Acoustic and Mechanical properties of particulate composites

Transcription

1 3rd International Non-Destrutive Testing Symposium and Exhibition, Istanbul Turkey, April 008 For all papers o this publiation lik: Aousti and Mehanial properties o partiulate omposites E. Sideridis, V.N. Kytopoulos, J.N. Prassianakis and I. Sakellaris The aousti and mehanial properties o a lass o partile illed polymers have been investigated using destrutive and non-destrutive testing tehniques. The veloities Cl and Ct o the longitudinal and transverse waves were evaluated rom the aousti properties. From these and rom the density o the material, the modulus o elastiity, the shear modulus, and the Poisson ration were evaluated by the appropriate relationships. The results were ompared with those obtained rom tensile experiments and also with those obtained rom theoretial ormulae. Finally, to investigate the eet o requeny, the results obtained rom ultrasoni experiments were ompared with those obtained rom dynami experiments arried out on iron-epoxy omposites. It was ound that the results rom ultrasoni tests are loser to those obtained rom dynami experiments than to those rom stati ones. INTRODUCTION Partiulate omposites are omposites reinored with partiles having dimensions o the same order o magnitude. Partiulate omposites are produed rom a polymeri matrix, into whih a suitable metal powder has been dispersed. One role o the matrix is to protet the iller rom the orrosive ation o the environment and to ensure interations between the illers by mehanial, physial, and hemial eets. Epoxy resins are the most suitable polymers or omposite matrixes, and extensive researh has been arried out on their rheologial behaviour [1,] and their mehanial properties [3,4]. The interrelationship o mehanial and optial properties has been investigated previously or various amounts o plastiiser [5] and aousti properties determined or plastiised epoxies and orrelated with the orresponding mehanial properties [6,7]. The mehanial and aousti properties o the epoxy polymers an hange by adding dierent amounts o iller. Metal oxides and metal powders have been used in ombination with epoxy matrixes to reate omposites. The mehanial and thermal properties o suh resins illed with iron partiles have been investigated, and the eet o partile size on the same properties o iron illed epoxies has been extensively studied [8,9]. A rigorous desription o a omposite system onsisting o a matrix, in whih iller partiles have been dispersed, is diiult to undertake. Many geometrial, topologial, mehanial, et., parameters are neessary, the majority o whih vary statially or are unknown. Theoretial treatments usually attempt to exploit as muh readily available inormation as possible, whih generally onsists o the mehanial properties o matrix and iller and the volume ration o the latter. Appropriate assumptions must be used or the missing data. Ultrasoni tehniques have been widely used or non-destrutive inspetion and evaluation (NDE) o omposite materials. Hale and Ashton [10] related strength redution and hange in ultrasoni attenuation o progressively damaged glass reinored plastis. Williams et al. [11] used the NDE tehnique o ultrasonis to haraterise separation mode and rature strength or adhesively bonded ibre reinored plastis. In addition, ultrasoni testing an be used to indiate the ibre diretions in a omposite material [1] and or general evaluation and quality ontrol o omponents by attenuation and analysis o requeny or spetrosopy [13,14]. The use o ultrasoni tehniques or the determination o the mehanial properties in omposite materials has been desribed by Smith [15] and by Dean and Loket [16]. In the present work the aousti and mehanial behaviour o an epoxy polymer, reinored with dierent amounts o iron partiles at ambient temperature, was investigated. Aousti properties were ompared with the orresponding mehanial properties obtained rom tensile experiments. The omparison revealed large disrepanies depending on

