The single-fibre pull-out test. 1: Review and interpretation

Composites: Part A 27A (1996) 591-612 Copyright 0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 1359-835X/96/$15.00

ELSEVIER

The single-fibre pull-out test. 1: Review and interpretation

C6lene Loctite

Di Francis” Corporation,

and Thomas

1001 Trout Brook Crossing, Rocky Hill, CT 06067-3910,

USA

C. Ward

Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, VA 2406 I- 02 12, USA

and Richard

0. Claus

Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0117, USA (Received 30. January 1995; revised 17 November 1995)

For the first time, the load versus extension trace generated by the single-fibre pull-out test is thoroughly interpreted and mathematically modelled. The single-fibre pull-out test is employed experimentally to model the failure of fibre-reinforced composite materials. The interpretation of this model, however, varies between laboratories. In this paper, the test methodologies and the experimental and mathematical interpretations of various scientists are presented and discussed, as is some preliminary work employing optical fibres embedded in various neat resins. Also, a more complete description of the experimental events is presented and described mathematically via the critical strain energy release rate for crack initiation and propagation, the interfacial shear stress of the bond and the coefficient of friction. Copyright ((i 1996 Elsevier Science Limited (Keywords: single-fibre pull-out test; load-extension

trace; review; interpretation)

INTRODUCTION Research in the area of fibre pull-out has considered the fracture mechanics and shear stresses of fibre-matrix failure’- 74. Various mechanistic models for the initiation of crack propagation between fibre and resin, as well as the continuation of this crack with the frictional dissipation of energy, have been presented. Since the late 1950s and early 1960s embedding and removing a single fibre or filament from neat resin has been used to model the failure of a composite material14. More specifically, this model has been implemented to compare various fibre surface treatments and embedding matrices. As research progressed, the interpretation of data evolved with the development of models through the shear lag hypothesis as applied by Greszczuk6 and interfacial fracture energy as applied by Outwater and Murphy’. *To whom corresondence

should

be addressed

Various fibre/resin combinations and many sample configurations have been used in the single-fibre models. ‘Fibres’ of interest have included metal ro&3,8.1

l-lS,27.35,37.40,,ar~on~~aments9,25,30,4l.49,54-56,6l,62,

glass fibres 4 17,20-22,25,26.34.38.41,42.51,53.59.62.68 and polymer fibres such as Kevlar26’41342,4”.57 and ultra-high density polyethylene6’. These fibres were embedded in matrices of concrete14’15’35 epoxy 8.9.11 - 14.17.20.21.25--27.37.38.40-42. 46.49,51.54-57,59,61,67.68’ polycarbonate’ 3, poly(butylene terepthalate)34, polyethylene4>21, and polyesterg3’t, to name a few. Specimens for the single-fibre pull-out test have taken the form of droplets3434’,“3,cylinders13’27337, ,,~oCks10,25.30,42,67 , or thick films situated at the end of the fibre35.55,68,pastilles at each end of the fibre’ and fibres completely embedded in a block of resin 14,51.59 . The interpretation of the load versus displacement trace for the single-fibre pull-out experiment has changed with the understanding of the failure events. Historically, the interpretation of the microdrop results was inaccurate due to the inability to monitor the debonding

597

The single-fibre pull-out

test. 1: C. DiFrancia et al.

process visually coupled with the inability to resolve the debonding events instrumentally”. A recent observation was made regarding the actual onset of the interfacial crack between fibre and resin of small-scale specimens: it was noted that initiation did not necessarily correspond to the maximum in the load versus extension trace”. To address the interpretation of this load-displacement trace, classic work by Kelly’, Takaku and Arridge” and Bowling and GrovesI has been extensively discussed72. Regarding the interpretation of single-fibre pull-out test results via the fracture energy approach, the reader is referred to the work of Morrison et a1.35, Jiang and Penn67 and Gao et a1.33.Also, regarding the interpretation of single-fibre pull-out test results via the shear lag avenue, the reader is referred to the work of Greszczuk6, and those researchers implementing the Greszczuk model. The characterization of the failure mechanism for the single-fibre pull-out test has been discussed by many researchers. Early work primarily consisted of reporting the experimentally observed maximum load. Later, research efforts incorporated the propagation of the interfacial fibre/resin crack and some pull-out parameters. Finally, a fracture mechanics approach to modelling the experimental results was employed. The difficulties, acknowledged by all researchers in the field, include the experimental handling of samples and/or the ability to observe the failure events instrumentally or visually with sufficient detail. The present paper gives a more complete description of the failure events for the single-fibre pull-out test. Included in this effort are not only the visual observation of crack propagation via birefringence patterns, but also the characterization of various physical events during failure. A theoretical load versus extensions trace was generated as a consequence of this research effort. This trace is supported with a significant amount of experimental data, as presented here and in the second paper in this series”. Values for the critical strain energy release rate as well as the strain energy release rate for crack propagation have been determined. The data were also quantified in terms of the interfacial shear stress of the bond, the debonded fibre and the sliding fibre. The coefficient of friction was also calculated. The details of the research and the complete interpretation of the load versus extension trace are addressed here.

