- Email: [email protected]
Detection and measurement of very small interfacial gaps in GRP
Composites Science and Technology 22 (1985) 135-152
Detection and Measurement of Very Small lnterfacial Gaps in GRP
J. P. Sargent and K. H. G. Ashbee H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Tyndall Avenue, Bristol BS8 1TL (Great Britain)
SUMMARY In situ detection and measurement of gaps of molecular dimensions between fibre and matrix materials in epoxy and polyester resin composites can be achieved by examination of the manner in which light is transmitted in a direction transverse to the fibre axis. Using the phenomenon of optical tunnelling following frustrated total internal reflection, it has been possible to detect and measure gap widths down to approximately 5 nm. It has been demonstrated that the presence of absorbed water gives rise to a small (~0.3 %)permanent increase in refractive index of the matrix resin.
INTRODUCTION
The principle of fibre reinforcement requires load transfer from matrix to fibres. In resin composites it is known, from measurements of mechanical properties, that realisation of load transfer is progressively impaired during water uptake from humid in-service environments. Loss of load transfer amounts to loss of interfacial adhesion and/or loss of the mechanical contact that gives rise to interfacial friction. Physically, this implies the creation of gaps at the interface. The same phenomenon in transparent composites of the kind used for transparent roofing panels, for example, is known as fibre whitening, or fibre prominence. This is the process whereby glass fibres in glass fibre 135 Composites Science and Technology 0266-3538/85/$03.30 (~3 Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain
136
J. P. Sargent, K. H. G. Ashbee
reinforced plastics become more visible as time goes on. For aesthetic reasons, manufacturers try to match the refractive index of the plastic (polyester or epoxy resin) with that of the fibreglass. Fibre whitening is certainly associated with water uptake and has been variously attributed to each of several phenomena, including the following: (i)
Change of refractive index (#) of the matrix resin and, since ]Awater < ]Aresin,it is usually assumed that incorporation of diffused water reduces the refractive index of the matrix. (ii) Resin shrinkage onto the fibres leading to localised densification and hence to increase of refractive index on the resin immediately adjacent to the fibres. (iii) Creation of interfacial gaps at the resin/fibre interfaces. These gaps may be filled with air or water, or a mixture of air and water. (iv) Chemical etching of the fibres. Water which has diffused in from the external surface is unlikely to be pure water by the time it collects at the resin/fibre interfaces. The presence in polyester and epoxy resins of acidic and of alkaline groups is well known. So, too, is the presence of alkaline network-modifying oxides in fibreglass compositions. Dissolution by diffused water of any of these materials may well produce solutions which are sufficiently corrosive to etch fibreglass. The purpose of the present work is to establish which, if any, of the above phenomena actually contribute to fibre whitening. P R E L I M I N A R Y OBSERVATIONS Photomicrographs of glass fibre composites, known to have sustained mechanical damage or to have been subjected to weathering, frequently show fibres which exhibit a characteristic pattern of light and dark bands parallel to the fibre axis when viewed in transmitted light. In addition, close inspection of individual fibres often reveals areas of interracial contrast which in some cases are lighter and in other cases darker than elsewhere. For example, Fig. 1 is a transmission optical photomicrograph of an isolated fibre in an epoxy/glass fibre composite which has been immersed for 24 h in distilled water at 95 °C. In general, this contrast is due partly to the creation of an interfacial gap and partly to the development of a refractive index mismatch between the fibre and matrix material.
Detection and measurement o f very small interfacial gaps in GRP
137
Fig. 1. Transmission optimal photomicrograph of a debonded glass fibre in an epoxy matrix, showing regions in which the interracial gap contains both air (large dark areas) and water.
REFRACTIVE I N D E X CHANGES If there is intimate contact between fibre and resin such that there is no interfacial gap, and if there is no refractive index mismatch between fibre and resin, then the fibre will be invisible when viewed under transmitted light. Under these conditions the only way in which the fibre may be seen is when viewed between crossed polars; residual stress birefringence in either material, resulting from resin cure shrinkage and/or differential thermal contraction between fibre and matrix materials, shows up as regions of bright contrast. Figure 2 shows the pattern of stress birefringence for such a fibre photographed under crossed polars with the microscope objective focused on the plane of the fibre axis. The example shown in Fig. 2 is an epoxy/glass fibre composite. The specimen was subsequently immersed in distilled water for 2.7 h at 92 °C
Fig. 2.
