mechanical stress relaxation in complex materials after high speed collisions
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XIII. International Conference on Khariton’s Topical Scientific Readings , March 14-18, 2011, Sarov , Russia „ Extreme State of Substance . Detonation . Shock Waves .” Session 3. – Dynamic Strength of Materials. - PowerPoint PPT PresentationTRANSCRIPT
Mechanical Stress Relaxation in Complex Materials After High
Speed Collisions
XIII. International Conference on Khariton’s Topical Scientific Readings,
March 14-18, 2011, Sarov, Russia„Extreme State of Substance. Detonation. Shock Waves.”
Session 3. – Dynamic Strength of Materials
Dr. László A. Gömze1, University of Miskolc, Miskolc, Hungary Milla Gömze2, IGREX Engineering Service Ltd. Igrici, Hungary
[email protected] [email protected] Tel.: +36 30 746 2714 Tel.: +36 30 746 2713
Our Aims
• Understand the phenomena of high speed collisions of bodies made from different materials.
• Analyse the mechanical model of hetero-modulus and hetero-viscous complex materials and their behavior during and after high speed (u≈1000 m/sec or higher) collisions.
• On the basis of ceramics develop hetero-modulus and hetero-viscous complex materials systems capable endure high speed collisions with flying metallic and other objects without damages.
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Typical Destruction of Ceramic Composites Under High Speed (HS) Collisions (u≥1000 m/sec)
Typical destruction of ceramic composites (L=3 mm) during high speed collision
Typical destruction of ceramic composites (L=4 mm) during high speed collisions
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
The Energy Conception of HS Collisions
WK = WE + WH+ WP + WS + WV, [Nm] (1)
WE: Energy engorgement through elastic deformation , [Nm].
WH: Energy engorgement through heating and recrystallization (phase transformation), [Nm].
WK: Kinetic energy of flying object, [Nm].
WP: Fracture energy engorgement through pressure stress, [Nm].
WS: Fracture energy engorgement through shear stress, [Nm].WV: Energy engorgement through viscous deformation, [Nm].Mechanical Stress Relaxation in Complex Materials After High Speed Collisions
[email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
The Energy Engorgement Through Fractures and Deformation of Traditional Materials and Ceramics
• Material has only one Young’s modulus (E=const.)• Flying (hit) object has inhomogeneous density (ρ≠const.)
ν1: the Poisson ratioρi: density of the „i-th”component of flying object; [kg/m3] A1i and A2i: surfaces of fractures caused by „i-th” density component of flying object [m2] i=1, 2, …, n: the number of different density components of flying object l1i and l2i: deep and „movement” of fractures, caused by „i-th” density component of flying
object [m]RP and RS: the pressure and shear strength of ceramic body [N/m2] Vi: volume of „i-th” component of flying object [m3]
(2)
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
n
i
n
iHEii
Sii
pn
iii NmWWlA
ERlA
ER
Vu1 1
22
2
11
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2
][;)1(22
Advantages of Hetero-Modulus Materials
• Multiple values of Young’s modulus
• High damage tolerance
• Ability to absorb and dissipate the elastic energy during crack propagation
• Good thermal shock resistance
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
The Energy Engorgement Through Fractures and Deformation of Hetero-Modulus Materials
• Material has several Young’s modulus (E=var.)• Flying (hit) object has inhomogeneous density (ρ≠const.)
