A study of the effect of dual shot peening on the surface integrity of carburized steel: combined experiments with dislocation density-based simulations

Abstract

As a novel processing technology for high surface integrity, dual shot peening enables improvement in residual compressive stress, hardness gradient, and a reduction in surface roughness, thus effectively enhancing the fatigue resistance of mechanical components. The modelling and experiments on the dual shot peening of 18CrNiMo7-6 carburized gear steel have been conducted. A dual-shot peening finite element model based on the dislocation density constitutive equation that considers hardness gradient, residual stress, and surface roughness has been developed. Extensive peening tests and surface integrity characterisation using TEM and EBSD were conducted. The correlation between peening parameters and surface integrity and the underlying mechanism have been explored. The results from modelling and the experimental dual shot peening tests are in good agreement, with the maximum errors of residual stress and microhardness less than 15.1% and 7.4%, respectively. For an effective dual shot peening process, high-intensity peening with medium shots is recommended as the first step, and low-intensity peening as the second step. This process increases the surface residual compressive stress and hardness to-950 Mpa and 790 HV, respectively, while maintaining a reduced surface roughness.

Full text

Vol.:(0123456789)
Archives of Civil and Mechanical Engineering (2024) 24:83
https://doi.org/10.1007/s43452-024-00893-x
ORIGINAL ARTICLE
A study oftheeffect ofdual shot peening onthesurface integrity
ofcarburized steel: combined experiments withdislocation
density‑based simulations
JizhanWu1· PeitangWei1 · MarioGuagliano2· JinghuaYang3· ShengwenHou3· HuaijuLiu1
Received: 18 October 2023 / Revised: 25 January 2024 / Accepted: 3 February 2024
© Wroclaw University of Science and Technology 2024
Abstract
As a novel processing technology for high surface integrity, dual shot peening enables improvement in residual compressive
stress, hardness gradient, and a reduction in surface roughness, thus effectively enhancing the fatigue resistance of mechanical
components. The modelling and experiments on the dual shot peening of 18CrNiMo7-6 carburized gear steel have been
conducted. A dual-shot peening finite element model based on the dislocation density constitutive equation that considers
hardness gradient, residual stress, and surface roughness has been developed. Extensive peening tests and surface integrity
characterisation using TEM and EBSD were conducted. The correlation between peening parameters and surface integrity
and the underlying mechanism have been explored. The results from modelling and the experimental dual shot peening tests
are in good agreement, with the maximum errors of residual stress and microhardness less than 15.1% and 7.4%, respectively.
For an effective dual shot peening process, high-intensity peening with medium shots is recommended as the first step, and
low-intensity peening as the second step. This process increases the surface residual compressive stress and hardness to -950
Mpa and 790 HV, respectively, while maintaining a reduced surface roughness.
Keywords Carburized steel· Dual shot peening· Surface integrity· Grain refinement
1 Introduction
As basic mechanical components of machines, gears are
widely used in aviation, aerospace, wind power, automobile,
and shipbuilding industries. Modern machines are designed
for higher reliability and longer lifetimes, necessitating more
exacting requirements for the fatigue resistance of gears [1,
2]. Anti-fatigue manufacturing technologies play an essen-
tial role in guaranteeing gear fatigue resistance and have
become a focus of research in academia and industry.
Among these manufacturing processes, shot peening is a
typical surface strengthening method, widely used in gears,
bearings, blades and other components [3]. Shot peening is
used to eliminate the tensile residual stress generated during
machining, such as grinding and turning [4], to minimise
the influence of undesired micro-structures formed on gear
surfaces during heat treatment [5], and to effectively allevi-
ate stress concentrations caused by tool marks or structural
factors such as grooves, holes, and transition fillets [6]. It is
widely acknowledged that shot preening can improve sur-
face hardness, refine material microstructure, and increase
dislocation density [4], thus achieving considerable improve-
ments in both fatigue life and the limits of components [6].
Overall, the load-bearing capacity of components such as
gears enables it to be improved by adopting an appropri-
ate shot peening treatment. Reports in the engineering lit-
erature have established an increase in the tooth bending
fatigue limit of carburized gears by 10–30% as a result of
shot preening, while the gear contact fatigue limit has been
increased by 5–20%. For example, Chen etal. [7] studied the
effect of shot peening on the bending fatigue performance
of 18CrNiMo7-6 carburized gears and observed an increase
* Peitang Wei
peitangwei@cqu.edu.cn
1 State Key Laboratory ofMechanical Transmission
forAdvanced Equipment, Chongqing University,
Chongqing400044, China
2 Department ofMechanical Engineering, Politecnico di
Milano, 20156Milan, Italy
3 Shaanxi Key Laboratory ofGear Transmission, Shaanxi Fast
Auto Drive Co., Ltd, Xi’an710119, China

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 2 of 22
from 460 to 603MPa due to the enhanced residual stress and
surface hardness induced by shot peening. Zhang etal. [8]
carried out a series of contact fatigue tests for 18CrNiMo7-6
carburized gears in the grinding and shot peening states.
They found that shot peening increased the contact fatigue
limit of gears from 1570 to 1765MPa. Moreover, some stud-
ies have found that shot peening led to an increase in the
scuffing and wear resistance of surfaces. Zammit etal. [9]
investigated the effect of shot peening on scuffing behaviour
and found that shot-peened specimens exhibited increased
scuffing resistance by an order of magnitude due to the high
residual compressive stress and hardness generated during
the process. Han etal. [10] investigated the tribological
behaviour of different austempered AISI 5160 steel speci-
mens after shot peening and demonstrated that the wear of
specimens was reduced by up to 73%, greatly improving the
wear resistance.
Combined manufacturing processes have been proposed
as an approach to improve surface integrity and service
performance. The composite process represented by dual
shot peening has a significant effect on the fatigue resist-
ance of high surface integrity processing and service per-
formance. Appreciable research has been conducted on
the application of composite processes. In particular, the
composite shot peening process considers the improvement
of residual compressive stress and the reduction of surface
roughness. Fu etal. [11] have studied the effect of compos-
ite shot peening on 18CrNiMo7-6 steel and reported that
the 0.50 + 0.30 + 0.15 mmA shot peening process enabled
an increase in the maximum compressive residual stress to
−1467MPa, and the surface microhardness to 1174 HV.
Lin etal. [12] found that dual-shot peening increases surface
residual compressive stress with reduced surface roughness.
Moreover, the authors noted that the subsurface location of
the maximum residual compressive stress was shifted closer
to the surface. Composite strengthening processes that com-
bine shot peening with other processes can also have a sig-
nificant effect, notably the combination of shot peening with
heat treatment which can significantly improve the carburi-
zation effect. Wu etal. [13] explored the effect of pre-shot
peening on carburizing efficiency and the surface integrity
of carburized steel rollers. The pre-shot peening served to
increase carburizing efficiency by 66.7%, greatly reducing
the production cost. In addition, shot peening combined with
surface finishing technology works well in the synergistic
machining of residual stress and roughness. Zhang etal.
[14] proposed a combined manufacturing treatment with
shot peening and barrel finishing, which increased surface
residual stress while reducing surface roughness.
Dual shot peening has the characteristic of being simple
and convenient to implement and can be readily applied in
engineering practice. Lambert etal. [15] investigated the
gear bending fatigue limit of dual shot peened made from
20CrMn5 steel and reported an improvement in the bend-
ing fatigue limit from 546 to 598MPa. Matsumura and
Hamasaka [16] assessed double hard shot peening (WHSP)
technology. They employed a first-step shot peening process
with a shot diameter of 0.8mm, followed by a second-step
peening with a diameter less than 0.1mm, which increased
the maximum compressive residual stress by more than
200MPa, achieving a lightweight design for the transmis-
sion system. Current research on dual-shot peening mainly
focused on direct application, and studies exploring the pro-
cess rules and standard methods of dual-shot peening are
limited. Ongtrakulkij etal. [17] have considered the effect
of shot types and diameters on hardness, roughness, and
residual stress after dual-shot peening. They reported that
compressive residual stress and surface hardness were signif-
icantly higher when treating with the smaller diameter shots
during the second step. Wang etal. [18] investigated the
changes in surface integrity of WC–CO cemented carbide
after dual shot peening treatment and observed an improved
uniformity of macroscopic and microscopic residual stresses
due to peening. Heydari Astaraee etal. [19] developed a
numerical model for dual shot peening of surface hardened
gear that incorporates variation of material properties with
thickness. They demonstrated that a local 3D cubic cell
model can be used to predict the final distribution of residual
stresses and surface roughness.
However, there has been little research on the genera-
tion rule for surface integrity in dual-shot peening, and the
related mechanism. This adds considerable limitations to the
practical application of dual-shot peening. The relationship
between dual shot peening processing parameters and sur-
face integrity must be investigated. The strengthening mech-
anism and application require further exploration. Based on
simulations and experiments, this study explores the influ-
ence of dual shot peening process parameters and the dual
peening sequences on surface integrity. Furthermore, a
mechanism for the surface integrity of dual shot peening at
the micro level has been proposed, which provides theoreti-
cal and data support for the practical implementation of the
dual shot peening process.
2 Experimental procedure
2.1 Samples andshot peening
A typical low-carbon carburizing gear steel 18CrNiMo7-6
was used for this study, which is widely used in high-speed
and heavy-duty transmission components. The chemical
composition of the steel (in wt.%) is C (0.17), Mn (0.75), Cr
(1.63), Ni (1.65), Mo (0.30), P (0.020), Si (0.32), S (0.030),
and Fe-Balance. Roller samples were used to conduct shot
peening and dual shot peening experiments. The diameter

