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1 M O D E L O W A N I E I N Y N I E R S K I E n r 4 7, I S S N X A N A L Y S I S O F T E M P E R A T U R E D I S T R I B U T I O N I N C O M P O S I T E P L A T E S D U R I N G T H E R M A L F A T I G U E A n d r z e j K a t u n i n 1 a 1 I n s t i t u t e o f F u n d a m e n t a l s o f M a c h i n e r y D e s, i Sg in l e s i a n U n i v e r s i t y o f T e c h n o l o g y a a n d r z e j. k a t u n n p o l s l.p l S u m m a r y T h e p a p e r d i s c u s s e st h e c h a r a c t e r o f t h e -h s eelaft i n g t e m p e r a t u r e d i s t r i b u t idounr i n g t h e r m a l f a t i g u e o f lia-m n a t e d c o m p o s i t e c a n t i l e v ep r l a t e i n t h e s t r e s s r e l a x a t i o n. m ot dhee t e m p e r a t u r e d i s t r i b u t i o n s a n d t h e i r e v o l u t i o n w e r e a c q u i r e d o n t h e o w n -d e s i g n e d t e s t r i g u s i n g i n f r a r e d c a m et rh a e. t h e r m o g r a m s w e r e c o m p a r e d w i t h f o r c e a n d v e l o c i t yo f d i s p l ae cm e n t m e a s u r e m e n t s a n d d y n a m i c p r o p e r t i e s o f t h e i n v e s t i g a t e d c o m p o s i to e r d ei r n t o eav- l u a t e c h a r a c t e r i s t i c d i s t r i b u t i o n s o f a t e m p e r a t u r e f o r v a r i o u s p h a s e s o f f a t i g u e : t h e t h ie n is te i-h l af et ai to in n g o, f t h e r m o m e c h a n i c a l d e g r a d a t i o n, i n i t i a t i o n a n d p r o p a g a t i o n o f c r a c k s e t c. B a s i n g o n o b t a i n ehd e rceosrurletls a tti o n b e t w e e n se l f-h e a t i n g t e m p e r a t u r e,s t r e s s r e l a x a t i o n a n d d y n a m ip cr o p e r t i e s w a s p r e s e n t e d. T h e c h a r a c t e r i s t i c t e m p e r a t u r e d i s t r i b u t i o n s w e r e j u s t i f i e d b a s i n g o n p l a t e t h e o r i e s. K e y w o r d s : s e l f-h e a t i n g t e m p e r a t u r e d i s t r i b u t, i to hn e r m a l f a t i g u, ed y n a m i c p r o p e r t i e s A N A L I Z A R O Z K A D U T E M P E R A T U R Y W P Y T A C H K O M P O Z Y T O W Y C H P O D C Z A S Z M C Z E N I A C I E P L N E G O S t r e s z c z e n i e A r t y k u o m a w i a c h a r a k t e r r o z k a d u t e m p e r a t u r y s a m o r o z g r z a n i a p o d c z a s z m* c z e n i a c i e p l n e g o l a m i n o w a n e j k o m p o z y t o w e j p y t y w s p o r n i k o w e j w w a r u n k a c h r e l a k s a c j i n* a p re. R o z k a d y t e m p e r a t u r y i i c h z m i e n n o ć z ao -s t y z m i e r z o n e n a z a p r o j e k t o w a n y m s t a n o w i s k u b a d a w c z y m z w y k o r z y s t a n i e m k a m e r y t e r m o w i z y j n e j. T e r m o gm ry a p o rƒ w n a n o z p o m i a r a m i s i y i p r z y s p i e s z e p r z e m i e s z c z e o r a z z w a c i w o c i a m i d y n a m i c z n y m i b a dk ao nm ep g o - z y t u w c e l u o c e n y c h a r a k t e r y s t y c z n y c h r o z k a dƒ w t e m p e r a t u r y w rƒ n y c h f a z a c h z m* c z e n i a : i n i cm jo ar co jzi - s a g r z a n i a, d e g r a d a c j i t e r m o m e c h a n i c z n e j, i n i c j a c j i i p r o p a g a c j i p* k n i* ć i t d. N a p o d s t a w i e u zyyn sikkƒ a nw y c h w p r z e d s t a w i o n o k o r e l a c j* p o m i* d z y t e m p e r a t u rs ąa m o r o z g r z a n i a, r e l a k s a c j ą n a p r* e i w a c i w o c i a m i d yzn -a m i c n y m i. C h a r a k t e r y s t y c z n e r o z k a d y t e m p e r a t u r y z o s t a y u z a s a d n inoa n e p o d s t a w i e t e o r i p y t. S o w a k l u c z o w e : r o z k a d t e m p e r a t u r y s a m o r o z g r z a n i, az m* c z e n i e c i e p l n, ew a c i w o c i d y n a m i c z n e 1. I N T R O D U C T I O N T h e p r o c e s s o f e n e r g y d i s s i p a t i o n i n v i s c o e l oa -s t i c t up r e i n c r e a s e s t o s o m e s m a l l v a l u e a n d t h e n s t a b i l i z e s. l y m e r i c c o m p o s i t e ss u b j e c t e d t o c y c l i c l o a d il ne g a d s t o T h i s i n c r e a s e r e v e a l s n e g l i g i b l e i n f l u e n c e o n m e c h a n i c a l i n i t i a t i o n o f t h e -hs e al tf i n g e f f e c t, i. e. t h e d i s s i p a tp er d o p e r t i e s o f t h e s ttru ur ce a n d t h e f a t i g u e p r o c e s s e n e r g y i s s t o r e d i n t o t h e s t r u c t u r e, w h i c h c a u s