A Novel Method for the Pushout Test in Composites

Transcription

1 A Novel Method or the Pushout Test in Composites Rebecca Sinclair and Robert J. Young Manchester Materials Science Centre, UMIST/University o Manchester, Grosvenor Street, Manchester, M1 7HS UK. SUMMARY: The indentation or pushout test is a widespread method o evaluating composite interaces. Pushout tests have been perormed on three types o α-alumina ibre embedded in epoxy resin: Nextel 610, PRD-166; and Saphikon. It has been ound that all three ibres exhibit a well-deined luorescence spectrum consisting o two approximately Lorentzian peaks; and that when compressive strain is applied, the peaks in the spectrum shit towards lower wavenumbers. The shit, measured in cm-1, is linear with respect to applied strain. The luorescence spectra o the ibres were ound to shit by approximately 8-10 cm-1 or each 1% o applied strain. This inormation was used to calculate the point-to-point axial strain variation in the embedded ibres. The luorescence probe method o evaluating pushout tests is capable o producing sensitive and accurate inormation that is useul or understanding the stress distributions in the test. KEYWORDS: Micromechanics, Pushout, Fluorescence Spectroscopy, Alumina ibres. INTRODUCTION The pushout or indentation test has become a widespread method or evaluating the interace strength o ibre composites. Marshall [1] proposed an indentation method (also known as pushout or push-in) or measuring rictional stresses in ceramic matrix composites in A standard Vickers-type pyramid indenter was used to apply orce to the end o a ibre, which is lush with the surrounding matrix in a polished composite specimen. The rictional orce was calculated using the amount o slippage o the ibre end and the peak load required to produce it. Since Marshall s proposal, it has become possible to measure the load and orce continuously throughout the test. Although in real use, most composites are not designed to undergo compressive loading, the test has become a popular method or evaluating the strength o interaces in ceramic matrix composites and any composites containing ibres that are too brittle or pullout. As with the pullout test, it has become common practice to evaluate the eect o embedded length on the calculated strength o the interace. Conventional analysis calculates the average the interacial shear stress, τ a : 1

2 rσ τ a = (1) Le where τ a is the average interacial shear stress, r is the ibre radius, σ is the stress on the ibre and is the embedded length. The analysis is essentially the same as Kelly and Tyson s analysis o the pullout test []. Fluorescence Ruby and sapphire in their naturally occurring orms consist o high-quality α-alumina crystals with Cr 3+ and other impurities. It is known that Cr 3+ enters oxide lattices substitutionally and occupies sites o trigonal symmetry [3]. This causes level splittings in the ground and excited energy states, which show up in the luorescence spectrum. Clear spectra can be obtained by stimulating the luorescence with a single requency light source. A typical spectrum or an oxide lattice containing Cr 3+ or other ions in the (3d) 3 sequence has two well-deined peaks on a lat baseline. The shape o these peaks has been successully modelled using a combination o Gaussian and Lorentzian unctions [4]. Typical spectra are shown in Fig 1. It has been ound that the application o stress on these crystals causes the luorescence peaks to shit in requency. This eect can be explained by cubic ield theory [5,6]. Measuring the shit in the peak positions when known pressures were applied to a ruby crystal in a diamond anvil cell meant that the luorescence lines could be used to measure stress [7] Intensity (Arbitrary units) PRD-166 Nextel 610 Saphikon Fluorescence Wavenumber (cm -1 ) Fig 1: Typical luorescence spectra or the three ibres. Measuring the stress in alumina based materials can be o use in composite testing in cases where the matrix material is transparent to laser illumination and luorescent emissions. A number o optically transparent materials are suitable, or example epoxy resin (particularly Araldyte LY505) and E-glass. The luorescence shit with applied stress is irst measured in a single ree ibre, and then the luorescence spectrum o any position along an embedded ibre can be used to calculate the stress at that point. Fluorescence spectroscopy has been successully used to analyse the ragmentation test in this way [8,9,10]. The use o luorescence in the ragmentation test by Young and co-workers was based on earlier work with Raman spectroscopy [11,1,13]. This method has been applied to ragmentation, microbond and pullout tests.

