The Determination of Inner Surfaces in Composites by X-Ray Refraction

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1 The Determination of Inner Surfaces in Composites by X-Ray Refraction A. H. Hampe, K.-W. Harbich, M. P. Hentschel and H.-V. Rudolph Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany SUMMARY: A X-ray refraction method is presented which reveals the inner surface and interface concentrations of nanometer dimensions due to the short X-ray wavelength near 10-4 µm. Sub-micron particle, crack and pore sizes are easily determined by "X-ray Refractometry" without destroying the structure by cutting or polishing for microscopic techniques. Beyond this analytical potential for (integral) analysis, spatial resolution can be achieved, when the sample is scanned across a narrow X-ray beam. This is possible within relatively short time, as the scattered intensity at very small angles of few minutes of arc is much higher than in conventional wide angle X-ray scattering (WAXS). In this case we have "X-ray Refraction Topography". The performance of the method is demonstrated by partly damaged samples of composites. KEYWORDS: X-ray refraction, inner surface, composites, matrix cracks, interfacial cracks, non destructive evaluation INTRODUCTION Inner surfaces are an important characteristic of a material. In the case of fibre reinforced composites such surfaces are formed by the interface of fibres and matrix, the voids in the matrix and by an incomplete wetting of the fibres. Under load additional inner surfaces appear: First micro cracks in the matrix, the fibres and the interface and then larger cracks as delaminations. The knowledge of the amount of inner surfaces in a composite would allow estimation of the damage state and thus the mechanical performance. For the determination of inner surfaces in materials a nondestructive method was developed using the refraction of X-rays. In contrast to the well known X-ray diffraction techniques, which are based on coherent scattering of electromagnetic waves at atomic lattices and particles, the X-ray refraction is based on the deflection at surfaces of materials with different electron densities (similar to the refraction of light at the surfaces of transparent materials). The measurement of X-ray diffraction in the wide angle range (WAXS) allows to investigate the molecular order with results like the determination of the crystalline structure or molecular orientation and in the small angle range (SAXS) it allows the determination of superstructures and orientation of fibres. The X-ray refraction is measured at small angles

2 due to the X-ray refractive index of materials, which is nearly 1. Surfaces between material and air exhibit much higher refraction intensities then the surfaces between fibre and matrix, since the difference of the material refractive indexes is smaller than For the detection of a surface a gap of 10 nm is sufficient. EXPERIMENTAL The physics of X-ray refraction is quite similar to the well known refraction of light by optical lenses and prisms, which is governed by Snell`s law. However a major difference from optics is the deflection at very small angles, as the refractive index n of X-rays in matter is in the region of one [1]: n = 1 - ε (ε ~ ρ λ 2, ε ~ 10-5 for glass/8kev radiation) (1) ε is the real part of the complex index of refraction, ρ the electron density and λ the X-ray wavelength. With n < 1 the converging effect of convex lenses changes to divergence in case of X-rays. Fig. 1 demonstrates the effect of small angle scattering by refraction of cylindrical lenses: A bundle of 15 µm glass fibers as used for composites (GFRP) deflects collimated parallel X-rays within several minutes of arc. The oriented intensity distribution is collected by X-ray film and the straight (primary) beam is omitted by a beam stop. Monochromatic radiation below 20 kev is applied like in crystallography, which is relatively soft for NDT purposes. The shape of the intensity distribution of cylindrical objects is always the same even for very different materials, if the scattering angle is normalized to the "critical angle" θ C of Fig. 1: Effect of oriented small angle scattering by refraction of glass fibers Fig. 2: The normalized shape of the angular intensity distribution of cylindrical objects 2

3 total reflection (Fig. 2). This parameter depends only on the refractive index: θ 2 C = 2ε. The experimental setup is shown in Fig. 3. The monochromatic X-ray (e.g. Cu-k, nm) passes after collimation the sample with the effects of absorption and refraction. The intensity of the refracted ray (I R ) is detected at an angle of about 0.05 degree. In order to get an information about the absorption effect (and beam stability) the intensity of the fluorescence (I T ) of a fluorescent foil is monitored. The beam cross section is about Detector Refraction Detector Scattering Foil Collimator Beamstop Sample X-Ray Source Fig. 3: Schematic experimental setup for the measurement of the X-ray refraction 0.05mm*2mm. By using a motor driven sample holder a refraction scanning topography at 50 µm resolution is possible. The additional refraction intensity of a refracting object can be measured according to [2] T I () θ = I () θ I () θ = Cd I () θ, with C = k S/V (2) R R A The refraction factor C is proportional to the inner surface density (surface/volume ratio) S/V and the sample thickness is d. I A (θ) is the scattering background under sample absorption and k is a constant of the apparatus, determined by a reference sample of known specific surface. APPLICATIONS The diffraction effect of a fiber which is scanned by a narrow X-ray beam is shown in Fig. 4. The behavior is exactly the same as in an optical experiment. Any diffraction effect would result in a symmetric intensity above background level. 3

4 Fig. 4: X-ray refraction by a 125 µm polymer fiber is demonstrated by scanning a fiber through a narrow X-ray beam and collecting the intensity at each position. Single fiber debonding, a central parameter of composites characterization in composites, is measurable by X-ray refractometry. The basic principle can be understood by the optical analogue: compare the focussing properties of a lens (fiber) in air and in a liquid (fiber in matrix)! The refraction effect is lower in the second case. The density difference between fiber and matrix determines the X-ray scattering effect as well. A model composite has been made in order to demonstrate the refraction behavior of a debonded and a bonded 140 µm saphire fiber in wax matrix (Fig. 5, left) 2. The upper ray crosses the bonded fiber matrix interface causing a small amount of deflected intensity. At the debonded fiber and at the matrix surfaces (lower ray) much more X-rays are deflected, as the larger density difference between the materials and air corresponds to a higher index of refraction. Fig. 5: Model of X-ray refraction at interfaces of bonded and debonded fibers of a composite, X-ray topography of model, investigation of single fiber debonding at different fiber volume ratios. The middle of Fig. 5 shows the resulting intensity distribution of a refraction scan of the model composite. The wax channel is clearly separated from the fiber surface. The bonded 4

