Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 39

Consider a hypothetical material that has a grain diameter of \(2.1 \times 10^{-2} \mathrm{~mm}\). After a heat treatment at \(600^{\circ} \mathrm{C}\) for \(3 \mathrm{~h}\), the grain diameter has increased to \(7.2 \times 10^{-2} \mathrm{~mm}\). Compute the grain diameter when a specimen of this same original material (i.e., \(\left.d_{0}=2.1 \times 10^{-2} \mathrm{~mm}\right)\) is heated for \(1.7 \mathrm{~h}\) at \(600^{\circ} \mathrm{C}\). Assume the \(n\) grain diameter exponent has a value of 2 .

Short Answer

Expert verified
Question: Given the initial grain diameter of 2.1 x 10^(-2) mm and a final grain diameter of 7.2 x 10^(-2) mm after 3 hours of heat treatment at 600°C, calculate the final grain diameter of the same original material after 1.7 hours of heat treatment at the same temperature, using the grain growth equation. (Grain diameter exponent, n=2) Answer: To calculate the final grain diameter after 1.7 hours of heat treatment at 600°C, use the given information and the grain growth equation as explained in the step-by-step solution provided. The final grain diameter is ________ mm. (Fill in the calculated value from the solution steps)

Step by step solution

01

Determine the time and temperature dependent constant, \(k\)

To find the constant \(k\), plug the initial conditions into the grain growth equation: \((7.2 \times 10^{-2})^{2} - (2.1 \times 10^{-2})^{2} = k \cdot 3\) Calculate the value of \(k\): \(k = \frac{(7.2 \times 10^{-2})^{2} - (2.1 \times 10^{-2})^{2}}{3}\)
02

Compute the final grain diameter for the new heat treatment time, \(1.7h\)

Now that we have the value of \(k\), we can plug in the new heating time into the grain growth equation and solve for the final grain diameter, \(d\): \((d)^{2} - (2.1 \times 10^{-2})^{2} = k \cdot 1.7\) To solve for \(d\), perform the following steps: 1. Replace \(k\) with the value obtained in Step 1 2. Add \((2.1 \times 10^{-2})^{2}\) to both sides of the equation 3. Take the square root of both sides of the equation to isolate \(d\) After performing these steps, you will get the final grain diameter for the specimen of the original material heated for \(1.7 \mathrm{~h}\) at \(600^{\circ} \mathrm{C}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A bar of a steel alloy that exhibits the stressstrain behavior shown in Figure \(6.22\) is subjected to a tensile load; the specimen is \(375 \mathrm{~mm}(14.8 \mathrm{in}\).) long and has a square cross section \(5.5 \mathrm{~mm}(0.22 \mathrm{in}\).) on a side.(a) Compute the magnitude of the load necessary to produce an elongation of \(2.25 \mathrm{~mm}(0.088\) in.). (b) What will be the deformation after the load has been released?

(a) A single crystal of a metal that has the BCC crystal structure is oriented such that a tensile stress is applied in the \([100]\) direction. If the magnitude of this stress is \(4.0 \mathrm{MPa}\), compute the resolved shear stress in the \([1 \overline{11}]\) direction on each of the \((110),(011)\), and \((10 \overline{1})\) planes. (b) On the basis of these resolved shear stress values, which slip system(s) is (are) most favorably oriented?

A single crystal of zinc is oriented for a tensile test such that its slip plane normal makes an angle of \(65^{\circ}\) with the tensile axis. Three possible slip directions make angles of \(30^{\circ}, 48^{\circ}\), and \(78^{\circ}\) with the same tensile axis. (a) Which of these three slip directions is most favored? (b) If plastic deformation begins at a tensile stress of \(2.5 \mathrm{MPa}\) (355 psi), determine the critical resolved shear stress for zinc.

Consider a single crystal of nickel oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a \([\overline{101}]\) direction and is initiated at an applied tensile stress of \(13.9 \mathrm{MPa}\) (2020 psi), compute the critical resolved shear stress.

Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a [112] direction. If slip occurs on a (111) plane and in a [011] direction, and the crystal yields at a stress of \(5.12 \mathrm{MPa}\), compute the critical resolved shear stress.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Modern Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Measurements

Read Explanation

Physics of Motion

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free