2 requeny. The elasti modulus obtained rom ultrasoni tests was then ompared with the elasti modulus o the same material obtained rom dynami experiments. ULTRASONIC EQUIPMENT AND MEASUREMENT PROCEDURES Energy pulse propagation through the struture at requenies above the audible range, an be related to the material properties. The veloity propagation an be measured sine modulus = density x veloity (Re. 5). However, the main aim o the ultrasoni testing o materials is to searh and evaluate loations in the materials whih ontain disontinuities and to determine the eets o interation between sound waves and material properties. The basi parameters required or all ultrasoni measuring methods are sound veloities and sound attenuation through the material in whih the sound wave travels. Sound veloities l and t o the longitudinal and transverse waves, respetively, and the density ρ o the material are used or the evaluation o the elasti modulus E, the Poisson ratio v, and the shear modulus G via the ollowing relationships E v G = ( 1+ v )( 1 v ) ( 1 v ) ( l t ) ( / ) 1 1/ / 1 = t l t ρ 1 = ρ (1) Figure 1 shows a shemati diagram o the ultrasoni pulse-eho measuring system used. The system onsists o a broad band ( MHz) ultrasoni pulser-reeiver law detetor (Krautkramer) whih an generate and reeive eletri pulses up to 15 MHz. KG and KN probes were used as transmitting reeiving transduers o sound waves, produing ultrasounds o and 4 MHz, respetively. A simple mahine oil was used as the transduer/speimen interae ouplant. A ontat load or both probes o 9 88 N was applied to the transduer/speimen interae. (1a) (1b) The pulser setion produes and injets ultrasoni pulses into the speimen through the transduer and the releted signals produed are ampliied by the reeiver setion o the equipment and displayed on the osillosope. The sound veloity using the relationship o the longitudinal waves o eah speimen was evaluated x l

3 x l d x = l () d g where l is the sound veloity o the reerene blok, dx is the real speimen thikness, and d is the equivalent thikness o the speimen, whih is measured on the sreen o the g osillosope. MATERIAL AND EXPERIMENTAL WORK Testing material The speimens used onsisted o a matrix material, whih was a old setting system based on a diglyidyl ether o bisphenol-a resin having an epoxy equivalent o , a visosity o 15Nsm - at 5 C, and moleular mass between 370 and 384, ur ed with 8 wt-% triethylenetetramine illed with iron partiles o average radius 75 µm. The elasti moduli o the matrix and iller were 3 5 and 10 GNm -, respetively, and their Poisson ratios were 0 36 and 0 9, respetively. Tensile experiments Dogbone speimens with onstant dimensions o measuring area 6x3 mm and length 45 mm were used during the tensile tests whih were arried out with an Instron type testing mahine at room temperature. The speimens were tested at a rate o extension o 1 mm min -1. Five iller volume rations υ and ive speimens or eah volume ration were used and the values given orrespond to their arithmeti mean value. For the obtention o the stress-strain diagrams, strain gauges (KYOWA type, gauge ator k = 1 99) were loated on the speimen to measure the strains. Ultrasoni experiments The NDE tehnique used in the present work was the ultrasoni pulse-eho tehnique [17]. When ultrasoni pulses are introdued into a speimen, they relet on a disontinuity or on the bak wall o the speimen. The magnitude o the eho reletions depends on the hanges in the impedane aross the speimen. To determine the veloities o longitudinal and transverse waves, ive speimens rom eah volume ration o the omposite material were tested ultrasonially at ambient temperature. During eah experiment the quantities obtained rom the osillosope sreen were the equivalent thikness d o the partile illed omposite and the eho heights. g Measurements at three dierent points in eah o the ive speimens were arried out. From these quantities and using equation (), the veloity l was evaluated. A suitable probe or the longitudinal waves with requeny 4 MHz was used. For the evaluation o the veloity t, a suitable probe or transverse waves with requeny MHz was used. From the analogous equation () this veloity was alulated x t d x = t (3) d g RESULTS Figure shows the variation o the longitudinal and transverse wave veloities versus the iller volume ration. From these urves it an be observed that as the amount o inlusions inreases, both veloities derease. Figure 3 presents the variation o the elasti modulus and shear modulus versus the volume ration as obtained rom the ultrasoni measurements. It an be observed that as the amount o inlusions inreases both moduli inrease.

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5 Figure 4 shows the variation o stress σ υ. the longitudinal strain ε or various iller rations (0, 0 05, 0 10, 0 15, 0 0, and 0 5 vol.-%) o the iron partile reinored epoxy polymer as obtained rom tensile experiments. By omparing these urves it an be observed

6 that as υ inreases, the linear portion o the stress-strain urve inreases. This is due to the matrix being a visoelasti material while the illers are elasti materials. The addition o iron partiles reinores the elasti behaviour o the omposite. Figure 5 presents the variation o the tensile stress at rature, σ F versus the iller volume ration υ obtained rom the tensile experiments. For omparison the igure also shows the urves obtained rom the theoretial ormulae o Nielsen [18] and Niolais and Marshelkar [19] given by equations (9) and (10): see Appendix. It an be observed that σ F, dereases as the iller volume ration inreases. The experimental values are in good agreement with the theoretial ones.

