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THE INITIATION OF EXPLOSIVE CRYSTALS BY SHOCK OR IMPACT
C. Coffey
To cite this version:
C. Coffey. THE INITIATION OF EXPLOSIVE CRYSTALS BY SHOCK OR IMPACT. Journal de
Physique Colloques, 1987, 48 (C4), pp.C4-253-C4-263. �10.1051/jphyscol:1987418�. �jpa-00226650�
JOURNAL DE PHYSIQUE
Colloque C4, supplement au n.9, Tome 48, septembre 1987
THE INITIATION OF EXPLOSIVE CRYSTALS BY SHOCK OR IMPACT
C.S. COFFEY
Naval Surface Weapons Center, White Oak Laboratoru, Silver Spring, MD 20903-5000, U.S.A.
Rbsum6 La formation des points chauds est une &tape primordiale pour
l'initiation par choc ou impact des cristaux explosifs. Par cons6quent. toute tentative pour comprendre l'initiation des cristaux explosifs passe par 1'6tude pr6alable de la localisation de 1'6nergie du choc ou de l'impact pour former des points chauds. Plus g6n6ralement, il apparait que la localisation de 1'6nergie a lieu dans tous les solides cristallins, qu'ils soient inertes ou 6nerg6tiques, d&s qu'ils sont soumis B une d6formation plastique induite par choc ou par impact. Cet article est en partie une revue de nos recherches en cours qui visent b comprendre le processus de localisation de 1'6nergie B un niveau microscopique en examinant la dissipation de l'bnergie dans les mouvements des dislocations. La production des dislocations et leur mouvement constituent le mkcanisme fondamental de la dkformation plastique. L'bnergie dissipee dans le champ de phonons engendr6 par le mouvement des dislocations est d6termin6e et l'on montre qu'elle est B la fois localis6e et intense. Les vitesses de dissipation de 1'6nergie sont calcul6es pour des chocs et impacts mod6r6s. Pour des chocs intenses, on montre que le pompage des niveaux d'6nergie interne des mol6cules pr&s du centre de dislocation est possible et qu'il peut produire une dissociation mol6culaire rapide. La formation de bandes de cisaillemnt est mod6lis6e. Ces bandes de cisaillement proviennent de
l'accumulation de nombreuses dislocations dans de petites rdgions de cisaillement intense dans le cristal et elles sont consid6r6es comme sites macroscopiques des points ch'auds.
A b s t r a c t The f o r m a t i o n o f h o t s p o t s i s an e s s e n t i a l s t e p i n t h e process o f i n i t i a t i n g e x p l o s i v e c r y s t a l s by shock o r impact. Consequently, any a t t e m p t t o understand t h e i n i t i a t i o n o f e x p l o s i v e c r y s t a l s must f i r s t e s t a b l i s h how t h e energy o f t h e shock o r impact i s l o c a l i z e d t o form h o t spots. More g e n e r a l l y , i t appears t h a t energy l o c a l i z a t i o n o c c u r s i n a l l c r y s t a l l i n e s o l i d s , b o t h i n e r t and e n e r g e t i c , when t h e y a r e s u b j e c t e d t o shock o r impact induced p l a s t i c
deformation. T h i s paper i s i n p a r t a r e v i e w o f o u r c u r r e n t r e s e a r c h t o
understand t h e process o f energy l o c a l i z a t i o n on a m i c r o s c o p i c l e v e l by examining t h e energy d i s s i p a t e d by moving d i s l o c a t i o n s . D i s l o c a t i o n g e n e r a t i o n and m o t i o n a r e t h e fundamental mechanism o f p l a s t i c d e f o r m a t i o n . The energy d i s s i p a t e d i n t h e phonon f i e l d generated by moving d i s l o c a t i o n s i s determined and shown t o be b o t h l o c a l i z e d and i n t e n s e . Energy d i s s i p a t i o n r a t e s 'are c a l c u l a t e d f o r m i l d shocks and impacts. For h i g h l e v e l shocks i t i s shown t h a t d i r e c t pumping o f t h e i n t e r n a l energy l e v e l s o f t h e m o l e c u l e s near t h e d i s l o c a t i o n c o r e i s p o s s i b l e which can produce r a p i d m o l e c u l a r d i s s o c i a t i o n . The g e n e r a t i o n of shear bands i s modelled. These shear bands a r e formed by t h e accumulation o f many d i s l o c a t i o n s i n s m a l l r e g i o n s o f i n t e n s e shear i n t h e c r y s t a l and a r e t a k e n t o be t h e
macroscopic s i t e s o f t h e h o t s p o t s .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987418
C4-254 JOURNAL DE PHYSIQUE
I n t r o d u c t i o n
There i s s u b s t a n t i a l e x p e r i m e n t a l evidence t h a t t h e i n i t i a t i o n o f an e x p l o s i v e c r y s t a l by shock o r impact i s 'due t o p l a s t i c d e f o r m a t i o n o f t h e c r y s t a l . Furthermore, t h i s p l a s t i c d e f o r m a t i o n i s n o t a b u l k o r continuum process b u t r a t h e r o c c u r s i n s m a l l l o c a l r e g i o n s o f t e n r e f e r r e d t o as h o t spots. The energy l o c a l i z a t i o n o r c o n c e n t r a t i o n t h a t occurs i n t h e s e l o c a l h o t s p o t r e g i o n s p r o v i d e s t h e means by which t h e e x p l o s i v e molecules a r e e x c i t e d t o d i s s o c i a t i o n w h i c h i n t u r n p r o v i d e s t h e a d d i t i o n a l energy t o cause r e a c t i o n t o b e g i n t o spread t h r o u g h o u t t h e c r y s t a l .