(3)
νj: the Poisson ratio of „j-th” Young’s modulus component of hetero-modulus body [m3]
ρi: density of the „i-th” component of flying object; [kg/m3]
A1j and A2j: surface of fractures of „j-th” Young’s modulus component of hetero-modulus body [m2]
A3j: surface of deformed „j-th” Young’s modulus component of hetero-modulus body [m2]Ej: The Young’s modulus of the „j-th” component of hetero-modulus body ; [N/m2]
i=1, 2, …, n: the number of different density components of flying objectj=1, 2, …, n: the number of different Young’s modulus components of hetero-modulus body l1j and l2j: deep and „movement” of fractures of „j-th” Young’s modulus component of hetero-modulus body [m]
l3j: Size of deformation of „j-th” Young’s modulus component of hetero-modulus body [m]RPj and RSj: the pressure and shear strength of „j-th” Young’s modulus component of hetero-modulus body [N/m2]
Vi: volume of „i-th” component of flying object [m3] Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
N
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22
The Thermic Part of the Collision Energy
WH = WHS + WRC + WRM , [Nm] (4)
WH: Energy engorgement through heating, [Nm]WHS: Energy engorgement of thermal deformation in place and
surrounding of the collision and fall; [Nm]WRC: Energy engorgement through recrystallization of particles
in place and surrounding of collision and fall; [Nm]WRM: Energy engorgement through spraying and
recrystallization of falling (metallic) body [Nm]
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Advantages of Hetero-Modulus and Hetero-Viscous Complex Materials
• High damage tolerance• Higher deformation tolerance• Ability to absorb and
dissipate the collision energy• Relax by time mechanical
stress developed in body during high speed collisions.
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Some Complex Materials Having Excellent Dynamic Strength
Automobile tyres Asphalt mixturesCeramics made from hetero-modulus and
hetero-viscous particles
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
The Energy Engorgement Through Fractures and Deformation of Hetero-Modulus and Hetero-Viscous Complex Materials
• Complex material has several Young’s modulus (E=var.) and viscosity (η=var.)• Flying (hit) object has inhomogeneous density (ρ≠const.)
(5)
ρi: density of the „i-th” component of flying object; [kg/m3]
A1j and A2j: surface of fractures of „j-th” Young’s modulus component of hetero-modulus body [m2]
A3j: surface of deformed „j-th” Young’s modulus component of hetero-modulus body [m2]Ej: The Young’s modulus of the „j-th” component of hetero-modulus body ; [N/m2]
i=1, 2, …, n: the number of different density components of flying objectj=1, 2, …, n: the number of different Young’s modulus components of hetero-modulus body l1j and l2j: deep and „movement” of fractures of „j-th” Young’s modulus component of hetero-modulus body [m]
l3j: Size of deformation of „j-th” Young’s modulus component of hetero-modulus body [m]RPj and RSj: the pressure and shear strength of „j-th” Young’s modulus component of hetero-modulus body [N/m2]
Vi: volume of „i-th” component of flying object [m3] Mechanical Stress Relaxation in Complex Materials After High Speed Collisions
[email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
K
kkkk
M
jjjjspH
n
iii lAlAEWWWVu
144
133
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=
1312111 aaal
2322212 aaal
321 nnnn aaal
•••
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Mechanical Model of Complex Materials We Want to Develop Using Nanoceramics and CMCs
321 aaal
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Shear Stresses in Hetero-Modulus and Hetero-Viscous Complex Materials
011 1
2
110
nn
nnn
ee
Where:η1, η2 and ηe: viscosities of elasto-viscoplastic, elasto-viscous parts and effective viscosity of the hybrid hetero-modulus, hetero-viscous body
τ0 and τ: static yield point of body and shear stress developed during deformation and destruction in the materialnτ and nγ : stress relaxation time and delay time of elastic deformation
τ and τ : first and second derivatives of shear stresses developed in hetero-modulus and hetero-viscous ceramic and CMC bodies during high speed collison with flying objects
(6)
. ..
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Where:η1, and η2: viscosities of elasto-viscoplastic, elasto-viscous parts of hybrid
hetero-modulus, hetero-viscous body τ0: yield stress developed during deformation and destruction in the material
nτ and nγ : stress relaxation time and delay time of elastic deformation
γ, γ and γ : first, second and third derivatives of deformation gradients
The Effective Viscosity of Hetero-Modulus and Hetero-viscous Complex Materials
(7)
.