e s its hme a i n l y d e t e r m i n e d b y m e c h a n i c a l d e g r a d a t i o n. S o m e h e a t i n g-u p o f i t. A s i t s w ad e s c r iebd i n e a r l y s t u d i e s e x a m p l e s o f s u c h c a s e s c o u l d b e f o u n d i n [ 4 ]. H o w e v e r, i n t h i s a r e a [ 1 ] a n d v a l i d a t e d i n t h e p r e v i o u s s t u dw ih e s n t h e a m o u n t o f t h e d i s s i p a t e d e n e r g y e x c e e d s m u c h [ 2, 3 ], t h e s-h e el af t i n g e f f e c t m a y i n f l u e n c e m u c h o n t h e t h e c o n v e c t i o n b o u n d a r y c o n d i t i o n s t h e -hs e al tf i n g f a t i g u e p r o c e s s D. e p e n d i n g o n t h e a m o u n t o f t h e d iis-s e f f e c t d o m i n a t e s a n d n tie n s i f i e s t h e f a t i g u e p r o c e s s. p a t e d e n e r g y t h e f a t i g u e p r o c e s s m a y e v ofl ov le l o w i n g t w o s c e n a r i o s.i n t h e f i r s t o nte h e s e l-hf e a t i n g t e m p e ra - 99

2 A N A L Y S I S O F T E M P E R A T U R E D I S T R I B U T I O N I N C O M P O S I T E P L A T E S D U R I N G T h e s t u d i e s o n t h e t h e r m a l f a t i g u e olf y mpeor s a n d p o l y m e r i c c o m p o s i t e s w e r e c a r r i e d o u t b y o n l y s e v e r a l r e s e a r c h e r s. L u o e t a l. [ 5 ] i n v e s t i g a t e d t h e t e m p e r a t u r e e v o l u t i o n i n a c r y l o n i t r i-b l eu t a d i e n e-s t y r e n e d u r i n g t e n s i l e l o a d i n g. T h eu y s e d f o r t e s t s h e a l t h y a n d ai r- t i f 2. T H E T H E R M O V I S C O E L A S T I C I T Y T h e d e s c r i p t i o n o f l i n e a r t h e r m o v i s c o e l a s tc io cu il td y b e g i v e n b y t h e m o d i f i e d B o l t z m -V a no l t e r r a i n t e g r a l c i a l l y d a m a g e d s p e c i m e n s a n d c o m p a r e t h e e x t e r n a l e q u a t i o n : w o r k d u r i n g t h e c y c l i c l o a d i n g t o t h e g e n e r a t e d h e a t a n d t s t a t e d t h a t t h e p a r t o f d i s s i p a t e d e n e r g y, w h i c h t u r n s t t E i n t o h e a t m a y a c h i e v e u p t o 7 % i n t h e c a s e o f p r e s e n c e Rt, dt o f c r a c k s.i n t e r e s t i n g r e s u l t s w e r e p r e s e n t e d b y t h e, ( 1 ) a u t h o r s o f [ 6 ]. T h e y t e s t e d g l-f a si sb e r r e i n f o r c e d pao-l y w h e r e σ (t) a n d ε (t) a r e t h e s t r e s s a n d s t r a i n h i s t o r i e s m i d e 6 6 s p e c i m e n s u n d e r t h e v a r i o u s e x c i t a t i o n fnr-e q u e r e s p e c t i v e l y θ, i s t h e t e m p e r a t u r e E, (θ ) i s a t e m p ea r- c i e s a n d s t r a i n r a t e s. T h e a u t h o r s a n a l y z e d t h e s t rteu srs e d e p e n d e n t i n s t a nt a n e o u s m o d u l u s o f e l a s t i c iτ t y i, s a n d t e m p e r a t u r e e v o l u t i o n d u r i n g f a t i g u e a n d p r o p o s e d t h e r e l a x a t i o n t i m e a n R d (t-τ, θ ) i s t h e t er m- p e s i m p l e f i t t i n g r e l a t i o n s h i p i n o r d e r t o e d e st ch re i b a t u r e d e p e n d e n t r e l a x a t i o n k e r n e l. p r o c e s s.t h e m o r e a c c u r a t e d e s c r i p t i o n w i t h t h e o r e t i c a A l p p l y i n g t h e F o u r i e r t r a n s f o r m t o e q u a t i o n ( 1 ) i, s i t f o u n d a t i o n s o f t h e s-h e le fa t i n g t e m p e r a t u r e g r o w t h p o s s i b l e t o p r e s e n t a n e q u a t i o n o f t h e r m o v i s c o e l a s t i c i t y d u r i n g t h e r m a l f a t i g u e w a s p r o p o s e d i n [ 7 ]. T h e a u t h o i r n s t h e f r e q u e n c y d o m a i: n t e s t e d p o l y a m i d e 6, 6 s p e c i m e n s i n t h e c r e e p m o d e. T h e y * a l s o p r e s e n t e d a n e x p l i c i t f lo ra m uo f t e m p e r a t u r e g r o w t h R (, ), ( 2 ) b a s i n g o n t h e l o s s c o m p l i a n c e i n f u n c t i o n o f a n a - e x c i t t i o n f r e q u e n c y. S o m e t h e o r e t i c a l a n d e x p e r i m e n t a l w h e r e R * (ω,θ ) i s t h e f r e q u e n c y a n d t e m p e r a t u r e dn e- p e s t u d i e s o f t h e r m a l f a t i g u e a n d c r a c k p r o p a g a t i o n h a v d e n t r e l a x a t i o n k e r n e l. B a s i n g o n ( 2 ) t h e c o m p l ed x - m o b e e n c a r r i e d o u t b y R i t t e l -1 1 [] 8. H e u s e d u l u s c o u l d b e i n t r o d u c e d : p o l y ( c a r b o n