Crossed polars transmission optical photomicrograph of a glass fibre in an epoxy matrix before exposure to water.
138
J. P. Sargent, K. H. G. Ashbee
and, with the microscope modified so that the specimen could be illuminated with parallel light from a laser, photomicrographs were taken with the objective lens focused in the plane of the fibre axis (Fig. 3(a)) and at a distance of 200/~m above the fibre axis (Fig. 3(b)). Images similar to those recorded in Fig. 3(a) and (b) can be generated simply by immersion of a glass fibre in immersion oils. Thus, in Fig. 4(a) and (b), we show images of a single S-glass fibre covered with drops from two oils of
Fig. 3. Transmission optical photomicrograph for the specimen shown in Fig. 2 but viewed with laser light and after 2.7 h immersion in distilled water at 92 °C. (a) Objective focused on the plane of the fibre axis; (b) objective focused 200#m above the fibre axis.
differing refractive index, and focused (a) in the plane of the fibre axis and (b) at a distance of 200 #m above the fibre axis. The refractive index of the oil differs from that of the fibre by + 0.005 on the right of the image and by - 0 . 0 0 5 on the left, a refractive index gradient existing in the oil mixture between these two regions. In the middle of the image the refractive index of the fibre and immersion oil exactly match and no fibre can be seen. Comparing Figs 3 and 4 it is evident that a small increase in refractive index of the resin due to water uptake has occurred and that this causes
Detection and measurement of very small interracial gaps in GRP
139
Fig. 4. Transmission optical photomicrograph for an isolated glass fibre immersed in immersion oils. On the left of the image the refractive index mismatch with the oil is - 0.005 and on the right the refractive index mismatch is + 0.005. (a) Objective focused on the plane of the fibre axis; (b) objective focused 200 #m above the fibre axis.
the fibre to behave as a very weak diverging lens to give a region of dark axial contrast. A decrease in resin refractive index during water uptake would have resulted in a bright axial region, i.e. behaviour expected for a weak converging lens. A noteworthy feature is that the increase of refractive index recorded here was permanent. It was not reversed by a subsequent further post-cure in air at 150 °C which removed the diffused water.
INTERFACIAL GAPS If debonding occurs and an interfacial gap is created, then focusing of the transmitted light occurs. The focused rays envelope a caustic surface, on the inside Of which the intensity of light is enhanced and on the outside of which it is zero: that is, a bright-edged shadow is created and this shadow
140
J. P. Sargent, K. H. G. Ashbee
dominates the microscope image. Figure 5 is a geometrical optics ray diagram reconstruction of the bright-edged shadow for a glass fibre embedded in resin and with a water-solution-filled gap at the interface. In a real composite the interfacial gap will, of course, be much smaller than that illustrated in Fig. 5(a). Figure 5(b) shows the corresponding wavefront diagram, computed using an optical path length of approximately 42 between wavefronts and with a wavelength (2) of 546nm. The consequence of reducing the gap size is to reduce the thickness of the shadow as demonstrated in Fig. 6(a) and (b). It should be noted that in these diagrams no allowance has been made for multiple reflections from a single surface, nor for diffraction effects. In reality, the resin/fibre interface behaves as a diffraction edge. Figures 7 and 8, respectively, are ray and wavefront diagrams computed for a composite in which air has replaced the water solution in the interfacial gap. If the interfacial gap is very small (less than ~ 2/2), internal reflection is not total; a transmitted wave appears beyond the gap. Following Feynman, 1 even though light is totally internally reflected from the resin/water solution interface, there are electric fields in the water solution which extend beyond the interface to a distance of the order of a wavelength, the amplitude of this 'transmitted' or evanescent wave dropping off exponentially with increasing distance from the interface. Thus, if another interface is sufficiently close (specifically the water solution/fibre interface in our case) the 'interfaces' in effect disappear, and some light is transmitted. This phenomenon is known as frustrated total internal reflection. Employing Feynman'sl equation: E t ---
E~ e +_k~xei(O~t-kyy)
E t = transmitted electric field vector, k~ = wave number for the transmitted w a v e , ky = component of k along the y-axis, o9 = angular frequency, and E 0 relates to the summation of two vectors, one for the incident and one for the reflected wave) light incident upon a single interface has been mathematically modelled in order to deduce the resulting transmitted light intensity. The results are shown in Fig. 9(a) and (b) for gaps filled with water solution and with air, respectively, and for interfacial gap widths of 2/2, 2/10 and 2/100 in each case. Figure 10 shows a sequence of images for a polyester/glass fibre composite which was immersed in distilled water at 95 °C. The specimen was removed periodically from the water, air dried for 10 min at 105 °C in (where
Detection and measurement o f very small interfacial gaps in GRP
141
b
Fig. 5. (a) Ray diagram reconstruction for a glass fibre embedded m resin with a water solution at the interface. Fibre diameter is 10 pm; interfacial gap is ~ ½a fibre diameter. (b) Same as (a) but showing the wavefronts. Wavefronts plotted at 4 2 optical path length intervals.