3 Ma and Clarke measured the stress distribution along a short sapphire ibre embedded in an aluminium alloy matrix [14]. They achieved this by ocusing a laser beam through an objective lens with a short depth o ield into the ibre end. The beam was ocused at successive depths along the ibre and the luorescence measured at each depth using an optical microprobe. However, the depth o ocus was not zero, so the measured requency shit o the luorescence was actually the average taken over the eective excitation volume. To solve this problem, Ma and Clarke measured the depth o ield unction o the microscope lens and used the results to perorm a deconvolution algorithm on their results. Elastic ield analysis was also used to resolve the contributions o radial and axial stresses to the measured stress. The laser used in Young and co-workers methods was plane polarised in the direction o the ibre axis, so that all the stress measured was axial. This enabled a simpler analysis than that o Ma and Clarke [14]. Pullout tests perormed using Raman spectroscopy [13] have revealed that Cox s shear lag assumption can be used successully to model the stress in all three tests beore debonding occurs, and ater debonding, Piggott and Kelly Tyson models can be used. Thereore it is proposed that the Cox model can be applied to pushout tests prior to debonding. Cox [15] proposed a model which described the stress distribution o short ibres ully embedded in a composite. An important assumption o the model, known as the shear-lag assumption, said that the ibre contained only axial stresses and that shear stresses were concentrated at the interace. Cox also assumed that there was perect adhesion between the ibre and the matrix. Cox s equations can be reinterpreted or the pullout test [16], and because o the similarity in the geometry o pullout and pushout tests, it can be used without alteration or this experiment. I a stress σ app is applied to the protruding section o a ibre with radius r, there will be a stress σ in the embedded portion o the ibre that will decrease with distance x rom the point where the ibre enters the block: d σ σ = n () d x r The parameter n is given by: Em 1 1 n = (3) E ln( R / r) 1+υm where E and E m are the ibre and matrix Young s modulus and ν m is the matrix Poisson s ratio. R represents the radius o an imaginary cylinder o matrix around the ibre. Originally this was a ibre-spacing parameter but in single ibre model composites it loses its physical meaning. Since it is unmeasurable, R, or n as a whole, is simply adjusted to it the results or each experiment. With the assumption that there is no bonding across the ibre end, Eqn can be integrated with the boundary conditions σ = σ app at x = 0 and σ = 0 at x = (the embedded length): sinh[ n( Le x) / r] ε = ε app (4) sinh[ nle / r] where ε and ε app are the ibre and applied strains, respectively. Eqn 4 is illustrated in Fig (b) below. 3

4 Fibre strain, e (%) Total Adhesion: = 000µm, E = 80GPa, r = 6µm, E m = 3GPa, ν m = 0.35, R/r = 50, n = 0.045, e m = 0.8% Total Debonding: = 000µm, E = 80GPa, r = 6µm, E m = 3GPa, ν m = 0.35, R/r = 50, n = 0.045, e m = 0.5%, m = 1.0, τ =.1MPa (b) 0.1 (a) Distance along ibre, x (µm) Fig Theoretical plots o the strain distribution in ibres during pullout using the parameters indicated. (a) The Cox model (ull bonding). (b) The Kelly Tyson model (total debonding) [17]. The interacial shear stress τ is obtained by taking the dierential o the strain unction in the ibre with respect to x: dε r τ = E (5) d x so rom Eqn 4 and Eqn 5; n cosh[ n( Le x) / r] τ = E ε app (6) sinh[ nle / r] Eqn 6 is illustrated in Fig 3 (b) below. ISS, τ i (MPa) (a) Total Adhesion: = 000µm, E = 80GPa, r = 6µm, E m = 3GPa, ν m = 0.35, R/r = 50, n = 0.045, e m = 0.8% Total Debonding: = 000µm, E = 80GPa, r = 6µm, E m = 3GPa, ν m = 0.35, R/r = 50, n = 0.045, e m = 0.5%, m = 1.0, τ =.1MPa 10 (b) Distance along ibre, x (µm) Fig 3 Theoretical plots o the interacial shear stress distribution in ibres during pullout using the parameters indicated. (a) The Cox model (ull bonding). (b) The Kelly Tyson model (total debonding) [17]. 4

