Vol.:(0123456789) 1 3 Metals and Materials International https://doi.org/10.1007/s12540-019-00317-z Physics‑Based Constitutive Model of Porous Materials for Die/Isostatic Compaction of Metallic Powders Yujin Seong 1  · Dami Yim 1  · Min Ji Jang 1  · Jeong Min Park 1  · Seong Jin Park 2  · Hyoung Seop Kim 1 Received: 21 March 2019 / Accepted: 30 May 2019 © The Korean Institute of Metals and Materials 2019 Abstract A physics-based constitutive model of porous materials is proposed to enhance the accuracy of numerical analysis in die/ isostatic compaction. The correlation between the yield function and equivalent work equation was derived, and the numerical integration method was modifed with the correlation. It is found that the apparent work of porous materials is lower than the product of relative density and equivalent work of solid materials at the beginning of compaction, implying the kinematic motion of powders and the resultant particle rearrangement. For verifcation of the proposed model, fnite element analyses were performed for the die/isostatic compaction of three metal powders: Ti, SUS316L, and Al6061 powders. Compared with two conventional constitutive models, the proposed model improves the accuracy of the densifcation behaviors in all the stage during die/isostatic compaction. Furthermore, this study is a groundwork to link the densifcation behavior of porous materials at bulk scale to the particulate behavior of powders at microscale. Keywords Constitutive model · Powder metallurgy · Die compaction · Porous material · Finite element method 1 Introduction Powder metallurgy (PM) is widely used in the production of complex engineering parts due to the economic advantage of mass production in various industrial felds such as auto- mobiles [1, 2], aerospace [3], and electronics. PM process- ing has three steps: pressing, sintering, and fnishing. The mechanical properties of the fnal products processed by PM signifcantly depend on the deformation behavior of powders during these three steps. In particular, densifcation behavior of the powders during die-pressing is very important for the performance and reliability of the fnal product. The numerical simulation of the powder compaction pro- cess is an alternative approach of experiments to investi- gate the densifcation behavior of powders due to efciency and cost. The fnal aim of the numerical simulation is to control processing conditions, such as strain rate, pressure, and lubrication, and to optimize the mold design. Thus, it is important to use an appropriate constitutive model to cor- rectly describe strain/stress distributions and density change of porous materials during the PM process. Depending on the scale, there are two types of studies that develop constitutive models: phenomenological and micro-mechanics based approaches. In phenomenological studies, a powder bed is considered as continuous media, which is suitable for industrial applications. Meanwhile, micro-mechanics based approaches give us insight into the particulate behavior of the powder [4–10]. In their studies, a small representative volume element is employed to allow the particulate behavior to be taken in full account because each particle is simulated. Their fnal goal is to link the deformation behavior of porous materials at bulk scale to the particulate behavior at microscale. Two phenomenological models are most commonly used in the PM feld: The Green/Shima type model and the Drucker–Prager model. The Green/Shima type model [11–15] is a quadratic function of efective stress q and hydrostatic pressure p, as shown in Eq. (1), (1) A(R)q 2 + B(R)p 2 = (R)Y 2 0 = Y 2 R , * Hyoung Seop Kim hskim@postech.ac.kr 1 Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea 2 Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea