In the present research, a numerical modeling approach of the initial stage of consolidation during spark plasma sintering on the microscopic scale is presented. The solution of a fully coupled thermo-electro-mechanical problem also accounting for grain boundary and surface diffusion is found by using a staggered way. The finite-element method is applied for solving the thermo-electro-mechanical problem while the finite-difference method is applied for the diffusion problem. A Lagrange-based non-linear formulation is used to deal with the detailed description of plastic and creep strain accumulation. The numerical model is developed for simulating the structural evolution of the involved particles during sintering of powder compacts taking into account both the free surface diffusion of the particles and the grain boundary diffusion at interparticle contact areas. The numerical results obtained by using the two-particle model—as a representative volume element of the powder—are compared with experimental results for the densification of a copper powder compact. The numerical and experimental results are in excellent agreement.

在本研究中，在微观尺度上提出了火花等离子体烧结过程中固结初期的数值模拟方法。通过使用交错方式找到了一个解决了晶界和表面扩散的完全耦合的热电机械问题的解决方案。有限元方法用于解决热电机械问题，而有限差分方法用于解决扩散问题。基于拉格朗日的非线性公式用于处理塑性和蠕变应变累积的详细描述。建立了数值模型，用于模拟粉末压块烧结过程中涉及的颗粒的结构演变，同时考虑了颗粒的自由表面扩散和颗粒间接触区域的晶界扩散。通过使用两颗粒模型（作为粉末的代表性体积元素）获得的数值结果与用于铜粉坯的致密化的实验结果进行了比较。数值和实验结果吻合得很好。