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L I T E R A T U R E C I T E DA. P. Polesh ko, "Co mpr ess ive tests of gl as s, " Problo Prochn. ~ No. 12, 101-103 (1975).Yu. K. Znachkov, R. A. Veselo vskii , and B. A. Lyashenko, "Glued joints on the bas is of poly -mers with interpenetrating grids," in: Glues and Their Technical Applications [in Russian]~Leningradsk ii Dora Nauchno-Tekhni cheskoi Informat sii, Leningrad (1975), pp. 40-45.L. Sachs, Statisti cal Evaluation [Russian transl ation] , Statistik a, Moscow (1976 }.

D A M P I N G C A P A C I T Y O F C A S T I R ON W I T HD I F F E R E N T S H A P E S O F G R A P H I T E I N C L U S I O N S

S . A . G o l ov i n , V . A . K uz m e nko ,G . D . Pe t ru sh in , N . N . P i s 'm enny i ,and I. I . Ren ne

UDC 669.13:534.833

One of the chief requiremenf~s of engineering that materials have to fulfill is their ability to dampdeleterio us vibrations, i. e. , to have high damping capacity. Part s that are exposed in operation tothe effect both of stati c and of rev ers ed cyclic loads are often made of cas t iron. This mate rial ischaracte rized by heterogeneous stru ctur e on account of graphite inclusions in the metal basel in conse -quence, it has advantages compared with steel, such as low sensitivit y to stres s rai ser s and high levelof dissipation of vibrational energy.

It was noted in a numb er of works [1-3] that one of the import ant facto rs dete rminin g the internaldissip ation of the energy of elast ic vi bration s in str uct ura lly in_homogeneous mat eria ls is the nonuni-form distribution of st res ses and strains in microvolu mes of the material, occurring during loading,and the plastic flow in the most highly stress ed microvol umes, caused by this.

Since the microinhomogeneity of the str es s- st ra in state of cast iron is associated with stressconcentrati ons in the matri x near the graphite incl usions, it must be assu med that the level of the dam-ping capacity of cast iron must to a certa in extent be correlated with the peculiari ties of developmentof rnicroinhomogeneity of stre ss es and strains determined by the configuration and distribution of theinclusions.

The presen t work investigates the dissipation of the vibrational energy in ferri te- bas e cast ironwith spherical, flaky, and lamella r graphite inclusions under two consid erably differing loading fre=quencies, and also the peculiariti es of the microinhomogeneity of the state of st res s and st rain of thesetypes of cas t iron upon loading in dependence on the nature of thei r stru ctu re.

a~ /

I

I

2 f z ~ --.=...z f

ll Z a O / O _ 1 0 a ~ b ~ ~ 1 7 6 Q ~ Q 8 ~ 1 7 6

Fig. 1. Dependence of the logari thmicdecrem ent of the vibrations of cast ironon the stress amplitude referred to theendurance limit, under different loadingfrequencies: a) f = 30-40 Hz; b) f ~ 1.5kHz;c) f~ 1.5 kHz. (1) gra y cas t iron; 2)malleable cast iron; 3) high-strengthcast iron. )

Institute of the Strength Pro bl em s, Acade my of Sciences of the Ukrainian SSR, Kiev. Transl atedfrom Pro bl emy Proc hno sti , No. 3, pp. 91-94, M arch, 1980. Original art ic le submitted May 3, 1979.

360 0039-2316/ 80/1203-0 360507.50 9 1980 Plenum Publishing Corpora tion

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F i g . 2 . D i s t r i b u t i o n f i e l d s o f l o c a l s t r a i n s i n m i c r o r e g i o n s o f c a s t i r o n : a , b ) h i g h -s t r e n g t h c a s t i r o n w i th tw o d e g r e e s o f l o a d in g ; c ) m a l l e a b l e c a s t i r o n ; d) g r a y c a s t i r o n .( D a r k a r e a s : g r a p h i t e i n c l u s i o n s ; n u m b e r s n e x t t o th e c u r v e s : ( e 1 - e2) , % . )