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 3 of 22 83
and width of the samples were 60mm and 9mm, respec-
tively. The detailed manufacturing process is schematically
illustrated in Fig.1. After carburizing and grinding, the sur-
face hardness reached 690 HV, the thickness of the hardened
layer was 2.2mm, and the arithmetic mean height (Sa) was
0.62μm.
The commercial pneumatic shot peening machine
(MT25-G80IIE/1/R) was used for the treatment, as shown
in Fig.2a. The equipment utilizes a 180° flip turntable, ena-
bling simultaneous loading and shot peening. The blasting
gun has a diameter of 8mm and is positioned 150mm from
the target body with a shot peening angle set as 90°. The
schematic diagrams in Fig.2b illustrate conventional shot
peening and dual shot peening. The 430 stainless steel shots
were steel wire pellets with diameters 0.4, 0.6, and 0.8mm
(see Fig.2c). In addition, the roundness grade of the shots
is at G2 level. The shot peening intensity was adjusted to
0.20, 0.35, and 0.50 mmA, and the shot peening coverage
was fixed at 200% according to the SAE J2277 standard.
The shot peening processing parameters are given in
Table1. A total of six batches of shot peening and dual
shot peening experiments were conducted. The conditions
involving different shot peening intensities are denoted
CSP1, CSP2, and CSP3, and represent conventional shot
peening. The different intensities were achieved by adjusting
the shot peening pressure and flow rate. Differences in shot
Fig. 1 Manufacturing process of the18CrNiMo7-6 roller samples
Fig. 2 Shot peening and dual shot peening process of the roller samples. a Shot peening experimental process; b Shot peening and dual shot
peening schematic diagram; c 0.4mm, 0.6mm, 0.8mm steel wire cutting shots morphology

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 4 of 22
diameter are denoted CSP2, CSP4, and CSP5. In addition,
DSP1 represents dual shot peening with a first peening step
at 0.35 mmA and a second step peening intensity reaching
0.50 mmA.
2.2 Surface integrity characterizations
Residual stress was tested by portable residual stress
meter (PULSTEC μ-360s, Cr target, 30kV, 1.5mA)
using ASTM E915 standard. The Proto-8818 electrolytic
polishing machine with saturated sodium chloride solution
as electrolyte was used to measure residual stress gradient
along the depth. The voltage and current of the polishing
machine were 60V and 2 A, respectively. In addition, the
corrosion depth was measured using a depth micrometer,
with an accuracy of 1μm. The testing depth of residual
compressive stress was up to 400μm.
The surface roughness was measured with the white
light interferometer of the surface measurement module
(RTEC MFT-5000) and a selection of 10 × magnification.
The spot size length and width were 1.11mm and 0.89mm,
respectively. Each position was measured three times to
confirm the accuracy of the measurements according to ISO
25178 standard. The surface topography of the shots and the
rollers were examined using a scanning electron microscope
(SEM, TESCAN VEGA 3 LMH). An XRD diffractometer
(PANalytical Empyrean) was used to determine the phase of
the specimen; a ceramic Cu target X-ray tube was employed
with a maximum power of 2.2kW.
The microhardness was measured on a digital automatic
turret micro-hardness tester (MHVS-1000AT) by ISO
6507 standard. The loading force was 500g and the load
retention time was 10s. Three separate measurements were
made for each condition and used to determine an average
microhardness. The width of a single measurement point
was around 40μm, so the surface depth of the first test point
was about 40–50μm.
Electron backscatter diffractometry (EBSD) was conducted
using an FE field emission scanning electron microscope
(LIBRA 200) to determine the microstructure and crystal ori-
entation of the material surface with ISO 24173 standard. The
sample was cut into an approximately 2 × 2 × 0.5 mm3 sample
block, placed in anhydrous ethanol with ultrasonic cleaner for
10min, and mechanically polished using water sandpaper until
there was no scratch on the surface. The sample was then sub-
jected to vibration polishing with nano-SiO2 as the polishing
solution.
TEM analysis was performed using a ChemisStem
Technology transmission electron microscope (FEI G2
60-300) operated at 200kV. Specimens for TEM were
prepared using the focused ion beam (FIB) method with a
gallium ion source. The sample was cut into 2 × 2 × 0.5 mm3,
ground to 40μm thickness with sandpaper, thinned to less
than 20μm through pits, finally obtaining a film area with a
thickness of less than 5000Å with ion thinning.
3 Numerical modelling
3.1 Dislocation density‑based constitutive
equations
Macroscopic plastic deformation occurs due to the high-speed
impact of shots in shot peening. Microscopically, the disloca-
tion slip systems are activated and dislocation proliferation
occurs, it gradually increasing dislocation density, and forming
a dislocation cell structure [20]. The dislocation cell structure
is generally composed of dislocation cell interiors and dislo-
cation cell walls [21]. The evolution of dislocation density
𝜌w
on the dislocation cell wall and the dislocation density
𝜌trial
c
inside the dislocation cell follows different rules, as shown in
(1) and (2) [22],
(1)
Δ
𝜌c=
𝛼∗MΔ𝜀
p
𝜌w
3b
−6𝛽∗MΔ𝜀p
bd(1−f)
1
3
−kcMΔ𝜀p𝜌cMΔ𝜀p
𝛾 0−
1
nc
,
Table 1 Processing parameters
of shot peening and dual shot
peening tests
First shot peening process parameters Dual shot peening process parameters
Parameters Pressure (MPa) Flow rate
(kg/min) Parameters Pressure (MPa) Flow rate
(kg/min)
CSP1 0.35 mmA-200%-0.6mm 0.4 12
CSP2 0.20 mmA-200%-0.6mm 0.15 10
CSP3 0.50 mmA-200%-0.6mm 0.5 6
CSP4 0.20 mmA-200%-0.4mm 0.2 5
CSP5 0.20 mmA-200%-0.8mm 0.1 8
DSP1 0.35 mmA-200%-0.6mm 0.4 12 0.50 mmA-
200%-
0.6mm
0.5 6