a t e ) a n d p o l y ( m e t hl ym e t h a c r y l a t e ) s p ei c- * m e n s i n f a t i g u e t e s t s a n d d e s c r i b e d t h e o b t a i n e d s t r e s s E E(, ) E (, ),( 3 ) a n d t e m p e r a t u r e c u r v e s i n o r d e r t o e v a l u a t e t h e f a i l u r e m e c h a n i s m s o f t h e s e p o l y m e r s u n d e r t h e t h e r m a l f a t i g u e w h e r e c o n d i t i o n s. I t w a s r e p o r t e d e a r l i e r [ 3 ], t h a t t h e t h e r m a l f a t i g u e p r o c e s s c o u l d b e d i v i d e d t o t h r e e c h a r a c t e r i s t i c p h a s e s E(, ) Et, sin tdt, ( 4 ) w i t h r e s p e c t t o t h e c h a r a c t e r o f -h es ae tl if n g t e m p e r a t u r e e v o l u t i o n. T h e f i r s t p h a s e i s d o m i n a t e d b y t h-e s e l f h e a t i n g e f f e c t, i. e. t h e t e m p e r a t u r e g r o w s e x p o n e n t i a l l y. E (, ) T h e s e c o n d p h a s e r e v e a l s q u a-l s i n ea r g r o w t h o f t h e Et, costdt t e m p e r a t u r e, w h i c h c a u s e d b y m e c h a n i c a l d e g r a d a t i o n o f ( 5 ) a s t r u c t u r e. A t t h e e n d o f t h e s e c o n d p h a s e t h e t h e r ma rl e t h e s t o r a g e a n d l o s s m oi d, u l r e s p e c t i v e l y. T h e id-i s s f a t i g u e c r a c k i n i t i a t i o n o c c u r s. T h e l a s t p h a s e ci-s c hpa ar ta e d e n e r g y a v e r a g e d o v e r a c y c l e c o u l d b e t h e n rd-e t e t e r i z e d b y r a p i d n o n l i n e a r g r o w t h o f t h e t e m p e r a t u rm e i n e d f r o m : u n t i l b r e a k d o w n. esv e r a l p h e n o m e n a h a v e a n d i n f l u e n c e o n t h e t e m p e r a t u r e g r o w t h i n t h i s p h a s e : a m o n g t h e 2 2 ij Q( t) ij dt. s t i f f n e s s l o s s r e s u l t e d f r o m t h e i n c r e a s e d t e m p e r a t u r e t h e dt ( 6 ) i n i t i a t e d c r a c k p r o p a g a t e s a n d a d d i t i o n a l l y i n t e n s i f i e s t h e p r o c e s s. T h e a i m o f t h i s s t u d y i s t o i n v e s t i gh a tr e a c ct e r i s t i c d i s t r i b u t i o n s o f t h e -hs e al tf i n g t e m p e r a t u r e d u r i n g T h e s e l f-h e a t i n g t e m p e r a t u r e e v o l u t i o n c o u l d b e rd -e t e m i n e d f r o m s u b s t i t u t i o n o f ( 6 ) i n t o h e a t t r a n s fae-r e q u t i o n a s a s o u r c e f u n c t i[ o1 n 2 ]. T h e s i m p l i f i e d r e l a t i o n o f w h o l e p r o c e s s o f t h e t h e r m a l f a t i g u e o f p o l y m e mr -i c c os e l f-h e a t i n g t e m p e r a t u r e e v o l u t i o n w a s p r o p o s e d i n [ 1 3 ] : p o s i t e s a n d t o f i n d t h e c o r r e l a t wi io tn h s t h e s t r e s s 2 d r e l a x a t i o n a n d d y n a m i c p r o p e r t i e s e v o l u t ai no d n r e la - t i o n s h i p s w i t h t h e o r e t i c a l af mu en nd t a l s o f t h i s p r o c e s s. dt 2c p E,, ( 7 ) O b t a i n e d r e s u l t s c o u l d b e u s e f u l f o r c o n d i t i o n rm -o n i t o w h e r e Δθ d e n o t e s t h e t e m p e r a t u r e i n c r e m e n t f r o m t h e i n g p u r p o s e s o f t h e s t r u c t u r e s m a d e o f p o l y m e r s a n d i n i t i a l t e m p e r a t u r ρ e, i s t h e m a s s d e n s i t y a n cd p o l y m e r i c c o m p o s i t e s. p i s t h e s p e c i fc i h e a t a t c o n s t a n t p r e s s u r e. 1

3 Andrzej Katunin 3. in Fig.2. The solid line denotes temperature, the dashed line denotes displacements envelope and the dotted line denotes the force envelope. The characteristic points were chosen as follows: a (3 s) for phase I of the thermal fatigue, b (18 s) for the stabilization of an exponential growth (the beginning of phase II of the thermal fatigue), c (3 s),d (44 s) for phase II of the thermal fatigue, e (56 s) for the crack initiation (beginning of phase III of the thermal fatigue and f (632 s) for the crack propagation. TESTS AND ANALYZES The tested specimens were fabricated from glass/epoxy laminate with a symbol of EP GC 21 and supplied by Izo-Erg S.A. The laminate consisted of 12 unidirectional layers with total thickness of 2.5 mm. A detailed description of specimens manufacturing and preliminary strength tests could be found in [14]. The specimens of width of 1 mm and lengths of 4, 45, 5 and 55 mm were prepared for tests. During the tests the specimens were loaded cyclically with various