Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 15AAP
To determine
The time necessary to increase the carbon content.
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To increase hardness of steel gear, it was carburized at 1040°C by introducing 1.5%C at its
steel surface. What will be the final carbon content 0.0014 m beneath the surface if this
treatment was lasted for 12 hours. The initial carbon content of steel is 0.1%C. (gas constant
is 8.31 J/mol K).
Given that a component is made of 0.1 wt.%C steel is carburized by introducing 1.0 wt.% carbon at its surface at 980ºC. Calculate the carbon content at 0.5 mm below the surface of this component after 1 hour.Do= 0.2 cm^2/s and Qd=40,000 cal/mol.
For a steel alloy it has been determined that a carburizing heat treatment of 18 h duration at 885°C will raise the carbon concentration
to 0.46 wt% at a point 2.0 mm from the surface. Estimate the time necessary to achieve the same concentration at a 8.4 mm position
for an identical steel and at a carburizing temperature of 1120°C. Assume that Do is 2.5 x 10-4 m2/s and Qa is 104 kJ/mol.
Chapter 5 Solutions
Foundations of Materials Science and Engineering
Ch. 5.7 - Prob. 1KCPCh. 5.7 - Write an equation for the number of vacancies...Ch. 5.7 - Prob. 3KCPCh. 5.7 - Prob. 4KCPCh. 5.7 - Describe the substitutional and interstitial...Ch. 5.7 - Prob. 6KCPCh. 5.7 - What factors affect the diffusion rate in solid...Ch. 5.7 - Write the equation for Ficks second law of...Ch. 5.7 - Prob. 9KCPCh. 5.7 - Prob. 10KCP
Ch. 5.7 - (a) Calculate the equilibrium concentration of...Ch. 5.7 - Prob. 12AAPCh. 5.7 - Determine the diffusion flux of zinc atoms in a...Ch. 5.7 - The diffusion flux of copper solute atoms in...Ch. 5.7 - Prob. 15AAPCh. 5.7 - Prob. 16AAPCh. 5.7 - Prob. 17AAPCh. 5.7 - A gear made of 1020 steel (0.20 wt% C) is to be...Ch. 5.7 - Prob. 19AAPCh. 5.7 - The surface of a steel gear made of 1020 steel...Ch. 5.7 - Prob. 21AAPCh. 5.7 - If boron is diffused into a thick slice of silicon...Ch. 5.7 - Prob. 23AAPCh. 5.7 - Prob. 24AAPCh. 5.7 - Prob. 25AAPCh. 5.7 - Prob. 26AAPCh. 5.7 - Prob. 27AAPCh. 5.7 - Prob. 28AAPCh. 5.7 - Prob. 29AAPCh. 5.7 - Prob. 30AAPCh. 5.7 - The diffusivity of copper atoms in the aluminum...Ch. 5.7 - Prob. 32AAPCh. 5.7 - Prob. 33SEPCh. 5.7 - Prob. 34SEPCh. 5.7 - Prob. 37SEPCh. 5.7 - Prob. 38SEPCh. 5.7 - The activation energy of nickel atoms in FCC iron...Ch. 5.7 - Prob. 40SEPCh. 5.7 - The self-diffusion of iron atoms in BCC iron is...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Prob. 44SEPCh. 5.7 - Prob. 45SEPCh. 5.7 - Prob. 46SEPCh. 5.7 - Prob. 47SEPCh. 5.7 - Prob. 48SEPCh. 5.7 - Prob. 49SEPCh. 5.7 - Prob. 50SEP
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- For a steel alloy it has been determined that a carburizing heat treatment of 16 h duration at 731°C will raise the carbon concentration to 0.40 wt% at a point 3.9 mm from the surface. Estimate the time necessary to achieve the same concentration at a 7.9 mm position for an identical steel and at a carburizing temperature of 1060°C. Assume that Do is 1.9 x 105 m²/s and Quis 108 kJ/mol, 3.89 -land Madin harrow_forwardDetermine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 3.1 mm into an iron-carbon alloy that initially contains 0.12 wt% C. The surface concentration is to be maintained at 1.2 wt% C, and the treatment is to be conducted at 1080°C. Assume that Do = 5.8 x 10-5 m²/s and Qd = 156 kJ/mol. The table Tabulation Error Function Values may be useful.arrow_forwardProblem 2 Consider the gas carburizing of a gear 1020 steel at 927°C. Calculate the time (in minute) necessary to increase the carbon content to 0.40 wt% at 0.5 mm below the surface. Assume that the carbon content at the surface 0.9 wt% and that the steel has a nominal carbon content of 0.2 wt%. Given: Diffusivity of C in Fe at 9270C is 1.28 x 10-11 m²s-1, activation energy is 148 kJmol-1, gas constant is 8.31 Jmol-1K-1, if erf (Z) = 0.7143, Z = 0.755. %3Darrow_forward
