Oct 6, 1989 - B. Mobasher is Member, Technical Staff, USG Corporation, 700 North. Highway 45, Libertyville, IL 60048. A. Castro-Montero is Graduate Reo.
A Study of Fracture in Fiber-reinforced Cement-based Composites Using Laser Holographic Interferometry by B. Mobasher, A. Castro-Montero and S.P. Shah
ABSTRACT--Micromechanisms of matrix fracture in Portland cement-based fiber composites were studied by means of reflection holographic interferometry and quantitative image analysis. An experimental investigation was conducted with different volume concentrations of polypropylene fibers. Uniaxial tensile specimens were loaded within a strain range of up to three percent. The deformation history was recorded as interference holograms. The holograms were acquired in an image-analysis system. After enhancement, they were analyzed for crack density, length, opening profile, and spacing. The evolution of microcracks, their propagation, distributed microcracking and the material response beyond the characteristic damage state are also discussed.
Introduction The use of fiber-reinforced concrete is currently limited to applications of low fiber contents, where the contribution of the fibers is apparent primarily in the post-peak region of the response o f the composite. As the volume fraction of fibers increases and they become more uniformly distributed, the possibility that they can hinder the growth of microcracks (prior to initiation of localization) through an arrest mechanism increases. Hence the matrix fracture toughness can be enhanced. Tensile stress-strain response of the specimens reinforced with relative large volume fraction (13.4 and 8.7 percent) of continuous uniaxial polypropylene fibers are shown in Fig. 1. The contribution of Portland cementpaste matrix was calculated by subtracting from the overall response of the composite. The contribution of the fibers was estimated from a separate series of tests. The calculated average response of the matrix is plotted on the inset of Fig. 1. It can be seen that the tensile strength of the matrix can be as high as 15 MPa, and that
B. Mobasher is Member, Technical Staff, USG Corporation, 700 North Highway 45, Libertyville, IL 60048. A. Castro-Montero is Graduate Reo search Assistant, Department of Civil Engineering, and S.P. Shah (SEM Member) is Professor, Department o f Civil Engineering and Director o f NSF Science and Technology Center for Advanced Cement-based Materials, Northwestern Univemity, Evanston, 11+60208. Original manuscript submitted: October 6, 1989. Final manuscript received." April 25, 1990.
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matrix can contribute as much as 8 MPa even at an average tensile strain of two percent. The maximum contribution o f the matrix occurred at about the point when the composite response first deviated from linearity. This point is defined as the bend over point (BOP). The value of strain at BOP was observed to be as high as 0.1 percent, which is an order of magnitude higher than the tensile strain corresponding to the peak tensile stress of the unreinforced matrix. Thus it seems likely that the presence of the fibers can substantially enhance the loadcarrying capacity properties of matrix. In an attempt to understand this favorable interaction between the fibers and matrix, a theoretical and experimental investigation was conducted using the acoustic emission, quantitative fluorescent microscopy, and holographic interferometry? .2 Earlier research using thin-section microscopy and acoustic emission' indicates the existence of microcracking in the initial (prior to BOP) loading stages. Detection of the microcracks in early stages by using microscopy is quite difficult, since the microcracks are small, and limited in number. The high magnification required for the observation o f microcracks results in a very narrow field of view. The use of acoustic-emission techniques is also restricted since continuous microcracking results in a constant change in the material through which the acoustic waves must travel. Hence, correct interpretation of the test results is difficult. The current investigation is based on the use of reflection holographic interferometry to characterize the initiation and propagation of microcracks in polypropylene fiber-reinforced cement-based composites. Holographic interferometry offers a field of view orders of magnitude larger than that of optical microscopy; yet the displacement sensitivity remains in the order of one #m. The nondestructive nature of holographic-interferometric measurements allows for the characterization of the response at various strain levels for the same specimen. Unlike optical microscopy, which measures the total number of cracks developed, holographic interferometry is an incremental-displacement measurement technique. Thus, it is possible to differentiate between previously existing and active cracks (i.e., cracks that open or propagate) at any load level.