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 5 of 22 83
where
nw
and
nc
are constants related to temperature.
𝛼∗
,
𝛽∗
,
kc
and
kw
are constants related to dislocation generation
and annihilation, respectively.
𝛾 0
denotes the reference
decomposed shear strain rate,
b
represents the maximum
Burgers vector,
d
refers to the grain size,
f
represents the
volume fraction of the dislocation cell wall,
Δ𝜀p
refers to
the increment of equivalent plastic strain [21], and
M
is the
Taylor coefficient.
Equations(1) and (2) consist of three terms. The first term
represents the intra-grain dislocation proliferation caused by
the activation of the Frank-Read source. The second term
deals with the transfer of dislocation in the grain to the grain
boundary. The last term represents the reciprocal annihilation
associated with the cross-slip of the intracellular screw
dislocation and the climb of the edge dislocation.
The overall dislocation density can be expressed as the
weight of the dislocations on the dislocation cell wall and the
dislocations inside the dislocation cell, as shown in (3).
where
f
is represented by [23],
and
f0
and
f∞
are the initial state value and the saturation
state value of the volume fraction of dislocation cell wall
f
,
respectively, and γ  is a constant [22]. The average grain size
d
is assumed to be inversely proportional to the square root
of the overall dislocation density,
K
is the parameter that expresses cumulative plastic strain,
where
K0
and
K∞
are the initial state value and the saturation
state value of
K
, respectively, and β is a constant [24]. The
mechanical behaviour of the material is simulated by a con-
stitutive model in the finite element numerical framework of
(2)
Δ𝜌w=
√3
𝛽
∗MΔ
𝜀
p(1−f)√
𝜌w
fb +
6
𝛽∗MΔ𝜀
p
(
1
−f)
2
∕
3
bdf
−kwMΔ𝜀p𝜌w
(
MΔ𝜀p
𝛾 0)
−1
nw,
(3)
𝜌t=f𝜌w+(1−f)𝜌c,
(4)
f=f∞+

f0−f∞

exp

−MΔ𝜀
p
𝛾
,
(5)
d
=
K
√
𝜌
t
.
(6)
K
=K
∞
+
(
K
0
−K
∞)
exp
(
−𝛽Δ𝜀
p),
shot peening. The Von-Mises yield criterion is adopted with
the flow stress expressed by
where
𝜎1
refers to the strain-independent initial stress that
hinders dislocation slip, and can be calculated from the
initial yield strength.
𝜎2
originates from the interaction
between dislocations and is related to the strain. In addition,
the hardness can be converted to a yield strength, which
allows material hardness to be added to the target. The
correlation between hardness and strength is based on the
Pavlina-Tyne formula [25],
where
𝜎y
is the yield strength, and H refers to the micro-
hardness. In addition, the resolved shear stress and shear
strain are related to the equivalent plastic strain via the
Taylor coefficient and
𝜎2
:
The shear stress can be calculated as follows [26],
where
G
is the shear modulus,
m∗
refers to the reciprocal of
the strain rate sensitivity coefficient, and
𝛼
is a constant [22].
The material parameters in the dislocation density-based
constitutive equation are listed in Table2 [24]. In summary,
the model considers plastic deformation, dislocation density
evolution, and initial material hardness. The calculation of
flow stress is based on integral and iterative algorithms. The
dislocation density constitutive equation is implemented
using the VUMAT subroutine in the finite element model
by Abaqus.
(7)
σ=𝜎1+𝜎2,
(8)
𝜎y=−90.7 +2.876H,
(9)
𝜏
r
=
𝜎
2
M,
(10)
𝜏r
=M𝜀.
(11)
𝜏r=f𝜏r
w+(1−f)𝜏r
c,
(12)
𝜏
r
w=𝛼Gb
√
𝜌w(MΔ𝜀
p
𝛾 0
)
1∕m∗
,
(13)
𝜏
r
c=𝛼Gb
√
𝜌c(MΔ𝜀p
𝛾
0
)
1∕m∗
,
Table 2 Material parameters
for a carburized gear used in the
dislocation-based constitutive
model
M
𝛼∗
𝛽∗
kc
kw
nc
nw
f0
f∞
γ
3.06 1.05 0.097 26.15 35.95 69.09 99.54 0.25 0.06 3.2
K0
K∞
β
G
(MPa)
m∗
𝛼
b
(mm)
𝜌t
=
0
w
(mm−2)
𝜌t
=
0
c
(mm−2)
100 1 0.26 82,000 108.92 0.25 2.48 × 10–7 5 × 1072.5 × 107

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 6 of 22
3.2 Dual shot peening finite element model
In this section, we address the development of the dual-shot
peening numerical model. The model was developed based on
a single shot peening numerical model which was established
first, as shown in Fig.3. The size of the target in this model is
5 × 5 × 10 mm3, and the shot peening area is 1 × 1 mm2. The
coverage was calculated using the Avrami Equation [25],
where C refers to the peening and shot peening coverage,
considered to be 100% as coverage reaches 98%. a is the
crater radius formed by a single shot impacting the target
surface, and N represents the number of shots required to
reach 100% coverage. The value can be calculated based on
Hertzian contact theory or the single-shot peening model.
In this study, we use the calculation method combined with
the Hertzian contact theory [25]. In addition, the coordinate
distribution of the shots in space takes a random functional
form,
(14)
C
=100
(
1−e−𝜋a2N
),
where,
Xi
,
Yi
,
Zi
represent the spherical center coordinates of
the i-th shots. It embodies different shot diameters and shot
impact velocities required to achieve the desired intensity.
The shot peening intensity may exhibit the same arc height,
but the shot peening velocity and shot diameter can be differ-
ent [27]. The realisation determination of peening intensity
is inconceivable not possible without conceptualising the
parameters such as peening flow, peening distance, and shot
diameter. According to the empirical formula [25], the shot
velocity can be calculated under different peening intensi-
ties, as shown in Table3,
It is necessary to reconstruct initial residual stress,
geometric parameters, and mechanical properties before
including shot peening in the model, and the surface must
be modelled by restructuring with reverse engineering.
The three-dimensional surface point cloud data obtained
from the surface roughness test was reconstructed in this
(15)
X
i
=Rand.uniform(−0.5, 0.5),
Y
i=Rand.uniform(−0.5, 0.5)
,
Z
i=10 +i
2
+i×i,
(16)
V
=
163.5 ×p
1.53 ×m+10 ×p
+
295 ×p
0.598 ×D+10 ×p
+48.3 ×p
.
Fig. 3 Shot peening finite element model and initial surface roughness, residual stress, hardness, reconstruction

