E-Journal of Advanced Maintenance Vol. 11 No. 2 (2019) 79-85
Japan Society of Maintenology

Numerical Investigation on Persistence of Modified Residual Stresses Due
to Shot Peening
Kazuki IKUSHIMA1, *, Yusuke YAMADA1, Masakazu SHIBAHARA1, Koichi AKITA2 andSatoru NISHIKAWA3
1Osaka Prefecture University, 1-1 Gakuencho, Naka-ku, Sakai, Osaka 599-8531, JapanTokyo City University, 1-28-1, Tamatsutsumi, Setagawa-ku, Tokyo, 158-8557, Japan
3
Iwate University, 4-3-5, Ueda, Morioka, Iwate, 020-8551, Japan
2

ABSTRACTIn this research, to investigate the persistence of compressive stress on a shot peened surface, the residual stresses
in a multi-pass welded pipe joint after shot peening were analyzed. Then, the variation of the stress distribution in
the welded pipe was examined by elastic plastic analyses under axial tension and compression with considerationof the shot peened residual stress distribution. As a result, it was found that the stress distribution remains incompression by applying tension followed by compression. It was also found that the compressive stress candecrease by applying compression followed by tension. From the above results, it can be said that the persistenceof compressive stress due to shot peening should be discussed before the peening operation, especially a large
load can be assumed to act on the shot peened part.
KEYWORDS
Shot peening, Residual stresses, Multi-pass welding, Elastic-plastic
analysis, Finite element analysis

1.

ARTICLE INFORMATION
Article history:
Received 15 October 2018
Accepted 11 September 2019

Introduction

Welding can cause a high tensile residual stress to occur on the surface of a part. This residual
stress affects the initiation of a fatigue crack and stress corrosion cracking (SCC) [1]. To improve thetensile residual stress on the surface due to welding, various peening techniques are commonly
employed [2, 3]. In the peening process, an impulsive load acts on the target surface and the stress stateon the target surface is improved.
The residual stress distribution after peening has been predicted in several reports [4, 5]. To
investigate the residual stress distribution in weld joints after shot peening, the authors previously
proposed an analysis system [6]. In the study, the reaction force under the collision of shot was modeled
as the equivalent load model. Large numbers of shot collisions were considered in a large-scaled
dynamic elastic plastic analysis in the previous research.
On the other hand, various loads act on shot peened structures under operation. Thus, it is important
to discuss the persistence of the compressive stress introduced by shot peening. The effect of external
force has been discussed in several reports [7, 8]. But, to the best of the author’s knowledge, very few
reports considered the shot peened residual stress distribution on the entire target surface.
In this research, to investigate the persistence of the stress distribution after shot peening undervarious load conditions, the proposed analysis system [6] is applied to the prediction of residual stresses
in a multi-pass welded pipe joint after shot peening. After that, with the obtained residual stress
distribution, the variation of the stress distribution is investigated by conducting elastic plastic analyses.
Through these investigations, the importance of prior assessment for the persistence of the residual
stress distribution after shot peening is discussed.

2.

Analysis System of Residual Stress Distribution After Shot Peening
In shot peening, 1 mm or smaller shots collide with the target surface numerous times and*Corresponding author, E-mail: ikushima@marine.osakafu-u.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

79

P

v1

P

Reaction force : P

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening

Plastic
deformation

Elastic
deformationr

r

Distance from collision : r(b) Elastic deformation(c) Start of plastic
deformation

v2

P

P

P

(a) Start of collision

No forcerr(e) End of plastic deformation(d) Plastic deformationr(f) End of collision

