7.13
We are asked to compute the critical resolved shear stress for Zn.
As stipulated in the problem,
φ
=
65
°
, while possible values for
λ
are 30
°
, 48
°
, and 78
°
.
(a)
Slip will occur along that direction for which (cos
φ
cos
λ
) is a maximum, or, in this case, for the
largest cos
λ
.
Cosines for the possible
λ
values are given below.
cos(30
°
) = 0.87
cos(48
°
) = 0.67
cos(78
°
) = 0.21
Thus, the slip direction is at an angle of 30
°
with the tensile axis.
(b)
From Equation 7.4, the critical resolved shear stress is just
τ
crss
=
σ
y
(cos
φ
cos
λ
)
max
= (2.5 MPa)
cos(65
°
) cos(
30°
)
[
]
= 0.90 MPa
(130 psi)

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