142
J. P. Sargent, K. H. G. Ashbee
/
.~"~_-i
,J
~ "
il
I
b Fig. 6. (a) Ray diagram reconstrucUon for a glass fibre embedded in resin with a water solution at the interface. Fibre diameter is 10 #m; interfacial gap is 2/2. (b) Same as (a) but showing the wavefronts. Wavefronts plotted at 42 optical path length intervals.
Detection and measurement of very small interfacial gaps in GRP
l! ! E
L
i
!i
!
,'
t
" I
i
I
Fig. 7.
i
?,5
I
55
1
S a m e as Fig. 5, but with an air gap.
143
144
J. P. Sargent, K. H. G. Ashbee
17
Fig. 8,
Same as Fig. 6, but with an air gap.
Detection and measurement of very small interfacial gaps in GRP ,~.
.....b
145
c
t,,J
O
./
..:
FIBRE
8 TRANSMITTED
[bl
108
FLUX
....--'- f - - - - - - .y-"
'0 FIBRE
0 TRANSMITTED
188 FLUX
%
Fig. 9. (a) Calculated transmitted intensity distribution across a fibre radius for parallel light incident from the left. Only one quarter of the fibre cross-section is shown, The interfacial gaps are (a) 0.52, (b) 0,1 2 and (c) 0.01 2. Interface refractive index, 1.37; fibre/resin refractive index, 1.55; one interface, parallel light. (b) The same as in (a), except that the gap contains air. Interface refractive index, 1.0; fibre/resin refractive index, 1.55; one interface, parallel light.
order to drive off the absorbed water, and examined in the microscope with the objective lens focused in the plane of the fibre axis. The fibre was at a depth of 85 #m from the nearest free surface. It is just possible to make out the fibre outline in the photograph taken before water immersion, indicating the existence of a small initial refractive index mismatch. Evidence for the gradual development of an interracial gap can be seen by inspection of the fibre end where dark bands appear and increase in both width and density. In order to reduce diffraction effects, these photographs were taken with illumination from a mercury discharge lamp and with a condenser lens so arranged as to provide a cone of light with a semi-apex angle of approximately 7 °. In order to relate the intensity distributions shown in Fig. 10 to that deduced theoretically it is necessary to take into account both the approximation due to nonparallelism of the incident light and, if it is assumed that the fibre debonds uniformly around its circumference, the presence of two interfaces.
146
J. P. Sargent, K. H. G. Ashbee
Fig. 10. Sequence of optical transmission photomicrographs for a polyester/glass fibre specimen immersed in distilled water at 92 °C after (a) 0 h, (b) 4-2 h, (c) 7.7 h and (d) 10-5 h.
Detection and measurement of very small interfacial gaps in GRP
147
0 o
0..
0
Transmitted flux (%)
100
Fig. 11. The calculated transmitted intensity distribution across a fibre radius for divergent light incident with cone angle of 14 °. The interfacial gaps are (a) 0.5 2, (b) 0.1 and (c) 0.01 )~.
This problem has been solved over one half the width of a fibre by numerical integration of the intensity contributions at the fibre midplane, for each of 100 discrete subdivisions within the angular spread of the cone of light. The resulting intensity distributions are shown in Fig. 11 for gap widths of 2/2, )~/10 and 2/100. Using microdensitometer scans taken from the upper end portion of the fibre shown in Fig. 10, and matching these to the calculated intensity distributions, gap width estimates have been obtained, amounting to 2/100, 2/10 and ~./50 after 4.2, 7.7 and 10.5 h immersion, respectively. Figures 12 and 13, respectively, show a similar development of interfacial gaps in S-glass fibre/epoxy and in Kevlar fibre/epoxy composites, during water uptake at 95 °C.
