Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 17AAP
To determine
The carbon content below the surface of the gear.
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Determine 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.
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
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.
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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- A 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_forwardIn a binary Fe-Fe3C system, what is a transformation that occurs when cooling an austenistic mixture of 2% C by weight from 1100°C to below the eutectoid temperature? What is the microstructure, and how is it formed? What are the total and partial phases? Given:Eutectoid temperature=723°C; Eutectoid concentration=0.76% C; Limit concentration of ferrite=0.022%; Limiting concentration of cementite: 6.7%.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_forward
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