excitation frequencies: 2, 25 and 3 Hz. The tests were performed on own-designed test rig, which allowed for cyclic excitation of the cantilever specimen in the stress relaxation mode with constant definable frequency. The measurement system contained an infrared camera, force sensor mounted on the excitation rod and a laser vibrometer used for measurement of velocity of displacements of the specimen near the clamp. The picture of the test rig is presented in Fig.1. The detailed description of the measurement system could be found in [2,3]. Fig. 1. A test rig during measurements Fig. 2. Self-heating temperature, displacements and force curves with corresponding thermograms in characteristic points 3.1 ANALYSIS OF THE TEMPEATURE DISTRIBUTION It could be observed that the temperature distribution is non-uniform along the width, i.e. the edges of the specimen have lower temperature. This phenomenon is resulted by several factors. The main reason of such a shape of distribution is the stress distribution in the specimen: following the Kirchhoff-Love plate theory (see e.g. [15]), during the bending of a cantilever plate two components of the stress tensor (bending stress and transverse shear stress) influences on this distribution. Moreover, there is an influence of the thermal convection, which is greater on the edges, because of additional convection surfaces perpendicular to the observed one. The characteristic changes in self-heating temperature distributions in various phases of thermal fatigue were compared with other acquired signals during the tests. Moreover, the characteristic points of the storage and loss moduli and phase lag acquired in dynamic mechanical analysis (DMA) [14] were also compared with the thermograms. The comparison of a typical set of discussed parameters for the specimen of the length of 45 mm excited with a frequency of 2 Hz was presented 11

4 A N A L Y S I S O F T E M P E R A T U R E D I S T R I B U T I O N I N C O M P O S I T E P L A T E S D U R I N G I n t h e F i g. 2 t h e c h a r a c t e r i s t i c d r o p t hoe n f o r c e w i t h d i s t r i b u t i o n s i n h e a l t h y s p e c i m e n s t h e a d d i t i o n a l c u r v e a n d i n c r e a s e o nd i s p l a c e m e n t s c u r v e i s o b s e r v a b l e t e s t s w e r e c a r r i e d o u t. T h e s p e c i m e n s w e r e a r t i f i c i a l l y i n t h e l o c a t i o n o f t h e p o i n t d. T h i s d r o p c o u lx d - b e d ea m a g e d o n v a r i o u s d i s t a n c e s r o fm t h e c l a m p ( 2. 5, 5 p l a i n e d b y t h e t w-t o e r m M a x w e l l -W i e c h e r t r h e o l o g i c a l a n d 1 m m ), t h e c r a c k d e p t h s i n e a c h c a s e w a s. 5 m m. m o d e l, w h i c h d e s c r i b e s t h e i n v e s t i g a t e d m a l t e r[ i1a6 ]. T h e t e s t s w e r e c a r r i e d o u t f o r s p e c i m e n s w i t h t h e l e n g t h I t c o u l d b e a l s o o b s e r v e d t h a t t h e t e m p e r a t u r e g r a d i e no t f 5 m m e x c i t e d w i t h a f r e q u e n c y o f 3 IH n z. o r d e r t o m o v e s i n t h e d i r e c t i o n o f s p e c i m e n s c l a m p d u r i n g t ha e n a l y z e t h e c h a r a c t e r o f t h e -hse altf i n g t e m p e r a t u r e i n c r e a s e o f t h e t e m p e r a t u r e. T h i s p h e n o m e n o n i s c a u s e gd r o w t h t h e m e a s u r em e n t p o i n t w a s d e f i n e d o n t h e b y l o c a l d r o p o f t h e s t i f f n e s s i n t h e h o t t e s t r e g i o n t h ea rn md o g r a m s i n t h e l o c a t i o n a s i t w a s s h o w n i n F i g. 2, t h u s t h e s t r e s s c o n c e n tiroan t i n t h i s r e g i o n, w h i c h a l s i o. e. i n t h e h o t t e s t r e g i o n. T h e t e m p e r a t u r e h i s t o r i e s w e r e e x p l a i n t h e r e g i o n o f t h e c r a c k i n i t i a t i o n. F o r d pe rt ea is el n t e d i n F i g. 4 F. o r t h e c o m p a r i s o n p u r p o s e s t h e a n a l y s i s o f t h e s t i f f n e s s d r o p t h e e v a l u a te iv o n l u ot if o n t e m p e r a t u r e h i s t o r y d e f i n e d i n t h e s a m e w a y w a s a d d e d o f d y n a m i c p r o p e r t i e s o f t h e c o m p o s i t e c o u l d br e - p e t o t h e p r e v i o u s t h r e e c a s e s i n F i g. 4. f o r m e d b a s i n g o n D M A -l i k e t e m p e r a t u r e p l o t s ( F i g. 3 ). F o r t h is p u r p o s e