Abstract

Steels are usually stronger at low temperatures than at high temperatures. But low temperatures are, particularly in combination with high strain rates and high stress triaxiality ratios, known to cause embrittlement. The common understanding is that the ductility of steels decreases dramatically below a threshold temperature known as the ductile-to-brittle transition temperature. This study explores the ballistic performance of Strenx 960 Plus steel plates at both low temperatures and room temperature. We describe a ballistic setup where target plates were cooled down to as low as −60 °C before we present results from ballistic impact tests with three different projectile types. The ballistic limit velocities from tests at low temperatures were higher than the ballistic limit velocities from tests at room temperature, indicating that brittle fracture does not take place. An analytical approach based on the Johnson–Cook constitutive relation, the Cockcroft–Latham ductile failure criterion, and a simple brittle fracture criterion is presented. The model suggests that ductile fracture prevails for most realistic material state histories, both in the ballistic impact tests as well as for quasi-static and dynamic tensile tests. This supports previous observations that brittle fracture is unlikely to occur in modern steels even when subjected to rapid loading and low temperatures.

References

1.
Dieter
,
G.
,
1988
,
Mechanical Metallurgy
, 3rd ed.,
McGraw-Hill
,
New York
.
2.
Tu
,
S.
,
Ren
,
X.
,
Kristensen
,
T. A.
,
He
,
J.
, and
Zhang
,
Z.
,
2018
, “
Study of Low Temperature Effect on the Fracture Locus of a 420-MPa Structural Steel With the Edge Tracing Method
,”
Fatigue Fract. Eng. Mater. Struct.
,
41
(
8
), pp.
1649
1661
.
3.
Perez-Martin
,
M. J.
,
Holmen
,
J. K.
,
Thomesen
,
S.
,
Hopperstad
,
O. S.
, and
Børvik
,
T.
,
2019
, “
Dynamic Behavior of a High-Strength Steel at Low Temperatures
,”
J. Dyn. Behav. Mater.
,
5
(
3
), pp.
241
250
.
4.
Anderson
,
T. L.
,
2005
,
Fracture Mechanics: Fundamentals and Applications
,
CRC Press
,
Boca Raton, FL
.
5.
Bao
,
Y.
, and
Wierzbicki
,
T.
,
2004
, “
On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space
,”
Int. J. Mech. Sci.
,
46
(
1
), pp.
81
98
.
6.
Bai
,
Y.
, and
Wierzbicki
,
T.
,
2008
, “
A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence
,”
Int. J. Plast.
,
24
(
6
), pp.
1071
1096
.
7.
Dæhli
,
L. E.
,
Morin
,
D.
,
Børvik
,
T.
, and
Hopperstad
,
O. S.
,
2018
, “
A Lode-Dependent Gurson Model Motivated by Unit Cell Analyses
,”
Eng. Fract. Mech.
,
190
, pp.
299
318
.
8.
Xie
,
J.
,
Zhao
,
X.
, and
Yan
,
J.-B.
,
2018
, “
Mechanical Properties of High Strength Steel Strand at Low Temperatures: Tests and Analysis
,”
Constr. Build. Mater.
,
189
, pp.
1076
1092
.
9.
Jia
,
B.
,
Rusinek
,
A.
,
Bahi
,
S.
,
Bernier
,
R.
,
Pesci
,
R.
, and
Bendarma
,
A.
,
2019
, “
Perforation Behavior of 304 Steel Plates at Various Temperatures
,”
J. Dyn. Behav. Mater.
,
5
(
4
), pp.
416
431
.
10.
Rodríguez-Martínez
,
J. A.
,
Pesci
,
R.
,
Rusinek
,
A.
,
Arias
,
A.
,
Zaera
,
R.
, and
Pedroche
,
D. A.
,
2010
, “
Thermo-Mechanical Behaviour of TRIP 1000 Steel Sheets Subjected to Low Velocity Perforation by Conical Projectiles at Different Temperatures
,”
Int. J. Solids Struct.
