DEFORMATION OF LONG- LENGTH EXPLOCLAD SHEETS: MATHEMATICAL MODELING

DEFORMATION OF LONGLENGTH EXPLOCLAD SHEETS:
MATHEMATICAL MODELING
А. Yu. Muizemnek, I. V. Denisov, О. L. Pervukhina,
А. Е. Rosen, I. S. Los’ and Yu. A. Gordopolov
2
Object:
Experimentally-theoretical research of longitudinal
deformations of making layers of a multilayer material at
explosion welding
Research Technique
1. Computer simulation of deformation process of large-size sheets at
explosion welding by means of LS-DYNA.
2. Experimental research of large-size sheets deformation by means of
fixed points method.
3. Analysis of computer simulation and experimental results.
3
Explosion welding scheme
1 – clad plate ; 2 – base plate ; 3 – air technological gap ; 4 - sand background
Initial data
The geometrical
sizes
Thickness,
mm
Length,
mm
Width,
mm
clad plate
4
6000
1500
base plate
26
5900
1500
gap
8
explosive
50
5900
1400
sand background
100
5900
1400
PHYSICOMECHANICAL PROPERTIES
OF MATERIALS
Steel plate:
– Density ρ = 7800 kg/m3;
– Young modulus E = 192 GPa;
– Yield strength σт = 350 MPa;
– ultimate strength σв = 500 MPa;
– unit elongation δ = 21%;
– coefficient of thermal expansion α = 11,4
ºС-1 (100ºС).
Explosive
- apparent density ρВВ = 740 kg/m3
- velocity of detonation D = 2100 m/s.
Sand
- apparent density ρпес = 2800 kg/m3
- compression strength σсж = 140 MPa
4
Mathematical simulation by means of LS-DYNA
software for the following situations :
1. Porous background, dissimilar metals
(steel+stainless steel) under the assumption that both
plates material behaves as a solid body, technological
gap between clad and base plates.
2. Porous background, dissimilar metals, under the
assumption that a clad material behaves as a liquid, a
base material behaves as a solid body, technological gap
between clad and base plates.
5
The description of used finite-element mesh
– Quantity of elements ~ 1000000 ;
– Quantity of units ~ 2000000 ;
– The maximal size of an element – 0.5 mm.
Finite-element mesh
Used models of materials and state equations.
Explosive :
– material model - #9 (Wilkins-Geyrouch);
– state equation - # 2 (JWL).
Metal plate :
– material model - #15 (Johnson – Cook);
– state equation - # 4 (Mi – Gruneisen);
Sand background :
– zero-material - #9;
– state equation of porous material - # 8.
Technological gap :
– vacuum model - #140.
6
The first variant of calculation
Porous background, dissimilar metals under the assumption that both plates material
behaves as a solid body, technological gap between clad and base plates.
a
b
Distribution of material density in calculation area at t = 3 ms:
a – the beginning clad process; b – the termination clad process
It is established that the left butt of clad and base plates is extended by
16,1 mm and 29 mm. The right butt of clad and base plates is extended by
71 mm and 61,3 mm accordingly.
7
The second variant of calculation
Porous background, dissimilar metals, under the assumption that a clad material behaves as a
liquid (base material behaves as a solid body), technological gap between clad and base plates
a
b
Distribution of material density in calculation area at t = 3 ms
a – the beginning clad process; b – the termination clad process
It is established that clad plate isn’t extended and base plate is extended by 35 mm.
8
clad plate
1
base plate
t = 1000 μs
t = 1500 μs
t = 2000 μs
Change of pressure longitudinal along sheets
2
9
clad plate
1
base plate
t = 2500 μs
t = 2750 μs
t = 3000 μs
Change of longitudinal stress along the sheets
2
10
The scheme of sheet deformation revealing after
explosion welding
Before explosion welding
The beginning of initiation
clad plate
Matching clad and base plates
base plate
Labels
After explosion welding
The beginning of initiation
clad plate
base plate
Places of matching clad and base plates
Labels
11
Results of experiments
Before explosion welding
After explosion welding
Matching clad and base plates
The top view
12
The generalized results of explosion welding simulation
Plate
base
clad
base
clad
base
Moving from the initiation
point
Variant of
calculation
Experimental data
at V0=2100 km/s
1
2
to the right, mm
16,1
0
0
to the right, mm
29
0
0
to the left, mm
61,3
35
25 – 28
to the left, mm
71
0
0
1500
1300
1200
the beginning of process of
lengthening, mm
Conclusions:
1. On the deformation behavior and change of geometric sizes of clad and
base sheet influence the next parameters:
– the initial geometric size of plates;
– characteristics of physical-mechanical properties of welded plates
materials and explosive.
2. The residual elongation of plates occurs nonuniformly from 80% of
sheet length. The maximal residual deformation is near the opposite butt
from the initiation point.
3. Calculation and experimental results showed that the clad sheet
behaves as a viscous liquid and the base sheet behaves as a metal in solid
state.
4. Tensile deformation of base sheet due to the impact of clad sheet goes
ahead of the contact point along the full thickness to the joint formation.
Consequently explosion welding at the end areas goes along the moving
surface of base sheet.
Анимация 2. Движение материала в расчётной области
(Начало процесса сварки)
Анимация 3. Движение материала в расчётной области
(окончание процесса сварки)
Для описания поведения материалов листов была использована модель
Джонсона-Кука со следующими значениями параметров модели:
$
*MAT_JOHNSON_COOK
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
mid
ro
g
e
pr
dtf
vp
4
7.8
0.808
2.03
0.300
0.0
0.0
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
A
B
n
c
m
tm
tr
epso
350.25E-5 275.0E-5
0.36
0.022
1.0
1400.0
30.0
1.0e-5
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
cp
pc
SPALL
IT
D1
D2
D3
D4
477.0E-8
0.0
0.0
1.0
100.0
0.0
0.0
0.0
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
D5
0.0
$
*EOS_LINEAR_POLYNOMIAL
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
eosid
c0
c1
c2
c3
c4
c5
c6
4
0.0
1.4
0.0
0.0
0.0
0.0
0.0
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
e0
v0
0.0000000
1.0
$
MID – идентификатор материала в виде уникального номера; RO – массовая плотность; G – модуль сдвига;
SIGY – предел текучести; PC – предельное давление при растяжении; SPALL – тип разрушения; EPS –
эффективная пластическая деформация; ES – эффективное напряжение; EOSID – метка уравнения состояния;
Е0 – начальная внутренняя энергия; V0 – начальный относительный объем.
Для описания поведения ВВ была использована модель
MAT_HIGH_EXPLOSIVE_BURN и уравнение состояния JWL со
следующими значениями параметров модели:
$
*MAT_HIGH_EXPLOSIVE_BURN
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
mid
ro
D
PCJ
BETA
K
G
SIGY
5
0.740
0.2100
0.01360 0.0000000 0.0000000 0.0000000 0.0000000
$
*EOS_JWL
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
eosid
a
b
r1
r2
omeg
e0
v0
5
0.06142
0.01352
5.4
1.4
0.25
0.00673
1.0
$
MID – идентификатор материала в виде уникального числа; RO – массовая плотность; D – скорость
детонации; PCJ – давление Чэпмена-Жуге; EOSID – метка уровня состояния; V0 – начальный
относительный объем.
Для описания поведения песка была использована модель MAT_NULL
для пористого материала со следующими значениями параметров:
$
*MAT_NULL
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
mid
ro
pc
mu
terod
cerod
ym
pr
6
2.5
0.00
0.0e+3
1.0e-5
0.00
$
*EOS_TABULATED_COMPACTION
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$
eosid
gama
e0
v0
6
0.0
0.0
1.0
$------+-------1-------+-------2-------+-------3-------+-------4-------+-------5
$
ev1
ev2
ev3
ev4
ev5
0.0
-0.04
-0.08
-0.12
-0.16
$
ev6
ev7
ev8
ev9
ev10
-0.20
-0.24
-0.28
-0.32
-0.36
$
c1
c2
c3
c4
c5
0.8e-11
0.8e-4
2.4e-4
5.6e-4
12.0e-4
$
c6
c7
c8
c9
c10
24.8e-4
50.5e-4
101.6e-4
204.0e-4
409.0e-4
$
t1
t2
t3
t4
t5
0.0e+6
0.0e+6
0.0e+6
0.0e+6
0.0e+6
$
t6
t7
t8
t9
t10
0.0e+6
0.0e+6
0.0e+6
0.0e+6
0.0e+6
$
k1
k2
k3
k4
k5
40.0e-4
40.0e-4
80.0e-4
160.0e-4
320.0e-4
$
k6
k7
k8
k9
k10
640.0e-4
1280.0e-4
2560.0e-4
5120.0e-4
10240.0e-4
$
MID – идентификатор материала в виде уникального номера; RO – массовая плотность; PC – предельное
давление при растяжении; MU – коэффициент вязкости; TEROD – относительный объем для разрушения при
растяжении; GEROD – относительный объем для разрушения при сжатии; YM – модуль Юнга (используется
только для нулевых балочных и оболочечных элементов); PR – коэффициент Пуассона (используется только для
нулевых балочных и оболочечных элементов).
Выражение Джонсона (Johnson) и Кука (Cook) для напряжения текучести
.
p n 

 y   A  B 1  c ln  *1  T *m 



Уравнение состояния JWL задает давление в виде


   R1V
   R2V E
e
e
p  A1 
 B1 

R
V
R
V
V
1 
2