t h e t e m p e r a t u r e p l o t s o f d y n a m i c p r o p e r t i e s f o r t e s t i n g f r e q u e n c y w a s r e c o n s t r u c t e d f r o m t h e m a s t e r c u r v e s p r e s e n t e d i n [ 1T4 h] e. s o l i d l i n e d e n o t e s s t o r a g e m o d u l u s, t h e d o t t e d l i n e d e n o t e s l o s s m o d u l u s a n d t h e d a s h e d l i n e d e n o t e s t a n g e n t o f t h e p h a s e s h i f t. I t c o u l d b e n o t i c e d t h a t t h e p r e s e n c e o f c r a c k a n d i t s p o s i t i o n h a s a g r e a t i n f l u e n c e o f t h e t e m p e r a t uor -e h i s t r i e s. I t c o u l d b e e x p l a i n e d b y t h e r e l o c a t i o n s to rf e sts h e g r a d i e n t t o t h e p o s i t i o n o f a c r a c k d u e t o t h e l o c a l s o f t e n i n g o f m a t e r i a l i n t h e a r e a o f a c r a c k l o c a t i o n. T h i s F i g. 3. D y n a m i c p r o p e r t i e s o f t h e i n v e s t i g a t e d c o m p o s i t e t h fe o r c a u s e s m o r e r a p i d t e m p e r a t u r e i n c r e a s e a n d s h o r t e r e x c i t a t i o n f r e q u e n c y o f 2 H z f a t i g u e l i f e c y c l e s. E a c h o tf e mt ph e r a t u r e c u r v e f o r t h e p r e -c r a c k e d s p e c i m e n s c o n s i s t s s i n g u l a r i t i e s, w h i c h w e r e A s i t c o u l d b e n o t i c e d, t h e r e i s a m o n o t o n i c d e c r e a s c a u s e d b y t h e r e l o c a t i o n o f a s t r e s s g r a d i e n t. I n o r d e r t o o f t h e s t o r a g e m o d u l u s ( 4 ) a n d t h e m o n o t o n i c i n c r e a s e i n v e s t i g a t e t h e s e s i n g u l a r i t i e s t h e s e t o f t h e r m o g r a m s f o r o f t h e l o s s m o d u l u s ( 5 ). T h e s t o rmao gde u l u s r e p r e s e n t s t h e p r e-c r a c k e d s p e c i m e n o n t h e d i s t a n c e o f 2. 5 m m w a s e l a s t i c p a r t o f t h e c o m p l e x m o d u l u s ( 3 ), w h i l e t h e l o s s p r e s e n t e d i n F i g. 5. m o d u l u s t h e v i s cuo s p a r t o f ( 3 ). T h e d e c r e a s e t h oe f s t o r a g e m o d u l u s i n t h e t e m p e r a t u r e r e g i o n o f i n t e r e s t e x p l a i n s t h e s o f t e n i n g o f t h e m a t e r i a l a n d s t r e sns - c o n c e t r a t i o n n e a r t h e l acm p o f a s p e c i m e n. T h e i n c r e a s e o f t a n g e n t o f t h e p h a s e s h i f t i n t h i s t e m p e r a t u r e r e g i o n d e n o t e s t h e i n c r e a s e o f t h e a r e a o f a h y s t e r e s i s l o o p, t h u s t h e d i s s i p a t i o n e n e r g y a m o u n t s t i l l i n c r e a s e A N A L Y S I S O F T H E T E M P E A T U R E D I S T R I B U T I O N O F P R E -C R A C K E D S P E C I M E N S F i g. 4. S e l f-h e a t i n g t e m p e r a t u r e h i s t o r i e s o f t h -c e rpar ce k e d a n d h e a l t h y s p e c i m e n s I n o r d e r t o a n a l y z e t h e s p e c i f i c t e m p e r a t u r e ud -i s t r i bf i g. 5. S e l e c t e d t h e r m o g r a m s f o r t h e p-c r re a c k e d s p e c i m e n o n t i o n s i n t h e p-c r er a c k e d s p e c i m e n s a n d c o m p a r e t h e m t h e d i s t a n c e o f 2. 5 m m, m a x. t e m p e r a t u r e a : 2a 6. 4 C, b a C, c a C, d a C, e a C, f a C 12

5 A n d r z e j K a t u n i n T h e s t r e s s c o n c e n t r a t i o n i s c l e a r l y v i s i b l e f r o m f it rh se t s t e p s o f a t e s t ( s e e F i g. 7 a, b ). F r o m t h e n g b e g i n n i f i r s t s t e p s o f t h e a n a l y s i s ( s e e F i g. 5 a, b ). T h i s e - p h e no of ma t e s t t h e h i g h e s t v a l u e s o f a t e m p e r a t u r e wb e- r e o n o n c o u l d b e u s e d f o r t h e f a t i g u e d a m a g e d e t e c t i o n a nsd e r v e d n e a r t h e c l a m p, a s f o r t h e h e a l t h y s p e c i m e n s ( c f. l o c a l i z a t i o n. B a s e d o n t h e s e o b s e r v a t i o n s t h e m e t h o d Foif g. 2 ). T h e t h e r m a l f a t i g u e p r o cpers os c e e d s a l m o s t t h e n o n -d e s t r u c t i v e d a m a g e e v a l u a t i o ( n N D E ) w a s d e v e l - s a m e w a y a s f o r t h e h e a l t h y s p e c i m e n, w h i c h c o n f i r m e d o p e d [ 1 7 ].T h e s i n g u l a r i t i e s o b s e r v en d t ih e t e m p e r a t u r e h i s t o r y c u r v e i n F i g. 4 w e r e c a u s e d b y t h e mmeonvt e t h e t e m p e r a t u r e h i s t o r i e s p r e s e n t e d i n F i g. 4 f o r t h e s e c a s e s. o f t h e t e m p e r a t u r e gr a d i e n t d u r i n g p r o p a g a t i o n T h e d a m a g e p r o p a g a t i o n o f t h e cs ae o f p r-c e r a c k e d o f a c r a c k ( c f. F i g.