5 Kelly and Tyson proposed a dierent model o the stresses in the pullout test [18]. They took the shear lag assumption, but assumed that the orces at the ibre-matrix interace were rictional only and that the interacial shear stress was a constant, τ. This gave rise to a orce balance: F = πr τ (7) i.e. the peak orce required to cause sliding F is proportional to the area o ibre surace in contact with the matrix and the interacial shear stress. This gives rise to: dσ τ = d x r (8) and integrating Eqn 8 with σ = 0 at x = gives: (L e x) ε = τ. (9) re Eqn 9 is illustrated Fig (b) above. See also Fig 3 (b) or an illustration o the interacial shear stress assumption. Later authors [19] deined the interacial shear stress as: τ = µσ 0 (10) Where µ is the coeicient o riction and σ 0 is the radial stress acting on the interace. EXPERIMENTAL The pushout tests were perormed on three types o α-alumina ibre embedded in epoxy resin: Nextel 610, a 1 µm diameter, smooth, polycrystalline ibre containing 99% α-alumina; PRD- 166, an 18 µm diameter, rough, polycrystalline ibre containing 80% α-alumina and 0% zirconia; and Saphikon, a 130 µm diameter, single crystal ibre o industrial white sapphire. It has been ound that all three ibres exhibit a well deined luorescence spectrum consisting o two approximately Lorentzian peaks superimposed on a lat baseline; and that when compressive strain is applied, the peaks in the spectrum shit towards lower wavenumbers. The matrix material was a two-part resin consisting o 100 parts by weight o Araldite LY505 resin to 38 parts by weight o Araldite HY505 hardener, cured or 1 week at room temperature. The luorescence spectrum o the alumina-based materials was measured using a Raman microprobe system. This consists o a Spex 1403 Double Monochromator connected to a Nikon BGSC microscope, which has been modiied to take laser radiation, and a 15mW Melles-Griot helium-neon laser. The system does not need to be modiied to measure luorescence rather than Raman scattering. The 63.8nm laser line is used to illuminate the specimen, producing luorescence in the alumina ibre. The luorescence is collected and separated into a spectrum in two stages by the two diraction gratings o the Double Monochromator. It alls onto a charge-coupled device (CCD) which counts the number o photons o each wavenumber across the desired range. For alumina materials the range used was to 14460cm -1 and the typical exposure time was 5s. All spectra were measured at a magniication o 50x. The signal rom the CCD is collected by a computer, which plots intensity versus wavenumber and saves the plot as a spectrum ile. Each spectrum ile taken rom an alumina specimen was itted to two Lorentzian curves and a straight baseline using an 5

6 iterative itting program supplied by Renishaw Raman System Sotware. The peak positions in terms o wavenumber o both curves were recorded. To obtain calibrations o the relationship between R peak shit and strain, single lengths o each o the three types o ibre were adhered to the surace o rectangular PMMA our-point bend beams. The beams were strained so as to place the ibre either in tension or compression. As the axial ibre strain was increased in steps, the position o the R peak was recorded. The R peak was ound to shit linearly with strain. The peak was ound to shit by 8-10 cm-1 or each 1% o applied strain. This inormation was used to measure the stress distribution in single ibre model composites during indentation testing. The specimens consist o a length o ibre embedded horizontally in a 3 mm cube o coldcured epoxy resin (see Fig 4). The ibre protrudes on one side, and stress is applied stepwise by pushing a lat block onto the protruding ibre end. At each compression level, the strain distribution is measured by taking luorescence spectra at several points along the ibre. Fig 4: The pushout specimen RESULTS AND DISCUSSION Example strain proiles rom the pushout tests shown in Fig 5 to Fig 7 were itted to Eqn 4 (the shear lag model or strain variation along a ibre). At zero applied strain, a version o Eqn 4 suitable or evaluating residual strain in ragmentation specimens [9]. For the Nextel 610 and PRD-166 specimens, the zero strain data was indicative o signiicant compressive residual strain, which indicates that there was resin shrinkage during the cold curing process. For Saphikon the zero stain data was indicative o zero residual strain. The dierence between the three specimens may be due to the dierence in the sizes o the ibres. At applied strains above zero, the strain variation along the ibres was modelled by adding the appropriate strain proile at zero applied load to Eqn 4. The results are shown in Fig 5 to Fig 7 as solid lines. For the Nextel 610 and PRD-166 specimens the shear lag model (Eqn 4) provided a good it. For Saphikon, Eqn 4 provided an acceptable it; however, it would also have been possible to model the data using Eqn 9. The modelled curves or each data set were dierentiated to give an estimate o interacial shear stress, τ i using [0]: E r d ε τ i = (11) d x d ε where E is the ibre modulus, r is its radius and is the rate o change o measured strain d x with respect to distance along the ibre. The interacial shear stress proiles shown in Fig 8 to Fig 10 were calculated using Eqn 11. 6

7 measured strain (%) =830µm r=6.4µm n 0 =0.01 n=0.034 E =375 GPa -0.1% -0.16% distance along ibre (µm) Fig 5: Axial strain distributions obtained rom a Nextel 610 ibre embedded in epoxy resin measured strain (%) =830µm r=7.9µm n 0 =0.014 n=0.033 E =375 GPa -0.09% -0.0% Distance along ibre (µm) Fig 6: Axial strain distributions obtained rom a PRD-166 ibre embedded in epoxy resin measured strain (%) =600µm r=65.5µm n= % -0.9% distance along ibre (µm) Fig 7: Axial strain distributions obtained rom a Saphikon ibre embedded in epoxy resin. 7

