HW8 ENME382 S10 Section0201 solution

HW8 ENME382 S10 Section0201 solution - ENME 382 Section...

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ENME 382 Section 0201 Homework 8 Due in class: April 26, 2010 1. a) The critical resolved shear stress for copper is 0.48 MPa (70 psi). Determine the maximum possible yield strength for a single crystal of Cu pulled in tension. Solution In order to determine the maximum possible yield strength for a single crystal of Cu pulled in tension, we simply employ Equation 8.5 as σ y = 2 τ crss = (2)(0.48 MPa) = 0.96 MPa (140 psi) bi) 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 MPa, compute the resolved shear stress in the [1 1 1] direction on each of the (110), (011), and (10 1 ) planes. bii) On the basis of these resolved shear stress values, which slip system(s) is (are) most favorably oriented? Solution (a) This part of the problem asks, for a BCC metal, that we compute the resolved shear stress in the [1 1 1] direction on each of the (110), (011), and (10 1 ) planes. In order to solve this problem it is necessary to employ Equation 8.2, which means that we first need to solve for the for angles λ and φ for the three slip systems. For each of these three slip systems, the λ will be the same—i.e., the angle between the direction of the applied stress, [100] and the slip direction, [1 1 1]. This angle λ may be determined using Equation 8.6 λ = cos - 1 u 1 u 2 + v 1 v 2 + w 1 w 2 u 1 2 + v 1 2 + w 1 2 ( ) u 2 2 + v 2 2 + w 2 2 ( ) where (for [100]) u 1 = 1, v 1 = 0, w 1 = 0, and (for [1 1 1]) u 2 = 1, v 2 = –1, w 2 = 1. Therefore, λ is determined as λ = cos - 1 (1)(1) + (0)( - 1) + (0)(1) (1) 2 + (0) 2 + (0) 2 [ ] (1) 2 + ( - 1) 2 + (1) 2 [ ]
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= cos - 1 1 3 = 54.7 ° Let us now determine φ for the angle between the direction of the applied tensile stress—i.e., the [100] direction—and the normal to the (110) slip plane—i.e., the [110] direction.
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HW8 ENME382 S10 Section0201 solution - ENME 382 Section...

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