-f 5 ) b. s p e c i m e n o n t h e d i s t a n c e o f 5 m m w a s n o t t y p i c a l, t h u s T h e t e m p e r a t u r e d i s t r i b u t i o n s i n o t h e r t w o c a s ets h e v i s u a l i n s p e c t i o n tohfe f r a c t u r e d s p e c i m e n a f t e r o f t h e p r e-c r a c k e d s p e c i m e n s r e v e a l s l i g h t d i f f e r e a n t t e s t w a s c a r r i e d o u t. T h e r e s u l t e d o b s e r v a t i o n s s h o w s, b e h a v i o u r. T h e s e l e c t e d t h e r m o g r a m s f o r t h e s e c a s e s t h a t t h e c r a c k p r o p a g a t e d i n t h e d i r e c t i o n t o a c l a m p a n w e r e p r e s e n t e d i n F i g. 6 a n d F i g. 7, r e s p e c t i v e l y. c a u s e d a d d i t i oanl d e l a m i n a t i o n. F u r t h e r d e t a i l e d ro-b s e v a t i o n s w e r e c a r r i e d o u t u s i n g c o n f o c a l m i c r o s c o p e, t h e r e s u l t s o f o b s e r v a t i o n w e r e p r e s e n t e d i n t h e n e x t c - s u b s e t i o n M I C R O S C O P I C E V A L U A T I O N O F T H E F R A C T U R E D S P E C I M E N S T h e o b s e r v a t i o n s w e r e c a r r i e d o u t o n tc ho e n f o c a l s t e r e o s c o p i c m i c r o s c o p e w i t h t h e m a g n i f i c a t i o n o f 1 x. T h e r e s u l t e d m i corp h o t o g r a p h s w e r e p r e s e n t e d ifn i g s F i g. 6. S e l e c t e d t h e r m o g r a m s f o r t h e p-c r re a c k ed s p e c i m e n o n t h e d i s t a n c e o f 5 m m, m a x. t e m p e r a t u r e : a a C, b a C, c a C, d a C, e a C, f a C F i g. 7. S e l e c t e d t h e r m o g r a m s f o r t h e p-c r re a c k e d s p e c i m e n o n t h e d i s t a n c e o f 1 m m, m a x. t e m p e r a t u r e : a a C, b a C, c a C, d a C, e a C, f a C F i g. 8. M i c r o p h o t o g r a p h o f t h e p r-ce r a c k e d s p e c i m e n o n t h e d i s t a n c e o f 2. 5 m m I n t h e c a s e o f a -c p rrea c k e d s p e c i m e n o n t h e sd -i t a n c e o f 5m m a t t h e b e g i n n i n g o f a t e s t t h e h i g h e s t v a l u e s o f a s t r e s s a n d a t e m p e r a t u r e w e r e l o c a t e d i n t h e c r a c k p o s i t i o n ( F i g. 6 a ), f u r t h e r t h e s t r e s s / t e m p e r a t u r e d i s t r i b u t i o n h o m o g e n i z e s ( F i g. 6 b ) a n d t h e n t h e g r a d i e n t m o v e s t o t h e c l a m p ( F i g. c -e 6 ). D u r i n g t h e rfs it p h a s e o f t h e t h e r m a l f a t i g u e t h e c r a c k p o s i t i o n i s s t i la l - d e t e c t b l e, b u t i n f u r t h e r p h a s e s t h e m o v e m e n t o f a g r a d i e n t i s o b s e r v e d. T h i s m o v e m e nt i s c a u s e d b y e x c e e d i n g o f t h e l o c a l m a t e r i a l s o f t e n i n g w i t h r e s p e c t t o t h e d r o p o f s t i f f n e s s n e a r t h e c l ac ma pu s e d b y t h e s e-h l fe a t i n g e f f e c t. I n t h e l a s t i ng va et se td i c a s e o n l y t h e b o u n d a r y F i g. 9. M i c r o p h o t o g r a p h o f t h e p r-ce r a c k e d s p e c i m e n o n t h e o f a s t r e s s / t e m p e r a t u r e d i s t r i b u t i o n i s o b s e r v e d i n dt ihse t a n c e o f 5 m m 13

6 A N A L Y S I S O F T E M P E R A T U R E D I S T R I B U T I O N I N C O M P O S I T E P L A T E S D U R I N G F i g. 1. M i c r o p h o t o g r a p h o f t h e p r-ce r a c k e d s p e c i m e n o n t h e d i s t a n c e o f 1 m m o f d e g r a d a t i o n a n d f rtaucr e p r o c e s s e s. T h e a n a l y s i s o f t h e t e m p e r a t u r e d i s t r i b u t i o n s t o g e t h e r w i t h t h e s t r e s s r e l a x a t i o n a n d d i s pcle am e n t c u r v e s a n d t h e c u r v e s o f d y n a m i c p r o p e r t i e s o f ac o m p o s i t e i n f u n c t i o n o f a t e m p e r a t u r e a l l o w s f o r g l o ba nl a l y s i s o f t h e s- e l f h e a t i n g p h e n o m e n o n d u r i n g w h o l e l i f e c y c l e o f t h e i n v e s t i g a t e d s p e c i m e n s. A d d i t i o n a l t h e r m a l a n d o m- i c r s c o p i c a n a l y z e s o f -c p rrea c k e d s p e c i m e n s g i v e n e w i n f o r m a t i o n a b o u t s p e c i f i c t y p e