Fig. 1. Schematic illustration of equivalent load model for shot collisioncompressive stress is introduced. The authors previously proposed an analysis system that can predictthe residual stress distribution after shot peening by using the large-scale nonlinear mechanical analysis
method named Idealized Explicit FEM [6] together with the parallelization on a graphics processing
unit (GPU) [9]. In this research, the proposed analysis system is applied to the prediction of the residual
stress distribution after shot peening.
In dynamic elastic plastic analyses using Idealized Explicit FEM, the semi-discretized equation of
motion by FEM is discretized for time by using Newmark’s beta method and the linearized equation
shown in Eq. (1) from the Newton-Raphson is used as fundamental equation:[𝐾𝑒𝑓𝑓 ](𝑘){Δ𝑈} =(𝑘)(1){𝐹𝑒𝑓𝑓 }

where [𝐾𝑒𝑓𝑓 ], {𝛥𝑈}, and {𝐹𝑒𝑓𝑓 } are the effective stiffness matrix, the displacement increment vector,
and the effective load vector, respectively. The left superscript (k) is the iteration number in the NewtonRaphson method. The details of each term is shown in the reference [10].
Adding the virtual inertial term and the virtual damping term yields the following equation:[𝑀𝑑𝑢𝑚 ]{𝑈̈𝑑𝑢𝑚 } + [𝐶𝑑𝑢𝑚 ]{𝑈̇𝑑𝑢𝑚 } + [𝐾𝑒𝑓𝑓 ]{𝑈𝑑𝑢𝑚 }𝜏 = {𝐹𝑒𝑓𝑓 }
𝜏

𝜏

(2)

where [𝑀𝑑𝑢𝑚 ] and [𝐶𝑑𝑢𝑚 ] are the virtual mass matrix and the virtual damping matrix, respectively.
{𝑈̈𝑑𝑢𝑚 } , {𝑈̇𝑑𝑢𝑚 }, and {𝑈𝑑𝑢𝑚 } are the acceleration vector, the velocity vector, and the displacement
vector at virtual time τ, respectively. The displacement vector is defined as {𝑈𝑑𝑢𝑚 } = {𝛥𝑈}.
Discretizing Eq. (2) by the central difference and advancing the time steps until the virtual inertial
term and the virtual damping term become negligibly small, that is, advancing the virtual time 𝜏 in Eq.
(2). The displacement vector obtained by advancing the virtual time 𝜏 is used as a solution. By using
these steps, it is expected that the same solution as that by solving Eq. (1) can be obtained. The virtual
mass and damping matrix ([𝑀𝑑𝑢𝑚 ] and [𝐶𝑑𝑢𝑚 ]) are utilized only to obtain the converged solution. The
formulation of these matrices to reduce the time steps for convergence, are employed as shown in [6].
A load on the collision of a shot is considered in the above dynamic elastic plastic analysis method.
As shown in Fig. 1, the history of the load distribution during the collision of a shot is modeled as anequivalent load model, which is introduced as an external force [6].
In addition, the persistence of the compressive stress introduced by peening is investigated byconducting elastic plastic analyses after shot peening. Therefore, the following series of analyses are
conducted in this research. First, welding residual stresses are predicted by thermal elastic plastic
analysis. Subsequently, shot peening process is analyzed by the abovementioned analysis system.
Finally, the variation of the stress distribution after shot peening is obtained by elastic plastic analysis.

80

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening

3.