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 7 of 22 83
study. Redundant information was removed from the
measured point cloud data, and the spatial topological
relationship matrix was constructed. The three-dimensional
surface was then characterised after accounting for the
reconstruction. The processed point cloud data was used
as the input in Creo software for three-dimensional surface
reconstruction of 1 × 1 × 1 mm3, as shown in Fig.3. The
initial hardness enables to be imported into the dislocation
density constitutive model according to Eq.(8). The initial
hardness gradient before shot peening can be represented
by the yield strength in constitutive model. The state of
residual compressive stress in different directions of each
depth position must be measured and added in the “pre-
defined field” in the finite element Abaqus software [28].
The residual stress in the X direction is added as “Sigma
11”, and the residual stress in the Y direction is added as
“Sigma 22”, as shown in Fig.3.
The dual-shot peening process was simulated and
modelled based on the single-shot peening finite element
model. Sequential inheritance of the results of the first
shot peening process simulation was carried out using the
import function embedded in Abaqus. A flow diagram for
the single shot peening and dual shot peening is shown
in Fig.4. The hardness of the shots is about 700 HV, the
yield strength is 1900MPa, Poisson's ratio is 0.3, the
elastic modulus is 210 GPa, and the density of 18CrN-
iMo7-6 is 7.85 × 10–9kg/mm3. The contact between the
shots and the target is set to surface-to-surface contact,
and the friction coefficient is set to 0.2 [3]. The mesh size
of the central shot peening area is set to 0.002mm, the
mesh type is C3D8R, and the mesh of the transition area
is slightly increased. An infinite element type is applied
to the rest of the target solid, which reduces the impact
of shots on the shock wave of the target. After explicit
dynamics calculation, the spring-back calculation based on
Table 3 Shot peening numerical
process parameters Shot peening parameters Pressure (MPa) Flow rate (kg/
min) Speed (m/s)
CSP1 0.35 mmA-200%-0.6mm 0.4 12 49.3
CSP2 0.20 mmA-200%-0.6mm 0.15 10 33.3
CSP3 0.50 mmA-200%-0.6mm 0.5 6 57.4
CSP4 0.20 mmA-200%-0.4mm 0.2 5 39.4
CSP5 0.20 mmA-200%-0.8mm 0.1 8 26.1
Fig. 4 Schematic diagram of modelling process of shot peening and dual shot peening
Table 4 Parameters in dual shot
peening First shot peening process parameters Dual shot peening process parameters
DSP1 CSP1:0.35 mmA-200%-0.6mm CSP3:0.50 mmA-200%-0.6mm
DSP2 CSP1:0.35 mmA-200%-0.6mm CSP2:0.20 mmA-200%-0.6mm
DSP3 CSP1:0.35 mmA-200%-0.6mm CSP4:0.20 mmA-200%-0.4mm
DSP4 CSP1:0.35 mmA-200%-0.6mm CSP5:0.20 mmA-200%-0.8mm

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 8 of 22
the implicit statics (ABAQUS/Standard) step and output-
ting the numerical simulation results are conducted. The
implicit statics' spring-back calculation is mainly utilized
to remove elastic wave effects in the shot-peening model.
Finally, we extracted and analysed surface roughness,
residual stress, microhardness, and microstructure. The
simulation parameters for dual shot peening are given in
Table4. The DSP1 and DSP2 parameters were used to
explore the influence of shot peening intensity in dual shot
peening; DSP3 and DSP4 were used to study the influence
of the shot diameter in dual shot peening.
4 Results
4.1 Model validation
To validate the dual shot peening model, the simulated
results with experimental measurements have been com-
pared. The residual stress, hardness gradient, and sur-
face roughness obtained from CSP1, CSP2, CSP3, and
DSP1 were assessed. As shown in Fig.5a–d, intense
plastic deformation introduced with shot peening in the
subsurface layer resulted in a residual compressive stress
Fig. 5 Verification of predicted surface integrity: a–d Comparisons of
residual stress between experiment and simulation for CSP1, CSP2,
CSP1, and DSP1, respectively. e–h Comparisons of micro-hardness
between experiment and simulation for CSP1, CSP2, CSP1, and
DSP1, respectively. i,j Comparisons of Sa and Sz between experiment
and simulation for CSP1, CSP2, CSP1, and DSP1, respectively

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 9 of 22 83
distribution that initially increased and then decreased. In
addition, it can be found that the simulated and measured
residual stress profiles show good agreement. In the case
of surface residual stress (CSP2), the experimental and
numerical results are −965 and −819MPa, respectively,
with a maximum error of 15.1%, as illustrated in Fig.5b.
The comparative results for microhardness can be
compared in Fig.5e,f. The simulated hardness shows an
upward trend closer to the surface, which then decreases
in the direction of depth. As the surface hardness
cannot be measured due to limited instrument accuracy,
a near-surface hardness depth of about 40–50μm was
measured. Overall, the simulated values of hardness
distributions, and depth with the maximum hardness,
match the measured values. The results of numerical and
experimental data also agree along the depth direction,
with a maximum error of only 7.24% when treated by
CSP2.
The surface roughness is represented by Sa and Sz [3].
As shown in Fig.5i–j, the numerical and experimental
results of Sa and Sz are almost identical. The maximum Sz
error of 0.3μm when treated by CSP3 represents a predic-
tion error ratio of 17.6%; the maximum prediction error
ratio is 13.2% for the arithmetic mean height Sa. Based
on the comparison results of hardness, residual stress, and
surface roughness, we can conclude that the experimental
and numerical results are in good agreement, establishing
the validity and accuracy of the dual-peening models.
4.2 Effect ofshot peening intensity
In the case of carburized gears, the most important shot-
peening treatment parameters are peening intensity and
shot diameter [25]. The effect of shot peening intensity and
dual shot peening with different intensities on the residual
stress are shown in Fig.6. To explore the effect of different
Fig. 6 Residual stress results obtained with different singleshot peen-
ing intensities and dual shot peening with simulation: a Top view of
residual stress distribution; b Side view of residual stress distribution;
c Residual stress distribution profile; d Surface and maximum resid-
ual stress; e Maximum residual stress depth and the influence on the
depth of residual stress

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 10 of 22
peening intensities, the diameter of the shot was fixed at
0.6mm and the peening coverage was maintained at 200%.
The residual stress distribution, surface residual stress, and
the maximum residual stress obtained with different shot
peening intensities for dual shot peening were examined in
detail with numerical calculations.
As shown in Fig.6a and b, an increased shot peening
intensity resulted in greater uniformity of the surface residual
compressive stress. This response, in terms of uniformity, is
more evident in dual-shot peening. Moreover, the surface
residual compressive stress gradually decreased with an
increase in shot peening intensity, while the maximum
residual compressive stress increased. Following the dual
shot peening treatment, the surface residual compressive
stress and the maximum residual compressive stress
improved significantly. The surface residual compressive
stress increased from about −650 MPa to greater than
−850MPa, and the maximum residual compressive stress
was in excess of −1100MPa (see Fig.6c and d). In addition,
an increase in shot peening intensity from 0.20 to 0.50 mmA
resulted in an increase in the depth of the residual stress
layer, with a further increase following dual shot peening.
Close examination has revealed that a combination of
medium-intensity in the first shot peening and high-intensity
in dual shot peening serves to maximize the depth of the
residual compressive stress layer.
The hardness distribution of different peening intensities
of CSP1 ~ CSP3 and dual shot peening is shown in Fig.7a.
The corresponding hardness gradient profiles and resultant
maximum hardness are shown in Fig.7b and c, respectively.
As the peening intensity increased from 0.20 to 0.50 mmA,
the maximum hardness gradually increased from 750 to 768
HV, with further improvement following dual-shot peening.
In the combination of medium-intensity followed by high-
intensity peening of DSP1, the increase in the maximum
hardness is most pronounced, reaching 785 HV. It shows
that as the shot peening energy gradually increases, the sur-
face hardness also increases correspondingly. In contrast, the
affected depth of hardness remained unchanged in the com-
bination of high-intensity peening and dual-shot peening.
The surface topography that results from different shot
peening intensities and dual shot peening is illustrated
in Fig.8a1–a4 and b1–b4. Clear grinding marks can be
observed on the surface after low-intensity peening. As
the shot peening intensity increased, a large proportion of
bumpy shot impact craters were eliminated, and the uneven-
ness of the surface decreased when treated with dual shot
peening. As shown in Fig.8c1–c5, the resulting surface
roughness after dual-shot peening is significantly reduced
compared with single-shot peening. When the medium-
intensity shot peening (CSP1: Sa 1.13μm) was performed
first, followed by high-intensity shot peening (CSP3: Sa
1.55μm), the surface roughness of DSP1 decreased to Sa
1.10μm. When medium-intensity shot peening (CSP1: Sa
1.13μm) was carried out first, and then followed by low-
intensity shot peening (CSP3: Sa 1.04μm), the surface
roughness decreased significantly to Sa 0.91μm. These
Fig. 7 Hardness results obtained with different shot peening intensities and dual shot peening with simulation: a Map of hardness distribution; b
Hardness distribution profile; c The maximum hardness with different shot peening intensities and dual shot peening

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 11 of 22 83
results indicate that dual-shot peening has a significant effect
on reducing surface roughness.
To facilitate a comprehensive comparison, the distri-
bution of residual stress, surface roughness, and hardness
of dual shot peening of DSP1 and DSP2 are presented in
a spider diagram (see Fig.9). The surface residual stress,
maximum residual stress, and surface roughness of DSP2 are
significantly higher than DSP1. In contrast, DSP1 is signifi-
cantly higher than DSP2 with respect to maximum hardness,
influence depth of the residual stress layer, and the depth of
maximum residual stress. We accordingly propose adopting
Fig. 8 Surface topography results obtained with different shot peen-
ing intensities and dual shot peening treated: a1–a3 Surface marks by
SEM experimental of CSP1, CSP2, CSP1, and DSP1. b1–b3 Surface
topography by experimental of CSP1, CSP2, CSP1, and DSP1. c1–c5
Surface topography by numerical of CSP1, CSP2, CSP1, DSP1, and
DSP2

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 12 of 22
a lower shot peening intensity for the second shot peening
pass to improve the overall effect of dual shot peening.
4.3 Effect ofshot diameter
The surface integrity results attained with different shot
diameters and dual shot peening are presented in Fig.10.
CSP4 and CSP5 represent the cases with shot diameters of
0.4mm and 0.8mm, respectively. As can be seen in Fig.10a
and c, the depth of maximum residual stress and the maxi-
mum residual compressive stress increased gradually with
an increase in shot diameter, while the surface residual com-
pressive stress decreased gradually. When the shot diameters
were 0.4mm (CSP4), 0.6mm (CSP2) and 0.8mm (CSP5),
the maximum residual compressive stress was −988MPa,
−999MPa, −1126MPa, respectively, which increased to
−1144MPa for DSP3 and −1434MPa for DSP4. When
the medium-intensity shot peening (CSP1) was performed
first, followed by a low-intensity large shot diameter (DSP4),
Fig. 9 Radar diagram of the residual stress, surface roughness, hard-
ness of dual shot peening of DSP1 and DSP2
Fig. 10 Surface integrity results obtained with different shot diameters and dual shot peening: a Residual stress distribution; b Hardness profile;
c Distribution of residual stress characteristics; d Surface roughness parameters of Sa and Sz

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 13 of 22 83
surface residual stress was increased to −953MPa and the
maximum residual stress reached −1434MPa.
The hardness gradient achieved with different shot
diameters and dual shot peening is illustrated in Fig.10b.
The maximum hardness was increased to 793 HV when
treated with dual shot peening, an increase of 40 ~ 50 HV
compared with the initial shot peening alone. The surface
roughness (Sa and Sq) with different shot diameters and dual
shot peening is shown in Fig.10d. The resulting arithmetic
mean height Sa was 0.859, 1.058 and 1.253μm, respectively,
with a shot diameter of 0.4, 0.6, and 0.8mm. The surface
roughness (Sa 1.27μm) was reduced after dual shot peening
to 0.806μm (DSP3) and 1.088μm (DSP4).
The spider diagram given in Fig.11 depicts the residual
stress, surface roughness, and hardness after dual shot peen-
ing of DSP3 with small-sized diameter shots, and DSP4 with
large-sized diameter shots. The surface residual stress, maxi-
mum residual stress, depth of the residual stress layer, and
maximum residual stress of DSP4 are higher than that of
DSP3. It is well established that small-sized dual-shot peen-
ing significantly improves surface roughness and increases
the depth of maximum residual stress. For components oper-
ated under conditions with more stringent roughness require-
ments such as gear tooth flank and bearings, the second shot
peening step in the dual shot peening treatment allows the
use of low-intensity and small-diameter shots. The use of
dual shot peening with low-intensity and larger diameter has
a more pronounced effect when the roughness requirements
are not stringent, potentially in applications such as gear
tooth root.
5 Discussion
A mechanistic examination of surface integrity in dual-
shot peening requires a full consideration of plastic defor-
mation behaviour. The contour of residual stress with a
dual shot peening process (DSP1) is presented in Fig.12a.
The distribution of plastic deformation with DSP1 is given
in Fig.12b. It can be found that the plastic deformation
distribution is consistent with the residual stress, and the
depth of maximum plasticity and residual compressive
stress both appear at about 0.05mm. Cumulative plastic
deformation and residual stress distribution are shown in
Fig.12c–e for CSP1(0.35 mmA-0.6mm-200%), CSP3(0.5
mmA-0.6mm-200%), and DSP1(CSP1 + CSP3), where a
similar pattern for the disturbance of residual stress and
plastic deformation can be observed. The maximum resid-
ual compressive stress appears at the depth of maximum
plastic deformation. As the cumulative plastic deformation
approaches 0, the residual compressive stress due to shot
peening is negligible. Rousseau etal. [29] reported that
residual stress is generated primarily because of plastic
deformation based on finite element multi-impact simu-
lations using the crystal plasticity law. Lainé et. al [30]
reported similar results by comparing shot peening and
laser shock peening of titanium alloys, where the varia-
tion depth of plastic deformation and residual stress were
similar. Due to the larger cumulative impact energy, the
magnitude and depth of plastic deformation in dual-shot
peening increased slightly. As a result, the surface residual
compressive stress, the maximum residual compressive
stress, and the depth of residual compressive stress intro-
duced by dual shot peening increased. However, there is
the greater impact energy of dual shot peening, the maxi-
mum plastic deformation position is equivalent to a single
shot peening shallower. Thus, the position of the maxi-
mum residual compressive stress gradually moves close
to the surface [31].
The results presented in Fig.7 suggest significant
improvement in hardness following dual shot peening. To
account for this enhancement in hardness, microstructure
characterisation was conducted by SEM, EBSD, and TEM.
The distribution of retained austenite and martensite is
shown in Fig.13a–c for CSP1, CSP3, and DSP1. The phase
composition is captured by the EBSD chrysanthemum pond
diffraction pattern. The retained austenite phase is coloured
red while the grey denotes the martensite phase. As shown
in Fig.13, the residual austenite is dispersed in a granular
form at the martensite grain boundary. The content of aus-
tenite decreased and the martensite phase increased with
an increase in shot peening intensity and dual shot peen-
ing treatment. This can explain the significant increase in
Fig. 11 Rader diagram of the residual stress, surface roughness, hard-
ness of dual shot peening of DSP3 and DSP4

