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Time-Efficient Prediction of the Surface Layer State after Deep Rolling using
Similarity Mechanics Approach
Daniel Trauth, Fritz Klocke, Patrick Mattfeld, Andreas Klink
Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University
Director: Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. Fritz Klocke
Agenda
Conclusion and outlook 5
Prediction of the surface layer state using similarity mechanics approach 4
FE-Modeling of the deep rolling process 3
Experimental examination of deep rolling and identification of significant process parameters 2
Motivation, objective and approach 1
Motivation and objective
Processing highly stressed technical
components using deep rolling is currently
based on individual know how of
experts, elaborate experiments and
subsequent time- and cost-intensive
measurements
Process modeling using finite element
method requires a high expertise of the
users as well as high computation times
For these reasons, a new method is
required, which enables an efficient and
also quantitive process design regarding
Residual stresses and
Strain hardening
in the surface layer
Motivation Objective
Development of an innovative method to
predict the residual stresses and the
strain hardening by
Developing FE-models to create a
comprehensive dataset of residual stresses
and strain hardening for different input
parameters
Deriving correlations between input and output
parameters using similarity mechanics
approach
Input Output
Analysis
Experiments
Simulation and
Verification
Interpretation of
the exp. and
num. results
Literature
review State of the
art
Time-efficient
prediction of the
surface layer state
Modeling
Strain
hardening
Abstract
Verification
= ?
Real. Sim.
Simulation
F, x...
Similarity
mechanics
Surface
roughness Residual
stresses Deep rolling
Evaluation
- +
Significance
analysis
A
B
A
B
𝜋 = 𝐿1𝑀−2𝑇1
Database
1s
Analyze
F v
Approach
Conclusion and outlook 5
Prediction of the surface layer state using similarity mechanics approach 4
FE-Modeling of the deep rolling process 3
Experimental examination of deep rolling and identification of significant process parameters 2
Motivation, objective and approach 1
Agenda
Test parameters
Deep rolling tools (Ecoroll AG, Germany)
– Hydraulic tool types: HG6 and HG13
Hydraulic power unit (Ecoroll AG)
– Type: HGP 400
Material to be tested
– Heat treated steel
42CrMo4 (ASTM: A322-4140)
– Ductile cast iron
GGG60 (ASTM: A536-80-55-06)
– Nickel-based alloy
IN718 (ASTM: B637)
Sample geometry
– Lateral surface area
– Outer radius
– Borehole
Experimental set-up
Three jaw chuck
Sample
Sleeve
Deep rolling tool
GGG60 IN718 42CrMo4
Borehole
(hidden) Outer radius Lateral surface
area
Lathe
Experimental examination of deep rolling
Significance analysis for maximum strain hardening at the lateral surface area acc. to DOE
Str
ain
ha
rde
nin
g
[H
RC
]
20
30
40
50
60
100 400
Walzdruck Rolling velocity v Rolling overlap o Ball diameter d Rolling pressure p
mm mm/s bar %
42CrMo4 42CrMo4
GGG60
IN718 IN718
-1400
-1200
-1000
-800
100 400
Rolling pressure p
-1400
-1200
-1000
-800
HG6 HG13
Ball diameter d
-1400
-1200
-1000
-800
0.3 0.8
Rolling overlap o
Re
sid
ua
l str
esse
s σ
RS [M
Pa
]
-1400
-1200
-1000
-800
70 150
Rolling velocity v
Significance analysis for maximum residual stresses at the lateral surface area acc. to DOE
mm mm/s bar %
better
better
Identification of significant process parameters
20
30
40
50
60
HG6 HG13
20
30
40
50
60
0,3 0,8
20
30
40
50
60
70 150
Conclusion and outlook 5
Prediction of the surface layer state using similarity mechanics approach 4
FE-Modeling of the deep rolling process 3
Experimental examination of deep rolling and identification of significant process parameters 2
Motivation, objective and approach 1
Agenda
FE-Modeling of material characteristics
-1200
-800
-400
0
400
800
1200
-3% -2% -1% 0% 1% 2% 3%
Sp
an
nu
ng
[M
Pa]
Dehnung [%]
Bauschinger-Versuch bei 42CrMo4
-1200
-800
-400
0
400
800
1200
-3% -2% -1% 0% 1% 2% 3%
Sp
an
nu
ng
[M
Pa]
Dehnung [%]
Bauschinger-Versuch bei GGG60
-1200
-800
-400
0
400
800
1200
0 20 40 60 80S
tres
s σ
[M
Pa
]
Time t [s]
GGG60 [2%]
Simulation and validation
Material modeling
Simulation Experiment
0
Strain ε [%]
GGG60
Str
es
s σ
[M
Pa
]
0
+2 -2
+400
+800
-800
-400
Tensile
load
Compressive
load Tensile
load
F F FE-Model
F
Experimental cyclic
compression-tension-test with
2%, 4% and 6% total strain
Tests were performed for all
three materials to determine the
parameters of the combined
cyclic nonlinear isotropic and
kinematic plasticity model acc.
