P1. A sheet of BCC iron 1 mm thick was exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other side at 725°C. After having reached steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were determined to be 0.012 and 0.0075 wt%. Compute the diffusion coefficient if the diffusion flux is 1.4*10^-8 kg/m2-s. Hint: Use Equation to convert the concentrations from weight percent to kilograms of carbon per cubic meter of iron.
P2. The diffusion coefficients for silver in copper are given at two temperatures:
T (°C) D (m2/s)
650 5.5 × 10–16
900 1.3 × 10–13
(a) Determine the values of D0 and Qd.
(b) What is the magnitude of D at 875°C?
P3. Aluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of Al in this silicon material is known to be 3x1019 atoms/m3. The drive-in diffusion treatment is to be carried out at 1050°C for a period of 4.0 h, which gives a junction depth xj of 3.0 micro meter. Compute the predeposition diffusion time at 950°C if the surface concentration is maintained at a constant level of 2x1025 atoms/m3. For the diffusion of Al in Si, values of Qd and D0 are 3.41 eV and 1.38x10^-4 m2/s, respectively.
P4. A cylindrical rod of copper (E = 110 GPa, 16x106 psi) having a yield strength of 240 MPa (35,000 psi) is to be subjected to a load of 6660 N (1500 lbf). If the length of the rod is 380 mm (15.0 in.), what must be the diameter to allow an elongation of 0.50 mm (0.020 in.)?
P5. Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225 lbf) produces an elastic reduction in diameter of 2.8x10^-4 mm (1.10x 10^-5 in.). Compute the modulus of elasticity for this alloy, given that Poisson's ratio is 0.30.
P6. A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.2 is produced when a true stress of 575 Mpa; for the same metal the value of K is 860Mpa; calculate the true strain that results from the application of a true stress of 600Mpa
P7. A yield strength of a polycrystalline material increases from 120 MPa to 220 MPa on decreasing the grain diameter from 0.04 to 0.01 mm. Find the yield strength for a grain size of ASTM 9.
P8. The yield strength of a polycrystalline material increases from 120 N/mm^2 on decreasing the average grain diameter from 0.04 mm to 0.01 mm. fine the yield strength for a grain size of 0.025 mm.
Solution-Click here
P2. The diffusion coefficients for silver in copper are given at two temperatures:
T (°C) D (m2/s)
650 5.5 × 10–16
900 1.3 × 10–13
(a) Determine the values of D0 and Qd.
(b) What is the magnitude of D at 875°C?
P3. Aluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of Al in this silicon material is known to be 3x1019 atoms/m3. The drive-in diffusion treatment is to be carried out at 1050°C for a period of 4.0 h, which gives a junction depth xj of 3.0 micro meter. Compute the predeposition diffusion time at 950°C if the surface concentration is maintained at a constant level of 2x1025 atoms/m3. For the diffusion of Al in Si, values of Qd and D0 are 3.41 eV and 1.38x10^-4 m2/s, respectively.
P4. A cylindrical rod of copper (E = 110 GPa, 16x106 psi) having a yield strength of 240 MPa (35,000 psi) is to be subjected to a load of 6660 N (1500 lbf). If the length of the rod is 380 mm (15.0 in.), what must be the diameter to allow an elongation of 0.50 mm (0.020 in.)?
P5. Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225 lbf) produces an elastic reduction in diameter of 2.8x10^-4 mm (1.10x 10^-5 in.). Compute the modulus of elasticity for this alloy, given that Poisson's ratio is 0.30.
P6. A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.2 is produced when a true stress of 575 Mpa; for the same metal the value of K is 860Mpa; calculate the true strain that results from the application of a true stress of 600Mpa
P7. A yield strength of a polycrystalline material increases from 120 MPa to 220 MPa on decreasing the grain diameter from 0.04 to 0.01 mm. Find the yield strength for a grain size of ASTM 9.
P8. The yield strength of a polycrystalline material increases from 120 N/mm^2 on decreasing the average grain diameter from 0.04 mm to 0.01 mm. fine the yield strength for a grain size of 0.025 mm.
Solution-Click here
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