207

# Materials Science and Engineering: An Introduction

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: REVISED PAGES EQA 184 - Chapter 7 I Dislocations and Strengthening Mechanisms (b) If slip occurs on a (110) plane and in a [111] direction, and the critical resolved shear stress is 30 MPa (4350 psi), calculate the magnitude of the applied tensile stress necessary to initiate yielding. Solution (a) A BCC unit cell along with the slip direction and plane as well as the direction of the applied stress are shown in the accompanying diagram. In order to solve this problem we must use Equation 7.2. However, it is first nec— essary to determine values for 95 and A, where, from the diagram below, (35 is the angle between the normal to the (110) slip plane (i.e., the [119] direc— tion) and the [010] direction, and It represents the angle between [111] and [010] directions. In general, for cubic unit cells, an angle 9 between directions 1 and 2, represented by [uivlwl] and [112921.02], respectively, is equal to (7.6) 6 = cos_1[ uluz + 0102 + wlwz ] V (in2 + of + wf){u§ + v5 + wé) For the determination of the value of 45, let [ululwl] = [110] and [ugvzwzl = [010] such that ¢ _ ms_1{ {1X0} + (1X1) + (0X0) } War + (1)2 + (error + (1)2 + (0):] = cos"(%) = 45° Normal to Slip direction [111] Direction of applied stress [010] However, for )1, we take [u1vlwl] : [111] and [H2U2W2] : [010], and (-1.J(0) + (1X1) + (1X0) V [(—1)2 + (1)2 + (1)2][(0)2 + (1)2 + (0)2] = cos“(%) = 54.7° Thus, according to Equation 7.2, 7R = 0 cos 4: cos A = (52 MPa)(cos 45“)(cos 54.7") : (52 MPa)(%)(%) = 21.3 MPa (3060 PS” )1 — cos_1[ ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern