A Finite Element Model to Predict the Effect of Porosity on Elastic Modulus in Low-Porosity Materials
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INTRODUCTION
A. Background
POROSITY can cause changes to a material’s behavior under loading that is different than predicted. In the extreme case, these changes, if unaccounted for, could lead to major safety and economic concerns. Therefore, the ability to accurately and easily model the effect of porosity is of paramount importance during the design and testing stages. While metals are typically not intended to contain significant pores, micro pores can be present due to manufacturing defects. These pores, which at first glance may appear inconspicuous, can increase in size during service in harsh environmental conditions. For example, in oil and gas pipelines and in hydrogen fuel tanks (typically found in aerospace), materials can be subject to high concentrations of hydrogen. Over time, hydrogen can diffuse into the material and recombine into H2, increasing the size of the initial voids and thus raising the porosity to a level that may effect the elastic modulus of the material.[1,2] As another example, in the emerging field of additive manufacturing, micro particles are being used to create parts via the bottoms-up method. However, this method often results in porosity in the part between 0 and LIAM S. MORRISSEY and SAM NAKHLA are with the Department of Mechanical Engineering, Memorial University of Newfoundland, 230 Elizabeth Avenue, P.O. Box 4200, St. John’s, Newfoundland and Labrador, A1C 5S7, Canada. Contact e-mail: [email protected] Manuscript submitted November 14, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
10 pct.[3] Overall, while the effect of low levels of porosity on the yield stress has been comprehensively studied and captured in finite element software, the effect on the elastic modulus requires further research.[4] B. Porosity and its Effect on Modulus Significant research has been completed on the relationship between porosity and elastic modulus. Models typically agree that the relationship falls into categories based on the level of porosity. For example, the work of Zhang and Wang in Reference 5 has recommended subdividing porosity levels into low, medium, and high porosity. Where low porosity is less than 10 pct, medium porosity is from 10 to 70 pct and, finally, high porosity is greater than 70 pct. Therefore, the approach taken to predict the effect of porosity on elastic modulus depends first on the degree of porosity in the material. For example in low-porosity materials, the fundamental assumption is that voids are distributed such that there is no pore interaction. This assumption then leads to the conclusion that only void fraction, and not void orientation or other material-specific constants, effects the reduction in elastic modulus.[6,7] However, when in intermediate porosity zone the distance between pores is such that pores interact and material-specific values must also be considered.[8] It is important to remember that the numbers in these ranges are not necessarily exact and could possibly be better described as extremely low porosity, extremely high porosity, and then the large middle
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