SCIENCE+ENGR.OF MTRLS.,SI ED.,ENHANCED
7th Edition
ISBN: 9780357447888
Author: ASKELAND
Publisher: CENGAGE L
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Chapter 5, Problem 5.51P
Determine the carburizing time necessary to achieve a carbon concentration of
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Diffusion
4) Determine the carburizing time necessary to achieve a
carbon concentration of 0.4wt% at a position 0.5 mm into
an iron-carbon alloy that initially contains 0.2wt% C. The
surface concentration is to be maintained at 0.9wt% and
the treatment is to be conducted at 927°C.
D @927 °C = 1.28 x 10" m'/s
Critical Resolved
Shear Stress
5) A single crystal of a metal has a critical shear stress of 2.2
MPa. If a stress of 5 MPa is applied along the [100]
direction of a unit cell then what will be the resolved
shear stress for the (111)[101] slip system? Will the
crystal exhibit slip?
Schmid's Law
Sie
Sie plane
crection
A•B/(A||B)
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 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
SCIENCE+ENGR.OF MTRLS.,SI ED.,ENHANCED
Ch. 5 - What is the driving force for diffusion?Ch. 5 - Give three examples of materials processes that...Ch. 5 - In the carburization treatment of steels, what are...Ch. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - A certain mechanical component is heat treated...Ch. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Compare the diffusion coefficients of carb on in...Ch. 5 - Prob. 5.18PCh. 5 - Activation energy is sometimes expressed as...Ch. 5 - Prob. 5.20PCh. 5 - The activation energy for the diffusion of copper...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Write down Fick’s first law of diffusion. Clearly...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - A 1-mm-thick BCC iron foil is used to separate a...Ch. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - A 0.001 in. BCC iron foil is used to separate a...Ch. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - Prob. 5.41PCh. 5 - Prob. 5.42PCh. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - Prob. 5.45PCh. 5 - Prob. 5.46PCh. 5 - Prob. 5.47PCh. 5 - Prob. 5.48PCh. 5 - Pure zinc is to be diffused into copper by dipping...Ch. 5 - Nitriding is a process in which nitrogen is...Ch. 5 - Determine the carburizing time necessary to...Ch. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - Prob. 5.56PCh. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Compare the rate at which oxygen ions diffuse in...Ch. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - Prob. 5.63PCh. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - A 0.80% C steel must operate at 950°C in an...Ch. 5 - Prob. 5.67PCh. 5 - Prob. 5.68PCh. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - Prob. 5.71PCh. 5 - Prob. 5.72PCh. 5 - Most metals and alloys can be processed using the...Ch. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - A ceramic part made from MgO is sintered...Ch. 5 - Prob. 5.78PCh. 5 - What are the advantages of using hot pressing and...Ch. 5 - Prob. 5.80PCh. 5 - Prob. 5.81DPCh. 5 - Design a spherical tank, with a will thickness of...Ch. 5 - Prob. 5.83DPCh. 5 - Prob. 5.84DPCh. 5 - Prob. 5.85DPCh. 5 - Prob. 5.86CPCh. 5 - Prob. 5.87CPCh. 5 - Prob. 5.88CPCh. 5 - Prob. 5.1KP
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- Problem 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_forwardDuring 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_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_forward
- 1. An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere that gives a surface carbon concentration constant at 1.0 wt%. If after 49.5 h, the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the temperature at which the treatment was carried out. 2. Consider a metal single-crystal oriented such that the normal to the slip plane and the slip direction are at angles of 60° and 35°, respectively, with the tensile axis. If the critical resolved shear stress is 20.7 MPa, will an applied stress of 45 MPa cause the single crystal to yield? If not, what stress will be necessary?arrow_forward(c) Consider an alloy that is undergoing carburizing process, initially has a uniform carbon concentration of 0.27 wt% and is to be treated at 950oC (1750oF). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.32 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_forwardCompare the diffusion coefficients (in cm²/s) of nitrogen in BCC and FCC iron at the allotropic transformation temperature of 912°C. Decc -153606 X Your response differs from the correct answer by more than 10%. Double check your calculations, cm²/s -1976-7 Dicc x Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm2/sarrow_forward
- For 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_forward6. (20%) Pure zinc is to be diffused into the copper by dipping copper into molten zinc at 450°C. Calculate how long would take to obtain 10wt% zinc at a depth of 0.5 mm beneath the copper surface. Is this commercially feasible? What practical problems might arise if we raise the temperature to 1000°C ? Use Table below for error function values as needed. At 450°C, the diffusion coefficient D = 6.3 10-17 m²/s.arrow_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
- 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 1Solutionarrow_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_forwardDiffusion of carbon into the surface of BCC steel at 600oC for 10 hours results in a carbon concentration of 0.2wt% at a depth of 1.5 mm below the surface. At what depth will the same concentration be obtained if the diffusion time is increased to 20 hours, leaving the temperature at 600oarrow_forward
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