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(dϕψ – do) = 1 s2[σ11cos2ϕ + σ12sin2ϕ + σ22sin2ϕ]sin2ψ
do 2

+ 1 s2[σ33cos2ψ + s1[σ11 + σ22 + σ33]
2

+ 1 + σ23sinϕ]sin22ψ
2 s3[σ13cosϕ

(4.13)

Where s1, s2 and s3 is the elastic compliance in GPa–1.
Since the direction for measuring residual stress re-
quire three orthogonal direction which is normal to each
other, positioning of sample should be consistant. There
also can be derived that, Equation 4.13 can deduced
based on the angle value given in Table 4.4. Based
on Equation ??. the strain for longitudinal, normal and
transverse direction

Table 4.4: The value given in radian for each direc-

tion of scanning angle used to obtain the diffraction

profiles or three orthogonal direction in residual stress

measurement. cosϕ sinψ cosψ
ϕ ψ sinϕ

(radian) (radian) (radian) (radian)

0◦ 90◦ 0 11 6.13x10–17
90◦ 90◦ 1 6.13x10–17 1 6.13x10–17
0◦ 0◦ 0
10 1

Each direction provide value for and ψ values as

91