K. M. Entwistle

Review: Current international research into cellulosic fibres and composites

The following paper summarises a number of international research projects being undertaken to understand the mechanical properties of natural cellulose fibres and composite materials. In particular the use of novel techniques, such as Raman spectroscopy, synchrotron x-ray and half-fringe photoelastic methods of measuring the physical and micromechanical properties of cellulose fibres is reported. Current single fibre testing procedures are also reviewed with emphasis on the end-use in papermaking. The techniques involved in chemically modifying fibres to improve interfacial adhesion in composites are also reviewed, and the use of novel fibre sources such as bacterial and animal cellulose. It is found that there is overlap in current international research into this area, and that there are complementary approaches and therefore further combining of these may make further progress possible. In particular a need to measure locally the adhesion properties and deformation processes of fibres in composites, with different chemical treatments, ought to be a focus of future research.

The fracture stress of float glass

A fracture test [1] which uses concentrically loaded square plates supported near their corners has been used to measure the fracture stress of float glass. The plates were 102mm square and 5.98mm thick. The maximum displacement at fracture was less than 0.4mm. Under these circumstances it has been shown that use of a linear finite element solution for the stress distribution and the plate deflections is justified. The glass plates had greater edge damage than had the alumina plates tested in an earlier investigation. In order to secure an adequate proportion of failures in the central plate region, it was necessary to move the supports inwards towards the centre of the plate. This reduced the ratio of the maximum edge stress to the maximum stress in the plate. Batches of plates were tested with loading circle diameters of 7.5 and 25mm, to measure volume effects, with the side of the plate that had been in contact with the liquid tin in tension. Median ranking was used in the statistical analysis and edge failures were treated as suspensions, it being assumed that the minimum fracture stress of the central region of the edge-fractured plates was the plate centre stress at the fracture load. The Weibull modulus was determined by a linear regression in which extreme members of the population were given reduced weighting using the relationship of Faucher and Tyson [3]. The average fracture stresses were 147.2 and 107.3 N mm−2 for the 7.5 and 25 mm loading circles, respectively, and the Weibull moduli were 4.49 and 5.44. These data are shown to agree well with Weibull statistics. Tests using a 7.5 mm diameter loading circle on plates with the non-tin side in tension gave a significantly higher average fracture stress of 242.1 N mm−2, confirming the fact that the non-tin side has a higher strength.

The derivation of the cellulose microfibril angle by small-angle X-ray scattering from structurally characterized softwood cell-wall populations

A method is presented for the measurement, using small-angle X-ray scattering (SAXS), of the microfibril angle and the associated standard deviation for the cellulose microfibrils in the S2 layer of the cell walls of softwood specimens. The length and orientation of over 1000 cell walls in the irradiated volume of the specimen are measured using quantitative image analysis. From these data are calculated the azimuthal variation of the scattered intensity. The calculated values are compared with the measured values. The undetermined parameters in the analysis are the microfibril angle (M) and the standard deviation (σΦ) of the intensity distribution arising from the wandering of the fibril orientation about the mean value. The two parameters are varied to give the best fit between the calculated and the measured values. Six separate pairs of values are determined for six different values of the angle of incidence of the X-ray beam relative to the normal to the radial direction in the specimen. The results show good agreement. The azimuthal distribution of scattered intensity for the real cell-wall structure is compared with that calculated for an assembly of rectangular cells with the same ratio of transverse to radial cell-wall lengths. Despite the existence of marked differences in the intensity distributions around the zero azimuth angle, the position of the extreme flanks of the distribution is very close for the real and the rectangular cells. This means that useful values of the microfibril angle can be obtained from the curve for the real cells using the Meylan parameter T derived by drawing tangents to the flanks of the intensity distribution and using M = kT. The value of k is M/(M + 2σΦ). Since both of these parameters are determined in the work now described, k is also determined. It is also demonstrated that for β = 45° (where β is the angle between the plane face of the wood specimens and the radial direction) the peaks in the azimuthal intensity distribution for the real and the rectangular cells coincide. If this peak position is Φ45, then the microfibril angle can be determined from the relation M = tan−1(tanΦ45/cos45°), which is precise for rectangular cells.