OBSERVATIONS WITH POLARISED LIGHT When the fibre is viewed between crossed polars and inclined at an angle of 45 ° to the crossed polars' directions, the regions of dark interracial contrast in Figs 10 and 12 show up bright against the dark background. This effect is shown in Fig. 14(b) for the polyester specimen from Fig. 10(b). Figure 15(b) shows the same effect for the epoxy specimen from Fig. 12(c). This is attributed to the fact that the interfacial gap imposes distinct polarisation axes (TM or TE) upon the evanescent wave. Thus, in
148
J. P. Sargent, K. H. G. Ashbee
d Fig. 12. Sequence of optical transmission photomicrographs for a glass fibre/epoxy specimen immersed in distilled water at 95 °C after (a) 0 h, (b) 377 h, (c) 519 h and (d) 844 h.
Detection and measurement of very small interfacial gaps in GRP
149
ta
C
Fig. 13. Sequence of optical transmission photomicrographs for a Kevlar fibre/epoxy specimen immersed in distilled water at 95 °C after (a) 0 h, (b) 377 h, (c) 519 h and (d) 844 h.
150
J. P. Sargent, K. H. G. Ashbee
Fig. 14. The specimen from Fig. 10 after (a) 0 h and (b) 4.2 h immersion, viewed between crossed polars showing the reorientation of polarisation axes following frustrated total internal reflection.
the absence of any reorientation of axes by stress birefringence, only that component of the light following frustrated total internal reflection (i.e. only that transmitted across gaps which are less than approximately 2/2 wide) passes through the analyser of the microscope and into the eyepiece.
G E N E R A L DISCUSSION A fundamental treatment of the bonding achieved between glass fibres and epoxy resins probably lies in the 'no man's land' between physisorption and chemisorption. In physisorption the electronic potentials between, say, an epoxy group and all molecules in a glass fibre would be integrated in order to obtain an effective potential for interaction with an approaching resin molecule. This would amount to a rather weak bond, say of the order of van der Waals forces. On the other
Detection and measurement of very small interfacial gaps in GRP
151
Fig. 15. The specimen from Fig. 12 after (a) 0 h and (b) 519 h immersion, viewedbetween crossed polars showing the reorientation of polarisation axes following frustrated total internal reflection.
hand, in chemisorption, the electronic potential between an epoxy group and a single molecule in the fibreglass surface would be considered and this would lead to identification of a strong bond such as a covalent bond. The nature of the interface is even more difficult to define when polar functional groups, such as silanol groups on the surfaces of u n b o n d e d glass or dipoles on the surface of interracial water, are present. Any attempt at calculating any potential fields for the interface will require sound knowledge of the thickness of air-filled and water-filled gaps. In the case of water, for example, the H - O - H b o n d angle is very close to the tetrahedral bond angle, 103 °-106 ° compared with 109 °, one consequence of which is that water molecules are expected to assemble into silica-like structures. 2 An interracial gap of 5 nm could accommodate of the order of l0 such corner-sharing tetrahedra.
152
J. P. Sargent, K. H. G. Ashbee
CONCLUSIONS 1. Using a transmission optical polarising microscope equipped with rectified optics, it is possible to observe the development of physical gaps as small as 5 nm at interfaces between matrix and fibres in glass fibre reinforced epoxy resins. 2. By comparing the intensity distributions of the observed contrast with that predicted from calculations, it is possible to distinguish between areas which are air-filled and areas which are water-filled. 3. The initial water uptake by epoxy resin composites is accompanied by a 0.3 ~ increase in the refractive index of the resin. 4. These two phenomena, creation of very small interfacial gaps and development of a mismatch between the refractive indices of the resin and fibre materials, are held responsible for the deterioration in visual appearance of G R P that is commonly referred to as fibre whitening.
ACKNOWLEDGEMENTS The authors gratefully acknowledge Dr C. Upstill for some helpful discussions. They are also grateful to the US Army for providing financial assistance (Grant No. DAJA45-83-C-0030).
REFERENCES 1. R. P. Feynman, R. B. Leighton and M. Sands, The Fevnman Lectures on Physics, Vol. 2, Addison-Wesley, Reading, Mass., 1964, p. 33-12. 2. J. D. Bernal and R. H. Fowler, J. Chem. Phys., 8 (1933) p. 515.