7 The variation o the elasti modulus E o the omposite versus the iller volume ration υ obtained rom tensile experiments is shown in Fig. 6. For omparison, the urve obtained rom a theoretial expression o the authors [3] given by equations (14) and (15) and the urves obtained rom the theoretial ormulae o Counto [0] and Kerner [1] given by equations (11) and (1) are also shown, see Appendix. It an be observed that the elasti modulus inreases as υ inreases. The experimental values lie between the two theoretial urves. In Fig. 6 ultrasoni and tensile values o the elasti modulus are also ompared. It an be observed that ultrasoni experiments give muh higher values than or tensile

8 experiments. This dierene appears to result rom the visoelasti behaviour o the polymer matrix, whih is a strongly visoelasti material and hene the elasti onstants hange during the tension test. This is not apparent, or example, in steel or whih visoelasti behaviour is insigniiant or the tension test and thus the elasti onstants measured either ultrasonially or rom tension tests are very similar. The behaviour o a visoelasti material, when subjeted to sinusoidally varying * G * ω loading, an be desribed by the omplex requeny dependent moduli E ( ω) and ( ) where ω = π is the angular requeny and is the requeny. The ollowing expressions hold ( ω) ( ω ) ( ω) ( ω) E* = E + ie (4) G* = G + ig (5) where primed symbols denote the storage modulus and double primed symbols denote the loss modulus o the material. The proedure by whih eetive omplex moduli o visoelasti materials an be determined, on the basis o analytial expressions or eetive elasti moduli, is known as the orrespondene priniple and was developed by Hashin []. For isotropi visoelasti materials a omplex Poisson ratio an be introdued ( ω) ( ω) v* = v + iv (6) on the basis o the relationship between the moduli

9 E * G* = 1 * ( + v ) (7) where E whih is the real part o the omplex modulus, is known as the dynami modulus and is proportional to the maximum energy stored during eah yle. Thus the expression or the veloity o a longitudinal wave in a medium an also be written l E ( 1 v ) ( 1+ v )( 1 v ) = ρ 1/ (8) Figure 7 shows the dynami storage modulus E o the iron partile reinored omposite material versus. requeny, as obtained rom dynami experiments arried out on a Dynastat and Dynalizer apparatus, whih an apply a sinusoidal load o maximum amplitude 100 N. The measurements were arried out at requenies rom 0 1 to 100 Hz at ambient temperature and are desribed in Re. 3. It an be observed that E inreases with requeny and i the urves obtained rom the experimental values are extended beyond 100 Hz, as shown by the disontinuous part o the urve, the moduli ahieved at approximately MHz, are lose to those obtained using ultrasonis. In visoelasti materials, the results or moduli obtained rom ultrasoni measurements appear to be loser to the results obtained rom dynami tests than to those rom stati tests, owing to the strong variations in the properties o these materials with requeny.

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11 CONCLUSIONS A omparison o the mehanial and aousti properties o iron partile reinored epoxy resin has been attempted. The veloities o longitudinal and transverse waves were onsidered as representative quantities o the ultrasoni behaviour by using pulse-eho measurements. It was shown that the veloity o ultrasoni longitudinal and transverse waves propagating in the iron partile reinored epoxy polymer dereases in a non-linear manner as the iller volume ration inreases. The veloity o longitudinal waves is determined more simply and with greater auray than the veloity o transverse waves beause these waves, produed by speial probes, show high attenuation when passing through the partile rilled polymers. The use o this type o wave presents diiulties or the study o the aousti behaviour o the partile reinored epoxy polymers. Conversely, the wave veloities are material properties that appear to depend on the disrete nature o the internal struture o the metal partile reinored epoxy polymer, whih may be altered by hanges in the iller ontent. In addition, these materials suer rom mirophysial damage aumulation in the orm o void ormation. The ourrene o a omplex series o events at the mirostrutural level (e.g. mirovoids or mirorak aumulation or iller agglomeration) in an initially intat material degrades strutural integrity. Tensile experiments arried out with the iron partile reinored epoxy resins showed that the tensile strength dereases but the elasti modulus inreases with iller volume ration. Comparison between tensile and ultrasoni determination o the elasti modulus revealed large disrepanies. The values obtained rom ultrasoni tests are muh higher than those obtained rom tensile tests. Finally, it an be onluded that in materials showing visoelasti behaviour suh as iron partile illed epoxy resins, the results or moduli obtained rom ultrasoni measurements are loser to the results obtained rom dynami experiments owing to the strong variations with requeny o the mehanial properties o these materials. APPENDIX TENSILE STRENGTH To determine tensile strength Nielsen [18] used the relationship / 3 ( ) σ = σ υ (9) F, F, m 1 where σ F, and σ F, m denote the tensile stress at rature o the omposite and the matrix, respetively, and υ is the iller volume ration. However, Niolais and Mashelkar [19] use /3 ( ) σ F, = σ F, m 1 1 1υ (10) ELASTIC MODULUS The Elasti Modulus o the omposite aording to the proedure derived by one o the authors in Re. 3 an be alulated as: ( 1 v ) λ υ ( 1 v ) 1 υ ( 1 λ ) ( 1 vm ) ( λυ 1) ( 1 vm ) + + = + E E Em 1 υ where the parameter λ is given as: ( v ) 3 1 m E λ = υ ( 1 v ) v E + ( 1 v )( 1 υ ) E m m m (11) (1)

