New Insight into Predicting the Compression Flow Behavior of Metal Foam
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al foams are frequently regarded as composite materials in which one phase is gaseous and the other a solid metal. Polyhedral voids separated by thin films result in the low relative density. The most distinguishing feature of metal foam is that the volume and porosity decrease steadily with the applied load.[1] Interestingly, the majority of metal foams present a monotonically increasing plastic flow behavior (Figure 1). To some extent, metal foams may be viewed as a heterogeneous compressible fluid. The density field will change with time as the load is exerted on metal foams. That is, q(r, t) is a function of space and time. However, it is quite hard to compute the real-time change of the density field because of the uncertainty of the deformation of thin metal films. On the base of the mean-field approximation, almost all researchers in this field
YONGLIANG MU and QIQI GE are with the School of Metallurgy, Northeastern University, Shenyang, Liaoning 110819, P.R. China. Contact e-mail: [email protected] GUOYIN ZU is with the School of Materials Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P.R. China. YONGDONG HE is with the School of Physical Science and Technology, Xinjiang University, U¨ru¨mqi, 830046, P.R. China. Manuscript submitted March 29, 2020 and accepted September 6, 2020.
METALLURGICAL AND MATERIALS TRANSACTIONS A
adopted the concept of average density, which will increase under the quasi-static compression condition. This is reminiscent of the isothermal reversible compression of the ideal gas. The pressure (P) obeys a power law relationship with specific volume (V) during compression, indicating an increasing density of ideal gas with increasing pressure. Over the past several decades, the research on metal foams has been focusing on the effect of structure parameters, especially average density, on the mechanical properties as well as deformation mechanisms.[2–5] Among these studies, the most influential and representative work on the structure-property relation is the unicell model developed against open-cell foam by Gibson and Ashby (G&A).[1] However, the introduction of a fraction u of solid contained in the cell faces for closedcell foam turns the G&A model into a semi-empirical model. Also, the equivalent inclusion method and meanfield approximation[2] as well as the finite element (FE) method[3,4,6–9] were used to study the elastic-plastic properties of cellular solids. Based on the principle of solid mechanics, previous studies successfully derived the quantitative relations between the elastic modulus (E) as well as yield strength (r) and average density (q) of metal foam through stress analysis and strength theory in the mesoscale.[1,2,5] On the other hand, it has recently been reported that the use of the 3D images obtained by X-ray computed tomography (XCT) to perform FE modeling can determine the deformation and fracture mechanisms of metal foams.[6–9] The collapse mechanisms were also replicated in the numerical approach. The formation of plastic hinges, bending, buck
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