Detection and Measurement of Very Small lnterfacial Gaps in GRP
J. P. Sargent and K. H. G. Ashbee H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Tyndall Avenue, Bristol BS8 1TL (Great Britain)
SUMMARY In situ detection and measurement of gaps of molecular dimensions between fibre and matrix materials in epoxy and polyester resin composites can be achieved by examination of the manner in which light is transmitted in a direction transverse to the fibre axis. Using the phenomenon of optical tunnelling following frustrated total internal reflection, it has been possible to detect and measure gap widths down to approximately 5 nm. It has been demonstrated that the presence of absorbed water gives rise to a small (~0.3 %)permanent increase in refractive index of the matrix resin.
INTRODUCTION
The principle of fibre reinforcement requires load transfer from matrix to fibres. In resin composites it is known, from measurements of mechanical properties, that realisation of load transfer is progressively impaired during water uptake from humid in-service environments. Loss of load transfer amounts to loss of interfacial adhesion and/or loss of the mechanical contact that gives rise to interfacial friction. Physically, this implies the creation of gaps at the interface. The same phenomenon in transparent composites of the kind used for transparent roofing panels, for example, is known as fibre whitening, or fibre prominence. This is the process whereby glass fibres in glass fibre 135 Composites Science and Technology 0266-3538/85/$03.30 (~3 Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain
136
J. P. Sargent, K. H. G. Ashbee
reinforced plastics become more visible as time goes on. For aesthetic reasons, manufacturers try to match the refractive index of the plastic (polyester or epoxy resin) with that of the fibreglass. Fibre whitening is certainly associated with water uptake and has been variously attributed to each of several phenomena, including the following: (i)
Change of refractive index (#) of the matrix resin and, since ]Awater < ]Aresin,it is usually assumed that incorporation of diffused water reduces the refractive index of the matrix. (ii) Resin shrinkage onto the fibres leading to localised densification and hence to increase of refractive index on the resin immediately adjacent to the fibres. (iii) Creation of interfacial gaps at the resin/fibre interfaces. These gaps may be filled with air or water, or a mixture of air and water. (iv) Chemical etching of the fibres. Water which has diffused in from the external surface is unlikely to be pure water by the time it collects at the resin/fibre interfaces. The presence in polyester and epoxy resins of acidic and of alkaline groups is well known. So, too, is the presence of alkaline network-modifying oxides in fibreglass compositions. Dissolution by diffused water of any of these materials may well produce solutions which are sufficiently corrosive to etch fibreglass. The purpose of the present work is to establish which, if any, of the above phenomena actually contribute to fibre whitening. P R E L I M I N A R Y OBSERVATIONS Photomicrographs of glass fibre composites, known to have sustained mechanical damage or to have been subjected to weathering, frequently show fibres which exhibit a characteristic pattern of light and dark bands parallel to the fibre axis when viewed in transmitted light. In addition, close inspection of individual fibres often reveals areas of interracial contrast which in some cases are lighter and in other cases darker than elsewhere. For example, Fig. 1 is a transmission optical photomicrograph of an isolated fibre in an epoxy/glass fibre composite which has been immersed for 24 h in distilled water at 95 °C. In general, this contrast is due partly to the creation of an interfacial gap and partly to the development of a refractive index mismatch between the fibre and matrix material.
Detection and measurement o f very small interfacial gaps in GRP
137
Fig. 1. Transmission optimal photomicrograph of a debonded glass fibre in an epoxy matrix, showing regions in which the interracial gap contains both air (large dark areas) and water.
REFRACTIVE I N D E X CHANGES If there is intimate contact between fibre and resin such that there is no interfacial gap, and if there is no refractive index mismatch between fibre and resin, then the fibre will be invisible when viewed under transmitted light. Under these conditions the only way in which the fibre may be seen is when viewed between crossed polars; residual stress birefringence in either material, resulting from resin cure shrinkage and/or differential thermal contraction between fibre and matrix materials, shows up as regions of bright contrast. Figure 2 shows the pattern of stress birefringence for such a fibre photographed under crossed polars with the microscope objective focused on the plane of the fibre axis. The example shown in Fig. 2 is an epoxy/glass fibre composite. The specimen was subsequently immersed in distilled water for 2.7 h at 92 °C
Fig. 2.