This paper discusses the development of a test method for quantitative evaluation of microcracking using the holographic-interferometry technique. The effectiveness of the experimental method and its benefits over the prior methodologies are also discussed.
Experimental Setup Fibrillated continuous-uniaxial-polypropylene fiber specimens were manufactured by means of a pulltrusion process as described in Ref. 2. The volume fraction of the fibers used was in the range of 8-12 percent by volume. Dogbone-shaped specimens of dimensions 10 x 15 x 110 mm (0.394 x 0.594 x 4.33 in.) were cast in Plexiglas molds and allowed to cure. The fiber-volume fractions for the six test specimens are shown in Table 1. Details about the matrix composition, the fiber type, and the curing conditions can be found in Refs. 1 and 2. The loading configuration used in these experiments was a direct tension setup using frictional wedge-type grips. The load was applied by manual operation o f a worm-gear-driven screw-nut assembly. In order to alleviate the crushing of the specimens at the loading grips, 1-mm thick aluminum plates were mounted on the contact regions of the specimens. The load was measured by means of a 2-kip capacity load cell. Elongation of the specimen was measured using a LVDT (linear variable differential transducer) of 0.05-in. (1.27-ram) range, mounted across a gage length of 3 in. (76.2 mm). The load-elongation response was continuously recorded using a chart recorder.
Optical Setup and Plate-holder Design Single-beam reflection holograms (Lippmann-Denisyuk type9 were used. A 10-mW He-Ne laser of wavelength 633 nm (red) and coherence length of approximately 80 mm was used as the source of light. Figure 2(a) shows the optical arrangement for the recording of the holograms. As shown in Fig. 2(a), the laser light incident on the plate is the reference beam. As the light transmitted through the plate is reflected from the object, it becomes the object beam. The interference between the object and reference wavefronts is recorded on the photographic emulsion of the plate forming the hologram. Interferometric fringes can be obtained by means of double-exposure holography, where interference takes place between the wavefronts reconstructed by two holograms of the same object at different states of deformation recorded on the same plate. An incremental displacement is applied to the specimen between exposures. The interferometric fringes include all the displacement sustained between exposures, including rigid-body motions.
However, if the holographic plate is rigidly attached to one point on the specimen, the only relative displacement o f the plate with respect to the specimen is that due to straining. This method, known as 'piggyback' holography was used by Boone,' and Neumann and Penn s to reduce the stability requirements during the exposure o f holograms in an industrial environment. The plate-holder assembly is shown in Fig. 2(b). By supporting the plates kinematically (at three contact points), it could be assured that the plate positioning is reproducible. The position of the plate on the plate holder is such that when attached to the specimen, the distance between the photosensitive emulsion and the specimen (6 ram) is less than 1/2 the coherence length of the laser light. The approximate field of view using this setup was 15 x 50 ram. Figure 2(c) shows the plate-tilting mechanism. The role of this tilting device will be discussed in the following section.
Interferometric Fringes and the Plate-tilting Mechanism Assuming that the material behaves elastically, uniaxial tensile loading results in a linear-displacement field (since the elongations are measured with respect to the point of contact of the plate holder and the specimen). The fringe pattern associated with this displacement field is a series of parallel fringes which are perpendicular to the loading direction. Figure 3(a) shows such a fringe pattern. The scale of all figures shown can be determined by considering that the width of the specimen is 15 ram. Note that, due to the geometry of the optical setup, the sensitivity vector 6 changes with the position on the object resulting in variable fringe spacing for constant strain. Furthermore, both fringes and transverse microcracking are perpendicular to the displacement gradient. Since microcracks are the discontinuities in the fringe patterns, their detection becomes difficult. A plate-tilting mechanism was designed which used a 40-pitch screw acting on a lever arm with a 10:1 ratio, tilting the plate out of plane. A 180-deg rotation of the
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TABLE1--SUMMARYOF
POLYPROPYLENE FIBER COMPOSITES USED IN THE PRESENT RESEARCH Specimen
Fiber Volume (percent)
BOP (M Pa)
Ultimate Strain (percent)
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Experimental Mechanics
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screw resulted in 32-#m out of plane motion of a point on the plate 45 mm away from the bottom edge [see Fig. 2(c)]. The homogeneous rigid-body motion of the plate controls the orientation of the fringes. Figure 3(b) represents the effect of rigid-body motion on a double-exposure hologram. The fringes introduced are due to rigid-body motion. Since the plate movement is out of plane, they are inclined with respect to the loading direction (the inclination angle depends on the amount of plate movement). The combined effect of plate tilting and incremental loading on the final fringe pattern significantly facilitates the microcrack detection as discussed below (Figs. 7-15).
