SolutionsHW5 - HW#5 Problem 7.12 a To Find Does the single...

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HW #5 Problem 7.12 a. To Find: Does the single crystal yield under the given applied stress? If not, at what stress will it yield? b. Given: = 43.1 o = 47.9 o CRSS = 20.7 MPa Applied stress = 45 MPa c. Assumptions: (i) The applied force is uniaxial (ii) Single crystal (iii) The metal is pure (alloying agents/impurities can change the value of CRSS . (iv) The testing is done at room temperature the value of CRSS can change with temperature. (v) The values of    CRSS and applied stress are accurate. d. Solution: Method 1: Calculate applied R and compare with CRSS. psi) (3181 MPa 22.0 = ) 47.9 )(cos 43.1 MPa)(cos (45 = cos cos = R   R > CRSS Method 2: Calculate yield strength and compare with applied stress. MPa 42.29 = ) 47.9 (cos ) 43.1 (cos / MPa) (20.7 = cos cos / CRSS Y > y The resolved shear stress is greater than the critical resolved shear stress. Hence, the single crystal will yield. The applied stress is greater than the yield strength. Hence, the single crystal will yield.
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Problem 7.13 a. To Find: (a) Most favored slip direction (b) CRSS b. Given: = 28.1 o = one of 62.4 o , 72.0 o , 81.1 o Yield strength y = 45 MPa c. Assumptions: (i) The applied force is uniaxial (ii) Single crystal (iii) The metal is pure alloying agents/impurities can change the value of CRSS .
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