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 14 of 22
hardness with high-intensity shot peening and the dual shot
peening treatment [27].
The surface phase analysis of three typical shot peening
processes and the dual shot peening by XRD is presented
in Fig.13d. Changes in diffraction peak intensity are
evident as is the displacement of the diffraction peaks
after different shot peening methods. A broadening and
reduction of diffraction peak intensity can be attributed to
grain refinement and strain induction. Dual-shot peening
can increase the FWHM and reduce grain size with an
increased degree of grain refinement [32]. The main phases
of steel 18CrNiMo7-6 with carburizing and quenching
generate diffraction peaks due to martensite (α) and retained
austenite (γ). Wu etal. [6] found that shot peening can
change the metallographic structure from retained austenite
to martensite. The diffraction peak intensity of retained
austenite (γ) decreases and that of martensite increases
with high-intensity shot peening and dual shot peening.
This serves to indicate that retained austenite gradually
transforms into martensite, thereby increasing hardness, in
line with the EBSD test results [33, 34].
The three-dimensional grain size distribution after shot
peening and dual shot peening is presented in Fig.14a,
which illustrates the gradient distribution of grain struc-
ture from surface to subsurface. The grain size and grain
orientation distribution of CSP1, CSP3, and DSP1 at the
surface level, at the depth of 50μm, and 200μm are shown
in Fig.14b–d. The grain orientation exhibits a random
non-uniform distribution with shot peening and there is no
obvious orientation preference phenomenon [35]. The grain
refinement can be seen from surface to subsurface, espe-
cially at a depth of 50μm. For example, in CSP1 the surface
grain size is about 430nm, the average grain size at 50μm
from the surface reaches 350nm, and the average grain size
gradually increases to 790nm at 200μm from the surface.
This response indicates that grain size first decreases and
then increases with shot peening [22, 36].
The degree of grain refinement is more obvious for the
average grain size with a high peening intensity and DSP
[37]. The average surface grain sizes of CSP1, CSP3, and
DSP1 are 430nm, 330nm, and 260nm, respectively. At a
depth of 50μm, the average grain size of CSP1, CSP3, and
Fig. 12 The distribution of residual stress and plastic deformation
with single shot peening and dual shot peening. a The distribution
of residual stress with DSP1, b The distribution of plastic deforma-
tion with DSP1, c Correspondence between residual stress and plastic
deformation with CSP1, d Correspondence between residual stress
and plastic deformation with CSP3, e Correspondence between resid-
ual stress and plastic deformation with DSP1

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 15 of 22 83
DSP1 reach 350nm, 270nm, and 200nm, respectively. At
a greater depth, the degree of grain refinement becomes less
pronounced. The grain size is around 790nm, almost the
same for CSP1, CSP3, and DSP1 at a depth of 200μm from
the surface.
Figure15a–c despite the pole figures for CSP1, CSP3,
and DSP1 at surface, depth of 50μm and 200μm, respec-
tively. There is no obvious weave structure with different
peening intensities or dual shot peening treatment, and
the grain orientation is random. It can be suggested that
the grain orientation is deformed from surface to subsur-
face, and the effect of grain refinement is accelerated with
shot peening and dual shot peening, resulting in increased
hardness [38, 39]. Chen etal. [40] reported a similar phe-
nomenon in their study and attributed it to deformation
strain accumulation on the specimen surface. Surface
strain caused dislocation slip, resulting in grain refinement
and a significant increase in strength and hardness [22].
After shot peening treatment, it can be observed that the
microstructure of the material undergoes a transformation
from austenite (BCC) to martensite (FCC), resulting in
an increase in hardness due to the emergence of a higher
hardness (FCC) texture within the material. Liu etal. [41]
reportedthat shot peening’s surface hardening primarily
results from internal texture alterations, as evidenced by
their two-step intense shot peening process.
TEM and FEM analyses were used to evaluate the
changes in the dislocation density of CSP1, CSP3, and
DSP1 at the surface, 50μm and 200μm depths, respec-
tively. The associated changes in dislocation density and
phase compositions are illustrated in Fig.16a. The rollers
were mainly composed of white retained austenite and black
martensite structures with the shot peening treatment, and
many dislocation tangles were also observed in the middle
of the rollers. There are obvious high-density dislocations
on the surface with shot peening, and the austenite structure
undergoes a bending deformation which generates regions
of dislocation. Dislocation movement is blocked at the car-
bide particles and the grain boundary attachment positions,
which causes dislocation entanglement [40]. No obvious
carbide particles were observed in the TEM microstruc-
ture analysis for high-intensity shot peening or dual shot
peening. This suggests that carbide particles are effectively
fragmented after mechanical impact, significantly reducing
grain size, which is beneficial for improving hardness and
strength [42].
Fig. 13 a The distribution of retained austenite and martensite of CSP1; b The distribution of retained austenite and martensite of CSP3; c The
distribution of retained austenite and martensite of DSP1; d X-ray diffraction patterns in the surface of shot peening and dual shot peening5

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 16 of 22
In addition, the dislocation density first increased and
then decreased from the surface to the subsurface, with the
dislocation density region increasing gradually from the
surface to a depth of 50μm in CSP1. At greater depths,
the dislocation density region decreased with some car-
bides appearing at a depth of 200μm. This observation may
indicate that some carbides break as a direct consequence
of the large impact energy of shot peening on the resur-
faced layer and the sub-surface layer, which contributes to
the dislocation winding phenomenon. The black structure
and dislocation winding area are more obvious with high-
intensity shot peening and dual shot peening. The increased
martensite structure and dislocation density can account for
the increased hardness [42]. In the microstructure of the
specimens, a large number of dislocations are seen in mar-
tensite and retained austenite after dual shot peening. The
occurrence of dislocation slip suggests that the dislocation
accumulation is caused by movement inside the grain during
the deformation process, which forms a high-density dislo-
cation band [43]. In addition, the presence of dislocations in
Fig. 14 a Three-dimensional
IPF diagram with singleshot
peening and dual shot peening,
b IPF diagram in the surface, c
IPF diagram at depth of 50μm,
d IPF diagram at a depth of
200μm

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 17 of 22 83
different directions may be due to the impact force of shots
exerted in different directions on the grains.
The dislocation density numerical simulation results
presented in Fig.16b illustrate that the dislocation density
first increased and then decreased from the surface to the
subsurface, which agrees with the test results. The disloca-
tion density increase is more obvious on the surface with
high-intensity-peening and dual-shot peening. The disloca-
tion density is almost unchanged at 3.125 × 107 mm−2 when
it reaches a depth of 200μm from the surface. However, the
change mechanism of shot peening and dual shot peening at
the micro level is verified and serves to increase the hardness
significantly [44].
The results relating to dislocation density, dislocation
cell size, and microhardness obtained from changes in
microhardness and microstructure are shown in Fig.17.
Attention is drawn to the remarkable agreement between
the dislocation density, dislocation cell size and grain size.
The density increased from a depth of 0–50μm and then
decreased and remained unchanged at a depth of 200μm.
This can be explained by an accumulation of dislocations in
the grains that twine to form a large number of dislocation
cells when treated with shot peening and dual shot peening,
and this leads to further grain refinement [22, 24, 45].
During shot peening and dual shot peening, the con-
tinuous impact of the shots causes the surface material to
undergo plastic strain, which increases the internal dislo-
cation of the material, as shown in Fig.18. Dislocation,
including dislocation slip, accumulation, and entanglement,
occurs in the initial grains, resulting in dislocation walls and
Fig. 15 a PF diagram in the surface; b PF diagram at a depth of 50μm; c PF diagram at a depth of 200μm

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 18 of 22
dislocation entanglement with high dislocation density [46].
This creates a dislocation cell structure that separates the
initial grains [46]. On the other hand, the annihilation and
rearrangement of dislocations occur first in the dislocation
walls and dislocation tangles with high dislocation density
when the plastic strain reaches a certain level, leading to
Fig. 16 a TEM images of CSP1, CSP3 and DSP1 at surface, 50μm and 200μm; b FEM results of CSP1, CSP3, DSP1 dislocation density

