In this paper, the influence of mesh sensitivity on the fracture predictions during penetration and perforation of hardened blunt-nose cylindrical steel projectiles in plates of Weldox 460E, Weldox 700E, and Weldox 900E steel has been studied. The main objective is to try to describe the experimentally obtained trend of a decrease in ballistic limit velocity with increased target strength when the plates are impacted by blunt projectiles. This behavior is due to the occurrence of highly localized shear bands as the target strength increases. The impact tests are analyzed using the explicit solver of a nonlinear finite element code. A thermoelastic-thermoviscoplastic constitutive model with coupled or uncoupled ductile damage was used in the simulations. It was found that the residual velocity continuously increases when the element size is decreased from 125μm to 15μm in the shear zone, and that this increase is significantly stronger for impact velocities close to the ballistic limit. The ballistic limit decreases by up to 25% when the size of the element is decreased from 125μm to 30μm; the decrease being somewhat greater for the two steels with the highest strength. Even with the finest mesh, the experimental trend of a decreasing ballistic limit with increasing target strength was not predicted in the simulations, neither with coupled nor uncoupled damage. Nonlocal simulations based on smoothing of the damage and temperature fields, which are the two variables causing the softening, were carried out for the Weldox steels and a mesh size of 30μm. These simulations indicate a reduction in the mesh sensitivity for both the coupled and uncoupled damage approaches when nonlocal averaging is employed.

1.
Backman
,
M. E.
, and
Goldsmith
,
W.
, 1978, “
The Mechanics of Penetration of Projectiles Into Targets
,”
Int. J. Eng. Sci.
0020-7225,
16
, pp.
1
99
.
2.
Corbett
,
G. G.
,
Reid
,
S. R.
, and
Johnson
,
W.
, 1996, “
Impact Loading of Plates and Shells by Free-Flying Projectiles
,”
Int. J. Impact Eng.
0734-743X,
18
(
2
), pp.
141
230
.
3.
Goldsmith
,
W.
, 1999, “
Review: Non-Ideal Projectile Impact on Targets
,”
Int. J. Impact Eng.
0734-743X,
22
, pp.
95
395
.
4.
Hadamard
,
J.
, 1903,
Leçons sur la propagation des ondes et les équations de l'hydrodynamique
,
Hermann
,
Paris
, Chap. 6.
5.
Bãzant
,
Z. P.
, 1986, “
Mechanics of Distributed Cracking
,”
Appl. Mech. Rev.
0003-6900,
39
(
5
), pp.
675
705
.
6.
Benallal
,
A.
, and
Bigoni
,
D.
, 2004, “
Effects of Temperature and Thermo-Mechanical Couplings on Material Instabilities and Strain Localization of Inelastic Materials
,”
J. Mech. Phys. Solids
0022-5096,
52
, pp.
725
753
.
7.
Needleman
,
A.
, 1988, “
Material Rate Dependent and Mesh Sensitivity in Localization Problems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
67
, pp.
69
85
.
8.
Perzyna
,
P.
, 1963, “
The Constitutive Equations for Rate-Sensitive Materials
,”
Q. Appl. Math.
0033-569X,
20
, pp.
321
332
.
9.
Zukas
,
J. A.
, and
Scheffler
,
D. R.
, 2000, “
Practical Aspects of Numerical Simulations of Dynamic Events: Effects of Meshing
,”
Int. J. Impact Eng.
0734-743X,
24
, pp.
925
945
.
10.
Voyiadjis
,
G. Z.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
, 2008. “
Constitutive Modeling and Simulation of Perforation of Targets by Projectiles
,”
AIAA J.
0001-1452,
46
, pp.
304
316
.
11.
Zhou
,
M.
,
Ravichandran
,
G.
, and
Rosakis
,
A. J.
, 1996b, “
Dynamically Propagating Shear Bands in Impact-Loaded Prenotched Plates—II. Numerical simulations
,”
J. Mech. Phys. Solids
0022-5096,
44
(
6
), pp.
1007
1032
.
12.
Li
,
S.
,
Liu
,
W. K.
,
Qian
,
D.
,
Guduru
,
P. R.
, and
Rosakis
,
A. J.
, 2001, “
Dynamic Shear Band Propagation and Microstructure of Adiabatic Shear Band
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
191
(
1–2
), pp.
73
92
.
13.
Li
,
S.
,
Liu
,
W. K.
,
Rosakis
,
A. J.
,
Belytschko
,
T.
, and
Hao
,
W.
, 2002, “
Mesh-Free Galerkin Simulations of Dynamic Shear Band Propagation and Failure Mode Transition
,”
Int. J. Solids Struct.
0020-7683,
39
(
5
), pp.
1213
1240
.
14.
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 Seventh International Symposium on Ballistics
, Hague, pp.
541
547
.
15.
Johnson
,
G. R.
, and
Cook
,
W. H.
, 1985, “
Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures
,”
Eng. Fract. Mech.
0013-7944,
21
, pp.
31
48
.
16.
Teng
,
X.
,
Wierzbicki
,
T.
, and
Couque
,
H.
, 2007, “
On the Transition From Adiabatic Shear Banding to Fracture
,”
Mech. Mater.
0167-6636,
39
, pp.
107
125
.
17.
Dey
,
S.
,
Børvik
,
T.
,
Hopperstad
,
O. S.
,
Leinum
,
J. R.
, and
Langseth
,
M.
, 2004, “
The Effect of Target Strength on the Perforation of Steel Plates Using Three Different Projectile Nose Shapes
,”
Int. J. Impact Eng.
0734-743X,
30
(
8–9
), pp.
1005
1038
.
18.
Solberg
,
J. K.
,
Leinum
,
J. R.
,
Embury
,
J. D.
,
Dey
,
S.
,
Børvik
,
T.
, and
Hopperstad
,
O. S.
, 2007, “
Localised Shear Banding in Weldox Steel Plates Impacted by Projectiles
,”
Mech. Mater.
0167-6636,
39
, pp.
865
880
.
19.
Børvik
,
T
,
Hopperstad
,
OS
,
Berstad
,
T
, and
Langseth
,
M.
, 2001, “
A Computational Model of Viscoplasticity and Ductile Damage for Impact and Penetration
,”
Eur. J. Mech. A/Solids
0997-7538,
20
, pp.
685
712
.
20.
Børvik
,
T.
,
Hopperstad
,
O. S.
,
Langseth
,
M.
, and
Malo
,
K. A.
, 2003, “
Effect of Target Thickness in Blunt Projectile Penetration of Weldox 460 E Steel Plates
,”
Int. J. Impact Eng.
0734-743X,
28
(
4
), pp.
413
464
.
21.
Hallquist
,
J. O.
, 2003,
LS-DYNA Keyword User’s Manual, Version 970
,
Livermore Software Technology Corporation
,
California
.
22.
Camacho
,
G. T.
, and
Ortiz
,
M.
, 1997, “
Adaptive Lagrangian Modelling of Ballistic Penetration of Metallic Targets
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
142
, pp.
269
301
.
23.
Lemaitre
,
J.
, 1992,
A Course on Damage Mechanics
,
Springer
,
Berlin
.
24.
Pijaudier-Cabot
,
G.
, and
Bãzant
,
Z. P.
, 1987, “
Nonlocal Damage Theory
,”
J. Eng. Mech.
0733-9399,
113
, pp.
1512
33
.
25.
Recht
,
R. F.
, and
Ipson
,
T. W.
, 1963, “
Ballistic Perforation Dynamics
,”
ASME J. Appl. Mech.
0021-8936,
30
(
3
), pp.
384
390
.
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