o f f r a c t u r e o f tc h- e s t r u t u r e s w i t h d e f e c t s O. b t a i n e d r e s u l t s m a y b e u s e f u l f o r t h e d e s i g n o f t h e l i f e c y c l e o f c o m p o s i t e e l e m e n t s a n d e v a l u a t i o n o f w o r k l o a d s a n d o t h e r o p e r a t i o n p a r a m e t e r s f o r e l e m e n t s m a d e o f t h e s e m a t e r i a l s. T h e p r e s e n t e d r e s u l t s c o u l d b e a l s o u s e d f o r e v a l u a t i o n o f s t r u c t u r a l h e a l t h o f t h e e l e m e n t s m a d e o f p o l y m e r i c c o m p o s i t e s. T h e o b s e r v a t i o n o f t h e r m o g r a m s d u r i n g s l i g h t h e a t i n g o f T h e m i c r o s c o p i c o b s e r v a t i o n s s h o w t h a t i n e a c h c a s se u c h s t r u c t u r e s a l l o w s f o r N D E a n d l o c a t i o n o f t h e s t r e s s o f t h e p r-c e r a c k e d s p e c i m e n s d i s c u s s e d i n t h e p r e v i o u s c o n c e n t r a t i o n a r e a s, w h i c h c o n f i r m e d t h e a u t h o r s o f [ 5 ]. s u b s e c t i o n t h e m o v e m e n t o f a s t r e s s / t e m p e r a t u r e a - g r d i e n t w a s c a u s e d b y t h e p r o p a g a t i n g d e l a m i n a t itohn i. s T h e f u n d a m e n t a l s o f t h e N D E m e t h o d o f s u c hm a t e r i a l s w a s d e v e l o p e d a n d p r e s e n t e d i n [ 1 6 ]. H o w e v e r, t h e r e a r e s p e c i f i c t y p e o f f r a c t u r e i s c a u s e d b y a s t r e s s a c- o n c esnetvre r a l o p e n q u e s t i o n s i n t h e i n v e s t i g a t e d p r otbhle e m. t i o n i n t h e c r a c k a r e a a n d s i m u l t a n e o uns el ay r t h e c l a m p. C o n s i d e r i n g t h e b e a m t h e o r y ( B e r n o u l l i o r o T- i m s h e n k o ) t h e h i g h e s t v a l u e s o f t h e s hs et ra er s s c o u l d b e m e c h a n i s m s o f s t r u c t u r a l d e g r a d a t i o n a n d f a i l u r e c o u l d b e d i f f e r e n t f r o m p o l y m e r t o p o l y m e r d u e t o t h e s p e c i f i c p r o p e r t i e s o f t h e s e a tme r i a l s. M o r e o v e r, i t i s e x p e c t e d o b t a i n e d o n t h e t o p a n d b o t t o m s u r f a c e s o f t h e i n- v e s t h a t t h e s e m e c h a n i s m s w i l l b e s t r o n g l y d e p e n d e n t o n t h e g a t e d s p e c i m e n s. I n t h e c a s e o f -c pr ra ec k e d s p e c i m e n s m a t e r i a l, t y p e a n d o r i e n t a t i o n o f t h e r e i n f o r c e m e n t i n t h e s h e a r s t r e s s d o m i n a t e d t h e b e n d i n g s t r e s s, w h i pc oh l y m e r i c c o m p o s i t e s. T h e g r e a t i n f l u e n c e o f t h e a - d e g r c a u s e s t h e s t r e s s p r o p a g a t i o n i n t h e p l a n a r d i r e c t id oa n t. i o n m e c h a n i s m s a n d f r a c t u r e m a y h a v e a l s o W h e n t h e d e l a m i n a t i o n for n t r e a c h e s t h e c l a m p l o c a t i o n t h e m a t e r i al a n i s o t r o p y o f t h e i n v e s t i g a t e d s t r u c t u r e s. t h e b e n d i n g s t r e s s b e c a m e d o m i n a n t d u e t o t h e m a t e r i a l T h u s t h e a d d i t i o n a l t us d i e s s h o u l d b e c a r r i e d o u t s o f t e n i n g i n t h i s a r e a c a u s e d b y t h -h e e sa et li fn g e f f e c t. i n o r d e r t o c o n f i r m t h e f i n d i n g s a n d s t a t e m e n tes - p r T h u s, t h e f u r t h e r p r o p a g a t i o n o f a c r a c k o c c u r r es d e n t e d i n t h e f o l l o w i n g p a p e r. in t h e d i r e c t i o n n o r m a l t o t h e s u r f a c e o f a s p e c i m e n. 4. C O N C L U S I O N S A c k n o w l e d g e m e n t s T h e a u t h o r w o u l d l i k e t o a c k n o w l e d g e M r. W i t o l d M a l e c P r e s e n t e d r e s e a r c h w a s c o n c e n t r a t e d o n t h e t er m-p e f r o m t h e I n s t i t u t e o f N-F o en r r o u s M e t a l s o f t h e P o l i s h a t u r e d i s t r i b u t i o n o f p o l y m e r i c l a m i n act oe md p o s i t e A c a d e m y o f S c i e n c e s f o r a p o s s i b i l i t y o f a c q u i s i t i o n o f p l a t e s d u r i n g t h e t h e r m a l f a t i g u e. T h e a n a l y z e d o f t h e t h e m i c r o p h o t o g r a p h s o f p r e -c r a c k e d s p e c i m e n s. t e m p e r a t u r e h i s t o r i e s a n d t h e r m o g r a m s d u r i n g t h i s p r o c e s s a l l o w t o e