- •You are case-hardening a tool made of BCC (α) iron in the presence of a carbonaceous material. A heat treatment at 600 oC for 100 minutes results in a carbon concentration of 0.75 wt% at a position 0.5mm below the surface. How long would it take to obtain the same concentration at the same position if the heat treatment were conducted at 900 oC? x12/D1t1= x22/D2t2 Arrhenius equation: D=D0e^(〖-Qd〗∕RT) Qd = Activation energy of diffusion D0 = Pre-exponential diffusion factor R = gas constant = 8.314 J/(mol*K) Use the Arrhenius equation to calculate D1 and D2. Calculate the time to satisfy the problem statement.arrow_forwardDetermine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 1.2 mm into an iron-carbon alloy that initially contains 0.18 wt% C. The surface concentration is to be maintained at 1.1 wt% C, and the treatment is to be conducted at 1200°C. Assume that Do 6.5 x 10-5 m2/s and Qd = 168 kJ/mol. The following table may be useful. %3D Table 5.1 Tabulation of Error Function Values erf(z) erf(z) erf(z) 0.55 0.5633 1.3 0.9340 0.0282 0.0564 0.025 0.60 0.6039 1.4 0.9523 0.05 0.10 0.65 0.70 0.75 0.6420 1.5 0.9661 0.1125 0.6778 1.6 0.9763 0.15 0.1680 0.7112 1.7 0.9838 0.20 0.2227 0.80 0.7421 1.8 0.9891 0.85 0.90 0.25 0.2763 0.7707 1.9 0.9928 0.9953 0.9981 0.30 0.3286 0.7970 2.0 0.35 0.3794 0.95 0.8209 2.2 0.8427 0.8802 0.40 0.4284 1.0 2.4 0.9993 0.45 0.4755 1.1 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999arrow_forwardTo increase the hardness of a steel gear, it was carburized at 850oC by introducing 1.3%C at its steel surface. What will be the final carbon content 1.4 mm beneath the surface if this treatment was lasted for 26 hours. The initial carbon content of steel is 0.1%C. (gas constant is 8.31 j/mol.K)arrow_forward
- During freezing of a Cu-Zn alloy, we find that the composition is non-uniform. By heating the alloy to 600°C for 3 hours, diffusion of zinc helps to make the composition more uniform. What temperature would be required if we wished to perform this homogenization treatment in 30 minutes?arrow_forwardA 50%Ni-50%Cu alloy is slowly cooled from 1400°C to 1200°C. Determine: At 1300°C, estimate the weight fractions of the solid and liquid.arrow_forwardFor a steel alloy it has been determined that a carburizing heat treatment of 11.4h duration will raise the carbon concentration to 0.410 wt% at a point 2.10 mm from the surface. Estimate the time necessary to achieve the same concentration at a 4.60 mm position for an identical steel and at the same carburizing temperature. iarrow_forward
- A certain component is to be carburized to obtain 0.592 wt % C at a depth of 2.0 mm. After carburizing (for 1.2 hours) the heat treater finds that he achieved 0.4 wt % C at a depth of 2.0 mm His furnace only operates at a 900 *C and maintains a constant atmosphere of 1 wt % C. The steel used has an initial carbon content of 0.2 wt %. How long (in hours) should he carburize to achieve his goal?arrow_forwardConsider an alloy that is undergoing carburizing process, initially has a uniform carbon concentration of 0.27 wt% and is to be treated at 950°C (1750°F). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.32 (c) wt%, how long will it take to achieve a carbon content of 0.85% at a position 0.7 mm below the surface? The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s; assume that the steel piece is semi-finite.arrow_forwardIf the initial composition of the carbon steel is c0=0.3 wt%, calculate the carbon concentration (in wt%) at a distance 0.2mm from the surface of the component after 1 hour of decarburization.arrow_forward
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