Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6.13, Problem 57AAP
A specimen of commercially pure titanium has a strength of 140 MPa. Estimate its average grain diameter using the Hall–Petch equation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The yield stress of AISI 1020 steel with a grain size of 200 μm is 200 MPa.Estimate the yield stress for a grain size of 10 μm if the Hall--Petch constantk = 0.8 MN/m3/2.
3. An uncold-worked brass specimen of average grain size 0.01 mm has a yield strength of 150
MPa (21,750 psi). Estimate the yield strength of this alloy after it has been heated to 500°C for
1000 s, if it is known that the value of σo is 25 MPa. (Note that the axis has logarithmic scale).
Grain diameter (mm)
(Logarithmic scale)
1.0
0.1
0.01
1
10
850°C
800°C
700°C
102
Time (min)
(Logarithmic scale)
600°C
500°C
103
104
The yield stresses (σY) have been measured using steel and aluminum specimens of various grain sizes given in the attached image.On the basis of data answer the following questions:
(a) Determine the coefficients σ0 and kY in the Hall- Petch for these two materials.(b) Determine the yield stress in each material for a grain size of d=26 μm.
Chapter 6 Solutions
Foundations of Materials Science and Engineering
Ch. 6.13 - (a) How are metal alloys made by the casting...Ch. 6.13 - Why are cast metal sheet ingots hot-rolled first...Ch. 6.13 - What type of heat treatment is given to the rolled...Ch. 6.13 - Describe and illustrate the following types of...Ch. 6.13 - Describe the forging process. What is the...Ch. 6.13 - What is the difference between open-die and...Ch. 6.13 - Describe the wire-drawing process. Why is it...Ch. 6.13 - Distinguish between elastic and plastic...Ch. 6.13 - Define (a) engineering stress and strain and (b)...Ch. 6.13 - Define (a) modulus of elasticity, (b) yield...
Ch. 6.13 - (a) Define the hardness of a metal. (b) How is the...Ch. 6.13 - What types of indenters are used in (a) the...Ch. 6.13 - What are slipbands and slip lines? What causes the...Ch. 6.13 - Describe the slip mechanism that enables a metal...Ch. 6.13 - (a) Why does slip in metals usually take place on...Ch. 6.13 - Prob. 16KCPCh. 6.13 - What other types of slip planes are important...Ch. 6.13 - Define the critical resolved shear stress for a...Ch. 6.13 - Describe the deformation twinning process that...Ch. 6.13 - What is the difference between the slip and...Ch. 6.13 - Prob. 21KCPCh. 6.13 - Prob. 22KCPCh. 6.13 - What experimental evidence shows that grain...Ch. 6.13 - (a) Describe the grain shape changes that occur...Ch. 6.13 - How is the ductility of a metal normally affected...Ch. 6.13 - (a) What is solid-solution strengthening? Describe...Ch. 6.13 - What are the three main metallurgical stages that...Ch. 6.13 - Describe the microstructure of a heavily...Ch. 6.13 - Describe what occurs microscopically when a...Ch. 6.13 - When a cold-worked metal is heated into the...Ch. 6.13 - Describe what occurs microscopically when a...Ch. 6.13 - When a cold-worked metal is heated into the...Ch. 6.13 - Prob. 33KCPCh. 6.13 - Prob. 34KCPCh. 6.13 - Prob. 35KCPCh. 6.13 - Prob. 36KCPCh. 6.13 - Prob. 37KCPCh. 