Abstract

Selection of flow stress models and fracture models to model sheet deformation at high strain rates is of great concern. The same is attempted in the present work during shock tube impact forming of 1-mm-thick AA 5052-H32 sheet using a rigid nylon striker. Lab scale experiments and finite element simulations using DEFORM 3D are conducted for the purpose. Johnson–Cook flow stress model and Modified Johnson–Cook flow stress model along with fracture models like normalized Cockcroft and Latham model, Rice and Tracey model, Oyane model, and McClintock model are tested for their accuracy and consistency. The fracture strain and fracture pattern evaluation suggest that the modified Johnson–Cook flow stress model and Rice and Tracey fracture model are suitable for fracture prediction, and it is better to use these together for fracture evaluation. An alternate method of evaluating rate-dependent tensile properties of sheet at higher strain rates is proposed and delivered acceptable fracture prediction results. Finite element simulations using Hollomon power law predict a strain rate of 1925/s at a striker velocity of 49.79 m/s, which is in the range of values in literature for explosive forming. Systematic shock tube forming experiments for calibrating the fracture models are acceptable.

References

1.
EEA Report, No 15/2018
,
2017
, “Monitoring CO2 Emissions From New Passenger Cars and Vans,”.
2.
Das
,
S. K
,
Green
,
J. A. S.
, and
Kaufman
,
J. G.
,
2007
, “
The Development of Recycle-Friendly Automotive Aluminum Alloys
,”
JOM
,
59
, pp.
47
51
.
3.
Tong
,
C.
,
Rong
,
Q.
, and
Yardley
,
V. A.
,
2020
, “
New Developments and Future Trends in Low-Temperature Hot Stamping Technologies: A Review
,”
Metals (Basel)
,
10
(
12
), pp.
1
27
.
4.
Smerd
,
R.
,
Winkler
,
S.
, and
Salisbury
,
C.
,
2005
, “
High Strain Rate Tensile Testing of Automotive Aluminum Alloy Sheet
,”
Int. J. Impact Eng.
,
32
(
1–4
), pp.
541
560
.
5.
Deng
,
H.
,
Mao
,
Y.
,
Li
,
G.
, and
Cui
,
J.
,
2019
, “
A Study of Electromagnetic Free Forming in AA5052 Using Digital Image Correlation Method and FE Analysis
,”
J. Manuf. Process.
,
37
, pp.
595
605
.
6.
Ahmed
,
M.
,
Kumar
,
D. R.
, and
Nabi
,
M.
,
2017
, “
Enhancement of Formability of AA5052 Alloy Sheets by Electrohydraulic Forming Process
,”
J. Mater. Eng. Perform.
,
26
(
1
), pp.
439
452
.
7.
Saxena
,
A.
,
Dwivedi
,
S. P.
,
Srivastava
,
A. K.
,
Sharma
,
S.
, and
Kotkunde
,
N.
,
2022
, “
A Computational Investigation on the Influence of the l/d Ratio and Strain Rate on the Deformation Behavior of Rolled and Homogeneous Armor Steel in the Split Hopkinson Pressure Bar Test Process
,”
Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng.
,
236
(
1
), pp.
138
148
.
8.
Broomhead
,
P.
, and
Grieve
,
R. J.
,
1982
, “
The Effect of Strain Rate on the Strain to Fracture of a Sheet Steel Under Biaxial Tensile Stress Conditions
,”
ASME J. Eng. Mater. Technol.
,
104
(
2
), pp.
102
106
.
9.
Grolleau
,
V.
,
Gary
,
G.
, and
Mohr
,
D.
,
2008
, “
Biaxial Testing of Sheet Materials at High Strain Rates Using Viscoelastic Bars
,”
Exp. Mech.
,
48
(
3
), pp.
293
306
.
10.
Bhaduri
,
A.
,
2018
, “High-Energy Rate Forming. In: Mechanical Properties and Working of Metals and Alloys,”
Springer Series in Materials Science, vol 264
,
Springer
,
Singapore
.
11.
Psyk
,
V.
,
Risch
,
D.
,
Kinsey
,
B. L.
,
Tekkaya
,
A. E.
, and
Kleiner
,
M.