x p l a i n t h e p h y s i c s o f te hn oe m ep nh o n R e f e r e n c e s 1. O l d y r e v P. P., T a m u z h V. P. : E n e r g y d i s s i p a t i o n o f g-r l ae si sn f o r c e d p l a s t i c d u r i n g p r o l o n g e d c y c l i c d e f o r. m a t i o n P r o b l e m y P r o c h n o s t i , V o l. 3, p K a t u n i n A. : C r i t i c a l s-h e el af t i n g t e m p e r a t u r e d u r i n g f a t i g u e o f p o l y m e r i c c o m p o s i t e s u n d e r c y c l i c. l o a d i n g C o m p o s i t e s T h e o r y a n d P r a c t i c e 2 1 2, 1, V o l. 1 2, - p K a t u n i n A., F i d a l i M. : F a t i g u e a n d t h e r m a l f a i l u r e o f p o l y m e r i c c o m p o s i t e s s u b j e c t e d t o cn yg c. l iac d -l o a d i v a n c e d C o m p o s i t e L e t t e r s 2 1 2, 3, V o l. 2 1, p K a t u n i n A., F i d a l i M. : E x p e r i m e n t a l itdiefn i c a t i o n o f -s n otn a t i o n a r y s e-h l fe a t i n g c h a r a c t e r i s t i c s o f l a m i n a t e d c o m p o s i t e p l a t e s u n d e r t h e r e s o n a n t v i b r a. t Ki o mn p o z y t y 2 1 1, 3, V o l. 1 1, p L u o W., Y a n g T., L i Z., Y u a n L. : E x p e r i m e n t a l s t u d i e s o n t h e t e m p e r a t u r e f l u c t iu n a tdieofnos r m e d t h e r m o p - l a s t i c s w i t h d e f e. c tis n t e r n a t i o n a l J o u r n a l o f S o la in d s S t r u c t u r e s 2, V o l. 3p 7.,

7 A n d r z e j K a t u n i n 6. B e l l e n g e r V., T c h a r k h t c h i A., C a s t a i n g P. : T h e r m a l a n d m e c h a n i c a l f a t i g u e o f a g l ap sa s 6 6 / f i b e r s c o m p o s i t e m a t e r i a l. I n t e r n a t i o n a l J o u r n ao l f F a t i g u e 2 6, V o l. 2 8, p L i u Z. Y., B e n i w a l S., J e n k i n s C. H. M., W i n t e r R. TM h. e : c o u p l e d t h e r m a l a n d m e c h a n i c a l i n f l u e n c e o n a g l a s s y t h e r m o p l a s t i c p o l y a m i d e : N y l o n 6, 6 u n d e r v i-c br eo e p. M e c h a n i c s o f T i m e-d e p e n d e n t M a t e r i a l s 2 4, V o l 8., p R i t t e l D. : A n i n v e s t i g a t i o n o f t h e h e a t g e n e r a t e d d u r i n g c y c l i c l o a d i n g o f t w o g l a s s y p o l y m e r s. ri P a- r t I : E x p e m e n t a l. M e c h a n i c s o f M a t e r i a l s 2, V o l. 3 2, p R i t t e l D., R a b i n Y. : A n i n v e s t i g a t i o n o f t h e h e a t g e n e r a t e d cd yu cr li inc g l o a d i n g o f t w o g l a s s y p o l y m e r s. P a r t I I : T h e r m a l a n a l y s i s. M e c h a n i c s o f M a t e r i a l s 2, V o l. 3 2, p R i t t e l D., E l i a s h N., H a l a r y J. L. : H y s t e r e t i c h e a t i n g o f m o d i f i e d p o l y ( m e t h y l m e t h a c r y l a t e ), 2 P 3 o, l yvm oe l r. 4 4, p M o i s a S., L a n d s b e r g G., R i t t e l D., H a l a r y J. L. : H y s t e r e t i c t h e r m a l ob f e h a mv oi ro pr h o u s s e m i-a r o m a t i c p o l ya - m i d e s. P o l y m e r 2 5, V o l. 4 6, p K a t u n i n A. : A n a l y t i c a l m o d e l o f t h e -hs e al tf i n g e f f e c t i n p o l y m e r i c l a m i n a t e d r e c t a n g u l a r dpul rait neg s b e n d i n g h a r m o n i c l o a d i n g. E k s p l o a t a c j a i N i e z a w o d n oć a M a i n t e n a n c e a n d R e l i a b i l i t y 2 1, 4, V o l. 4 8, - p H e r z b e r g R. W., M a n s o n J. A. : F a t i g u e o f e n g i n e e r i n g p l a s t i c s. L o n d o n : A c a d e m i c P r e s s, K a t u n i n A., G n a t o w s k i A. : I n f l u e n c e o f h e a t i n g r a t e o n e v o l u t i o n o f d y n a m i c p r o p e r t i e s o f p o l y m e r i c. l a m i n a t e s P l a s t i c s R u b b e r a n d C o m p o s i t e s 2 1 2, 6, V o l. 4 1, p H j e l m s t a d K. D. : F u n d a m e n t a l s o f s t r u c t u r a l m e c h a n inc es w. -Y o r k : S p r i n g e r, K a t u n i n A., F i d a l im. : I n v e s t i g a t i o n o f d y n a m i c b e h a v i o u r l ao mf i n a t e d c o m p o s i t e p l a t e s u n d e r c y c l i c l o. a d i n g K o m p o z y t y 2 1 1, 3, V o l. 1 1, p K a t u n i n A., M o c z u l s k i W. : M e t h o d o f d e t e c t i o n o f d a m a gi en s p o l y m e r i c c o m p o s i t e s b y u s i n g t h oe vr im s i o n a n d s e l f-h e a t i n g e f f e c t P r z e g lą d M e c h a n i c z n y 2 1 3, 5, V o l 7. 2, p

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