6.13 - Why are nanocrystalline materials stronger? Answer...Ch. 6.13 - A 70% Cu30% Zn brass sheet is 0.0955 cm thick and...Ch. 6.13 - A sheet of aluminum alloy is cold-rolled 30% to a...Ch. 6.13 - Calculate the percent cold reduction when an...Ch. 6.13 - Prob. 42AAPCh. 6.13 - What is the relationship between engineering...Ch. 6.13 - A tensile specimen of cartridge brass sheet has a...Ch. 6.13 - A 0.505-in.-diameter rod of an aluminum alloy is...Ch. 6.13 - In Figure 6.23, estimate the toughness of SAE 1340...Ch. 6.13 - The following engineering stress-strain data were...Ch. 6.13 - Prob. 49AAPCh. 6.13 - A 0.505-in.-diameter aluminum alloy test bar is...Ch. 6.13 - A 20-cm-long rod with a diameter of 0.250 cm is...Ch. 6.13 - Prob. 52AAPCh. 6.13 - Prob. 53AAPCh. 6.13 - Prob. 54AAPCh. 6.13 - Prob. 55AAPCh. 6.13 - Prob. 56AAPCh. 6.13 - A specimen of commercially pure titanium has a...Ch. 6.13 - Prob. 58AAPCh. 6.13 - Prob. 59AAPCh. 6.13 - Prob. 60AAPCh. 6.13 - Prob. 61AAPCh. 6.13 - Prob. 62AAPCh. 6.13 - Prob. 63AAPCh. 6.13 - Prob. 64AAPCh. 6.13 - Prob. 65SEPCh. 6.13 - Prob. 66SEPCh. 6.13 - A 20-mm-diameter, 350-mm-long rod made of an...Ch. 6.13 - Prob. 68SEPCh. 6.13 - Prob. 69SEPCh. 6.13 - Consider casting a cube and a sphere on the same...Ch. 6.13 - When manufacturing complex shapes using cold...Ch. 6.13 - Prob. 74SEPCh. 6.13 - Draw a generic engineering stress-strain diagram...Ch. 6.13 - (a) Draw a generic engineering stress-strain...Ch. 6.13 - Prob. 77SEPCh. 6.13 - Prob. 78SEPCh. 6.13 - Prob. 79SEPCh. 6.13 - The material for a rod of cross-sectional area...Ch. 6.13 - What do E, G, v, Ur, and toughness tell you about...Ch. 6.13 - A cylindrical component is loaded in tension until...Ch. 6.13 - Referring to Figures 6.20 and 6.21 (read the...Ch. 6.13 - (a) Show, using the definition of the Poissons...Ch. 6.13 - A one-inch cube of tempered stainless steel (alloy...Ch. 6.13 - Prob. 87SEPCh. 6.13 - Prob. 88SEPCh. 6.13 - Prob. 89SEPCh. 6.13 - Prob. 90SEPCh. 6.13 - Prob. 91SEPCh. 6.13 - Prob. 92SEPCh. 6.13 - Prob. 93SEPCh. 6.13 - Prob. 94SEPCh. 6.13 - Starting with a 2-in.-diameter rod of brass, we...Ch. 6.13 - Prob. 96SEPCh. 6.13 - Prob. 97SEPCh. 6.13 - Prob. 98SEPCh. 6.13 - The cupro-nickel substitutional solid solution...Ch. 6.13 - Prob. 100SEP
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
A nozzle at A discharges water with an initial velocity of 36 ft/s at an angle with the horizontal. Determine ...
Vector Mechanics for Engineers: Dynamics
A number of common substances are
Some of these materials exhibit characteristics of both solid and fluid beha...
Fox and McDonald's Introduction to Fluid Mechanics
What is the importance of modeling in engineering? How are the mathematical models for engineering processes pr...
HEAT+MASS TRANSFER:FUND.+APPL.
The moment of inertia Iy for the slender rod in terms of the rod’s total mass m .
Engineering Mechanics: Statics & Dynamics (14th Edition)
Assume the following vectors are already defined: V1=[302]V2=[214]V3=[5131]V4=[0.50.10.20.2] For each of the fo...
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Select a mechanical component from Part 3 of this book (roller bearings, springs, etc.), go to the Internet, an...