Crossed polars transmission optical photomicrograph of a glass fibre in an epoxy matrix before exposure to water.
138
J. P. Sargent, K. H. G. Ashbee
and, with the microscope modified so that the specimen could be illuminated with parallel light from a laser, photomicrographs were taken with the objective lens focused in the plane of the fibre axis (Fig. 3(a)) and at a distance of 200/~m above the fibre axis (Fig. 3(b)). Images similar to those recorded in Fig. 3(a) and (b) can be generated simply by immersion of a glass fibre in immersion oils. Thus, in Fig. 4(a) and (b), we show images of a single S-glass fibre covered with drops from two oils of
Fig. 3. Transmission optical photomicrograph for the specimen shown in Fig. 2 but viewed with laser light and after 2.7 h immersion in distilled water at 92 °C. (a) Objective focused on the plane of the fibre axis; (b) objective focused 200#m above the fibre axis.
differing refractive index, and focused (a) in the plane of the fibre axis and (b) at a distance of 200 #m above the fibre axis. The refractive index of the oil differs from that of the fibre by + 0.005 on the right of the image and by - 0 . 0 0 5 on the left, a refractive index gradient existing in the oil mixture between these two regions. In the middle of the image the refractive index of the fibre and immersion oil exactly match and no fibre can be seen. Comparing Figs 3 and 4 it is evident that a small increase in refractive index of the resin due to water uptake has occurred and that this causes
Detection and measurement of very small interracial gaps in GRP
139
Fig. 4. Transmission optical photomicrograph for an isolated glass fibre immersed in immersion oils. On the left of the image the refractive index mismatch with the oil is - 0.005 and on the right the refractive index mismatch is + 0.005. (a) Objective focused on the plane of the fibre axis; (b) objective focused 200 #m above the fibre axis.
the fibre to behave as a very weak diverging lens to give a region of dark axial contrast. A decrease in resin refractive index during water uptake would have resulted in a bright axial region, i.e. behaviour expected for a weak converging lens. A noteworthy feature is that the increase of refractive index recorded here was permanent. It was not reversed by a subsequent further post-cure in air at 150 °C which removed the diffused water.
INTERFACIAL GAPS If debonding occurs and an interfacial gap is created, then focusing of the transmitted light occurs. The focused rays envelope a caustic surface, on the inside Of which the intensity of light is enhanced and on the outside of which it is zero: that is, a bright-edged shadow is created and this shadow
140
J. P. Sargent, K. H. G. Ashbee
dominates the microscope image. Figure 5 is a geometrical optics ray diagram reconstruction of the bright-edged shadow for a glass fibre embedded in resin and with a water-solution-filled gap at the interface. In a real composite the interfacial gap will, of course, be much smaller than that illustrated in Fig. 5(a). Figure 5(b) shows the corresponding wavefront diagram, computed using an optical path length of approximately 42 between wavefronts and with a wavelength (2) of 546nm. The consequence of reducing the gap size is to reduce the thickness of the shadow as demonstrated in Fig. 6(a) and (b). It should be noted that in these diagrams no allowance has been made for multiple reflections from a single surface, nor for diffraction effects. In reality, the resin/fibre interface behaves as a diffraction edge. Figures 7 and 8, respectively, are ray and wavefront diagrams computed for a composite in which air has replaced the water solution in the interfacial gap. If the interfacial gap is very small (less than ~ 2/2), internal reflection is not total; a transmitted wave appears beyond the gap. Following Feynman, 1 even though light is totally internally reflected from the resin/water solution interface, there are electric fields in the water solution which extend beyond the interface to a distance of the order of a wavelength, the amplitude of this 'transmitted' or evanescent wave dropping off exponentially with increasing distance from the interface. Thus, if another interface is sufficiently close (specifically the water solution/fibre interface in our case) the 'interfaces' in effect disappear, and some light is transmitted. This phenomenon is known as frustrated total internal reflection. Employing Feynman'sl equation: E t ---
E~ e +_k~xei(O~t-kyy)
E t = transmitted electric field vector, k~ = wave number for the transmitted w a v e , ky = component of k along the y-axis, o9 = angular frequency, and E 0 relates to the summation of two vectors, one for the incident and one for the reflected wave) light incident upon a single interface has been mathematically modelled in order to deduce the resulting transmitted light intensity. The results are shown in Fig. 9(a) and (b) for gaps filled with water solution and with air, respectively, and for interfacial gap widths of 2/2, 2/10 and 2/100 in each case. Figure 10 shows a sequence of images for a polyester/glass fibre composite which was immersed in distilled water at 95 °C. The specimen was removed periodically from the water, air dried for 10 min at 105 °C in (where
Detection and measurement o f very small interfacial gaps in GRP
141
b
Fig. 5. (a) Ray diagram reconstruction for a glass fibre embedded m resin with a water solution at the interface. Fibre diameter is 10 pm; interfacial gap is ~ ½a fibre diameter. (b) Same as (a) but showing the wavefronts. Wavefronts plotted at 4 2 optical path length intervals.
