Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets
The investigation of three-dimensional problem of normal and oblique interaction of yawed pro jectiles with ceramic plates in a velocity range up to 4000 m/s was carried out by the finite element method. The paper presents an advanced constitutive model of AD995 Alumina. The model of a damaged mediu...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2002
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| Zitieren: | Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets / V. A. Gorel’skii // Проблемы прочности. — 2002. — № 3. — С. 109-113. — Бібліогр.: 5 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-467932025-02-09T14:40:53Z Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets Численное моделирование при ударе по нормали и под углом к поверхности преграды Gorel’skii, V.A. Научно-технический раздел The investigation of three-dimensional problem of normal and oblique interaction of yawed pro jectiles with ceramic plates in a velocity range up to 4000 m/s was carried out by the finite element method. The paper presents an advanced constitutive model of AD995 Alumina. The model of a damaged medium is used; it is characterized by a possibility of crack initiation and propagation under impact loading. A kinetic fracture model of the active type developed earlier for the simulation of fracture in various materials is used for numerical modeling of ceramic failure at high velocity impact. Temperature effects are taken into account in the constitutive model. На основе метода конечных элементов исследовалась пространственная задача взаимодействия при ударе по нормали и под углом снаряда с керамической пластиной при скорости до 4000 м/с. Представлена усовершенствованная модель керамики AD995 Alumina, учитывающая температурное воздействие. Применяется также модель поврежденной среды, характеризующаяся возможностью моделировать возникновение и развитие трещины в условиях ударного нагружения. В процессе численного моделирования разрушения керамической пластины при высокоскоростном воздействии была использована кинетическая модель разрушения активного типа, разработанная ранее для моделирования разрушения различных материалов. На основі методу скінченних елементів досліджувалася просторова задача взаємодії при ударі по нормалі та під кутом снаряда з керамічною пластиною при швидкості до 4000 м/с. Представлено удосконалену модель кераміки AD955 Alumina, яка враховує температурну взаємодію. Використовується також модель пошкодженого середовища, для якої характерна можливість моделювання виникнення і розвитку тріщини в умовах ударного навантаження. У процесі числового моделювання руйнування керамічної пластини при високій швидкості було використано кінетичну модель руйнування активного типу, яку розроблено раніше для моделювання руйнування різних матеріалів. 2002 Article Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets / V. A. Gorel’skii // Проблемы прочности. — 2002. — № 3. — С. 109-113. — Бібліогр.: 5 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/46793 539.4 en Проблемы прочности application/pdf Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Gorel’skii, V.A. Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets Проблемы прочности |
| description |
The investigation of three-dimensional problem of normal and oblique interaction of yawed pro jectiles with ceramic plates in a velocity range up to 4000 m/s was carried out by the finite element method. The paper presents an advanced constitutive model of AD995 Alumina. The model of a damaged medium is used; it is characterized by a possibility of crack initiation and propagation under impact loading. A kinetic fracture model of the active type developed earlier for the simulation of fracture in various materials is used for numerical modeling of ceramic failure at high velocity impact. Temperature effects are taken into account in the constitutive model. |
| format |
Article |
| author |
Gorel’skii, V.A. |
| author_facet |
Gorel’skii, V.A. |
| author_sort |
Gorel’skii, V.A. |
| title |
Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets |
| title_short |
Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets |
| title_full |
Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets |
| title_fullStr |
Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets |
| title_full_unstemmed |
Computer Simulation of Normal and Oblique Impacts of Yawed Projectiles on Ceramic Targets |
| title_sort |
computer simulation of normal and oblique impacts of yawed projectiles on ceramic targets |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2002 |
| topic_facet |
