Additive manufacturing (AM) methods such as Aerosol Jet (AJ) printing allow the fabrication of structures via sintering of micro and/or nanoparticles, leading to microstructures that consist of various combinations of pore and grain sizes. It has been reported that AJ printed and sintered silver micropillars show an unusual behavior of high stiffness and high strain-to-failure for structures with high porosity and vice versa (Saleh et al. 2018 [1]). This behavior, however, is accompanied by the stiffer structures having smaller grain sizes and softer structures having larger grain sizes. To explain the physics of this behavior where a trade-off between hardening caused by size effects (grain refinement and gradients) and softening caused by porosity is expected to play a critical role, a multi-scale modeling approach is proposed in this paper. The model formulation consists of a continuum dislocation dynamics (CDD) framework, coupled with continuum plasticity and finite element analysis. The dislocation dynamics formulation is introduced into a user material subroutine and coupled with a finite element commercial solver, in this case, LS-DYNA, to solve the model in three-dimensional scale with the same size as the AM micropillars. The results from the model capture the general trends observed in compression tests of AM micropillars. In particular, it is shown that the grain size and dislocation density have a disproportionately higher influence over the mechanical deformation of metallic structures when compared to the porosity. These results show that the behavior of AM structures in the plastic regime is dominated by grain size effects rather than porosity. Some limitations of the model and possible future refinements are discussed. The paper provides an important analytical framework to model the mechanical behavior of AM structures with internal porosity in the plastic regime.

诸如Aerosol Jet（AJ）印刷之类的增材制造（AM）方法允许通过微米和/或纳米粒子的烧结来制造结构，从而导致由孔隙和晶粒尺寸的各种组合组成的微观结构。据报道，对于具有高孔隙率的结构，AJ印刷和烧结的银微柱表现出不寻常的高刚度和高应变破坏性能（反之亦然）（Saleh等人，2018 [1]）。然而，这种行为伴随有具有较小晶粒尺寸的较硬结构和具有较大晶粒尺寸的较软结构。为了解释这种行为的物理现象，其中尺寸效应（晶粒细化和渐变）导致的硬化与孔隙率造成的软化之间的权衡取舍有望发挥关键作用，本文提出了一种多尺度建模方法。该模型公式由连续位错动力学（CDD）框架，连续性可塑性和有限元分析组成。位错动力学公式被引入到用户材料子例程中，并与有限元商用求解器（在本例中为LS-DYNA）耦合，以在三维尺度上求解与AM微型桩相同大小的模型。该模型的结果反映了在AM微柱压缩测试中观察到的总体趋势。特别地，显示出与孔隙率相比，晶粒尺寸和位错密度对金属结构的机械变形具有不成比例的更高的影响。这些结果表明，AM结构在塑性状态下的行为主要受晶粒尺寸效应而不是孔隙率的影响。讨论了模型的一些局限性和未来可能的改进。本文提供了一个重要的分析框架，以模拟具有塑性状态下内部孔隙的AM结构的力学行为。