12 The Poisson ratio v o the omposite may be alulated with a great auray by the simple relation derived rom the inverse law o mixtures, whih is expressed by: 1 υ υm = + (13) v v v m where ν denotes the Poisson ratio o the iller, and v m the Poisson ratio o the matrix. Also the Counto [0] model uses the relationship or elasti modulus / υ 1 = + E E υ E + E ( 1 υ ) 1/ 1/ m m where E, Em, and E are the elasti moduli o the omposite, the matrix, and the iller, respetively. To determine the same parameter, Kerner [1] uses (14) E = Em 1 + ( 1 υ ) ( v ) υ 15 1 m 8 10vm (15) REFERENCES 1. P. S. THEOCARIS: Rheol. Ata, 196,, (), 9.. P. S. THEOCARIS: J. Appl. Polym. Si., 1964, 8, T. HIRAI and D. E. KLINE: J. Appl. Polym. Si., 197, 16, T. HIRAI and D. E. KLINE: J. Appl. Polym. Si., 1973, 17, P. S. THEOCARIS and J. PRASSIANAKIS: J. Appl. Polym. Si., 1978,, J. N. PRASSIANAKIS: J. Appl. Polym. Si., 1990, 39, B. KONSTANTELLOS and E. SIDERIDIS, Plast. Rubber Compos. Proess. Appl., 1994,, G. C PAPANIKOLAOU, S. A. PAIPETIS, and P. S. THEOCARIS: J. Appl. Polym. Si., 1977, 1, P. S. THEOCARIS, G. C. PAPANICOLAOU, and E. SIDERIDIS: J. Rein. Plast. Compos., 198, 1, J. M. HALE and J. N. ASHTON, Br. J. Non-Destr. Test., 1985, 1, J. H. WILLIAMS, J. R. SAMSON, S. LEE, and T. K. ANG: Compos. Mater., 1987, 1, G. DEAN: 'Charaterisation o ibre omposites using ultrasonis, omposite-standards, testing and design', 16; 1974, National Physial Laboratory, UK. 13. P. R. TEAGLE: Composites, 1983, 14, (), J. L. ROSE, J. M. CARSON, and D. L. LEIDEL: 'Analysis o the test methods or high modulus ibers and omposites', STP 51, 311; 1973, Philadelphia, PA, ASTM. 15. R. E. SMITH: J. Appl. Phys., 197, 43, (6), G. D. DEAN and F. J. LOCKET: 'Analysis o the test methods or high modulus ibers and omposites', STP 51, 36; 1973, Philadelphia, PA, ASTM. 17. J. KRAUTKRAMER and H. KRAUTKRAMER: 'Ultrasoni testing o materials'; 1977, Berlin, Springer-Verlag. 18. L. E. NIELSEN: J. Appl. Polym. Si., 1966, 10, L. NICOLAIS and R. A. MASHELKAR: J. Appl. Polym. Si., 1976, 0, U. J. COUNTO: Mag. Conr. Res., 1964, 16, 19.

13 1. E. H. KERNER: Pro. Phys. So, 1956, 69B, Z. HASHIN: Int. J. Solids Strut., 1970, 6, E. SIDERIDIS: Compos. Si. Tehnol, 1986, 7, 305.