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# HW7 - ME363 HW7 1 Fall 2011 No due date The tensile...

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ME363 HW7 Fall 2011 No due date 1. The tensile strength of a part produced by powder metallurgy can be empirically related to porosity as follows: 0 nP UTS UTS e = where P is the volume fraction of pores in solid, UTS 0 is the tensile strength at zero porosity, and the exponent ranges between 4 and 7 (assume to be 4 in this case). A fully dense ceramic has the properties of UTS 0 =180 MPa, E 0 = 300 GPA and density of 4000 kg/m 3 . (a) After compaction, it reaches 70% of the density of the solid material. If the linear shrinkage is 5% during sintering, determine the density after sintering. (b) Determine the UTS and modulus of elasticity of this material after sintering. 2. A ceramic has k 0 = 0.8 W/mK. If this ceramic is shaped into a cylinder with a porosity distribution given by ( )( ) 0.1 / 1 / , P x L x = L where x is the distance from one end of the cylinder and L is the total length, plot the porosity as a function of distance, evaluate the average porosity, and calculate the average thermal conductivity.
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