应变能（对于γ ′），有效扩散率以及γ ′′- γ和γ′ - γ界面能。N＆G模拟所选择的扩散率和界面能的适用性是通过它们在复制先前测得的速率常数以进行两个γ的扩散控制粗化的一致性而建立的′′和γ ′。通过Kampmann–Wagner方法离散化N＆G公式以获得数值（电子表格）解决方案。沉淀物的体积分数和平均尺寸随时间变化的模拟结果与实验测量结果吻合良好。还对模型预测对各种输入参数的敏感性进行了量化。