8 6 Interacial Shear Stress, τ i (MPa) =830µm r=6.4µm n 0 =0.01 n=0.034 E =375 GPa -0.1% -0.16% distance along ibre (µm) Fig 8 Derived interacial shear stress distribution or Nextel 610 pushout (data rom Fig 5). Interacial Shear Stress, τ i (MPa) =830µm r=7.9µm n 0 =0.014 n=0.033 E =375 GPa -0.09% -0.0% Distance along ibre (µm) Fig 9: Derived interacial shear stress distribution or PRD-166 pushout (data rom Fig 6). Interacial Shear Stress, τ i (MPa) =600µm r=65.5µm n= % -0.9% distance along ibre (µm) Fig 10: Derived interacial shear stress distribution or Saphikon pushout (data rom Fig 7). 8

9 CONCLUSIONS The luorescence probe method o evaluating pushout tests is capable o producing sensitive and accurate inormation that is useul or understanding the stress distributions in the test. Upon application o compressive load on the protruding ibre o a pushout specimen, compressive axial strain increases at the point o entry o the ibre into the matrix. For Nextel 610 and PRD-166, the observed strain increase above the existing residual strain decays away to zero within 1000µm. For Saphikon, the compressive strain increase extends along the whole ibre length, becoming zero at the opposite end o the embedded ibre. The dierence is likely to be due to the dierence in ibre diameter. In most cases, the interacial shear stress (ISS) proile in the pushout specimens exhibits a maximum at the point o entry o the loaded ibre into the matrix. In the case o the Saphikon specimen, the ISS proile is approximately lat at all applied strain levels. The maximum values o ISS were lower than the shear yield stress o epoxy resin (41MPa). ACKNOWLEDGEMENTS The authors are grateul to EPSRC or supporting this work in the orm o a studentship (RS) and a research grant (RJY). REFERENCES [1] D B Marshall, An indentation method or measuring matrix-iber rictional stresses in ceramic composites, Journal o the American Ceramic Society, 1 (1984) C59. [] A Kelly and W R Tyson, 'Tensile properties o ibre-reinorced metals: copper/tungsten and copper/molybdenum', Journal o Mechanics and Physics o Solids [3] E Feher and M D Sturge, Eect o stress on the trigonal splittings o d 3 ions in sapphire (α-al O 3 ), Physical Review 17 (1968) 44. [4] R G Munro, G J Piermarini and S Block, Model line-shape analysis or the ruby R lines used or pressure measurement, Journal o Applied Physics 57 (1985) 165. [5] R M Macarlane, Analysis o the spectrum o d 3 ions in trigonal crystal ields, Journal o Chemical Physics 39 (1963) [6] A L Schawlow, A H Piskis and S Sugano, Stain-induced eects on the degenerate spectral line o chromium in MgO crystals, Physical Review 1 (1961) [7] R A Forman, G J Piermarini, J D Barnett and S Block, Pressure measurement made by the utilization o ruby sharp-line luminescence, Science 1 (197) 84. [8] X Yang and R J Young, Determination o residual strains in ceramic-ibre reinorced composites using luorescence spectroscopy, Acta Metallurgica et Materialia, 43 (1995)

10 [9] R B Yallee, M C Andrews and R J Young, 'Fragmentation in alumina ibre reinorced epoxy model composites monitored using luorescence spectroscopy', Journal o Materials Science 31 (1996) [10] R B Yallee, Single ibre composite micromechanics, PhD Thesis, UMIST (1997). [11] I M Robinson, R J Young, C Galiotis and D N Batchelder, Study o model polydiacetylene/epoxy composites, Journal o Materials Science (1987) 364. [1] X Yang, X Hu, R J Day and R J Young, Structure and deormation o high-modulus alumina-zirconia ibres, Journal o Materials Science Letters 7 (199) [13] R J Young, Evaluation o composite interaces using Raman Spectroscopy, Key Enginerring Materials (1996) [14] Q Ma and D R Clarke, Measurement o residual stresses in sapphire iber composites using optical luorescence, Acta Metallurgica et Materialia 41 (1993) [15] H L Cox, 'The elasticity and strength o paper and other ibrous materials', British Journal o Applied Physics 3 (195) [16] P S Chua and M R Piggott, The glass ibre-polymer interace: 1 - Theoretical consideration or single ibre pull-out tests, Composites Science and Technology (1985) 33. [17] D J Bannister, Micromechanical and hydrothermal behaviour o single-ibre epoxy resin composites, PhD thesis UMIST (1996) [18] A Kelly and W R Tyson, 'Tensile properties o ibre-reinorced metals: copper/tungsten and copper/molybdenum', Journal o Mechanics and Physics o Solids [19] D K Shetty, Shear-lag analysis o iber push-out (indentation) tests or estimating interacial riction stress in ceramic matrix composites, Journal o the American Ceramic Society 71 C107. [0] A Kelly and N H MacMillan in Strong Solids 3 rd Edition, Clarendon Press, Oxord (1980). 10