Prediction of Residual Stress Distribution After Shot Peening

3.1. Analysis model and conditions
Figure 2 (a) shows the entire model. The detail of the welded part is shown in Fig. 2 (b). Welding
is carried out in 1 pass for each layer for a total of 10 passes. The welding condition is as follows:
current 180 A, voltage 10 V, and speed 1.33 mm/s. The heat efficiency is assumed as 80%. The assumed
temperature dependent material properties are shown in Figs. 3 and 4. The anneal temperature isassumed as 850°C where stress relief heat treatment of austenitic steel is conducted [10]. The effect ofwork hardening at high temperature is eliminated by setting the equivalent plastic strain to zero [11].
After the welding, the inner and outer surfaces are removed by machining. This process is modeledby disabling elements in the removal region. The redistribution of stress is analyzed by the static elastic
plastic analysis.
The target of shot peening is the region 25 mm left and right of the welding line and up to 70°
around the point 180° from the start point of welding. The target surface of shot peening is meshed withhexahedral elements of 0.2 mm and the numbers of elements and nodes are 3,004,664 and 3,494,600,
respectively. The radius of a shot is 0.8 mm and the projection velocity is set to 60 m/s. The analysis ofshot peening continues until the collision area ratio Rc reaches 50. Rc is the ratio of the sum of theloaded area by the equivalent load model to the target area [6].
In the above analysis, the following computer is employed: CPU is an Intel Core i7 3.5 GHz
processor, RAM is 128 GB, GPU is an NVIDIA GeForce GTX TITAN X processor.
3.2. Analysis results
Figure 5 shows the residual stress in axial direction (σx ) distribution after welding on the crosssection 180° from the start point of welding. The figure indicates that large residual stress occurs due
to welding. Figure 6 and 7 show the axial stress distribution after shot peening of the entire pipe and
210mm
50 mm

137.5mm

164.5mm

Removed by machiningA

Shotpeened

A´

z

10
9
8
7
6
5
4
3
2
1

Shot peened(50mm)xyzyWeld metal(Y316L)

Base metal(SUS316L)

Removed by machiningx(b) Zoomed view of welded part(a) Entire modelFig. 2. Analysis model for multi-pass welded pipe joint
9.0

9.0
8.0

6.0

Initial yield stress(102 MPa)
Heat conductivity
Poisson’s ratio(10-2 J/mm/°C)-1(10 )Linear expansion ratio (10-5)

5.0
4.0
3.0
2.0

Work hardening
(GPa)

1.0
0.0
0.0

300.0

600.0

Young’s modulus (102 GPa)

6.0
5.0

1200.01500.0Poisson’s ratio(10-1)

4.0
3.0

1.0

Work hardening
(GPa)
0.0

1800.0Linear expansion
Heat conductivity
ratio (10-5)(10-2 J/mm/°C)

2.0

0.0
900.0

Density (10-3 g/mm3)
Specific heat (102 J/kg/°C)

7.0

Material constants

Material constants

8.0

Density (10-3 g/mm3)
Specific heat (102 J/kg/°C)

7.0

300.0

600.0

Young’s modulus (102 GPa)
Initial yield stress (102 MPa)
900.0

1200.01500.01800.0Temperature (°C)

Temperature (°C)

Fig. 3. Temperaturedependentmaterial
constants of SUS316L (base metal)

Fig. 4. Temperaturedependentmaterial
constants of Y316L (weld metal)

81

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening
(MPa)
240
180
120
60
0
-60
-120
-180
-240
-300

z

x

y

Fig. 5. Axial residual stress distribution after
welding on the cross section at 180° from thestart of welding

(MPa)
450
350
250
150
50
-50
-150
-250
-350
z
-450
y
x
-550

Fig. 6. Axial stress distribution after shot
peening
400.0

Weld
metal

A

A´

(MPa)
400
300
200
100
0
-100
-200
-300
-400
-500

z

x

y

Stress (MPa)

200.0
0.0
-200.0σzσθ-400.0σz-600.0σθ

Shot peened-800.0
-60.0

-40.0

-20.0

0.0

20.0

Welding
XRD
IEFEM
XRD
IEFEM
Peening
XRD
IEFEM
XRD
IEFEM

40.0

60.0

Distance from weld line (mm)Fig. 8. Comparison of analyzed and measured
residual stress distribution after
welding and shot peening

Fig. 7. Axial residual stress distribution after shot
peening on the cross section at 180° fromthe start of weldingthat on the same cross section, respectively. From these figures, it is found that strong compressive
stress is introduced to the target surface.
Figure 8 shows the comparison of the residual stress distribution measured by XRD and calculatedby the analysis. Figure 8 shows that the analyzed axial and hoop residual stress distributions agree wellwith those measured by XRD after both welding and shot peening.
As shown here, the stress distribution predicted by using the proposed analysis system canreproduce the measured results well. The computing time of was about 10 days in total.