to Lemaitre-Chaboche (LCP-
Model)
FE-Setup of the
compression-tension-test
Fitting of the Parameters
𝑄∞, 𝑏, 𝐶 and 𝛾 of the LCP-
Model using Curve Fitting
Toolbox in Matlab
Validation of the results
LCP-Model:
Isotropic behavior:
𝜎0 = 𝜎0 + 𝑄∞ (1 − 𝑒−𝑏𝜀−𝑝𝑙)
Kinematic behavior:
𝛼 = 𝐶𝜀 𝑝𝑙(𝜎 − 𝛼)
𝜎0− 𝛾𝛼𝜀 𝑝𝑙
Bauschinger experiment
Boundary conditions
ωB
RC
rB
Workpiece
Rolling tool
Connector
FE-Modeling and simulation
Five rolling tools
Workpiece
(C3D8R, LC-Plasticity)
Averaged
evaluation path
σRS [MPa]
+1431 0
Rigid
y
x
z
ωC 𝑐
Modeling of process kinematics using
a special connector assembly
This makes the use of the Abaqus
mass scaling option usefull
Tests have shown, that a mass
scaling factor of 250 has no influence
on the results despite 15-times
acceleration of the computation time
Setup of 9 evaluation paths in the
model center to minimize numerical
instabilities
Evaluating residual stresses by
means of the Mises-stress-tensor and
strain hardening by the plastic
equivalent strain
FE-Modeling of the deep rolling process
-1500.00
-1000.00
-500.00
0.00
Res
idu
al s
tres
se
s σ
RS
,i
[MP
a]
Surface layer depth t [µm]
Exp. σx Exp. σy
Sim. σx Sim. σy
Exp. σRS,x
Sim. σRS,x
Exp. σRS,y
Sim. σRS,y
Surface layer depth t [µm]
Res
idu
al S
tres
s P
rofi
le
σR
S,i [
MP
a]
Verification Characterization
Maximum deviation of 1.1% for σRS,x
for the highest compressive residual
stresses
Good qualitative accordance of the
numerical residual stresses with the
experimentally measured stress
Thus, the FE-model is verified and
qualifies for further investigations
using similarity mechanics
This involves the characterization of a
typical residual stress depth profile by
significant values (𝜎0, 𝜎𝑚𝑖𝑛 , 𝜎𝑚𝑎𝑥)
𝜎𝑚𝑎𝑥
𝜎0
𝜎𝑚𝑖𝑛 𝑧𝑚𝑖𝑛 𝑧0 𝑧𝑚𝑎𝑥
Verification of the numerical deep rolling process
Conclusion and outlook 5
Prediction of the surface layer state using similarity mechanics approach 4
FE-Modeling of the deep rolling process 3
Experimental examination of deep rolling and identification of significant process parameters 2
Motivation, objective and approach 1
Agenda
-1200
-700
-200
300
0.0 1.0 2.0
Surface layer depth t [mm]
s_parallel
s_parallel_AM
s_senkrecht_AM
s_senkrecht
Res
idu
al s
tres
se
s σ
RS
[M
Pa
]
Sim. σRS,x
Est. σRS,x
Est. σRS,y
Sim. σRS,y
42CrMo4, 250 bar, HG6, 30%
-1200
-960
-720
-480
-240
0
-5.80E-03
-4.64E-03
-3.48E-03
-2.32E-03
-1.16E-03
0.00E+00
sm
in/E
[ -
]
Intensity number π8 [ - ]
σmin,x
σmin,y
42CrMo4
Analytic functions Estimation and validation
Significant dimensionless numbers
acc. to DOE and Buckingham
𝛱1= 𝑓
𝐷 𝛱2=
𝑣
𝐸𝜌
𝛱3= 𝑑
𝐷 𝛱8=
𝑝
𝐸
𝜎𝑚𝑖𝑛,𝑦
𝐸= −191721𝜋8
2 + 36,649𝜋8 − 0,0035
𝜎𝑚𝑖𝑛,𝑥𝐸
= −199054𝜋82 + 20,999𝜋8 − 0,0042
The significant values of a residual
stress profile can be well estimated
by the presented method (maximum
deviation of 5%)
In our paper, the authors propose a
function to connect the estimated
values to a representative profile
Prediction of the surface layer state
Conclusion and outlook 5
Prediction of the surface layer state using similarity mechanics approach 4
FE-Modeling of the deep rolling process 3
Experimental examination of deep rolling and identification of significant process parameters 2
Motivation, objective and approach 1
Agenda
Conclusion Outlook
This work presents significant process
input parameters acc. to DOE to
maximize residual stresses and strain
hardening for 42CrMo4, IN718 and
GGG60
Furthermore a verified FE-Model based
on a special connector is presented
which allows a comprehensive
investigation of the correlation between
input and output parameters
Hereby a very effective and simple
method could be developed, which
allows an estimation of process results
like residual stresses or strain
hardening using similarity mechanics
approach
Future work aims at the increase of
the amount of characteristic values of
a depth profile to make the application
of a connecting-function as presented
in the paper obsolete
Besides, the prediction of the fatigue
life using similarity mechanics will be
investigated. Therefore dimensionless
numbers relating the surface layer
state to a S/N curve are determined
Using experiments and FE-analyses,
suitable analytic functions allow the
prediction of the number of stress
cycles or the critical fatigue stress de-
pending on residual stresses, strain
hardening and the surface quality
Conclusion and outlook
The authors would like to thank the German Federal Ministry of Economics and Technology (BMWi)
for supporting this research project through the Central Innovation Programme for SME (ZIM).
Further, we express our graditute to K. Röttger and S. Fricke of ECOROLL AG Werkzeugtechnik for
their support in conducting the experiments cited in this paper.
Thank your very much for your attention
Acknowledgement