5 fiber is much less contrasted. A practical measurement of the fraction of debonded fibers in a real thermoplastic C-fiber composite is given on the right. There is a nonlinear dependence of debonding on the fiber volume fraction. This can be explained by the very viscous thermoplastic matrix, which is hindered to penetrate between densely packed fibers during melt impregnation processing. Formulas for the calculation of individual or collective fiber debonding have been given [3]. The measurement of the crack density in light weight materials can be performed by X-ray refractometry as well. The knowledge of the crack development is believed to play the key role in all long-term material behavior. Fig. 6 shows the refraction value for a short glass fiber reinforced Polyoxymethylene (POM) as a function of an ageing time. The ageing procedure consisted in storage of the samples in water of 98 C. The circles indicate the refraction values for the samples before mechanical testing, the triangles correspond to refraction values of samples after loading until fracture. The data reveal that the ageing is causing inner surfaces with a saturation effect and that the mechanical loading of the samples is producing additional surfaces (cracks). Fig. 7 correlates the refraction value with the tensile strength for the unloaded and loaded samples. 1 0,95 1 0,95 - after mechanical loading - before mechanical loading refraction value 0,9 0,85 0,8 - before mechanical loading 0,75 - after mechanical loading 0, ageing time [h] refraction value 0,9 0,85 0,8 0,75 0, tensile strenght σ [MPa] Fig. 6: Refraction values of POM/GF versus ageing in water of 98 C Fig. 7: Refraction values of the aged POM/GF samples versus tensile strength REFRACTION TOPOGRAPHY Scanning X-ray refraction localizes the projection of inner surface concentrations or individual edges of surfaces and interfaces such as sub-micrometer pores or cracks. The spatial resolution can be better than 10 µm, although this is not the main advantage of refraction techniques, as the signal level itself contains the information about inner surfaces. In Fig. 8 the picture of a scanned POM/GF sample, which passed a fatigue test of 1500 cycles at 1 Hz with a peak stress of 100 MPa, is shown. The pattern indicates clearly that the damage is concentrated in the middle of the sample. 5

6 Fig. 8: X-ray refraction topography of a POM/GF sample after a fatigue test Refraction value C m d 0, ,66 0, ,87 0, ,00 1, ,30 A severe problem of CFRP characterization relates to impact damages. Ultrasound C-scans resolve delaminations created by impact very well, but the single fiber debonding area, which develops at lower loads, is only detectable by X-ray refraction topography. In Fig. 9 seven impact areas are imaged at 1 mm resolution. The reduction of details compared to Fig. 10 is compensated by 100 times faster measurements (10 mm²/s). (The three bright capitals are not impacted, simply pencil written [graphite scattering].) Fig. 9: Large area X-ray Refraction Topography of seven impact areas at 1 mm resolution X-RAY REFRACTION COMPUTER TOMOGRAPHY Although two-dimensional Refraction Topography provides an effective new probe for analysing meso-structures of all kind of heterogeneous materials, it is sometimes interesting to have section images of transversal resolution as known from X-ray computer tomography in order to overcome the overlap of details by projection effects. FIG. 10 demonstrates the feasibility of X-ray Refraction Computer Tomography: The sample micrograph shows a 3 by 3mm bar of phenolic resin CFRP laminate, which is a standard precursor in C/C and C/SiC CMC processing [4]. The computer tomography experiment is carried out by 18 kev single beam scanning in a Kratky camera according to Fig. 4. Linear scans are performed for 360 angular positions, Fourier filtered for linear smearing on a PC and added up in an image file (filtered back projection). The reconstruction of detector signals I A shows a quite homogeneous density of 6

7 the conventional (absorption) computer tomographic image (Fig. 10, center). The final refraction image reveals the spatial interface/inner surface distribution free of absorption effects. The typical layer and crack structure of the micrograph can be recognized by a nondestructive technique. Fig. 10: X-ray refraction Computer-Tomography of CFRP laminate: micrograph, left; conventional absorption tomography, middle; interface tomography, right. X-ray refraction techniques combine analytical capabilities of sub-micrometer structure detection with the requirements of nondestructive full volume characterization. X-ray refraction therefore might help faster materials development, better understanding of meso structures and partly replace micro analysis and mechanical testing in advanced materials science. REFERENCES 1. Compton H. and Allison, S. K., X-ray in Theory and Experiment, Macmillan and Co. Ltd., London (1935) 2. Ekenhorst, D., Hentschel, M. P., Lange, A. and Schors, J., X-ray refraction: a new nondestructive evaluation method for analyzing the interface of composites in the nanometer range, Proceedings of the Tenth International Conference on Composites Materials, Whistler, B.C., Canada, August14-18th, 1995, 5:413, A. Poursartip, K. Street, eds., Woodhead Publishing Ltd., Cambridge (1995) 3. Hentschel, M.P., Harbich, K.-W. and Lange, A., Nondestructive evaluation of single fiber debonding in composites by X-ray refraction, NDT&E International 27:275 (1994) 4. Hentschel, M. P., Lange, A., Harbich, K.-W., Ekenhorst, D. and Schors, J. V., Röntgentopographische Verfahren, Materialprüfung 40 (1998) 5,