4.

Variation of Residual Stress After Shot Peening due to Various Loads

4.1. Analysis model and conditions
To investigate the persistence of the compressive stress introduced by shot peening, the variationof the stress field is discussed by applying external loads to the multi-pass welded pipe model after shot
peening. The analysis model and material properties are the same as those given in Section 3.
Figure 9 schematically shows the two cases of load conditions in this analysis. In Fig. 9 (a), a
tension is applied; after that, the same quantity of compression is given, and then the constraint isreleased. This case is defined as the tension-compression-release condition. Likewise, the compressiontension-release condition (Fig. 9 (b)) is also investigated. Four cases of applied tensile/compressive
strain are assumed: 0.15%, which is assumed to be within the elastic deformation; 0.5% and 0.7%,
which exceed the yield stress; and 1.0%, which assumes excessive loads such as great earthquakes.
4.2. Influence of tensile load
Figure 10 shows the deformed shape during tensile deformation with the axial stress distribution
at 1.0% tension. The deformation in this figure is magnified by ten times. The barrel-shaped deformation
is obtained by applying tension. The reason for this deformation is assumed as follows. The yield stress82

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening

Applied axial
strainPeak tension

Load step
Applied axial
strainRelease of
constraint
Load step

Release of
constraint
Peak compression(b) Compression-tension-release condition(a) Tension-compression-release condition

Fig. 9. Schematic illustration of loading conditionsof the weld metal is higher than that of the base metal. Thus, the deformation in the weld metal is smaller
than that in the base metal and the axial elongation due to tension becomes different. It can be assumed
that this difference can cause the bending deformation along axial direction and the barrel shaped
deformation.
Figure 11 shows the axial stress distribution under the applied tension on the cross section at 180°from the start point of welding. The tensile stress occurs over the entire cross section at the peak tension,
as shown in (a). This is because the large 1.0% tensile strain is applied. In the case that the compressive
strain is applied after the tension (b), almost the entire cross section has compressive stress. After the
release of the compressive strain (c), the strong compressive stress in the shot peened part recovers.
Figure 12 shows the axial stress distribution along line B-B´ after the tension-compression-releasecondition. Figure 13 shows the distribution of the plastic strain increment along line B-B´ after loading
under the tension-compression-release condition. The effect of first applying the tension remains at
(MPa)
620
530
440
350
260
170
80
-10
-100 zx-190 yFig. 10. Deformed shape of pipe joint and axial stress distribution during tensile deformation
(MPa)
540
480
420
360
300
240
180
120
60
0

z

x

(MPa)
0
-60
-120
-180
-240
-300
-360
-420
-480
-540

B

y
B´
(a) Tension
(MPa)
230 z
160
90
20 y
-50
-120
-190
-260
-330
-400

z

x

y

(b) Compression after tensionx(c) Release after tension and compression
Fig. 11. Distribution of stress in axial direction83

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening
0.0008B(shot peened)

B´

Axial stress (MPa)

200.0

0.0

-200.0As-peenedas-peened
0.15%
tension0.15%
tens-rel
0.50%
tension0.50%
tens-rel0.70%
tens-rel
0.70%
tension1.00%
tens-rel
1.00%
tension-400.0B(shot peened)

0.0006

Axial plastic strain increment

400.0-600.00.0004

0.70% tension
1.00% tension

0.00020.0000-0.0002-0.0004-0.0006-0.0008

0.0

2.0

4.0

6.0

8.0

10.0

0.0

2.0

Distance from point B (mm)600.0

B(shot peened)