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- In order to find out the effects of the grain sizes on the mechanical strength of a metal, three different grain sizes of 10 µm, 500 nm and 10 nm were produced. What will be the yield stresses of these same metals at different average grain sizes? The yield strength for a grain or reference point is 78 MPa, while the material proportional constant is 29.2 MPa-mm1/2.arrow_forwardThe yield strength for an alloy that has an average grain diameter of 4.7 × 102 mm is 134 MPa. At a grain diameter of 7.4 x 103 mm, the yield strength increases to 236 MPa. At what grain diameter, in mm, will the yield strength be 249 MPa?arrow_forwardQuestion The yield strength for an aluminum alloy that has an average grain diameter of 10 um is 400 MPa. As the grain diameter is increased to 80 um, the yield strength decreases to 260 MPa. When the grain diameter is 2 um, its yield strength is close to 760 MPa 668 MPa 566 MPa 419 MPaarrow_forward
- In an engineering application, the material is a strip of iron with a fixed crystallographic structure subject to a tensile load during operation. The part failed (yielded) during operation and needs to be replaced with a component with better properties. You are told that two other iron strips had failed at yield stresses of 110 and 120 MPa, with grain sizes of 30 microns and 25 microns respectively. The current strip has a grain size of 20 microns. The diameter of the rod is 1 mm and the load applied is 100 N. What is the yield stress of the new part C and would you recommend it for operation? Select one: a. 140.5, no Ob. 129.5, yes OC. 120.5 MPa, no O d. 133.5 MPa, yes O e. 123.5 MPa, yesarrow_forwardIn an engineering application, the material is a strip of iron with a fixed crystallographic structure subject to a tensile load during operation. The part failed (yielded) during operation and needs to be replaced with a component with better properties. You are told that two other iron strips had failed at yield stresses of 110 and 120 MPa, with grain sizes of 30 microns and 25 microns respectively. The current strip has a grain size of 20 microns. The diameter of the rod is 1 mm and the load applied is 100 N. What is the yield stress of the new part C and would you recommend it for operation? Select one: a.120.5 MPa, no b.140.5, no c.129.5, yes d.123.5 MPa, yes e.133.5 MPa, yesarrow_forwardIn an engineering application, the material is a strip of iron with a fixed crystallographic structure subject to a tensile load during operation. The part failed (yielded) during operation and needs to be replaced with a component with better properties. You are told that two other iron strips had failed at yield stresses of 110 and 120 MPa, with grain sizes of 30 microns and 25 microns respectively. The current strip has a grain size of 20 microns. The diameter of the rod is 1 mm and the load applied is 100 N. What is the yield stress of the new part C and would you recommend it for operation? Select one: a. O b. 129.5, yes C. 133.5 MPa, yes e. 120.5 MPa, no d. 140.5, no 123.5 MPa, yesarrow_forward
- In an engineering application, the material is a strip of iron with a fixed crystallographic structure subject to a tensile load during operation. The part failed (yielded) during operation and needs to be replaced with a component with better properties. You are told that two other iron strips had failed at yield stresses of 110 and 120 MPa, with grain sizes of 30 microns and 25 microns respectively. The current strip has a grain size of 20 microns. The diameter of the rod is 1 mm and the load applied is 100 N. What is the yield stress of the new part C and would you recommend it for operation?arrow_forwardThe yield strength for an alloy that has an average grain diameter of 5.2 x 102 mm is 110 MPa. At a grain diameter of 6.3 x 103 mm, the yield strength increases to 251 MPa. At what grain diameter, in mm, will the yield strength be 222 MPa? d = mmarrow_forward(b) The yield stress for a metal changes from 450 Nmm-2to 610 Nmm-2 when the average grain diameter decrease from 0.043 mm to 0.022 mm. Determine the yield stressfor the same metal with an average grain diameter of 0.030 mm.arrow_forward
- A copper-zine alloy has the properties shown in the table below. Grain Diameter (mm) Strength (MPa) 0.015 170 MPa 0.025 158 MPa 0.035 151 MPa 0.050 145 MPa Determine (a) the constants in the Hall-Petch equa- tion; and (b) the grain size required to obtain a strength of 200 MPa.arrow_forward3) The strength of a titanium piece is found to be 65,000 psi when the grain size is 17 x10-6 m and 82,000 psi when the grain size is 0.8 x10 m. What would be the 9- (a) Constants in the Hall-Petch equation Strength of this titanium piece when the grain size is reduced to 0.2 x10 m. (9)arrow_forwardCalculate the dislocation spacing of a low-angle tilt boundary in aluminumfor θ = 0.5◦. Take G = 26.1 GPa, v = 0.345, and rAl = 0.143 nm.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Explanation of Solidification of Metals & Alloys | Manufacturing Processes; Author: Magic Marks;https://www.youtube.com/watch?v=G5z9KknF_s8;License: Standard Youtube License