Научно-технический раздел |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/46793 |
| citation_txt |
Computer Simulation of Normal and Oblique Impacts of Yawed
Projectiles on Ceramic Targets / V. A. Gorel’skii // Проблемы прочности. — 2002. — № 3. — С. 109-113. — Бібліогр.: 5 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT gorelskiiva computersimulationofnormalandobliqueimpactsofyawedprojectilesonceramictargets AT gorelskiiva čislennoemodelirovaniepriudareponormaliipoduglomkpoverhnostipregrady |
| first_indexed |
2025-11-26T23:23:38Z |
| last_indexed |
2025-11-26T23:23:38Z |
| _version_ |
1849897172060864512 |
| fulltext |
UDC 539.4
Computer Simulation of Normal and Oblique Impacts of Yawed
Projectiles on Ceramic Targets
V. A. Gorel’skii
Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia
Численное моделирование при ударе по нормали и под углом к
поверхности преграды
В. А. Горельский
Томский госуииверситет систем контроля и радиоэлектроники, Томск, Россия
На основе метода конечных элементов исследовалась пространственная задача взаимо
действия при ударе по нормали и под углом снаряда с керамической пластиной при скорости
до 4000 м/с. Представлена усовершенствованная модель керамики AD995 Alumina, учиты
вающая температурное воздействие. Применяется также модель поврежденной среды,
характеризующаяся возможностью моделировать возникновение и развитие трещины в
условиях ударного нагружения. В процессе численного моделирования разрушения керами
ческой пластины при высокоскоростном воздействии была использована кинетическая мо
дель разрушения активного типа, разработанная ранее для моделирования разрушения
различных материалов.
Ключевые слова: ударное нагружение, керамика, метод конечных элемен
тов, модель разрушения.
Formulation of the Problem. A model of a damageable medium
characterized by microcavities (cracks and pores) is used. According to [1], the
total volume of the medium W consists of an undamaged part, which occupies
the volume Wc and is characterized by the density p c, and microcavities, which
occupy the volume WT. The density of the microcavities is assumed to be zero.
The mean density of the damageable medium is related to the parameters
introduced by the formula p = p c (Wc/W). The degree of damage of the medium
is characterized by the specific volume of cracks VT = WT /(Wp). A set of
equations describing time-dependent adiabatic motion of a compressible medium
(in the case of both elastic and plastic deformation) and taking into account the
growth and accumulation of microdamages consists of equations of continuity,
motion, and energy, and the equation that describes the variation of the specific
volume of cracks:
УДК 539.4
p dvi/dt =aij, j , (1)
dp/dt + div( pv ) = 0, (2)
dE/dt = (1/ p)Oij £ij, (3)
© V. A. GOREL’SKII, 2002
ISSN 0556-171X. Проблемы прочности, 2002, № 3 109
V. A. Gorel’skii
dVT
dt
0 for |pc| < P * or Pc > P * and VT = 0,
- sgn( Pc )K 4(| Pc| - P *)(V2 +Vt )
for Pc < -P * or Pc > P * and VT > 0,
(4)
where P = PkV\l(VT + V1); p is the density; vt are the components of the
velocity vector; E is the specific internal energy, £ j are the components of the
deformation-velocity tensor; aij = (P + Q)dij- + Sij are the stress-tensor
components; Pc is the pressure in the continuous component of the substance;
P = Pc(p/pc) is the mean pressure; Q is the artificial viscosity [2], and V1, V2,
Pk, and K 4 are material constants obtained experimentally. Simulation of
fracture was performed with the help of the kinetic model of fracture of active
type, which defines the growth of microcracks that continuously change the
material properties and cause the stress relaxation [3, 4]. Pressure in the
undamaged substance is a function of the specific volume, internal energy, and
specific volume of cracks, and in the whole range of loading conditions it is
defined by the equation of state of the Mie-Gruneisen type according to the
formula
where y 0 is the Gruneisen coefficient, Vo and V are the initial and current
specific volumes, a and b are constants of the Hugoniot adiabat, which is
defined by the linear relation
where D is the shock-wave velocity and um is the mass velocity of the
substance beyond the shock-wave front. Deviatoric components of the stress
tensor are obtained from the following relation:
The parameter X is equal to 0 in the case of elastic deformation. In the case of
plastic deformation, it can be found using the von Mises yield criterion:
P c = P0a2P + P0a2W- Y0 /2 + 2 b - 1)1^2 +
+ p0a 2 [2(1 - y 0/2)(b - 1) + 3(b - 1)2]a3 +y 0P0E,
P = V0/(V - Vt ) - 1,
D = a + bu
where
dSij dSj
d t~ = ^ t ~ - S ikW Jk - S j k W ik , 2W j = d v i / d x j - d v i / d x j ■
SjSj = 2/3 a 2.