The measurement of the micro-fibril angle in soft-wood

The paper explores the measurement, using X-rays, of the micro-fibril angle of the cellulose fibres in the S2 layers of the cell walls of soft-wood, particularly pinus radiata. It is demonstrated that unambiguous values of the micro-fibril angle can be obtained from small angle X-ray scattering patterns if the X-ray beam is directed at 45 degrees to both sets of cell walls, with the cell axes vertical. The theory of the method is presented and justified. Examples of the measurement of the micro-fibril angle in pinus radiata specimens are given. It is demonstrated that the scattering patterns obtained with the X-ray beam directed normal to one set of cell walls are not capable of yielding micro-fibril angle values. The wide-angle diffraction pattern from the (002) planes with the X-ray beam equally inclined to both sets of cell walls has been analysed. The analysis has been justified experimentally and it is shown that the S2 fibres give rise to eight intensity maxima round the (002) circle and that the azimuthal angles can be related to the micro-fibril angle. It has not been possible to resolve the eight peaks. Wide-angle diffraction patterns revealed four peaks, each comprising two merged adjacent peaks. The azimuth angle at the centre of each of the four peaks is the average of those for the two constituent peaks. It is demonstrated that values of the micro-fibril angle can be obtained from this average azimuth angle.

X-ray diffraction from cellulose micro-fibrils in the S2 layers of structurally characterised softwood specimens

A previous paper (K. M. Entwistle and N. J. Terrill, J. Mater. Sci35 (2000) 1675) reported measurements of the micro-fibril angle of the cellulose fibres in the S2 layers in softwood. The method involved irradiating a specimen with X-rays directed at 45° to the radial and to the transverse direction. The determination of the micro-fibril angle from the distribution of intensity round the (002) diffraction circle assumed an idealised structure in which all the cell walls were oriented precisely in either the radial or the transverse direction. The real cell structure diverges significantly from this ideal. The error involved in assuming the ideal structure has been assessed by making a quantitative image analysis of the length and orientations of the cell walls in a section of the specimen comparable in cross-section to that irradiated by the X-rays. The position of the S2 intensity peaks round the (002) diffraction circle has been calculated and compared with those predicted from the idealised structure. It is demonstrated that the error involved in extracting a value for the micro-fibril angle from the measured intensities using the assumed ideal cell structure of the previous paper (cited above) is not more than one degree in the range of micro-fibril angles 20°–30°. So the approximate analysis is adequate for many purposes.

The fracture of concentrically loaded square ceramic plates

A testing system is described which measures the fracture stress of square plates. The loading is concentric and the plate is simply supported at the corners. The effective stressed volume can conveniently be changed by varying the diameter of the loading circle. The test is used to measure the fracture characteristics of square alumina plates 103 mm square and 1 mm thick. The displacement of the centre of the plate at fracture is about 3 mm, so the elastic system is geometrically non-linear. A non-linear finite element analysis using the ABAQUS program gave a stress distribution that was found to be in very good agreement with measured stress. The finite element solution was used to calculate stress-volume and stress-area integrals, which are tabulated, and these give the effective volumes and areas, for loading circles of 25 and 7.5 mm diameter. Two batches of plates were fractured, one with a loading circle of 25 mm diameter and the other 7.5 mm. Weibull plots were made assuming zero threshold stress. The first plots used the maximum tensile stress in the plate derived from the measured load using the finite element solution. This stress occurs at the intersection of the plate diagonal with the loading circle. Different values ofm (19.58 and 15.48) were given for the two loading circle diameters. Plots based on the stress determined at the fracture origin gave nearly identical values ofm (13.92 and 13.72). Weibull statistics and the values of the stress-volume or the stress-area integrals were used to predict the ratio of the average fracture stress for the two loading circle diameters. The predictions showed good agreement with the measured values. The stress-area integrals, which are simpler to calculate, gave almost as good predictions as did the stress-volume integrals.

Small-angle X-ray scattering from cellulose micro-fibrils in the S2 layers of structurally characterised softwood specimens

AbstractA method was reported in a previous paper (Entwistle and Terrill, J. Mater. Sci.35 (2000) 1675) for the measurement of the micro-fibril angle in the S2 layers of softwood. The small-angle X-ray scattering pattern was recorded with the beam directed at 45° to the radial direction in the cell structure. A cruciform scattering pattern was produced and the micro-fibril angle was deduced from the angle between the arms of the cross. The analysis assumed that all the cell walls lay in either the radial or the tangential direction. Real cell structures do not conform to this ideal. The objective of the work now presented was to calculate the error in the deduced value of the micro-fibril angle arising from the assumption that the specimen cell walls all lie in either the radial or in the tangential direction. To this end, the length and orientation of over 1000 cell walls was measured on two specimens using an image analyser. From these data the azimuth angle at the peak of the scattered intensity was calculated as a function of the micro-fibril angle and the standard deviation of the spread of intensity. The true micro-fibril angle was determined by comparing these data with the measured azimuth angle at the peak intensity. A value for the micro-fibril angle was also calculated from the measured value of the azimuth angle at the peak intensity using the relation for a square-section cell structure

Interfacial effects in the flow-bead test for vitreous enamels

M = Atan(\surd 2^ * tan\phi ).