2
1
110
1
nnnn
ne
.. …
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Involving Following New Symbols
(8.2)
(8.3)
(8.4)
(8.5)
nnA
e
nB
1
2
1
2
1 11
nnC
0D
x (8.1)
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Transcription of Eq. (6) Using the New Symbols for Material Characteristics
(9.1)
(9.2)
0 DCxxBxA
(9.4)
0 CxxBxA (9.3)
tt eCeCx 2121
(9.5)AC
AB
AB 2
2
2,1 42
CDX * (9.6)
From where:
If:0D
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
The General Equation of Shear Stress Relaxation in Complex Hetero-Modulus and Hetero-Viscous Ceramics after High Speed
Collision
CDeCeC
tAC
AB
ABt
AC
AB
AB
2
2
2
2
422
421
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
(10)
Where:
C1 and C2: constants of integration
The Stress Relaxation in the Hetero-Modulus and Hetero-Viscous CMCs and Complex Material Systems After HS Collision
(11)
2
1
2
1
0
11
42
2
11
42
1
11
2
1
2
1
22
011
2
1
2
1
22
011
nn
eC
eC
tnn
nn
nn
tnn
nn
nn
ee
ee
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Particle Diameter (µm.)
Volume %
0
10
20
30
0
10
20
30
40
50
60
70
80
90
100
1.0 10.0 100.0 1000.0
Raw Material Powders for Development of Alumina-based Hetero-modulus and Hetero-Viscous CMCs
• Particle size distributions:
Particle Diameter (µm.)
Volume %
0
10
20
30
0
10
20
30
40
50
60
70
80
90
100
0.1 1.0 10.0 100.0
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Atomizer powders
Microstructure of Used Ceramic Raw Materials and Principle of Their Compaction
• Principle of the developed compacting method with HS flying punches:
flying punch
vacuum or nitrogen in specimen holder
specimen holder
specimen
vacuum or nitrogen
v
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
(v≥1000 m/s)
Our Principle of Compaction Using HS Flying Punches Could Be Adapted
(Was taken from Prof. Bragov and his group at State University of Nizny Novgorod)
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Achieved Microstructures After Dynamic Compacting
Phase transformation and crystal growth of Al2O3 components during dynamic
compactions in vacuum
Phase transformation of Si3N4 particles and c-Si3N4 diamond crystals development during dynamic
compactions in vacuumed nitrogen
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Conclusions• Using the advantageous of high energy dynamic compacting methods with high
speed flying punches, at the places and surroundings of hits and collisions new, cubic c-Si3N4 diamond particles have been developed with spinel crystalline structures.
• Understanding the mechanical phenomena in the collisions under high speeds and advantageous of hetero-modulus and hetero-viscous complex materials having several Young’s modulus simultaneously, new alumina matrix ceramic composite material was developed, reinforced with submicron and nanoparticles of AlN, Si2ON2, SiAlON and c-Si3N4 diamond particles.
• Understanding the energy engorgement during high speed collisions we could mathematically described (Eq. 10. and 11.) the relaxation of the mechanical stresses have developed in the hetero-modulus and hetero-viscous complex materials during the collisions.
○
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Acknowledgement
The authors acknowledge to IGREX Engineering Service Ltd. for technical and financial support of this presented research for several
years and to the young colleagues and PhD students at the Department of Ceramics and Silicate Engineering in the University of
Miskolc (Hungary) for laboratory tests and assistances.
○
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials
Thank you very much for your time and kind attention !
http://keramia.uni-miskolc.hu http://www.szte.org.hu/folyoirat
László A. GömzeUniversity of Miskolc
3515, Miskolc, [email protected]
Phone: +36 30 7462714
Liudmila N. GömzeIgrex Ltd.
3459, Igrici, [email protected]
Phone: +36 30 7462713
Mechanical Stress Relaxation in Complex Materials After High Speed [email protected] http://keramia.uni-miskolc.hu [email protected]
XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia
Session 3. – Dynamic Strength of Materials