,
47
(
9
), pp.
1268
1284
.
11.
Paik
,
J. K.
,
Kim
,
B. J.
,
Park
,
K.
, and
Jang
,
B. S.
,
2011
, “
On Quasi-Static Crushing of Thin-Walled Steel Structures in Cold Temperature: Experimental and Numerical Studies
,”
Int. J. Impact Eng.
,
38
(
1
), pp.
13
28
.
12.
Paik
,
J. K.
,
Lee
,
D. H.
,
Noh
,
S. H.
,
Park
,
D. K.
, and
Ringsberg
,
J. W.
,
2020
, “
Full-Scale Collapse Testing of a Steel Stiffened Plate Structure Under Axial-Compressive Loading Triggered by Brittle Fracture at Cryogenic Condition
,”
Sh. Offshore Struct.
,
15
(
Suppl. 1
), pp.
S29
S45
.
13.
Paik
,
J. K.
,
Lee
,
D. H.
,
Park
,
D. K.
, and
Ringsberg
,
J. W.
,
2021
, “
Full-Scale Collapse Testing of a Steel Stiffened Plate Structure Under Axial-Compressive Loading at a Temperature of −80 °C
,”
Sh. Offshore Struct.
,
16
(
3
), pp.
255
270
.
14.
Ehlers
,
S.
, and
Østby
,
E.
,
2012
, “
Increased Crashworthiness Due to Arctic Conditions—The Influence of Sub-Zero Temperature
,”
Mar. Struct.
,
28
(
1
), pp.
86
100
.
15.
Ritchie
,
R. O.
,
Knott
,
J. F.
, and
Rice
,
J. R.
,
1973
, “
On the Relationship Between Critical Tensile Stress and Fracture Toughness in Mild Steel
,”
J. Mech. Phys. Solids
,
21
(
6
), pp.
395
410
.
16.
Needleman
,
A.
, and
Tvergaard
,
V.
,
2000
, “
Numerical Modeling of the Ductile-Brittle Transition
,”
Int. J. Fract.
,
101
(
1/2
), pp.
73
97
.
17.
Nam
,
W.
,
Amdahl
,
J.
, and
Hopperstad
,
O. S.
,
2016
, “
Influence of Brittle Fracture on the Crashworthiness of Ship and Offshore Structures in Arctic Conditions
,”
Proceedings of the 7th International Conference on Collision and Grounding of Ships and Offshore Structures
,
Ulsan, South Korea
,
June 15–18
, pp.
1
6
.
18.
Nam
,
W.
,
Hopperstad
,
O. S.
, and
Amdahl
,
J.
,
2018
, “
Modelling of the Ductile-Brittle Fracture Transition in Steel Structures With Large Shell Elements: A Numerical Study
,”
Mar. Struct.
,
62
, pp.
40
59
.
19.
SSAB
, “
Strenx Performance Steel
,” https://www.ssab.com/products/brands/strenx, Accessed August 5, 2021.
20.
eCorr User Manual
,” https://www.ntnu.edu/kt/ecorr, Accessed July 22, 2021.
21.
Børvik
,
T.
,
Clausen
,
A.
, and
Dey
,
S.
,
2009
, “
Perforation Resistance of Five Different High-Strength Steel Plates Subjected to Small-Arms Projectiles
,”
Int. J. Impact Eng.
,
36
(
7
), pp.
948
964
.
22.
Børvik
,
T.
,
Langseth
,
M.
,
Hopperstad
,
O. S.
, and
Malo
,
K. A.
,
1999
, “
Ballistic Penetration of Steel Plates
,”
Int. J. Impact Eng.
,
22
(
9–10
), pp.
855
886
.
23.
Recht
,
R. F.
, and
Ipson
,
T. W.
,
1960
, “
Ballistic Perforation Dynamics
,”
ASME J. Appl. Mech.
,
30
(
3
), pp.
384
390
.
24.