Experimental Program A total of six polypropylene fiber-reinforced specimens were studied. Conditions of the experimental program are given in Table 1. A series of preliminary tests was con-
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ducted to calibrate for the exposure time, incremental displacement, and plate-rotation magnitude. Based on the preliminary results, it was decided to use an incremental strain of 60 #E and 180-deg rotation of the tilting screw. This magnitude was held constant for the specimens tested in this study. Since proper seating of the specimens in the supports prior to making of a hologram is required, specimens were loaded up to approximately 80 /ze. Beginning with this point consecutive holograms were shot. The BOP occurs at approximately 300-1000/~e (depending on the fiber-volume fraction); thus a total of four to nine holograms could be obtained in the initial quasilinear response. Beyond the BOP, the holograms were taken at specified strain values (i.e., 0.3, 1 and 3 percent).
Enhancementof Hologramsby Image Analysis The reflection holograms are capable of being reconstructed under ordinary white light. This is due to the fact that the primary interference fringes are parallel to the emulsion coating. Similar to the crystal lattices in an Xray diffraction, they act as diffraction gratings and allow components of white light with wavelengths satisfying Bragg's condition to be diffracted. A 200-watt fiber-optic lamp was used as the reference beam in reconstructing the holograms. The images were then fed into a Tracer Northern image-analysis system using a slow-scan high-resolution COHU camera. A schematic arrangement for reconstruction and acquisition of the holographic images is shown in Fig. 4. The acquired image contains a range of intensities (0-255) representing different grey levels. The image is thus represented by a 512 x 512 two-dimensional array of integers, each representing the average light intensity across an elemental area, referred to as a pixel (picture element). The size of the pixel determines the spatial resolution of the image. The bright and dark components of holographic fringes can be represented as a 'binary' image, whereas the pixel intensities assume an 'ON' or 'OFF' condition. Creation of a binary image requires enhancement of the initial grey image so that the edges are sharpened and differentia-
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Fig. 3(b)--An interference hologram obtained by tilting of the plate only
tion of components can be handled in an automatic, and objective manner. Due to the inhomogeneous nature of intensity distribution, it is possible for a bright fringe at one section of the image to have a lower intensity magnitude than the dark fringes at other segments of the image. Standard methods of image analysis such as segmentation of the image from a certain pixel intensity are thus not applicable. This situation is represented by the plot of Fig. 5(a). The twodimensional variations in pixel intensities can be idealized as a one-dimensionai intensity function, I(x), where x represents the location. The points of local maxima and minima indicate bright and dark fringes respectively. Assume that the grey image is represented as IMAGE 1. By applying a smoothing filter (moving weighted average) to IMAGE 1, the contrast of the image is decreased. Smoothing results in a spatial averaging of the image and is represented by the dashed line in Fig. 5(a), or symbolically as IMAGE 2. Note that magnitude of change is negative for high-intensity, and positive for low-intensity pixels. For optimum results, the size of the smoothing filter is selected as a function of the fringe spacing. (For fringe spacing of n pixels an n • n filter should be used.) A weighted subtraction of IMAGE 2 from IMAGE 1 results in IMAGE 3 and is represented as IMAGE3 = IMAGEI-X*IMAGE2
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