Prompted by t h e s e o b s e r v a t i o n s , t h a t p l a s t i c d e f o r m a t i o n i s e s s e n t i a l t o t h e i n i t i a t i o n o f e x p l o s i v e c r y s t a l s d u r i n g shock o r impact, a t h e o r e t i c a l
i n v e s t i g a t i o n was undertaken t o understand t h e fundamentals o f t h e d e f o r m a t i o n process. The a n a l y s i s focused on t h e m i c r o s c o p i c r o o t cause o f p l a s t i c
deformation, t h e g e n e r a t i o n and movement b f d i s l o c a t i o n s , and examined t h e r a t e a t which energy i s d i s s i p a t e d by r a p i d l y moving d i s l o c a t i o n s , how f a s t t h e s e d i s l o c a t i o n s move under an a p p l i e d shear s t r e s s , and how t h e y m i g h t be generated and congregate i n shear bands d u r i n g an a p p l i e d shock o r impact. T h i s p r e s e n t paper i s an e f f o r t t o draw t o g e t h e r t h e above mentioned r e s e a r c h and t o extend i t t o p r e d i c t t h e response o f a nominal e x p l o s i v e c r y s t a l t o e i t h e r m i l d impact o r t o a more v i o l e n t shock l o a d i n g .
A n a l y s i s
I n c r y s t a l s , p l a s t i c d e f o r m a t i o n occurs due t o t h e c r e a t i o n and m o t i o n o f d i s l o c a t i o n s . At t h e m i c r o s c o p i c 1 eve1 t h e s e d i s l o c a t i o n s r e p r e s e n t a
s u b s t a n t i a l d i s t o r t i o n o f t h e c r y s t a l l a t t i c e i n t h e r e g i o n near t h e c o r e o f t h e d i s l o c a t i o n . Here, a r e v i e w i s g i v e n d e s c r i b i n g t h e energy l o c a l i z a t i o n and d i s s i p a t i o n due t o t h e m o t i o n of edge d i s l o c a t i o n s i n a c r y s t a l 1 i n e l a t t i c e . T h i s summarizes t h e analyses o f r e f e r e n c e s (1, 2, 3) t o which t h e r e a d e r i s r e f e r r e d f o r d e t a i l s . These r e s u l t s a r e t h e n extended t o a t t e m p t t o u n i f y t h e shock and impact i n i t i a t i o n o f e x p l o s i v e s by e s t a b l i s h i n g t h a t t h e h o t s p o t -
energy l o c a l i z a t i o n process i s t h e same f o r b o t h events. The d i f f e r e n c e i n t h e response o f an e x p l o s i v e t o e i t h e r o f t h e s e s t i m u l i i s j u s t due t o t h e way t h e d i f f e r e n t l o a d i n g r a t e s and s t r e s s amp1 i t u d e s d r i v e t h e d i s l o c a t i o n s , and t h e r e s u l t a n t i n t e n s i t y o f energy 1 o c a l i z a t i o n .
The i n t e r a c t i o n Hamil t o n i a n t h a t d e s c r i b e s how a moving d i s l o c a t i o n
i n t e r a c t s w i t h t h e l a t t i c e can be w r i t t e n as
where i s t h e l o c a l s t r e s s f i e l d o f t h e d i s l o c a t i o n and Z' i s t h e l a t t i c e p e r t u r b a t i o n s t r a i n due t o t h e presence o f t h e moving d i s l o c a t i o n . For a moving edge d i s l o c a t i o n t h e l o c a l s t r e s s f i e l d can be approximated by i t s s t a t i o n a r y v a l u e which i n p o l a r c o o r d i n a t e s i s ( 4 )
where G i s t h e shear modulus, b i s t h e Burgers l e n g t h , v i s t h e Poisson r a t i o , r i s t h e r a d i a l d i s t a n c e f o r t h e d i s l o c a t i o n core, and 9 i s t h e p o l a r angle. The l o c a l s t r a i n f i e l d can be expressed i n terms o f i t s compressive and shear components as
and
, X - X
E = -
€Icos e dl
I