|NDT.net - December 2002, Vol. 7 No.12|
Micro damage structures of fiber reinforced polymers (FRP) can be characterized nondestructively by X-ray refraction topography, which images inner surfaces. The damage accumulation after fatigue treatment of short glass fiber reinforced polybutylene terephthalate (PBT-GF) is correlated to the applied load and the number of cycles. Micro cracks and fiber/matrix debonding during fatigue can be detected separately due to their different direction of X-ray small angle scattering. The residual strength over the crack surface decreases by a linear decay as 30 %, 60 % and 90 % of the materials lifetime is passed.
Fiber reinforced polymers (FRP) have been established more and more in constructions of automotive and aviation industry. For such applications the exact knowledge of the failure behavior of components under long-term cyclic load is desired. However, the failure mechanisms of fiber reinforced polymers are complex and far from being well understood. Traditionally the fatigue behavior of a material is characterized by the number of load cycles before their macroscopic failure at different stress amplitudes (Woehler-plot). This kind of mechanical spectroscopy is very time-consuming and gives no information about the relevant micro damages developing during dynamic loading. The micro structures after fatigue of short glass fiber reinforced injection molded tensile test samples of polybutylene-terephthalat (PBT-GF) can be characterized nondestructively by X-ray refraction (1). By this method it is possible to study the damage accumulation during fatigue as a function of load cycles and stress amplitudes. X-ray refraction topographs image the increase of cracks and fiber debonding during fatigue treatment.
The X-ray refraction technique utilizes X-ray small angle scattering which is well known in crystallography, where particle dimensions of a few nano meters are investigated. Different from this, larger micro structure give rise to such scattering as well, but at even smaller scattering angles, typically below five seconds of arc. It is dominated by the X-ray optical effects of refraction and total reflection at inner surfaces. The X-ray deflection occurs at interfaces of different index of refraction, similar to the refraction behavior of light at the surfaces of transparent materials. However one major difference to optical principles is the deflection with very small angles, as the refractive index of X-rays in condensed matter is nearly one (2). The refraction effect is sensitive to smallest fiber separations or cracks of nanometer dimensions up to the micrometer range and well suitable to find micro structural defects, which are formed in composite materials e.g. micro cracks, fiber cracks and fiber debonding. Beyond the determination of an average inner surface density at a spot, their spatial resolution is achieved by scanning the sample resulting in refraction topographs.
|Fig 1: X-ray refraction measuring principle.|
The X-ray refraction measuring principles are shown by Fig. 1. Modified conventional small angle X-ray scattering (SAXS) equipment can be employed. The collimation of the X-rays and the selection of the scattering angle is performed by a Kratky type small angle scattering camera. The primary beam passes the sample mounted to a two axes micro drive where it is partly absorbed to the intensity IA. It penetrates a scattering foil from which an absorption detector receives the proportional scattering. The intensity of the refracted beam IR is detected by a separate detector after passing a detection slit which is set to a small scattering angle close to two minutes of arc. For practical measurements the detection slit remains at a fixed scattering angle. The additional refraction intensity of a refracting object can be measured according to:
|C . d . IA = IR - IA , with C = k S/V||(1)|
The refraction factor C is proportional to the inner surface density S/V (surface/volume ratio) and the sample thickness is d. IA is the scattering background under sample absorption and k is a constant of the apparatus, determined by a reference sample of known specific surface.
During cyclic loading of injection molded PBT-GF test samples of high fiber orientation the damaging takes place essentially by micro cracking and fiber/matrix debonding (see Fig. 2). At interfaces the deflection of X-rays points towards the surface-normal. This causes oriented scattering by oriented interfaces (or surfaces). With respect to glass fibers of a composite they are usually aligned to a large extent along the extended axis of the tensile test samples (the flow direction during injection molding). Micro cracks which might develop under tensile stress along the long axes of the test sample take a perpendicular orientation. Thus by choosing the appropriate sample orientation during the refraction measurement the two kinds of damage structures can be detected independently. If the fiber direction is perpendicular to the scattering plane, the amount if scattered intensity is a proportional to their degree of debonding. Correspondingly the formation of micro cracks directly detectable if the sample is inclined by 90 degree about the crossing X-ray beam.
|Fig 2: The X-ray refraction technique reveals the separate detection of (A) fiber/matrix debonding (fibers perpendicular to the vertical scattering plane) and (B) the micro cracking (fibers parallel to the scattering level) in the scan area by turn of the sample around 90°.|
|Fig 3: Change of the relative inner surface over fatigue rate for two different cyclic loads (stress amplitude 125 MPa and 78 MPa). Curve (A) shows by fiber/matrix debonding, curve (B) by micro cracking developing relative inner surfaces. X-ray refraction topographs at top image the locations of the micro cracking within the scaned area. The signal levels relate to the crack population.|
The X-ray refraction topographs at the top of Fig. 3 characterize the damage process during fatigue regarding the micro crack growth at different stress amplitudes (125 MPa and 78 MPa). The gradual increase of the refraction signals with the fatigue rate (30, 60 and 90% of the number of load cycles up to failure) informs about a progressive damage of the composite by accumulation of micro cracks. However the much higher number of load cycles at the lower stress amplitude (right diagram) is related to a lower level of inner surfaces from both fiber/matrix debonding (plot A) and micro cracks (plot B).
|Fig 4: Decrease of residual strength as a function of the relative inner surface due to micro cracking after fatigue treatment and related fatigue rates (30, 60 and 90% of lifetime) at two different loads.|
Additional measurements of the residual strength reveal a marked decrease in correlation to the inner surface of cracks (Fig. 4). Compared to the plot of the 125 MPa treatment the decay is much faster after cycling at the lower load of 78 MPa (corresponding to over 2000 times more cycles). Although decreasing systematically with the number of cycles the residual strength is not only a function of crack surface. The damage accumulation during fatigue depends strongly on the stress amplitude and the number of cycles.
It is assumed that during a high number of load cycles at low stress amplitude relatively few large cracks emerge from initial smaller ones. The resulting reduction of local strain might prevent the creation of new cracks. However the cracks might grow in size rather than by number until they cause failure of the material. Larger cracks should have primarily a higher volume at smaller surface than more numerous smaller ones.
The investigations reveal new structure property relations of a thermoplastic composite after fatigue treatment. They also demonstrate the advantages of combining mechanical and advanced nondestructive methods for a better understanding of materials.
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