Acrystalline grain of nickel in a metal plate is situated so that a tensile load is oriented along the [111] crystal direction (a) if the applied stress if 0.45 mpa, what will be the resolved shear stress, trss, along the [101] direction within the (11 t) plane? (b) what tensile stress is required to produce a critical resolved shear stress, tcrss of 0.242 mpa

Given:

Applied stress,

Critical Resolved Stress,  

Solution:

a). According to the question, orientation of tensile load is along [1 1 1],

Now, for resolved shear stress,   along [1 0 1] within (1 1 T)

let  '' be the angle between [1 1 1] and [1 0 1], then by coordinate formula:

=

=

let  '' be the angle between [1 1 1] and [1  1 1], then by coordinate formula:

= 1

Now, for the resolved components along [1 0 1]

 =

= = 0.3673 MPa

b).  For required tensile stress to produce  :

we need to know the time interval during which the force acts. impulse of force = momentum change

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.