(10 points) Consider a single crystal of some hypothetical metal that has the FCC crystal structure, and its critical resolved shear stress is 3.42 MPa. The crystal is oriented such that a tensile stress is applied at an angle of 39.2 degrees to the slip plane. Slip can occur in two directions( 18.4 and 74.2 degrees to the tensile force). (a) (5 points) Which direction, is slip favored

Complete Question

(10 points) Consider a single crystal of some hypothetical metal that has the FCC crystal structure, and its critical resolved shear stress is 3.42 MPa. The crystal is oriented such that a tensile stress is applied at an angle of 39.2 degrees to the slip plane. Slip can occur in two directions( 18.4 and 74.2 degrees to the tensile force).

(a) (5 points) Which direction, is slip favored?

b)  (5 points)  What is the yield strength of this crystal during this tensile test ?

a

the slip would occur 18.4° to the tensile force

b

The yield strength is    

Explanation:

From the question we are told that

    The Resolved shear force is

     The angle in which the tensile stress is applied is

      The first direction of slip is

      The second direction of the slip is

Generally the condition for direction in which slip is likely to occur(

direction in which slip is favored )   is that  

Must be Maximum for that direction

   Since is constant for both direction we would  look at the the cos of the the angle for both direction

From this calculation we can see that the slip would occur 18.4° to the tensile force

   Generally critical resolved shear stress is mathematically represented as

Where is the  yield strength

Making   the subject

Substituting value

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explanation:

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.