Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 2 Tel.: Tel.:

Our Aims Understand the phenomena of high speed collisions of bodies made from different materials.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.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.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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 W K = W E + W H + W P + W S + W V,[Nm] W K = W E + W H + W P + W S + W V,[Nm] (1) W E : W E : Energy engorgement through elastic deformation, [Nm]. W H : W H : Energy engorgement through heating and recrystallization (phase transformation), [Nm]. W K : W K : Kinetic energy of flying object, [Nm]. W P : W P : Fracture energy engorgement through pressure stress, [Nm]. W S : W S : Fracture energy engorgement through shear stress, [Nm]. W V : W V : Energy engorgement through viscous deformation, [Nm]. Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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.)Material has only one Young’s modulus (E=const.) Flying (hit) object has inhomogeneous density (ρ≠const.)Flying (hit) object has inhomogeneous density (ρ≠const.) ν 1 : ν 1 : the Poisson ratio ρ i : ρ i : density of the „i-th”component of flying object; [kg/m 3 ] A 1i A 2i : A 1i and A 2i : surfaces of fractures caused by „i-th” density component of flying object [m 2 ] i=1, 2, …, n: i=1, 2, …, n: the number of different density components of flying object l 1i l 2i : l 1i and l 2i : deep and „movement” of fractures, caused by „i-th” density component of flying object [m] R P R S : R P and R S : the pressure and shear strength of ceramic body [N/m 2 ] V i : V i : volume of „i-th” component of flying object [m 3 ] (2) Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Materials Multiple values of Young’s modulusMultiple values of Young’s modulus High damage toleranceHigh damage tolerance Ability to absorb and dissipate the elastic energy during crack propagationAbility to absorb and dissipate the elastic energy during crack propagation Good thermal shock resistanceGood thermal shock resistance Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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.)Material has several Young’s modulus (E=var.) Flying (hit) object has inhomogeneous density (ρ≠const.)Flying (hit) object has inhomogeneous density (ρ≠const.) (3) ν j : ν j : the Poisson ratio of „j-th” Young’s modulus component of hetero-modulus body [m 3 ] ρ i : ρ i : density of the „i-th” component of flying object; [kg/m 3 ] A 1j A 2j : A 1j and A 2j : surface of fractures of „j-th” Young’s modulus component of hetero-modulus body [m 2 ] A 3j : surface of deformed „j-th” Young’s modulus component of hetero-modulus body [m 2 ] E j : E j : The Young’s modulus of the „j-th” component of hetero-modulus body ; [N/m 2 ] i=1, 2, …, n: i=1, 2, …, n: the number of different density components of flying object j=1, 2, …, n: j=1, 2, …, n: the number of different Young’s modulus components of hetero-modulus body l 1j l 2j : l 1j and l 2j : deep and „movement” of fractures of „j-th” Young’s modulus component of hetero-modulus body [m] l 3j : Size of deformation of „j-th” Young’s modulus component of hetero-modulus body [m] R P R Sj : R Pj and R Sj : the pressure and shear strength of „j-th” Young’s modulus component of hetero-modulus body [N/m 2 ] V i : V i : volume of „i-th” component of flying object [m 3 ] Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials

The Thermic Part of the Collision Energy W H = W HS + W RC + W RM,[Nm] W H = W HS + W RC + W RM,[Nm] (4) W H : W H : Energy engorgement through heating, [Nm] W HS : W HS : Energy engorgement of thermal deformation in place and surrounding of the collision and fall; [Nm] W RC : W RC : Energy engorgement through recrystallization of particles in place and surrounding of collision and fall; [Nm] W RM : W RM : Energy engorgement through spraying and recrystallization of falling (metallic) body [Nm] Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 toleranceHigh damage tolerance Higher deformation toleranceHigher deformation tolerance Ability to absorb and dissipate the collision energyAbility to absorb and dissipate the collision energy Relax by time mechanical stress developed in body during high speed collisions.Relax by time mechanical stress developed in body during high speed collisions. Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 mixtures Ceramics made from hetero-modulus and hetero-viscous particles Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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.)Complex material has several Young’s modulus (E=var.) and viscosity (η=var.) Flying (hit) object has inhomogeneous density (ρ≠const.)Flying (hit) object has inhomogeneous density (ρ≠const.) (5) ρ i : ρ i : density of the „i-th” component of flying object; [kg/m 3 ] A 1j A 2j : A 1j and A 2j : surface of fractures of „j-th” Young’s modulus component of hetero-modulus body [m 2 ] A 3j : surface of deformed „j-th” Young’s modulus component of hetero-modulus body [m 2 ] E j : E j : The Young’s modulus of the „j-th” component of hetero-modulus body ; [N/m 2 ] i=1, 2, …, n: i=1, 2, …, n: the number of different density components of flying object j=1, 2, …, n: j=1, 2, …, n: the number of different Young’s modulus components of hetero-modulus body l 1j l 2j : l 1j and l 2j : deep and „movement” of fractures of „j-th” Young’s modulus component of hetero-modulus body [m] l 3j : Size of deformation of „j-th” Young’s modulus component of hetero-modulus body [m] R P R Sj : R Pj and R Sj : the pressure and shear strength of „j-th” Young’s modulus component of hetero-modulus body [N/m 2 ] V i : V i : volume of „i-th” component of flying object [m 3 ] Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials

= Mechanical Model of Complex Materials We Want to Develop Using Nanoceramics and CMCs Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Where: η 1, η 2 and η e : viscosities of elasto-viscoplastic, elasto-viscous parts and effective viscosity of the hybrid hetero-modulus, hetero-viscous body τ 0 and τ: static yield point of body and shear stress developed during deformation and destruction in the material n τ and n γ : 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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials

Where: η 1, and η 2 : viscosities of elasto-viscoplastic, elasto-viscous parts of hybrid hetero-modulus, hetero-viscous body τ 0 : yield stress developed during deformation and destruction in the material n τ and n γ : 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)... … Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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) (8.1) Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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) (9.4) (9.3) (9.5) (9.6) From where: If: Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials (10) Where: C 1 and C 2 : constants of integration

The Stress Relaxation in the Hetero-Modulus and Hetero-Viscous CMCs and Complex Material Systems After HS Collision (11) Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials

Raw Material Powders for Development of Alumina-based Hetero-modulus and Hetero-Viscous CMCs Particle size distributions: Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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: Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 Al 2 O 3 components during dynamic compactions in vacuum Phase transformation of Si 3 N 4 particles and c-Si 3 N 4 diamond crystals development during dynamic compactions in vacuumed nitrogen Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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-Si 3 N 4 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, Si 2 ON 2, SiAlON and c-Si 3 N 4 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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials

Acknowledgement 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 Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March 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 ! László A. Gömze University of Miskolc 3515, Miskolc, Hungary Phone: Liudmila N. Gömze Igrex Ltd. 3459, Igrici, Hungary Phone: Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International Conference on Khariton’s Topical Scientific Readings, March XIII. International Conference on Khariton’s Topical Scientific Readings, March 14-18, 2011, Sarov, Russia Session 3. – Dynamic Strength of Materials