1. Modeling of structure formation processes in explosion welding of large-size multilayer materials Rozen A.E. Muyzemnek A.Y. Zhuravlyov E.A. Los I.S. Vorobyov E.V. Rozen A.A. 1 EPNM-2012 Strasbourg PENZA STATE UNIVERSITY, Russia E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

2. 2 EPNM-2012 Strasbourg 1. Cowan G.R., Holzman A. Flow configuration in cojliting plates // J. Appl. Phys. 1963. – 34, № 4. – P. 928-939. 2. Wolsh J.M., Shreffler R.G., Willing E.J. Limiting condition for jet formation in high velocity collisions // I big. – 1953 - 24, № 3. – P. 349-359. 3. Абрахамсон Г.Р. Остаточные периодические деформации поверхности по действием перемешивающей струи // Тр. Амер. о-ва инж.-мех. Сер. Е. Прикладная механика. – 1961. – 28. – 28. - № 4. – С. 45-55. 4. Гордополов Ю.А., Дрёмин А.Н., Михайлов А.Н. К вопросу о волнообразовании при высокоскоростном соударении металлических тел // Тр. Амер. о-ва инж.-мех. Сер. Е. Прикладная механика. – 1977. – 13, № 2. – С. 288 – 291. 5. Дерибас А.А. Физика упрочнения и сварки взрывом. – 2- изд., доп. И перераб. – Новосибирск: Наука, 1980. – 222 с. 6. Bahrani A.S., Black T.I., Crossland B. The mechanics of wave formation in explosive welding // Proc. Roy. Soc. – 1967. – A296, № 1445. – P. 123-136. 7. Cowan G.R., Bergman O.R., Holizman F.H. Mechanism of bond zone wave formation in explosion-clad metals // Met. Trans. – 1971. - 2, № 11. – P. 3145 – 3155. 8. Klein W. The flow path in the contact zone in explosion welding // 3-rd Int. conf. of the center for high energy forming. Wail Colorado. – July, 1971. - 18 p. 9. Лысак В.И., Кузьмин С.В. Сварка взрывом. – М.: Машиностроение, 2005. – 512 с. E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 The basic publications on a theme

3. The analysis of collision parameters in critical modes of wave formation enabled to reveal the following features of the process: for every fixed value of initial angle there is a critical value of motion rate of a flyer, below which the waves cannot be formed (this value grows with increase of initial angle between the plates); independent of initial angle for every combination of metals there is a certain critical value of a contact point velocity, below which the waves cannot be formed at all; there is also a minimal value of motion rate of a flyer, below which the collision is, apparently, elastic; wave formation takes place when the contact point velocity is less than velocity of sound in metals and the flow in moving coordinates is subsonic (having this condition met the waves are expected to be formed also in parallel positioning of plates, provided the detonation velocity of explosives applied is less than sound velocity). 3 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

4. Multilayer composition of Al+Cu+Al explosion welding schema 4 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

5. 5 E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 EPNM-2012 Strasbourg Experiment results

6. 6 E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 EPNM-2012 Strasbourg Copper surface

7. 7 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 Copper surface on the top on the bottom

8. 8 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 Copper surface α1α1 α2α2

9. 9 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 Asymmetric wave pattern

10. where p eos - is the pressure from the state equation, V – is the volume fraction, E – is the internal energy density by a unit of initial volume Fraction of burnout F is determined by the following correlation where where V CJ – is the volume fraction of Chapman-Jouguet, t – is the current moment of time. If F is more than 1, this parameter is bound to value 1. In case of such calculation of the burnout fraction, the value F usually reaches 1 in several time steps, resulting in “blurred” front of burnout in some elements. After the value F reaches 1, it remains constant. Besides that, before detonation it is possible to consider the explosive material as elastic, perfectly plastic. In this case the researchers use test elastic stress as a new stress tensor. 10 The pressure in explosive elements EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

11. Explosion welding schema EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 11

12. Explosion welding of three-layers material. Numerical simulation. EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 12

13. 13 Results of 2D modeling Al+Cu+Al (2 + 2 +2) D = 1600 м/с The size of the 8 nodal volumetric element is 0,05 millimeters. EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

14. Formation of a wave surface 14 a) 26,6 mks b) 27,6 mks c) 29,6 mks EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

15. 15 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 Comparison of settlement and experimental values Divergence – 27 %

16. Thank you for attention! 16 EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53

17. Resultant velocity EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 17

18. Resultant pressure EPNM-2012 Strasbourg E-mail: metal@pnzgu.rumetal@pnzgu.ru Тел. (841-2) 36-84-53 18