142
J. P. Sargent, K. H. G. Ashbee
/
.~"~_-i
,J
~ "
il
I
b Fig. 6. (a) Ray diagram reconstrucUon for a glass fibre embedded in resin with a water solution at the interface. Fibre diameter is 10 #m; interfacial gap is 2/2. (b) Same as (a) but showing the wavefronts. Wavefronts plotted at 42 optical path length intervals.
Detection and measurement of very small interfacial gaps in GRP
l! ! E
L
i
!i
!
,'
t
" I
i
I
Fig. 7.
i
?,5
I
55
1
S a m e as Fig. 5, but with an air gap.
143
144
J. P. Sargent, K. H. G. Ashbee
17
Fig. 8,
Same as Fig. 6, but with an air gap.
Detection and measurement of very small interfacial gaps in GRP ,~.
.....b
145
c
t,,J
O
./
..:
FIBRE
8 TRANSMITTED
[bl
108
FLUX
....--'- f - - - - - - .y-"
'0 FIBRE
0 TRANSMITTED
188 FLUX
%
Fig. 9. (a) Calculated transmitted intensity distribution across a fibre radius for parallel light incident from the left. Only one quarter of the fibre cross-section is shown, The interfacial gaps are (a) 0.52, (b) 0,1 2 and (c) 0.01 2. Interface refractive index, 1.37; fibre/resin refractive index, 1.55; one interface, parallel light. (b) The same as in (a), except that the gap contains air. Interface refractive index, 1.0; fibre/resin refractive index, 1.55; one interface, parallel light.
order to drive off the absorbed water, and examined in the microscope with the objective lens focused in the plane of the fibre axis. The fibre was at a depth of 85 #m from the nearest free surface. It is just possible to make out the fibre outline in the photograph taken before water immersion, indicating the existence of a small initial refractive index mismatch. Evidence for the gradual development of an interracial gap can be seen by inspection of the fibre end where dark bands appear and increase in both width and density. In order to reduce diffraction effects, these photographs were taken with illumination from a mercury discharge lamp and with a condenser lens so arranged as to provide a cone of light with a semi-apex angle of approximately 7 °. In order to relate the intensity distributions shown in Fig. 10 to that deduced theoretically it is necessary to take into account both the approximation due to nonparallelism of the incident light and, if it is assumed that the fibre debonds uniformly around its circumference, the presence of two interfaces.
146
J. P. Sargent, K. H. G. Ashbee
Fig. 10. Sequence of optical transmission photomicrographs for a polyester/glass fibre specimen immersed in distilled water at 92 °C after (a) 0 h, (b) 4-2 h, (c) 7.7 h and (d) 10-5 h.
Detection and measurement of very small interfacial gaps in GRP
147
0 o
0..
0
Transmitted flux (%)
100
Fig. 11. The calculated transmitted intensity distribution across a fibre radius for divergent light incident with cone angle of 14 °. The interfacial gaps are (a) 0.5 2, (b) 0.1 and (c) 0.01 )~.
This problem has been solved over one half the width of a fibre by numerical integration of the intensity contributions at the fibre midplane, for each of 100 discrete subdivisions within the angular spread of the cone of light. The resulting intensity distributions are shown in Fig. 11 for gap widths of 2/2, )~/10 and 2/100. Using microdensitometer scans taken from the upper end portion of the fibre shown in Fig. 10, and matching these to the calculated intensity distributions, gap width estimates have been obtained, amounting to 2/100, 2/10 and ~./50 after 4.2, 7.7 and 10.5 h immersion, respectively. Figures 12 and 13, respectively, show a similar development of interfacial gaps in S-glass fibre/epoxy and in Kevlar fibre/epoxy composites, during water uptake at 95 °C.