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 19 of 22 83
transformation into the sub-grain boundaries [12]. Sub-
grains then begin to appear inside the original grains, the
plastic deformation increases continuously, the orientation
difference between adjacent sub-grains increases under
the continuous impact of shots, and the sub-grain bounda-
ries are transformed into grain boundaries with large grain
boundary angles [47]. Dislocation activity proceeds in the
refined sub-grains and inside the grains as the plastic strain
increases further. The dislocation cell structure is formed
again, the sub-grains and grains are refined again, and fine
grains are gradually formed resulting in grain refinement
[48]. The degree of grain refinement is more pronounced due
to the higher impact energy of dual shot peening, generating
a higher maximum microhardness.
Plastic deformation begins in the subsurface of the
material, resulting in residual compressive stress in the
plastic deformation zone [49]. The maximum residual
compressive stress and the depth of residual compressive
stress increase gradually due to the enhanced plastic
deformation and deformation zone after dual shot peening.
In addition, the residual compressive stress on the surface
becomes larger, creating enhanced fatigue resistance [50].
The dual shot peening leads to a lower surface roughness
compared with a single-shot peening [12, 15, 51].
6 Conclusion
Simulations based on the dislocation density constitutive
behaviour were combined with extensive experimental tests
to facilitate an understanding of the mechanism of dual shot
peening of carburizing steel. The effects of parameters such
as peening intensity and shot diameter on surface integrity
were investigated and discussed in detail. The conclusions
can be summarised as follows:
1. A dual shot peening numerical model has been
developed based on dislocation density constitutive
equations, which enables to predict surface integrity
parameters such as residual stress, hardness gradient,
surface roughness, dislocation cell size and dislocation
density. The predicted accuracy has been validated,
the maximum prediction error of residual stress and
microhardness is less than 15.1% and 7.4%.
2. For dual-shot peening, the first step of high-intensity
peening with medium-size shots followed by the second
step of low-intensity peening is recommended. The
dual shot peening generates surface residual stress of
more than 900MPa and a maximum residual stress of
1200MPa, while remains a reduced surface roughness.
3. For the second-step low-intensity peening in dual shot
peening, small-size shots decrease surface roughness
and increase the maximum residual compressive stress.
However, large-size shots in the second-step improve the
surface residual stress and hardness, which are increased
to −950MPa and 790 HV.
4. Dual shot peening produces dislocation walls
and dislocation tangles with high dislocation
density, resulting in grain refinement. More phase
transformations from retained austenite to martensite
have been activated. Thus, it introduces larger surface
hardness and residual stress in a dual-shot peening
process.
Fig. 17 Dislocation density, dislocation cell size and microhardness
distribution with singleshot peening and dual shot peening

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 20 of 22
Acknowledgements The work is supported by the National
Key Research and Development Program (Grant no.
2023YFB4704302),Shaanxi Key Laboratory of Gear Transmission
Open Program (Grant no. SKLGT-2022-005) and Key research &
development program and achievement transformation plan project
of Inner Mongolia Autonomous Region (Grant no. 2023YFJM0006).
We would like to thank Analytical and Testing Center of Chongqing
University for the help of material microstructure measuring.
Funding The funding was supported by National Key Research and
Development Program,2023YFB4704302, Peitang Wei,Shaanxi Key
Laboratory of Gear Transmission Open Program, SKLGT-2022-005,
Huaiju Liu, Key research & development program and achievement
transformation plan project of Inner Mongolia Autonomous Region,
2023YFJM0006, Peitang wei.
Data availability The datasets used and analyzed during the current
study are available from the corresponding author on reasonable
request.
References
1. Song C, Li X, Yang Y, Sun J. Parameter design of double-circu-
lar-arc tooth profile and its influence on meshing characteristics
of harmonic drive. Mech Mach Theory. 2022;167:104567.
2. Zhao J, Zhou W, Tang J, Jiang T, Liu H. Analytical and experi-
mental study on the surface generation mechanism in shot peen-
ing. Arch Civil Mech Eng. 2022;22(3):111.
3. Wu J, Liu H, Wei P, Lin Q, Zhou S. Effect of shot peening cov-
erage on residual stress and surface roughness of 18CrNiMo7-6
steel. Int J Mech Sci. 2020;183:105785.
4. Lin Q, Liu H, Zhu C, Parker RG. Investigation on the effect of
shot peening coverage on the surface integrity. Appl Surf Sci.
2019;489:66–72.
5. Zhiming L, Laimin S, Shenjin Z, Zhidong T, Yazhou J. Effect
of high energy shot peening pressure on the stress corrosion
cracking of the weld joint of 304 austenitic stainless steel. Mater
Sci Eng A. 2015;637:170–4.
6. Wu J, Liu H, Wei P, Zhu C, Lin Q. Effect of shot peening coverage
on hardness, residual stress and surface morphology of carburized
rollers. Surf Coat Technol. 2020;384:125273.
7. Chen DF, Zhu JZ, Liu HJ, Wei PT, Mao TY. Experimental inves-
tigation of the relation between the surface integrity and bend-
ing fatigue strength of carburized gears. Sci China Technol Sci.
2023;66:33–46.
Fig. 18 Surface integrity forma-
tion diagram with shot peening
and dual shot peening

