Modeling the effects of pore arrays on the electrical and mechanical properties of copper
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The development of porous metals has led to the need for an accurate prediction of the physical and mechanical properties of the many possible fabricated structures. For applications where yield stress needs to be reduced, while maintaining a high conductivity, the optimization of the pore dimensions, volume fraction, and pore spacing is required. A finite element model has been developed to simulate the effects of these factors on the electromechanical behavior of porous copper. This model was validated against samples of copper with mechanically induced pores as well as a copper GASAR sample. Good agreement (within an error of 63%) was shown between the model and experimental data for the resistivity and effective modulus for both the mechanically induced pore and the GASAR samples, although the low ductility of the samples was not predicted and restricts the application of the simulation. ry ¼ r0 ð1 pÞ1þð2bÞ a
I. INTRODUCTION
Porous metals have been shown to have higher acoustic damping, reduced density, and greater energy absorption compared with their solid counterparts1 leading to a number of vibration-related applications. The introduction of pores into a solid structure, however, does also result in reduction of modulus, strength, and toughness. The variation in some properties can depend strongly on the number density, shape, and alignment of the pores present in the metal/alloy.2,3 The expansion of the range of applications in which porous metals would be beneficial requires that appropriate pore distributions are introduced into the solid metal. While an empirical approach can achieve this, the design of suitable porous structures would be accelerated if a verified model was available to simulate the behavior of these materials. Nakajima3 has shown that the resultant yield stress of a porous material can be calculated from Eq. (1). This is a 2D solution and does not account for pore distribution within the material. Good agreement was seen when compared with experimental data for pore fractions up to 40% porosity for modulus and ultimate tensile strength. However, yield strength in porous copper was poorly predicted, with up to 60% discrepancies being seen at pore fractions between 10–30% porosity (it was noted that these samples showed very little ductility). The relationship shown by Eq. (1) is based on the stress intensity factor of a pore; however, this equation does not resolve the shear stresses that would result when multiple pores interact. a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2013.188 J. Mater. Res., Vol. 28, No. 17, Sep 14, 2013
http://journals.cambridge.org
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ð1Þ
where ry and r0 are the yield stresses of the porous and solid material, respectively, p is the pore volume fraction, and a and b are the pore dimensions (a being the length perpendicular to the loading axis). A number of dissimilar material applications, e.g., metallization of ceramics or ceramic–metal joints, involve the application of thermal sc
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