金属3D打印熔融与凝固过程的SFEM-SPH模拟研究

Selective laser melting is an important issue in 3D printing problem, which usually involves complex physical processes associated with multi-scale, multi-physical field and multi-phase phenomena. It is difficult to observe specific physical phenomena through experimental approach. Meanwhile, the expensive development cycle of material technology test is time-consuming. It is therefore attractive to reveal the relevant mechanism of selective laser melting process using numerical approach so as to reduce the development cycle and cost of experiment. Moreover, it is difficult for the existing numerical methods to achieve the real coupling of flow-stress-temperature in 3D printing process. This project intends to develop a novel coupling approach of non-linear smooth finite element method (SFEM) with smoothed particle hydrodynamic (SPH) to simulate the selective laser melting in 3D printing process, i.e., metal powder melting, pool flow and solidification, thermal stress and deformation. The main contents are as follows: 1) Investigate the theory of nonlinear SFEM with multi-physical fields. Based on the smoothing strain technique, the smoothing strain rate technique, the smoothing temperature gradient technique, and the thermo-elastic-plastic constitutive model are developed to establish the nonlinear SFEM method for simulating the thermo-solid coupling problem. 2) Study the SPH method with phase change multi-physical field. The heat source model, surface tension model and phase change latent heat model are incorporated in the SPH model to simulate the powder melting, molten pool flow and solidification. 3) Develop the interface processing technology and the element-particle conversion technology. The coupling approach of SFEM with SPH is proposed to model the flow-stress-temperature interaction problems.

金属激光选区熔融是一类关键的3D打印技术，其工艺涉及多尺度、多物理场、多相的复杂物理过程。采用实验手段很难直接观察到具体物理现象，迫切需要发展可靠的数值模拟手段揭示其3D打印过程中流动-应力-温度耦合作用机理，以缩短产品研发周期，减少成本。本项目拟发展模拟金属激光熔融3D打印过程的非线性光滑有限元（SFEM）与光滑粒子流体动力学（SPH）耦合方法，实现3D打印过程中金属粉末熔化、熔池流动与凝固、热应力与变形的模拟。主要研究以下几方面的内容：1）研究多物理场非线性SFEM理论，发展光滑应变率技术与光滑温度梯度技术，引入热-弹塑性本构，建立模拟热-固耦合的非线性SFEM；2）研究含相变多物理场的SPH方法，发展热源模型、表面张力模型、相变潜热模型，建立模拟粉末熔化、熔池流动与凝固的SPH方法；3）研究界面处理技术与单元粒子相互转化技术，耦合SFEM与SPH方法，实现流动-应力-温度的真正耦合。

金属激光选区熔融是一类关键的3D打印技术，其工艺涉及多尺度、多物理场、多相的复杂物理过程。采用实验手段很难直接观察到具体物理现象，迫切需要发展可靠的数值模拟手段揭示其3D打印过程中流动-应力-温度耦合作用机理，以缩短产品研发周期，减少成本。项目主要通过分别利用光滑有限元（SFEM）构建热-固耦合模型和光滑粒子流体动力学（SPH）构建热-流耦合模型，并开发模拟热-流-固耦合问题的SFEM-SPH耦合方法，实现对金属粉末熔化、熔池流动和凝固过程模拟。依据项目申请书主要开展了以下研究：1）基于温度梯度光滑技术和光滑应变率技术，分别建立了基于更新拉格朗日格式求解瞬态热传导问题和结构运动变形的光滑有限元模型。并考虑温度与应力的耦合作用，发展了求解热-固耦合问题的非线性光滑有限元方法。2）发展了基于核函数梯度修正和人工粒子位移相结合的修正方法提高SPH方法的计算精度，基于质量、动量和能量守恒方程，建立了求解热-流耦合问题的SPH方法。3）提出了基于虚粒子方法的流固耦合算法和共轭传热算法，发展了模拟热-流-固耦合问题的SFEM-SPH耦合方法。4）发展了表面张力模型，提出了一种改进的SPH高精度格式，并引入高斯热源和相变潜热模型，发展了模拟金属粉末熔化、熔池流动及凝固过程的高精度SPH方法。5）基于单元粒子耦合算法及单元粒子转化算法，建立了模拟金属激光选区熔融3D打印过程的热-流-固SFEM-SPH耦合方法。综上，项目通过对系列热-固耦合、热-流耦合、热-流-固耦合及激光选区熔融过程数值算例，对本项目所提出算法的计算精度、效率等进行了验证。

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