Archives of Civil and Mechanical Engineering (2024) 24:83 Page 21 of 22 83
8. Zhang X, Wei P, Parker RG, Liu G, Liu H, Wu S. Study on the
relation between surface integrity and contact fatigue of carbur-
ized gears. Int J Fatigue. 2022;165:107203.
9. Zammit A, Abela S, Wagner L, Mhaede M, Wan R, Grech M.
The effect of shot peening on the scuffing resistance of Cu-Ni
austempered ductile iron. Surf Coat Technol. 2016;308:213.
10. Han X, Zhang Z, Hou J, Barber GC, Qiu F. Tribological behav-
ior of shot peened/austempered AISI 5160 steel. Tribol Int.
2020;145:106197.
11. Fu P, Zhan K, Jiang C. Micro-structure and surface layer proper-
ties of 18CrNiMo7-6 steel after multistep shot peening. Mater
Des. 2013;51:309–14.
12. Lin Q, Liu H, Zhu C, Chen D, Zhou S. Effects of different shot
peening parameters on residual stress, surface roughness and cell
size. Surf Coat Technol. 2020;398:126054.
13. Wu J, Wei P, Liu H, Zhang X, He Z, Deng G. Evaluation of pre-
shot peening on improvement of carburizing heat treatment of
AISI 9310 gear steel. J Mater Res. 2022;18:2784–96.
14. Zhang X, Liu H, Wu S, Li G, Wei P. Experimental investigation
on the effect of barrel finishing processes on surface integrity of
18CrNiMo7-6 carburized rollers. Proc Inst Mech Eng E J Process
Mech Eng. 2022;236:2095–105.
15. Lambert RD, Aylott CJ, Shaw BA. Evaluation of bending fatigue
strength in automotive gear steel subjected to shot peening tech-
niques. Procedia Struct Integr. 2018;13:1855–60.
16. Matsumura S, Hamasaka N. High strength and compactness of
gears by WHSP (double hard shot peening) technology. Komatsu
Tech Rep. 2006;52:1–5.
17. Ongtrakulkij G, Khantachawana A, Kajornchaiyakul J, Kondoh
K. Effects of the secondary shot in the double shot peening pro-
cess on the residual compressive stress distribution of Ti-6Al-4V.
Heliyon. 2022;8: e8758.
18. Wang C, Zhang H, Xiong X, Li M, Chen M, Liu H, Jiang C.
Changes in surface integrity of cemented tungsten carbide with
shot peening treatment. Surf Coat Technol. 2021;425:127710.
19. Heydari Astaraee A, Bagherifard S, Bradanini A, Duó P, Henze
S, Taylor B, Guagliano M. Application of shot peening to case-
hardened steel gears: the effect of gradient material properties and
component geometry. Surf Coat Technol. 2020;398:126084.
20. Estrin Y, Tóth LS, Molinari A, Bréchet Y. A dislocation-based
model for all hardening stages in large strain deformation. Acta
Mater. 1998;46:5509–22.
21. Wang C, Wang L, Wang X, Xu Y. Numerical study of grain
refinement induced by severe shot peening. Int J Mech Sci.
2018;146–147:280–94.
22. Hassani-Gangaraj SM, Cho KS, Voigt HJL, Guagliano M, Schuh
CA. Experimental assessment and simulation of surface nanocrys-
tallization by severe shot peening. Acta Mater. 2015;97:105–15.
23. Toth L, Molinari A, Estrin Y. Strain hardening at large strains as
predicted by dislocation based polycrystal plasticity model. J Eng
Mater Technol. 2002;124:71–7.
24. Lin Q, Wei P, Liu H, Zhu J, Zhu C, Wu J. A CFD-FEM numerical
study on shot peening. Int J Mech Sci. 2022;223:107259.
25. Pavlina E, Van Tyne C. Correlation of yield strength and ten-
sile strength with hardness for steels. J Mater Eng Perform.
2008;17:888–93.
26. Liu H, Wang W, Zhu C, Jiang C, Wu W, Parker RG. A microstruc-
ture sensitive contact fatigue model of a carburized gear. Wear.
2019;436–437:203035.
27. Wu J, Wei P, Liu H, Zhang B, Tao G. Effect of shot peening
intensity on surface integrity of 18CrNiMo7-6 steel. Surf Coat
Technol. 2021;421:127194.
28. Mahmoudi AH, Ghasemi A, Farrahi GH, Sherafatnia K. A com-
prehensive experimental and numerical study on redistribution of
residual stresses by shot peening. Mater Des. 2016;90:478–87.
29. Rousseau T, Nouguier-Lehon C, Gilles P, Hoc T. Finite element
multi-impact simulations using a crystal plasticity law based on
dislocation dynamics. Int J Plast. 2018;101:42–57.
30. Lainé SJ, Knowles KM, Doorbar PJ, Cutts RD, Rugg D. Micro-
structural characterisation of metallic shot peened and laser shock
peened Ti–6Al–4V. Acta Mater. 2017;123:350–61.
31. Walczak M, Szala M. Effect of shot peening on the surface prop-
erties, corrosion and wear performance of 17–4PH steel pro-
duced by DMLS additive manufacturing. Arch Civil Mech Eng.
2021;21(4):157.
32. Bagheri S, Guagliano M. Review of shot peening processes
to obtain nanocrystalline surfaces in metal alloys. Surf Eng.
2009;25:3–14.
33. Saleh B, Fathi R, Tian Y, Radhika N, Jiang J, Ma A. Fundamen-
tals and advances of wire arc additive manufacturing: materials,
process parameters, potential applications, and future trends. Arch
Civil Mech Eng. 2023;23(2):96.
34. Snopiński P, Król M, Pagáč M, Petrů J, Hajnyš J, Mikuszewski
T, Tański T. Effects of equal channel angular pressing and heat
treatments on the microstructures and mechanical properties of
selective laser melted and cast AlSi10Mg alloys. Arch Civil Mech
Eng. 2021;21(3):92.
35. Wang W, Politis NJ, Wang Y, Zhou X, Balint D, Jiang J. Solid-
state hot forge bonding of aluminium-steel bimetallic gears: defor-
mation mechanisms, microstructure and mechanical properties.
Int J Mach Tools Manuf. 2022;180:103930.
36. Lu J, Wu L, Sun G, Luo K, Zhang Y, Cai J, Cui C, Luo X. Micro-
structural response and grain refinement mechanism of commer-
cially pure titanium subjected to multiple laser shock peening
impacts. Acta Mater. 2017;127:252–66.
37. Tiamiyu AA, Pang EL, Chen X, LeBeau JM, Nelson KA, Schuh
CA. Nanotwinning-assisted dynamic recrystallization at high
strains and strain rates. Nat Mater. 2022;21:786–94.
38. Li BY, Li AC, Zhao S, Meyers MA. Amorphization by mechanical
deformation. Mater Sci Eng R Rep. 2022;149:100673.
39. Bertin N, Capolungo L, Beyerlein I. Hybrid dislocation dynam-
ics based strain hardening constitutive model. Int J Plast.
2013;49:119–44.
40. Chen G, Jiao Y, Tian T, Zhang X, Li Z, Zhou W. Effect of wet
shot peening on Ti-6Al-4V alloy treated by ceramic beads. Trans
Nonferrous Metals Soc China. 2014;24:690–6.
41. Liu H, Gan J, Jiang C, Wu W, Guagliano M. Work softening
mechanism and microstructure evolution of nanostructured
Mg-8Gd-3Y alloy during severe shot peening. Surf Coat Technol.
2022;441:128601.
42. Bagherifard S, Ghelichi R, Khademhosseini A, Guagliano M.
Cell response to nanocrystallized metallic substrates obtained
through severe plastic deformation. ACS Appl Mater Interfaces.
2014;6:7963–85.
43. Orozco-Caballero A, Jackson T, Da Fonseca JQ. High-resolution
digital image correlation study of the strain localization during
loading of a shot-peened RR1000 nickel-based superalloy. Acta
Mater. 2021;220:117306.
44. Zhang J, Dong X, Zhou Y, Liu J. Surface derusting of rust-covered
metallic surface via shot blasting: a smoothed particle hydrody-
namics simulation. Wear. 2023;514:204566.
45. Mercer C, Speck T, Lee J, Balint D, Thielen M. Effects of geom-
etry and boundary constraint on the stiffness and negative Pois-
son’s ratio behaviour of auxetic metamaterials under quasi-static
and impact loading. Int J Impact Eng. 2022;169:104315.
46. Bagherifard S, Fernandez-Pariente I, Ghelichi R, Guagliano M,
Vezzu S. Effect of severe shot peening on microstructure and
fatigue strength of cast iron. Int J Fatigue. 2014;65:64–70.
47. Zhang C, Zheng M, Wang Y, Gao P, Gan B. Effect of high energy
shot peening on the wear resistance of TiN films on a TA2 surface.
Surf Coat Technol. 2019;378:124821.

Archives of Civil and Mechanical Engineering (2024) 24:83 83 Page 22 of 22
48. Zielecfei W, Pawlus P, Perłowski R, Dzierwa A. Surface topog-
raphy effect on strength of lap adhesive joints after mechanical
pre-treatment. Arch Civil Mech Eng. 2013;13:175–85.
49. Shi Y, Shen X, Xu G, Xu C, Wang B, Su G. Surface integrity
enhancement of austenitic stainless steel treated by ultrasonic
burnishing with two burnishing tips. Arch Civil Mech Eng.
2020;20:1–17.
50. Wu J, Wei P, Liu G, Chen D, Zhang X, Chen T, Liu H. A
comprehensive evaluation of DLC coating on gear bend-
ing fatigue, contact fatigue, and scuffing performance. Wear.
2023;536–537:205177.
51. Pandey V, Chattopadhyay K, Srinivas N, Singh V. Role of ultra-
sonic shot peening on low cycle fatigue behavior of 7075 alu-
minium alloy. Int J Fatigue. 2017;103:426–35.
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