A t lo w f r e q u e n c y ( 3 0 - 40 H z ) , t h e a m p l i tu d e d e p e n d e n c e o f t h e l o g a r i t h m i c d e c r e m e n t o f t h e v i b r a -t i on s w a s d e t e r m i n e d o n a n in s t a l l a t io n t y p e D - 7 , d e s i g n e d b y t h e I n s t i t u te o f t h e S t r e n g t h P r o b l e m s ,A c a d e m y o f S c i e n c e s o f t h e U k r a i n i a n S S R , w i t h c y c l i c b e n d in g o f s p e c i m e n s w i t h a c r o s s s e c t i o n 2 x1 4 1 0 0 m m o f t h e w o r k i n g p a r t , b y t h e m e t h o d o f f r e e d a m p e d v i b r a t i o n s [ 4] . U n d e r c o n d i t i o n s o fh i g h - f r e q u e n c y c y c l i c b e n d in g o f t h e s p e c i m e n s ( ~ 1 . 5 k H z ), t h e d e p e n d e n c e o f t h e l o g a r i t h m i c d e c r e -m e n t o f t h e v i b r a t io n s o n t h e s t r e s s a m p l i t u d e w a s d e t e r m i n e d o n a n e l e c t r o d y n a m i c v i b r a t o r V I~ DS -2 00 A b y t h e m e t h o d o f t h e r e s o n a n c e c u r v e o n p r i s m a t i c s p e c i m e n s w i th f i ll e t s .

F i g u r e 1 sh o w s t h e a m p l i t u d e d e p e n d e n c e s o f t h e l o g a r i th m i c d e c r e m e n t o f v i b r a t io n s o f t h e i n -v e s t i g a t e d t y p e s o f c a s t i r o n w i t h l o w (a ) a n d h i g h (b ) l o a d i n g f r e q u e n c i e s , t h e c u r v e s w e r e p l o t t e d u n -d e r h o m o l o g o u s s t r e s s e s r e f e r r e d t o t h e e n d u r a n c e l i m i t d e t e r m i n e d in t e s t s w i th a f r e q u e n c y o f ~ 1 .5k H z .

A f e a t u r e c o m m o n t o a l l t y p e s o f c a s t i r o n i s i n c r e a s e d e n e r g y d i s s i p a t i o n w i th i n c r e a s e d s t r e s sa m p l i t u d e ; c a s t i r o n w it h i a m e l l a r g r a p h i t e h a s t h e h i g h e s t le v e l o f e n e r g y d i s s i p a t i o n w h i l e c a s t i r o nw i t h s p h e r i c a l g r a p h i t e h a s t h e l o w e s t v a l u e o f 6 i n t h e e n t i r e s t r e s s r a n g e . T h e d a m p i n g c a p a c i t y o fc a s t i r o n i n c r e a s e s f r o m t h e in i t ia l a m p l i t u d e s : W i t h t h e s h a p e o f t h e i n c l u s i o n s c h a n g in g f r o m s p h e r i -c a l t o l a m e l l a r , t h is d e p e n d e n c e b e c o m e s e v e r m o r e m a r k e d .

W h e n w e e x a m i n e t h e e f f e c t o f t h e f r e q u e n c y f a c t o r o n t h e a m p l i t u d e d e p e n d e n c e o f t h e l o g a r i t h -m i c d e c r e m e n t , w e s e e t h a t t he f r e q u e n c y d o e s n o t h a v e a s u b s ta n t i a l i n f l u e nc e o n t h e da m p i n g c a p a -c i t y o f c a s t i r o n c o n t a in i n g i n c l u s i o n s w i t h m o r e o r l e s s e q u i a x i a l s h a p e ( s p h e r i c a l o r f l a k y ) , a n d t h a ti t o n l y s l i g h t l y i n c r e a s e s t h e l e v e l o f e n e r g y d i s s i p a t i o n a t lo w f r e q u e n c y f o r c a s t i r o n w i t h i n e q u ia x i a l( l a m e l l a r ) g r a p h i t e .

