Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International...

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

mailto:[email protected]






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


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




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]



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]

(2)




n

i

n

iHEii

Sii

pn

iii NmWWlA

E

RlA

E

RV

u

1 122

2

11

2

1

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




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]



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]




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.




Some Complex Materials Having Excellent Dynamic Strength

Automobile tyres Asphalt mixturesCeramics made from hetero-modulus and

hetero-viscous particles




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 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 Collisions

[email protected] http://keramia.uni-miskolc.hu [email protected]



K

kkkk

M

jjjjspH

n

iii lAlAEWWWV

u

144

133

1

2

2

=

1312111 aaal

2322212 aaal

321 nnnn aaal

•••

n

iiFF

1

nllll ...21

Mechanical Model of Complex Materials We Want to Develop Using Nanoceramics and CMCs

321 aaal




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

(6)

. ..




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

.. …




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)




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)A

C

A

B

A

B

2

2

2,1 42

C

DX * (9.6)

From where:

If:0D




The General Equation of Shear Stress Relaxation in Complex Hetero-Modulus and Hetero-Viscous Ceramics after High Speed

Collision

C

DeCeC

tA

C

A

B

A

Bt

A

C

A

B

A

B

2

2

2

2

42

2

42

1




(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




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




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




(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)




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




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.

○




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.

○




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




Date post:	21-Jan-2016
Category:	Documents
Upload:	nathan-wilkerson
View:	212 times
Download:	0 times

Mechanical Stress Relaxation in Complex Materials After High Speed Collisions XIII. International...

Documents