Engineering, 22.04.2020 21:43, alexkrol30083
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 [121] direction. If slip occurs on a (101) plane and in a direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.9 MPa.
Answers: 1
between the slip direction [121] and [111]![\lambda = cos^{-1} [\frac{(u_1 u_2 + v_1 v_2 + w_1 w_2}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_2^2 + v_2^2 + w_2 ^2)} } ]](/tpl/images/0619/2658/9a22c.png)
are the directional indices ![\lambda = cos ^-[ \frac{(1) (-1) + (2) (1) + (1) (1)}{\sqrt{((1)^2 +(2)^2 + (1)^2)}\sqrt{((-1)^2 + (1)^2 + (1)^2 ) } } ]](/tpl/images/0619/2658/874e0.png)
![= cos^{-1} [\frac{2}{\sqrt{6} \sqrt{3} } ]](/tpl/images/0619/2658/712dc.png)
between the direction [121] and [101]![\O = cos^{-1} [\frac{(u_1 u_3 + v_1 v_3 + w_1 w_3}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_3^2 + v_3^2 + w_3 ^2)} } ]](/tpl/images/0619/2658/df225.png)
, 2 for 
, 1 for 
, 1 for 
, 0 for 
, and 1 for 
![\O = cos^{-1} [\frac{1* 1 + 2*0 + 1*1 }{\sqrt{1^2 + 2^2 + 1^2 } \sqrt{(1^2 + 0^2 + 1^2 )} } ]](/tpl/images/0619/2658/cf8f4.png)
![\O = cos^{-1} [\frac{2}{\sqrt{6} \sqrt{2} } ]](/tpl/images/0619/2658/1f76c.png)
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