is the strain free lattice spacing, E is the Young’s modulus,
ν
is Poisson’s constant and
σ
φ
is the residual
stress.
For this report, the first part of Equation 4 was used to calculate the strain (Equation 5), where the first measurement for
dspacing in Table 1 was considered as
d
0
.
ε
φψ
=
d
φψ

d
0
d
0
(5)
The measurements obtained from the XRD test and calculations for d spacing and strain are shown in Table 1.
Measurement
ψ
deg
sin
2
(
ψ
)
Peak pos (
2
θ
) deg
dspacing (nm)
Strain
1
0
0
99.589
0.117119
0
2
26.57
0.2
99.694
0.117029
0.000845
3
39.23
0.4
99.810
0.116929
0.001706
4
50.77
0.6
99.934
0.116823
0.002560
Table 1: Shotpeened steel spring d spacing and strain results from XRD test.
In order to calculate the residual stress, a graph
sin
2
(
ψ
)
vs
ε
φψ
was plotted (Figure 4), obtaining a linear graph
represented by Equation 6. Comparing Equation 4 with Equation 6, it can be deduced that slope 0.0043 is equal to
1+
v
E
σ
φ
. Using the properties of the material shown in Table 2 and Equation 7 the residual stress of 694.61 MPa was
obtained.
Figure 4: Graph
sin
2
(
ψ
)
vs
ε
φψ
for a shotpeened steel spring.
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y
=

0
.
0043
x
+ 3
x
10

6
(6)
Young Modulus (E) MPa
Poisson ratio (v)
Wavelength (
λ
) nm
210x10
3
0.3
0.178897
Table 2: Shot peened steel properties.
σ
φ
=

0
.
0043
E
1 +
v
=
(

0
.
0008)(210
x
10
3
)
1 + 0
.
3
=

694
.
61
MPa
(7)
2. Important is to realize the direction of the stress and if this is compressive or tensile! Draw an arrow in the image
below to indicate the direction of the measured stress in this experiment. Explain from the measured peaks why it
is compressive or tensile in this direction.
Shot peening is a process which affects plastic deformation on the surface, relieves surface tensile stresses and introduces
beneficial
compressive residual stresses
as shown in Figure 5.[
4
] The degree and sign of the residual stress depend on
degree and nature of the working process, and shot peening is a cold working process where peening is carried out on
the surface of a component with small spherical balls called shots.[5]
Figure 5:
Stress formation during shot peening process[5]
XRD is a linearelastic process which calculates residual stresses in the materials from the strain measured in the
crystal lattice. XRD processes do not have significant influence by the hardness of the material, degree of cold work,
or preferred orientation.[
4
] It is proficient of large spatial resolution, on the order of millimetres and depth resolution
on the order of microns. Thus, it can be applied to a wide variety of sample geometries. Through XRD methods,
the macroscopic residual stresses and the information associated with the degree of cold working can be achieved
simultaneously.[
4
] The shallow depth of infiltration of the xray beam, on the scale of 8
μ
m, is an aid for highresolution
6
MS43010  N
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25, 2019
subsurface profiles but can be a hindrance when trying to characterize a stress distribution generated by shot peening
with just surface measurements.[4]
An example of a typical shotpeened surface’s stress depth profile inducing over 400 MPa of compressive residual stress
on the subsurface layers of the component is shown in Figure 6. Within the depth, differences in the stress direction and
values are confirmed by Xray diffraction.[5]
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 Spring '18
 Dr. maarten bakker