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. Gömze 1 , University of Miskolc, Miskolc, Hungary Milla Gömze 2 , IGREX Engineering Service Ltd. Igrici, Hungary 1 femgomze@ uni-miskolc.hu 2 igrex2009@ yandex.ru Tel.: +36 30 746 2714 Tel.: +36 30 746 2713
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Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings,
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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
• 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.
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 ratio
ρi: 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]
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 object
j=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
jH
M
jjjjjj
N
j jj
jSjjj
j
pjn
iii NmWlAElA
E
RlA
E
RV
u
1 13322
1
2
11
2
1
2
][;)1(
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]
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 material
nτ 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
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.