OBSERVATIONS WITH POLARISED LIGHT When the fibre is viewed between crossed polars and inclined at an angle of 45 ° to the crossed polars' directions, the regions of dark interracial contrast in Figs 10 and 12 show up bright against the dark background. This effect is shown in Fig. 14(b) for the polyester specimen from Fig. 10(b). Figure 15(b) shows the same effect for the epoxy specimen from Fig. 12(c). This is attributed to the fact that the interfacial gap imposes distinct polarisation axes (TM or TE) upon the evanescent wave. Thus, in
148
J. P. Sargent, K. H. G. Ashbee
d Fig. 12. Sequence of optical transmission photomicrographs for a glass fibre/epoxy specimen immersed in distilled water at 95 °C after (a) 0 h, (b) 377 h, (c) 519 h and (d) 844 h.
Detection and measurement of very small interfacial gaps in GRP
149
ta
C
Fig. 13. Sequence of optical transmission photomicrographs for a Kevlar fibre/epoxy specimen immersed in distilled water at 95 °C after (a) 0 h, (b) 377 h, (c) 519 h and (d) 844 h.
150
J. P. Sargent, K. H. G. Ashbee
Fig. 14. The specimen from Fig. 10 after (a) 0 h and (b) 4.2 h immersion, viewed between crossed polars showing the reorientation of polarisation axes following frustrated total internal reflection.
the absence of any reorientation of axes by stress birefringence, only that component of the light following frustrated total internal reflection (i.e. only that transmitted across gaps which are less than approximately 2/2 wide) passes through the analyser of the microscope and into the eyepiece.
G E N E R A L DISCUSSION A fundamental treatment of the bonding achieved between glass fibres and epoxy resins probably lies in the 'no man's land' between physisorption and chemisorption. In physisorption the electronic potentials between, say, an epoxy group and all molecules in a glass fibre would be integrated in order to obtain an effective potential for interaction with an approaching resin molecule. This would amount to a rather weak bond, say of the order of van der Waals forces. On the other
Detection and measurement of very small interfacial gaps in GRP
151
Fig. 15. The specimen from Fig. 12 after (a) 0 h and (b) 519 h immersion, viewedbetween crossed polars showing the reorientation of polarisation axes following frustrated total internal reflection.
hand, in chemisorption, the electronic potential between an epoxy group and a single molecule in the fibreglass surface would be considered and this would lead to identification of a strong bond such as a covalent bond. The nature of the interface is even more difficult to define when polar functional groups, such as silanol groups on the surfaces of u n b o n d e d glass or dipoles on the surface of interracial water, are present. Any attempt at calculating any potential fields for the interface will require sound knowledge of the thickness of air-filled and water-filled gaps. In the case of water, for example, the H - O - H b o n d angle is very close to the tetrahedral bond angle, 103 °-106 ° compared with 109 °, one consequence of which is that water molecules are expected to assemble into silica-like structures. 2 An interracial gap of 5 nm could accommodate of the order of l0 such corner-sharing tetrahedra.
152
J. P. Sargent, K. H. G. Ashbee
CONCLUSIONS 1. Using a transmission optical polarising microscope equipped with rectified optics, it is possible to observe the development of physical gaps as small as 5 nm at interfaces between matrix and fibres in glass fibre reinforced epoxy resins. 2. By comparing the intensity distributions of the observed contrast with that predicted from calculations, it is possible to distinguish between areas which are air-filled and areas which are water-filled. 3. The initial water uptake by epoxy resin composites is accompanied by a 0.3 ~ increase in the refractive index of the resin. 4. These two phenomena, creation of very small interfacial gaps and development of a mismatch between the refractive indices of the resin and fibre materials, are held responsible for the deterioration in visual appearance of G R P that is commonly referred to as fibre whitening.
ACKNOWLEDGEMENTS The authors gratefully acknowledge Dr C. Upstill for some helpful discussions. They are also grateful to the US Army for providing financial assistance (Grant No. DAJA45-83-C-0030).
REFERENCES 1. R. P. Feynman, R. B. Leighton and M. Sands, The Fevnman Lectures on Physics, Vol. 2, Addison-Wesley, Reading, Mass., 1964, p. 33-12. 2. J. D. Bernal and R. H. Fowler, J. Chem. Phys., 8 (1933) p. 515.