Chemistry Reference
In-Depth Information
ψ
> 0
Δ
ε
φψ
Δ
ε
φψ
ε
φψ
ε
φψ
m
{
hkl
}
ψ
< 0
∂
ε
φψ
∂(sin
2
ψ
)
ε
φ
,
ψ
=0
sin
2
ψ
sin
2
ψ
(
a
)
(
b
)
Stress gradient
Δ
ε
φψ
ε
φψ
Texture
b
∂(Δ
ε
φψ
)
∂(sin 2
ψ
+
)
sin
2
ψ
sin 2
ψ
+
(
c
)
(
d
)
e
fhklg
fc
sin
2
c plot: (a) linear when t
f
¼ 0;
(b) c-split due to shear t
f
6¼ 0; (c) plot of De
fc
versus sin 2c
þ
; (d) curved due to texture, stress
gradient, or composition gradient.
FIGURE 9.5 Stress measurement from the
This method is often called the sin
2
cmethod. The interception of the e
fhklg
fc
-sin
2
c plot
with the e
fhklg
fc
axis is the strain measured with the tilt angle c ¼ 0,
e
fhklg
f;c¼0
¼ S
fhklg
ðs
11
þs
22
Þ
ð9
:
43Þ
1
In the case of biaxial stress with shear (only s
33
¼ 0), the shear strain results in a
deviation from the linear relation of the e
fhklg
fc
sin
2
c plot, as shown in Figure 9.5(b).
The deviations are both positive and negative from the linear relation depending on
the sign of the c-tilt angle. Therefore, it is also referred to as c-split. The shear stress
t
f
can be measured from the amount of c-split. Assuming the strain e
fhklg
fc
has been
measured at both positive and negative c-tilt angles, by subtracting Eq. (9.35) for c
þ
and c
and assuming sin 2c
¼sin 2c
þ
, we obtain
De
fc
¼
e
fhklg
fcþ
e
fhklg
2
S
fhklg
1
t
f
ðsin 2c
þ
sin 2c
Þ
2
fc
2
S
fhklg
2
t
f
sin 2c
þ
¼
¼
1
2
2
ð9
:
44Þ