Zukas
,
J. A.
,
1982
,
Impact Dynamics
, 1st ed.,
John Wiley & Sons, Inc
,
New York
.
25.
Holmen
,
J. K.
,
Johnsen
,
J.
,
Jupp
,
S.
,
Hopperstad
,
O. S.
, and
Børvik
,
T.
,
2013
, “
Effects of Heat Treatment on the Ballistic Properties of AA6070 Aluminium Alloy
,”
Int. J. Impact Eng.
,
57
, pp.
119
133
.
26.
Holmen
,
J. K.
,
Johnsen
,
J.
,
Hopperstad
,
O. S.
, and
Børvik
,
T.
,
2016
, “
Influence of Fragmentation on the Capacity of Aluminum Alloy Plates Subjected to Ballistic Impact
,”
Eur. J. Mech. A Solids
,
55
, pp.
221
233
.
27.
Goldsmith
,
W.
,
1999
, “
Non-Ideal Projectile Impact on Targets
,”
Int. J. Impact Eng.
,
22
(
2–3
), pp.
95
395
.
28.
Børvik
,
T.
,
Olovsson
,
L.
,
Dey
,
S.
, and
Langseth
,
M.
,
2011
, “
Normal and Oblique Impact of Small Arms Bullets on AA6082-T4 Aluminium Protective Plates
,”
Int. J. Impact Eng.
,
38
(
7
), pp.
577
589
.
29.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1983
, “
A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures
,”
Proceedings of the 7th International Symposium on Ballistics
,
The Hague, The Netherlands
,
Apr. 19–21
, pp.
541
547
.
30.
Roth
,
C. C.
, and
Mohr
,
D.
,
2014
, “
Effect of Strain Rate on Ductile Fracture Initiation in Advanced High Strength Steel Sheets: Experiments and Modeling
,”
Int. J. Plast.
,
46
, pp.
19
44
.
31.
Johnson
,
G. R.
,
Hoegfeldt
,
J. M.
,
Lindholm
,
U. S.
, and
Nagy
,
A.
,
1983
, “
Response of Various Metals to Large Torsional Strains Over a Large Range of Strain Rates—Part 1: Ductile Metals
,”
ASME J. Eng. Mater. Technol.
,
105
(
1
), pp.
42
47
.
32.
Bridgman
,
P. W.
,
1944
, “
The Stress Distribution at the Neck of a Tension Specimen
,”
Trans. Am. Soc. Metals
,
32
, pp.
553
574
.
33.
Le Roy
,
G.
,
Embury
,
J. D.
, and
Ashby
,
M. F.
,
1981
, “
A Model of Ductile Fracture Based on the Nucleation and Growth of Voids
,”
Acta Metall.
,
29
(
8
), pp.
1509
1522
.
34.
Børvik
,
T.
,
Hopperstad
,
O. S.
,
Berstad
,
T.
, and
Langseth
,
M.
,
2001
, “
Numerical Simulations of Plugging Failure in Ballistic Penetration
,”
Int. J. Solids Struct.
,
38
(
34–35
), pp.
6241
6264
.
35.
Børvik
,
T.
,
Hopperstad
,
O. S.
, and
Berstad
,
T.
,
2003
, “
On the Influence of Stress Triaxiality and Strain Rate on the Behaviour of a Structural Steel. Part II. Numerical Study
. Eur. J. Mech. A Solids
,
22
(
1
), pp.
15
32
.
36.
Roth
,
C. C.
,
Fras
,
T.
, and
Mohr
,
D.
,
2020
, “
Dynamic Perforation of Lightweight Armor: Temperature-Dependent Plasticity and Fracture of Aluminum 7020-T6
,”
Mech. Mater.
,
149
, p.
103537
.
37.
Holmen
,
J. K.
,
Solberg
,
J. K.
,
Hopperstad
,
O. S.
, and
Børvik
,
T.
,
2017
, “
Ballistic Impact of Layered and Case-Hardened Steel Plates
,”
Int. J. Impact Eng.
,
110
, pp.
4
14
.
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