110 ISSN 0556-171X. npo6n.eubi npounocmu, 2002, N2 3
Computer Simulation o f Normal and Oblique Impacts
Here G is the shear modulus and о is the dynamic yield strength. These
parameters are obtained with the help of the following relations:
G = G0 [1 + cp(1 + ,a)1/3 + d(T - 300)] V3 /(VT + V3) when T < Tm ,
G = 0 for T > Tm,
о = о 0 [1 + cp(1 + ц ) 1/3 + d(T - 300)](1 - VT /V4)
when T < Tm and VT < V4,
о = о p when VTK < VT < V4 and T < Tm ,
о = 0 when T > Tm or VT > V4 or о < p ̂ .
Here Tm is the substance melting temperature, о w is the stress in a shock wave,
c, d, Vз, and V4 are material constants defined experimentally. The temperature
is calculated according to [5]:
T = (E - Eox ) cp = [E - Eo - E1 ̂ - ( - E 1 + E2^ 2 -
- (E1 - 2E2 + E3)̂ 3 - (-E1 + 3E2 - 3E3 + E4 )̂ 4]/cp,
Eo =- 300cp, E 1 = y0Eo. E2 = (a2 + УоEoV2,
E 3 = (46a 2 + у 0 E 0 )/16, E 4 = (-2y 0 2 + 18b 2 a 2 + у 4 E 0 )/24,
where cp is the specific heat, and E0x is the cold component of the specific
internal energy.
To investigate the effects of fracture and temperature in a ceramic target
during oblique impact of yawed projectiles in the range of velocities up to
4000 m/s, a number of simulations were performed. The interaction of a steel
cylinder 7.6 mm in diameter and 50.8 mm in height with a 10 mm thick AD995
plate was modeled. The model parameters for AD995 ceramics were adjusted
using the data from plate impact experiments. The characteristics of the AD995
plate employed in computations were [6] as follows: p0 = 3890 kg/m ,
о0 = 4.7 GPa, G0 = 160.0 GPa, V1 = 1.46• 10-6 m3/kg, V2 = 0.875-10-7 m3/kg,
V3 = 5.83• 10-5 m3/kg, V4 = 1.75• 10-4 m3/kg, K4 = 0.5 (m-s)/kg, Pk = 0.45
GPa, a = 7700 m/s, b = 1.3, c = 10560 m/s, Tm = 2327 K, VTK = 1.0 • 10-5 m3/kg,
d = 1.6'10K, cp = 775.2 J/(kg • K), у 0 = 1.32, оp = 0.3 GPa, pfr = - 8.8 GPa.
The characteristics of the steel were: p0 = 7850 kg/m3, о0 = 1.01 GPa,
G0 = 79 GPa, V1 = 9.2-10-6 m3/kg, V2 = 5.7 -10-7 m3/kg, V3 = 2.55•Ю-5
m3/kg, V4 = 6.37 • 10-5 m3/kg, K4 = 0.54 (m • s)/kg, Pk = - 1.5 GPa, a = 4400
m/s, b = 1.55, c = 206 GPa, d = 1.6-10 K, cp = 446.7 J/(kg-K), у0 = 1.91.
ISSN 0556-171X. Проблемы прочности, 2002, N 23 111
V. A. Gorel’skii
Results of Numerical Calculations. Computations have been made for the
yaw up to 100. Figure 1 shows configurations of the projectile and plate during
interaction at the impact velocity 4000 m/s for the obliquity 45° and yaw 10° at 10
s. In this case, the computation evidences that the process of perforation is
observed and completed within 15 ,ws.
Fig. 1. Penetration processes at the im pact velocity 4000 m /s for the obliquity 45° and yaw 10°.