0.0012B´
Axial plastic strain increment

200.0
0.0

As-peenedas-peened
0.15% compression
0.15% comp-tens-rel
0.50%comp-tens-rel
compression
0.50%
0.70%comp-tens-rel
compression
0.70%
1.00%
1.00%comp-tens-rel
compression-400.0-600.0

6.0

8.0

10.0

Fig. 13. Comparison of plastic strain
increment
under
tensioncompression-release condition

400.0-200.04.0

Distance from point B (mm)Fig. 12. Comparison of axial stress (σx) under
tension-compression-release condition

Axial stress (MPa)

B´

0.15%
tens-comp-rel
As-peened
0.50%
tens-comp-rel
0.15%
tension0.70% tens-comp-rel
0.50%
tension
1.00% tens-comp-rel-800.0B(shot peened)

As-peened
0.15% compression
0.50% compression
0.70% compression
1.00% compression

0.00080.0004B´

0.0000-0.0004-0.0008

0.0

2.0

4.0

6.0

8.0

10.0

0.0

Distance from point B (mm)

2.0

4.0

6.0

8.0

10.0

Distance from point B (mm)Fig. 15. Comparison of plastic strain
increment under compressiontension-release condition

Fig. 14. Comparison of axial stress (σx) undercompression-tension-release condition

0.50% tensile strain and the compressive stress slightly decreases. In the case of 0.70% tensile strain,
the compressive plastic strain increment is larger than that at 0.50% tensile strain, and that is even larger
at 1.0% tensile strain. Especially, at 1.0% tensile strain, large compressive plastic strain is generated.
The compressive stress on the shot peened surface increases due to the increase of compressive plasticstrain.
In summary, in the case that the compression is applied after applying tension, the effect of tension
decreases and the compressive stress in the shot peened surface can be maintained.
4.3. Influence of compressive load
In the same way as the tension-compression-release condition, the variation of the stress
distribution is investigated in the case that the load conditions shown in Fig. 9 (b) is applied.
Figures 14 and 15 show the axial stress distribution and the axial plastic strain increment under thecompression-tension-release condition, respectively. For the conditions over the applied compressive
strain of 0.7%, the tensile plastic strain is pronouncedly generated, and the compressive stress on the
shot peened surface decreases. As shown here, it can be assumed that the compressive stress introducedby shot peening can decrease in case that the tension is applied after applying compression.
From these discussions of the numerical investigations, the compressive stress introduced by shot
peening can maintain unless excessively large loads are applied in the targeted weld joint. Therefore, it
can be said that the persistence of the compressive stress introduced by shot peening should be
investigated in advance, especially in the case that large load acts on the peened part.

5.

Conclusion
To numerically investigate the persistence of compressive stress on a surface due to shot peening,84

K. Ikushima, et al./ Numerical Investigation on Persistence of Modified
Residual Stresses Due to Shot Peening

this research analyzed the residual stress distribution of a multi-pass welded pipe joint after shot peening
using the analysis system proposed by the authors. With the analysis results of the residual stress
distribution, elastic plastic analyses were conducted under axial tension and compression, and thevariation of the residual stress distribution after shot peening due to the load conditions was investigated.
As a result, it was shown that the proposed analysis system can accurately simulate the residual stressdue to welding and shot peening in realistic computing time. It was seen that the compressive stressintroduced by shot peening can be maintained in the case that the compression is applied after thetension. It was also found that the compressive stress on the shot peened surface can maintain unlessexcessively large loads are applied in case that the tension is applied after the compression. These results
indicated that to evaluate the persistence of the compressive stress due to shot peeing, it is importantwhether large loads acted to the part.

Acknowledgement
A part of this study is the result of “Development of a Basic Technology for the Safety Assessmentof Residual Stress Improvement Method on Nuclear Power Plant Structures” carried out under theCenter of World Intelligence Project for Nuclear S&T and Human Resource Development by the
Ministry of Education, Culture, Sports, Science and Technology of Japan.

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