F i g u r e l c s h o w s t h e d e p e n d e n c e s 5 = 6 (a ) f o r c a s t i r o n s u b j e c t e d t o p r e l i m i n a r y c y c l i c l o a d in ga t h i gh f r e q u e n c y b y s t r e s s e s b e l o w t h e e n d u r a n c e l i m i t o n a b a s e o f 2 . 10 7 t o 2 -1 08 c y c l e s . A l l t h e

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TABLE 1. C hara cter ist ic s of the Micro-inhomog eneity of the Stra in State of the In-vestiga ted Types of Cast IronD e g r e eo f l o a d [ m a xing mm

G r a y c a s ti ron

I 0 9I1 1 2

I I I 1 7

K m a x c o ~2 9 0 3 73 5 0 4 83 2 0 4 4

Malleablecast ironKmax I2 12 02 1

High-stre gthcast irocos K m ax cos

0 2 6 t 9 0 2 60 2 5 : 1 8 0 2 4i

dependences are cha rac ter ize d by the exist ence of bends in the curves 5 = 5(a): At firs t the ievel ofenergy diss ipat ion increases , and then i t decrea ses .

The peculiar i t ies of the microi nhomoge neity of the state of st res s and strain of cast i ron withdifferent configurat ions of the graphite inclusions were studied by the opt ical polarizat ion method ofphotoelastic coatings. It is known that the use of pa rti cul arl y thin, optically active coatings makes itpossible to dete rmin e the chara cter ist i cs of the state of st rain: The difference between the principalstr ain s eq - e2 and the orientat ion of the principal de form atio n axes within the limits of micro sco pic al-ly small volumes [5]. Within the framew ork of the present work we invest igated the state of micro -str ain of cast iron in one -ti me static quasipu re bending of fiat spec imen s (55 5 x 2 mm) in mi cr or e-gions si tuated in tensioned f ibers of the specimen. The method of carr ying out such meas urem ent s andof proce ssing the ex perimental data was described previou sly [6, 7].

Figur e 2 shows the topographic distr ibuti on fields of equal levels of the differen ces of the prin-cipal str ai ns eq - ez in the mic roregio ns of the invest igated types of cast i ron at different stages ofthei r s tat ic loading, obtained by scanning interpretat io n of the inter ferenc e pat terns at a pi tch of 10#m.The sensit ivit y of the applied optical pola rizati on method with the actual thickne ss of the coatings (~1 0-15 #m) is l imited by the region of elastoplast ic and plastic st rain s. As the chara cter ist ic of the degreeof loading, we determined the bending force Pben and the correspondin g m aximum deflect ion of the spe-cimen fmax at a base of 50 mm. The obtained distr ibut ion f ields test i fy to the different local izat ion an dintensi ty of incre ase of local micro deform ations in the matr ix of cast i ron with different configurat ionof the graphite inclusions.

As a ru le, the reg ions of the highest value s e i - e2 are concentrated nea r accu mulat ions of gra-phi te inc lusions, and the orientat ion of these regions coincides with the direct ion in which the maxi-mum shear st r ess es act , i . e . , the regions are si tuated at an angle of ~/4 to the direct ion of the ma -croscopic s tre sse s a act ing in the microvolume in quest ion. In high-s treng th and malleable cast i ron,the r egions of the high est lev els of e 1 - e2 are si tuated in the necks of the mat r ix between graphite seg -regat ions. In gray cast i ron, these regions are local ized in the matr ix next to the graphite inclusionsorientated at an angle of ~/4 to the direct io n in which the macr ost res se s act . An incre ase in mac ro-scopic str ess es with subsequent increa se of the bending force is accompanied both by increased maxi-mum levels of s - 89 and by an incr ease of the regions with increa sed intensi ty of microd eformat ionsinitial ly formi ng in the matr ix (see Fig. 2a, b).

For compar ing the nature of the microinhomogenei t ies of the s t re ss- s t r a in s ta te of cas t i ronwith different configurat ion of the graphite inclusions, we used such par ame ters as the variat ion co-eff icient of the values of the differences of the principal st rains ~e and the local s t ra in concentrat ionfactors Kmax.

The varia tion coefficie nt o~ ~ ch ara ct eri zes the sc at ter of the values of eq - e2 within the investi-gated region due to struc tura l n onuniformity, and i t is deter mined by the known expression [7].