Figure 2 shows the histories of resistance force components during
penetration at the impact velocity 4000 m/s for the 45° obliquity. The curves show
that at the initial moment the vertical components of resistance forces are larger.
Beyond 6 ,ws, the horizontal components of the resistance forces are larger for
both angles of the yaw.
Fig. 2. H istories o f resistance force com ponents during penetration at the im pact velocity 4000 m/s
for the obliquity 45°: (1) F2, yaw = 0°; (1) F2, yaw = 10°; (2) F3, yaw = 0°; (2 ) F3, yaw = 10°.
We investigated the histories of temperature near the contact surface in the
target and projectile. The results obtained show that the temperature effects are
important for the impact velocity range over 4000 m/s and they are more
pronounced for the ceramic target. To further investigate the ceramic model, the
contours of specific volume of cracks were generated. The computations show
that the maximum damage occurred in the bottom of the ceramic target near the
impact axis for both angles of the yaw and only for the 10° yaw in the surface
layer of the ceramics near the leading edge of the projectile-target interaction
region. The effect of the yaw on fracture was clearly pronounced.
112 ISSN 0556-171X. npoôëeMbi npounocmu, 2002, N 3
Computer Simulation o f Normal and Oblique Impacts
In conclusion it may be said that the results of numerical simulations using
the shock-wave-propagation-based finite-element code revealed that both
temperature effects and fracture of ceramics are important at the velocity 4000 m/s.
We established the stages in the penetration process, the surfaces and contours of
temperature and specific volume of cracks for various instants of time. The results
show that the temperature effects in ceramic targets are clearly pronounced for the
impact velocity 4000 m/s. It was revealed that during the second stage of
penetration the values of the horizontal components of the resistance forces are
larger than the values of their vertical components. This results in the
normalization of the vector velocity of the projectile mass center during the
second stage of the penetration process at the 45° obliquity.
The research was supported by the Russian Foundation for Basic Research
(Grant No. 99-03-32200).
Р е з ю м е
На основі методу скінченних елементів досліджувалася просторова задача
взаємодії при ударі по нормалі та під кутом снаряда з керамічною пласти
ною при швидкості до 4000 м/с. Представлено удосконалену модель кера
міки AD955 Alumina, яка враховує температурну взаємодію. Використову
ється також модель пошкодженого середовища, для якої характерна можли
вість моделювання виникнення і розвитку тріщини в умовах ударного
навантаження. У процесі числового моделювання руйнування керамічної
пластини при високій швидкості було використано кінетичну модель руйну
вання активного типу, яку розроблено раніше для моделювання руйнування
різних матеріалів.
1. V. A. Gorel’skii and S. A. Zelepugin, “Numerical simulation of powder
compaction under an axially symmetric impact,” Poroshk. Metal., No. 4, 11
- 16 (1992).
2. V. A. Gorel’skii, I. E. Khorev, and N. T. Yugov, “Dynamics of a
three-dimensional process of asymmetric interjection between deformable
bodies and a rigid wall,” Prikl. Mekh. Tekh. Fiz., No. 4, 112 - 118 (1985).
3. V. A. Gorel’skii and S. A. Zelepugin, “Mathematical simulation of fracture
of ceramic obstacles in axially symmetric high-velocity impact,” Probl.
Prochn., No. 5-6, 87 - 94 (1995).
4. V. A. Gorel’skii and S. A. Zelepugin, “Vortex structures in ceramics under
high velocity impact,” Tech. Phys. Lett., 23, No. 24, 86 - 90 (1997).
5. W. H. Gust, “High impact deformation of metal cylinders at elevated
temperatures,” J. Appl. Phys., 53, No. 5, 3566 - 3575 (1982).
6. R. Subramanian and S. J. Bless, “Penetration of semi-infinite AD995
Alumina targets by tungsten long rod penetrators from 1.5 to 3.5 km/s,” Int.
J. Impact Eng., 17, 807 - 816 (1995).
R eceived 14. 11. 2001
ISSN 0556-171X. Проблеми прочности, 2002, № 3 113
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