,
2011
, “
Electromagnetic Forming—A Review
,”
J. Mater. Process. Technol.
,
211
(
5
), pp.
787
829
.
12.
Dariani
,
B. M.
,
Liaghat
,
G. H.
, and
Gerdooei
,
M.
,
2009
, “
Experimental Investigation of Sheet Metal Formability Under Various Strain Rates
,”
Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf.
,
223
(
6
), pp.
703
712
.
13.
Oliveira
,
D. A.
,
Worswick
,
M. J.
,
Finn
,
M.
, and
Newman
D.
,
2005
, “
Electromagnetic Forming of Aluminum Alloy Sheet: Free-Form and Cavity Fill Experiments and Model
,”
J. Mater. Process. Technol.
,
170
(
1–2
), pp.
350
362
.
14.
Babaei
,
H.
,
Mirzababaie
,
Mostofi
,
T.
, and
Armoudli
,
E.
,
2017
, “
On Dimensionless Numbers for the Dynamic Plastic Response of Quadrangular Mild Steel Plates Subjected to Localized and Uniform Impulsive Loading
,”
Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng.
,
231
(
5
), pp.
939
950
.
15.
Kanel
,
G. I.
,
Savinykh
,
A. S.
,
Garkushin
,
G. V.
, and
Razorenov
,
S. V.
,
2020
, “
Effects of Temperature and Strain on the Resistance to High-Rate Deformation of Copper in Shock Waves
,”
J. Appl. Phys.
,
128
(
11
), p.
115901
.
16.
Mandal
,
A.
, and
Gupta
,
Y. M.
,
2019
, “
Elastic-Plastic Deformation of Molybdenum Single Crystals Shocked to 12.5 GPa: Crystal Anisotropy Effects
,”
J. Appl. Phys.
,
125
(
5
), p.
055903
.
17.
Stoffel
,
M.
,
Schmidt
,
R.
, and
Weichert
,
D.
,
2001
, “
Shock Wave-Loaded Plates
,”
Int. J. Solids Struct.
,
38
(
42–43
), pp.
7659
7680
.
18.
Justusson
,
B.
,
Pankow
,
M.
,
Heinrich
,
C.
,
Rudolph
,
M.
, and
Waas
,
A. M.
,
2013
, “
Use of a Shock Tube to Determine the Bi-Axial Yield of an Aluminum Alloy Under High Rates
,”
Int. J. Impact Eng.
,
58
, pp.
55
65
.
19.
Ray
,
N.
,
Jagadeesh
,
G.
, and
Suwas
,
S.
,
2015
, “
Response of Shock Wave Deformation in AA5086 Aluminum Alloy
,”
Mater. Sci. Eng.: A
,
622
, pp.
219
227
.
20.
Bisht
,
A.
,
Ray
,
N.
,
Jagadeesh
,
G.
, and
Suwas
,
S.
,
2017
, “
Microstructural and Crystallographic Response of Shock-Loaded Pure Copper
,”
J. Mater. Res.
,
32
(
8
), pp.
1484
1498
.
21.
Koohbor
,
B.
,
Kidane
,
A.
, and
Lu
,
W.-Y.
,
2016
, “
Characterizing the Constitutive Response and Energy Absorption of Rigid Polymeric Foams Subjected to Intermediate-Velocity Impact
,”
Polym. Test.
,
54
, pp.
48
58
.
22.
Vilamosa
,
V.
,
Clausen
,
A. H.
,
Børvik
,
T.
,
Holmedal
,
B.
, and
Hopperstad
,
O. S.
,
2016
, “
A Physically-Based Constitutive Model Applied to AA6082 Aluminium Alloy at Large Strains, High Strain Rates and Elevated Temperatures
,”
Mater. Des.
,
103
, pp.
391
405
.
23.
Tian
,
Y.
,
Huang
,
L.
,
Ma
,
H.
, and
Li
,
J.
,
2014
, “
Establishment and Comparison of Four Constitutive Models of 5A02 Aluminium Alloy in High-Velocity Forming Process
,”
Mater. Des.
,
54
, pp.
587
597
.
24.
Song
,
P.