The local st rain concentrat ion factor characterizes the maximum strain concentrat ions in themat rix associa ted with the presence of graphite inclusions in the matr i x, and it is determined as

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Kmax ~ (81 -- 82)max(81 -- e2)mod '

where (e1 - e2)mod is the modal value (e1 - e2) within the investigated microregi on, i . e . , the level ofthe difference of the principal st rai ns of the ma tr ix with the highest frequency and determin ed by thekind of empiric al s t rain distr ibut ion densi ty. The values of Kmax and w 8 for d iffe rent st ages of load -hug the inves tigated kinds of ea st iron ar e pres ente d in Table 1.

I t can be seen from the data of the table that the cha ract eris t ics of inhomogeneity of high-s trengthand malleable cast i ron are at the same level whereas the local s t rain concentrat ion factor Kma x andthe variat ion coeff icient We of gray cast i ron are substant ial l y larg er . These data correspond to thedata on the level of dissipat ion of the vibrat ion energy in the above mat eri als , and this c onfirms thatstru ctur al inhomogeneity makes a substant ial contr ibut ion to the damping capaci ty of cast i ron.

The process of reve rsed cycl ic loading is accompanied by the continuous accumulat ion of plast icstrai ns in the micro volumes of the cas t i ron; this leads to a change in the boundaries of the elast ic andplast ic regions with an increa sing num ber of cycles and co rrespondi ngly to a change in the conditionsof nonuniform cumulat ion and redistr ibu t ion of local s t r ains. In consequence of a change in the bound-ary condit ions, the level of the stre ss concentrat ions somewhat drops, and this entai ls the effect ofincrea sed mobil i ty of the domains, blocked at the ini t ial s tage of loading by the highly stre ssed str uc-ture. The graphs in Fig. lc cle arly show that af te r lengthy cycl ic loading, the curves 5(~) assumed ashape typical of mate rial s in which magnetomec hanical hys tere sis is clea rly expressed: In the regionof medium levels of s t ress ampl i tudes , a d i s tinc t maximum formed characte r i s t ic for th i s mechanismof energy dissipat ion.

We want to point out another fact co nfirming the possibi l i ty that the above assumption is co rrec t ,namely: A magnetomech anical peak of energy dissipat ion i s found in specimens of high-s treng th castiron not subjected to previous cycling in which the blocking of the domains is slight in consequence ofthe lower level of st r ess concentrat ion on the spheric al graphite (see Fig. lb) . In the other curves, as imi lar maximum appears only af ter a cer ta in number of load cycles .

Moreov er, a magnetomecha nical maxim um occurs only on the high-f requen cy curves 5(a) . InFig. la it does not appear even on the curv e 5 (u) for hig h-s tre ngt h cast iron.

Thus, a low loading frequency does not always help reve al lo sses of energy expended on the re -orientat ion of the domains.

2.3.4.5.6.7.

L I T E R A T U R E C I T E DG. S. Pis are nko , Ene rgy Dissipa tion by Mechanical Vibrations [in Russia n], Izd. Akad. NaukUkr. SSR, Kiev (1962).V. T. Tro shchenko, , 'Energy dissipat ion in mat eri al s , Fiz. Tverd. Tela, 2, No. 6, 1060-1063(1960).M. A. Krishtal and S. A. Golovin, Internal Friction and the Structure of Metals [in Russian],Metallurgiya, Moscow (1976).G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Vibration-Damping Properties of Struc-tural Materials [in Russian], Naukova Dumlm, Kiev (1971).A. Ya. Aleksandrovand M. Kh. Akhmetzyanov, Optical Polarization Methods of the Mechanicsof Deformed Bodies [in Russian], Nauka, Moscow (1973).S. A. Golovin and I. I. Renne, Peculiarities of the development of mieroplastie strain in iron-base composition materials, Probl. Prochn., No. 4, 84-87 (1977).I. I. Renne, N. E. Kuz'mina, G. D. Petrushin, and O. A. Kazanskaya, Application of the op-tical polarization method to the investigation of strains in microregions of structurally inhomo-geneous materials, in: Problems of Metal Science and the Physics of Metals [in Russian], TulaPolytechnic Institute (1977), pp. 49-58.

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