Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 19AAP
To determine
The time necessary to increase the carbon content.
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Determine 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
0.9999
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
h
Consider the gas carburizing of a gear of 1020 steel at 927°C (1700°F) as in Example
Problem 5.2. Only in this problem calculate the carbon content at 0.50 mm beneath the sur-
face of the gear after 5 h carburizing time. Assume that the carbon content of the surface of
the gear is 0.90%, and that the steel has a nominal carbon content of 0.20%.
Danin=1.28 x 10-11 m2/s
1Solution
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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- 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_forwardFor 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.arrow_forwardProblem 2 Determine the carburizing time necessary to achieve a carbon concentration of 0.45 wt% at a position 2 mm into an iron-carbon alloy that initially contains 0.20 wt% C. The surface concentration is to be maintained at 1.30 wt% C, and the treatment is to be conducted at 1000 °C. Use the diffusion data for y-Fe in Table 5.2.arrow_forward
- 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.arrow_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_forwardA mechanism for hardening steel is called carburization. To achieve this process, the piece of steel is exposed to an atmosphere rich in hydrocarbon such as methane (CH4). Consider a steel with a carbide concentration of 0.25wt%, which must be treated at 950˚C. If the carbon concentration at the surface is suddenly increased to 1.20wt%, how long does it take for a penetration of 0.5mm from the surface to reach a concentration of 0.80wt%? . The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2s-1. Assume that the piece of steel is semi-finite. Use the table below.arrow_forward
- Decarburization of a steel occurs when carbon diffuses from the steel to the surface and enters the atmosphere. How long will it take for a 0.6 % C steel surface to decarburize below 0.1 % C for a depth of 2 mm if the FCC steel is held at 1250 °C in an atmosphere containing zero carbon? I need this question's answer. It's important for me.arrow_forwardA 1020 steel contains 0.20% carbon is carburized by a source that maintains a surface carbon content 0f 2.0% C. It is desired to produce a 0.80 wt% C concentration 0.1 cm below the steel surface after a 4-hour treatment. At what temperature should the carburization be carried out? R = 8.314 J/mol•K; DO = 2.3x10-5 m2 /s; Qd=148,000 J/mol erf(z) erf(z) erf(z) 0.55 0.5633 1.3 0.9340 0.025 0.05 0.0282 0.60 0.6039 1.4 0.9523 0.0564 0.65 0.6420 1.5 0.9661 0.10 0.1125 0.70 0.6778 1.6 0.9763 0.15 0.1680 0.75 0.7112 1.7 0.9838 0.20 0.25 0.30 0.2227 0.80 0.7421 1.8 0.9891 0.2763 0.85 0.7707 1.9 0.9928 0.3286 0.90 0.7970 2.0 0.9953 0.35 0.3794 0.95 0.8209 2.2 0.9981 0.40 0.4284 1.0 0.8427 2.4 0.9993 0.45 0.4755 1.1 0.8802 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999arrow_forwardAn FCC iron-carbon alloy initially containing 0.10 wt% C is carburized at an elevated temperature and in an atmosphere in which the surface carbon concentration is maintained at 1.10 wt%. If the treatment is conducted at 1050 °C, how long should the treatment be performed to reach a 0.30 wt% of carbon concentration at a position 4.2 mm below the surface?arrow_forward
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