,
Li
,
W.
,
Wang
,
X.
, and
Xu
,
W.
,
2019
, “
Study on Mechanical Properties and Constitutive Model of 5052 Aluminium Alloy
,”
Mater. Sci. Technol.
,
35
(
8
), pp.
916
924
.
25.
Barik
,
S. K.
,
Ganesh Narayanan
,
R.
, and
Sahoo
,
N.
,
2021
,
Failure Strain and Fracture Prediction During Shock Tube Impact Forming of AA 5052-H32 Sheet
,”
ASME J. Eng. Mater. Technol.
,
143
(
3
), p.
031009
.
26.
Barik
,
S. K.
,
Narayanan
,
R. G.
, and
Sahoo
,
N.
,
2022
, “
Assessment of Stress-Strain Constitutive Models and Failure Models on the Shock Tube Based Impact Forming of AA 5052-H32 Sheet
,”
J. Manuf. Process.
,
74
, pp.
573
591
.
27.
Wagoner
,
R. H.
, and
Chenot
,
J. L.
,
1996
,
Fundamentals of Metal Forming
,
John Wiley & Sons Inc.
,
New York
.
28.
Barlat
,
F.
,
Lege
,
D. J.
, and
Brem
,
J. C.
,
1991
, “
A Six-Component Yield Function for Anisotropic Materials
,”
Int. J. Plast.
,
7
(
7
), pp.
693
712
.
29.
Barlat
,
F.
,
Maeda
,
Y.
,
Chung
,
K.
,
Yanagawa
,
M.
,
Brem
,
J. C.
,
Hayashida
,
Y.
,
Lege
,
D. J.
, et al
,
1997
, “
Yield Function Development for Aluminum Alloy Sheet
,”
J. Mech. Phys. Solids
,
45
(
11–12
), pp.
1727
1763
.
30.
Banabic
,
D.
,
Aretz
,
H.
, and
Comsa
,
D. S.
,
2005
, “
An Improved Analytical Description of Orthotropy in Metallic Sheets
,”
Int. J. Plast.
,
21
(
3
), pp.
493
512
.
31.
Talebi-Ghadikolaee
,
H.
,
Naeini
,
H. M.
,
Mirnia
,
M. J.
,
Mirzai
,
M. A.
,
Gorji
,
H.
, and
Alexandrov
,
S.
,
2020
, “
Fracture Analysis on U-Bending of AA6061 Aluminum Alloy Sheet Using Phenomenological Ductile Fracture Criteria
,”
Thin-Walled Struct.
,
148
, p.
106566
.
32.
Pereira
,
A. F. G.
,
Prates
,
P. A.
,
Oliveira
,
M. C.
, and
Fernandes
,
J. V.
,
2020
, “
Inverse Identification of the Work Hardening Law From Circular and Elliptical Bulge Tests
,”
J. Mater. Process. Technol.
,
279
, p.
116573
.
33.
Iqbal
,
M. P.
,
Jain
,
R.
, and
Pal
,
S. K.
,
2019
, “
Numerical and Experimental Study on Friction Stir Welding of Aluminum Alloy Pipe
,”
J. Mater. Process. Technol.
,
274
, p.
116258
.
34.
Khodko
,
O.
,
Zaytsev
,
V.
,
Sukaylo
,
V.
,
Verezub
,
N.
, and
Scicluna
,
S.
,
2015
, “
Experimental and Numerical Investigation of Processes That Occur During High Velocity Hydroforming Technologies: An Example of Tubular Blank Free Bulging During Hydrodynamic Forming
,”
J. Manuf. Process.
,
20
, pp.
304
313
.
35.
Gurson
,
A. L.
,
1997
, “
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
,”
ASME J. Eng. Mater. Technol.
,
99
(
1
), pp.
2
15
.
36.
Hambli
,
R.
,
2001
, “
Finite Element Simulation of Fine Blanking Processes Using a Pressure-Dependent Damage Model
,”
J. Mater. Process. Technol.
,
116
(
2–3
), pp.
252
264
.
37.
Habibi
,
N.
,
Zarei-Hanzaki
,
A.
, and
Abedi
,
H.-R.
