Chapter 7 DISLOCATIONS AND STRENGTHENING MECHANISMS 1. Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1° and 47.9° , respectively, with the tensile axis. If the critical resolved shear stress is 22 MPa, will an applied stress of 50 MPa cause the single crystal to yield? If not, what stress will be necessary? 2. A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [110] direction. If the critical resolved shear stress for this material is 2.2 MPa, calculate the magnitude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the 101¸[101]and[011]directions. Hint: For each of these three slip systems, the ø will be the same-i.e., the angle between the direction of the applied stress, [110] and the normal to the (111) plane, that is, the [111] direction. The angle ømay be determined using Equation 9.6 as u,u, + v,v, + ww, O = cos (ui + v} + w} )(u} + v + w}) ]

Chapter 7 DISLOCATIONS AND STRENGTHENING MECHANISMS 1. Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1° and 47.9° , respectively, with the tensile axis. If the critical resolved shear stress is 22 MPa, will an applied stress of 50 MPa cause the single crystal to yield? If not, what stress will be necessary? 2. A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [110] direction. If the critical resolved shear stress for this material is 2.2 MPa, calculate the magnitude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the 101¸[101]and[011]directions. Hint: For each of these three slip systems, the ø will be the same-i.e., the angle between the direction of the applied stress, [110] and the normal to the (111) plane, that is, the [111] direction. The angle ømay be determined using Equation 9.6 as u,u, + v,v, + ww, O = cos (ui + v} + w} )(u} + v + w}) ]

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [2 2 1] direction. If slip occurs on a (2 1 1) plane and in a [-1 1 1] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.4 MPa.
5. 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 [102] direction. If slip occurs on a (111) plane and in a [101] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 3.42 MPa.
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 [11 2] direction. If slip occurs on a ( 111) plane and in a [0 11] direction, and the crystal yields at a stress of 5.12 MPa, compute the critical resolved shear stress. CRITICAL RESOLVED SHEAR STRESS • CRITICAL RESOLVED SHEAR STRESS (T, THE MOST FAVORABLY ORIENTED SLIP SYSTEM WHEN SHEAR STRESS IS AT J: SLIP IN A SYSTEM STARTS ON CRSS THIS CRITICAL VALUE • MINIMUM SHEAR STRESS REQUIRED TO INITIATE SLIP • SINGLE CRYSTAL PLASTICALLY DEFORMS WHEN: T, > T, CRSS OR TR(max) =T CRSS 'R Tcrss (cos o cos A)max
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.120.5 MPa, no b.140.5, no c.129.5, yes d.123.5 MPa, yes e.133.5 MPa, yes
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, yes
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. O b. 129.5, yes C. 133.5 MPa, yes e. 120.5 MPa, no d. 140.5, no 123.5 MPa, yes
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?