1-15.An enhanced finite element model considering multi strengthening mechanisms in particle reinforced metal matrix composites

B.L. Xiao1*, J.F. Zhang1, Heiko Andrä2, X.X. Zhang1, Q.Z. Wang1, Z.Y. Ma1

1.Institute of Metal Research, Chinese Academy of Sciences
2.Fraunhofer Institute for Industrial Mathematics, Fraunhofer-Platz 1, Kaiserslautern 67663, Germany

Abstract: The properties of particle reinforced metal matrix composites (PRMMC) depend on the ingredient of the matrix, the morphology of the reinforcement and the interfacial properties, etc. These diverse influencing factors make PMMMC highly designable, but also increase the complexity of the design. At present, the design of PRMMC uses the traditional trial and error method, which usually requires a large amount of experimental preparation and testing. It is time-consuming, labor-intensive, high in cost and poor in applicability. Taking advantage of simulation aided design, it can be low cost, short cycle and good applicability. At the same time, the influence of the preparation process on the mechanical properties of the composite can be studied. However, the current finite element simulation of PRMMC lacks consideration of polyphase characteristics of the composite. It is difficult to balance reasonable elastoplastic constitutive relations and realistic virtual microstructures. In order to solve this problem, it is necessary to construct a realistic virtual 3D microstructure and set a reasonable elastoplastic constitutive relation for the particles and the matrix.

      Considering that the strengthening effect of PRMMC is mainly due to load transfer strengthening, grain boundary strengthening, residual stress/strain strengthening and plastic strain gradient strengthening. Taking full account of all the strengthening factors can characterize the mechanical properties of PRMMC accurately and providing a basis for the design of metal matrix composites. Therefore, it is necessary to optimize the existing finite element model for these strengthening mechanisms. First of all, a reasonable virtual microstructure of PMMMC can reflect effect of load transfer accurately. Secondly, considering that the particles can refine the grain of the matrix, this study used the Hall-Petch relationship to introduce the grain refinement strengthening into the existing constitutive relation. Thirdly, the quenching process was introduced before the simulation of the tensile process, and the thermal residual stress-strain strengthening of the near-interface region in the matrix was obtained. Last, in order to introduce the influence of strain gradient, this study introduces the plastic strain gradient theory in the constitutive relation of the matrix. 

        15 vol. % SiCp/2009Al was studied in this work. The applicability of the model was evaluated by comparing the tensile stress-strain curves obtained from experiments and simulations. As shown in Fig. 1, it can be found that the simulation results agree well with the experimental results when considering the grain refinement strengthening. The yield strength of the PRMMC with small particle size was underestimated when the grain refinement strengthening (5 μm Simulation = 290 MPa) was neglected. Because the different particle sizes caused a different strain gradient in the matrix, as shown in Fig. 2, even when the grain refinement strengthening was neglected, there are still size effect in the results. By combining specific strengthening mechanisms, the model can also evaluate the effect of each strengthening mechanism. 

       This study introduced the thermal residual stress-strain and strain gradient strengthening mechanism to 3D realistic microstructure models of PRMMC. The strengthening effect of the near-interface region was accurately calculated. By comparing the effects of different strengthening mechanisms, the influence of load transfer, thermal residual stress/strain, strain gradient and grain refinement strengthening in the composite are clarified. This study provides a finite element model for predicting the mechanical properties of PRMMC more accurately, which can help design new PRMMC.

Keywords: Metal matrix composite; Finite element simulation; Residual stress; Strain gradient; Strengthening mechanisms

Fig. 1 The strain-stress curves of PRMMC with different particles sizes obtained from experiments and simulations. 

图 1 实验与模拟得到的具有不同颗粒尺寸的 PRMMC 单向拉伸曲线对比

Fig. 2 The distribution of the plastic strain gradient after 5% tensile loading 

图 2 经过 5 %单向拉伸之后，模型内部塑性应变梯度分布云图

 考虑颗粒增强金属基复合材料的多种强化机制的增强有限元模型

肖伯律 1*，张峻凡 1，Heiko Andrä2，张星星 1，王全兆 1，马宗义 1 

1.中国科学院金属研究所

2.Fraunhofer Institute for Industrial Mathematics, Fraunhofer-Platz 1, Kaiserslautern 67663, Germany 

摘要:颗粒增强金属基复合材料(PRMMC)性能取决于基体成分、增强体形貌、界面性质等， 这些多样化的影响因素使 PRMMC 具有很高可设计性，但也增加了设计的复杂性。目前 PRMMC 的设计使用传统的试错法，通常需要大量的实验制备和测试，耗时耗力，成本高周期长，而且 适用性差。通过模拟辅助设计，具有快速高效，成本低、周期短、适用性好的特点。同时，还 能模拟制备工艺对复合材料力学性能的影响。然而，目前对 PRMMC 的有限元模拟缺乏对多相 特征的考虑，很难兼顾合理的弹塑性本构关系和足够逼真的虚拟微观结构。为解决这一问题， 需要构建逼真的虚拟三维微观结构，并在此基础上，为增强体和基体设置合理的弹塑性本构关系。

        考虑到 PRMMC 的强化作用主要源于载荷传递强化，基体合金的晶界强化、残余应力应变 强化和塑性应变梯度强化。充分考虑基体的强化因素，就可以准确体现 PRMMC 的强化作用， 从而为金属基复合材料设计提供依据。所以需要针对这些强化机制，优化已有的有限元模型。 首先，能构建合理的 PRMMC 虚拟微观结构，可以准确体现载荷传递的强化作用。其次，考虑 到增强体颗粒具有显著的晶粒细化作用，本研究使用 Hall-Petch 关系对晶界强化作用开展了计 算，将基体合金的晶界强化引入到现有本构关系中。第三，本研究在拉伸过程模拟之前引入了 淬火热处理过程的模拟，从而获得了近界面基体区的热残余应力应变强化。最后，为引入应变 梯度的影响，本研究在基体的本构关系中引入了塑性应变梯度理论。本研究的研究对象为 15 vol. % SiCp/2009Al。通过对比实验与模拟得到的拉伸应力应变曲 线，评估模型的适用性。如图 1 所示，能够发现，在考虑晶界强化时，模拟结果与实验结果吻 合良好，而不考虑晶界强化时(5 μm Simulation =290 MPa)，小颗粒尺寸的 PRMMC 屈服强 度被低估。在没有考虑到晶界强化时，不同颗粒尺寸的 PRMMC 同样能够表现出尺寸效应，这 是由于不同颗粒尺寸会导致基体内部的应变梯度产生差异，如图 2 所示。通过调整模型和基体 本构关系，删减特定强化机制，该模型还能够评估每种强化机制的作用效果和发生作用的影响 因素。

      本研究通过引入热残余应力应变、应变梯度强化机制，解决了以往研究采用逼真三维结构 难以精确计算近界面区强化作用的问题。通过对比不同的强化机制的作用效果，阐明了载荷传 递、热残余应力应变、应变梯度和晶界强化在复合材料中发生作用的大小和影响条件。本研究 提供了一种更为准确地预测 PRMMC 力学性能的有限元模型，为复合材料设计提供了新方法。

关键词:金属基复合材料;有限元模拟;残余应力;应变梯度;强化机制