,
2015
, “
An Investigation Into the Fracture Mechanisms of Twinning-Induced-Plasticity Steel Sheets Under Various Strain Paths
,”
J. Mater. Process. Technol.
,
224
, pp.
102
116
.
38.
Heidari
,
A.
,
Ghassemi
,
A.
, and
Atrian
,
A.
,
2020
, “
A Numerical and Experimental Investigation of Temperature Effects on the Formability of AA6063 Sheets Using Different Ductile Fracture Criteria
,”
Int. J. Adv. Manuf. Technol.
,
106
(
5–6
), pp.
2595
2611
.
39.
Chow
,
C. L.
, and
Yang
,
X. J.
,
2001
, “
Prediction of the Forming Limit Diagram on the Basis of the Damage Criterion Under Non-Proportional Loading
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
215
(
4
), pp.
405
414
.
40.
Hashemi
,
R.
,
Abrinia
,
K.
, and
Faraji
,
G.
,
2015
, “
A Methodology for Determination of Extended Strain-Based Forming Limit Curve Considering the Effects of Strain Path and Normal Stress
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
229
(
9
), pp.
1537
1547
.
41.
Marciniak
,
Z.
, and
Kuczynski
,
K.
,
1967
, “
Limit Strains in the Processes of Stretch-Forming Sheet Metal
,”
Int. J. Mech. Sci.
,
9
(
9
), pp.
609
612
.
42.
Srinivas Naik
,
B.
,
Janaki Ramulu
,
P.
, and
Ganesh Narayanan
,
R.
,
2010
, “
Application of a Few Necking Criteria in Predicting the Forming Limit of Unwelded and Tailor-Welded Blanks
,”
J. Strain Anal. Eng. Des.
,
45
(
2
), pp.
79
96
.
43.
Cockcroft
,
M.
, and
Latham
,
D.
,
1968
, “
Ductility and the Workability of Metals
,”
J. Inst. Met.
,
96
, pp.
33
39
.
44.
Rice
,
J. R.
, and
Tracey
,
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids
,
17
(
3
), pp.
201
217
.
45.
McClintock
,
F. A.
,
1968
, “
A Criterion for Ductile Fracture by Growth of Holes
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
363
371
.
46.
Oyane
,
M.
,
Sato
,
T.
,
Okimoto
,
K.
, and
Shima
,
S.
,
1980
, “
Criteria for Ductile Fracture and Their Applications
,”
J. Mech. Work. Technol.
,
4
(
1
), pp.
65
81
.
47.
Wang
,
H.
,
Yan
,
Y.
,
Jia
,
F.
, and
Han
,
F.
,
2016
, “
Investigations of Fracture on DP980 Steel Sheet in Roll Forming Process
,”
J. Manuf. Process.
,
22
, pp.
177
184
.
48.
Takuda
,
H.
,
Mori
,
K.
, and
Hatta
,
N.
,
1999
, “
The Application of Some Criteria for Ductile Fracture to the Prediction of the Forming Limit of Sheet Metals
,”
J. Mater. Process. Technol.
,
95
(
1–3
), pp.
116
121
.
49.
Novella
,
M. F.
,
Ghiotti
,
A.
,
Bruschi
,
S.
, and
Bariani
,
P. F.
,
2015
, “
Ductile Damage Modeling at Elevated Temperature Applied to the Cross Wedge Rolling of AA6082-T6 Bars
,”
J. Mater. Process. Technol.
,
222
, pp.
259
267
.
50.
Talebi-Ghadikolaee
,
H.
,
Elyasi
,
M.
, and
Mirnia
,
M. J.
,
2020
, “
Investigation of Failure During Rubber Pad Forming of Metallic Bipolar Plates
,”
Thin-Walled Struct.
,
150
,
106671
.
51.
Modanloo
,
V.
,
Talebi-Ghadikolaee
,
H.
,
Alimirzaloo
,
V.
, and
Elyasi
,
M.
,
2021
, “
Fracture Prediction in the Stamping of Titanium Bipolar Plate for PEM Fuel Cells
,”
Int. J. Hydrogen Energy
,
46
(
7
), pp.
5729
5739
.
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