6 -On presente un c r i t e r e de courbure de f i s s u r e fond& sur sa s t a b i l i t i ! d i r e c t i o n n e l l e a i n s i qu'un c r i t e r e de r a m i f i c a t i o n necessi t a n t un f a c t e u r dynamique d ' i n t e n s i t@ de c o n t r a i n t e de r a m i f i c a t i o n e t l e c r i t e r e de courbure. Abstract -A crack curving c r i t e r i o n based on i t s d i r e c t i o n a l s t a b i l i t y and a crack branching c r i t e r i o n r e q u i r i n g a dynamic

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... hing s t r e s s i n t e n s i t y f a c t o r and t h e crack c u r v i n g c r i t e r i o n a r e presented. These c r i t e r i a are used t o p r e d i c t crack curvings and crack branchings i n Homalite-100 and polycarbonate f r a c t u r e specimens, and 'bursting s t e e l and aluminum pipes. Despite t h e many papers and a number o f comprehensive review a r t i c l e s on dynamic f r a c t u r e * papers on elastodynamic analyses o f crack c u r v i n g and branching a r e few. Among these are an approximate t h e o r e t i c a l s o l u t i o n f o r t h e c u r v i n g o f a s t a t i c crack w i t h nonvanishing mode I1 s t r e s s i n t e n s i t y f a c t o r s /1,2/, and an elastos t a t i c s s o l u t i o n s w i t h vanishing mode I1 s t r e s s i n t e n s i t y f a c t o r f o r p r e d i c t i n g t h e i n i t i a l angle o f crack branching /3r4/. A c r i t i c a l review o f s t a t i c crack branching a n a l y s i s i s provided by Lo / 5 / . Experimental observations o f crack c u r v i n g in b r i t t l e m a t e r i a l s /6-12/ show t h a t t h e curved crack path appears t o d i f f e r w i t h specimens and l o a d i n g conditions. For example, crack path i n a bend specimen under impact loading may have a charact e r i s t i c S-shape as t h e crack approaches t h e compression s i d e o f t h e specimen /6*7/; a double c a n t i l e v e r beam specimen under wedge l o a d i n g o f t e n y i e l d s a gradual c u r v i n g crack path a f t e r f r a c t u r e i n i t i a t i o n /&11/; s i n g l e d edge notch specimens under u n i a x i a l loading may have a s l i g h t l y d e f l e c t e d crack path /12/. Long . b e f o r e o t h e r e l a s t o s t a t i c s o l u t i o n s t o crack branching problems became available, Y o f f e l s pre-branching a n a l y s i s /13/ showed t h a t t h e maximum circumf e r e n t i a l s t r e s s * oget e x h i b i t s two symmetrical maximum along t h e crack a x i s a t a crack v e l o c i t y o f about C/C1 = 0.38# where Cl i s t h e d i l a t a t i o n a l wave v e l o c i t y . This c r i t i c a l v e l o c i t y , which s h i f t e d t h e maximum Gee away from t h e d i r e c t i o n o f s e l f -s i m i l a r crack propagation* was deemed t h e c o n d i t i o n f o r crack branching. Experimentally observed crack v e l o c i t i e s a t crack branching, unfortunate1 y, a r e much smaller than t h e t h e o r e t i c a l l y p r e d i c t e d c r i t i c a l crack v e l o c i t i e s f o r branching. Bowdeds e t al. /14/ experimental observations showed t h a t a crack propagated we1 l be1 ow t h e terminal v e l o c i t y before branching* b u t accelerated up t o t h e i n s t a n t of branching, and i s accompanied by a drop o f 5 t o 10 percent i n Article published online by EDP Sciences and available at http://dx.