THE SINGLE-FIBRE

PULL-OUT

TEST

Early observations of the single-jibre pull-out test One of the earliest descriptions of the single-fibre pullout test, which detailed the initial debonding, crack propagation, completion and fibre pull-out, was given by Kelly in 19708. It was recognised that if the embedded length of the fibre was greater than the length of catastrophic interfacial failure, complete debonding would not occur at once. This same type of load versus displacement curve was also reported by Takaku and Arridge in 197911. In their

598

interpretation of the load-extension trace they stated that the peak of the maximum load correlated to ‘the wire debond[ing] along the full embedded length from the matrix, i.e. crack initiation through to failure’. They did not, however, account for the time required for the debonding to occur and the initiation and steady-state or completion loads were not separated. Although early observations of the single-fibre pullout test included the onset of crack initiation as well as the propagation of this crack along the length of the interface, quantitative distinctions between the events were not made. Instead, the maximum load the system was able to withstand was used as the basis of comparison between sample sets. As efforts progressed, however, more details were recognised and more appropriate experimental interpretations presented. Incorporation of crack propagation in the evaluation of the single-jibre pull-out test In 1979, Bowling and Groves published a paper describing the pull-out of ductile wires from a brittle matrix14. In this paper, various events of crack propagation were presented and the role of fibre diameter and embedded length addressed. An excellent schematic representation of debonding and pull-out was presented. An important feature of their model is that, behind the crack front, the shear stress translates across the debonded region of the interface. Here, at sufficiently large crack lengths or debond values, the debonding stress exceeded the yield stress of the wire at which time the plastic radial contraction of the wire reduced the interfacial shear stress to zero. From this point until the end of the fibre was reached, the debonding front continued to propagate with a constant stress on the wire, i.e. with no additional frictional contribution to energy dissipation. As was observed with the data to be presented, Bowling and Groves found that pull-out generally occurred from one side only of the crack such that the pull-out process was a withdrawal of a ‘plug’ at one end of the wire. The length of this plug was the same as the length at the end of the wire in contact with the matrix at the moment of final debonding. Since the shear stress supported by the bonded fibre typically exceeded the shear stress transmitted after debonding, a load drop occurred at the commencement of pull-out. The pull-out load remained constant until the beginning of the plug reached the crack surface. The debonding plateau was, therefore, followed by a pull-out plateau. In their paper, the debonding plateau was fairly constant. Their comparisons and analysis were done using this debonding stress valuer4. Change offibre diameter with tensile load The issues to be addressed on the interpretation of the length of the plug during debonding and during pull-out are numerous. In the case of a ductile wire, Bowling and Groves depict the loaded wire as consisting of yielded

The single-fibre

and unyielded regions. The plugs at the ends of the wire corresponded to the unyielded zone and the inner length between the two plugs was the yielded zone14. For this material, the yielded wire diameter associated with debond completion did not recover when the load drop occurred. Instead, the diameter of the plug, i.e. the diameter of the embedded wire, and the diameter of the yielded length remained essentially the same as when the debonding process reached completion. In cases where the wire/fibre is not ductile, however, the profile of the fibre diameter is determined by the Poisson’s contraction of that fibre under a given load and is reversible. For the fibre with reversible radial contraction, the analogy of a plug at the end of the fibre still applies. However, the profile of the shear stress or interfacial friction cannot be assumed constant. This is because under a particular load, larger than that required to form a high frictional region or plug, the friction between the debonded fibre and matrix will be greatest behind the debond front and decrease continuously along the length. For a bi-directional fracture, the diameter profile will mirror itself with a high frictional zone behind each debond front which decreases symmetrically to the centre of the debond region. The total high friction plug length was defined as equivalent to half the total unyielded and debonded length of wire. Again, between these two high-friction or primary frictional zones was a length of fibre whose diameter, due to either yielding or Poisson’s contraction resulting from the load, was sufficiently decreased as to not contribute to the frictional dissipation of energy. For the non-ductile system, however, these values are not the same at debonding and pull-out. As will be discussed in the next section, the load on the fibre during pull-out (although dependent on fibre, resin and thermal history) is not the same as the load on the fibre during debonding. Thus, the resulting Poisson’s contraction along the length of the fibre typically resulted in a shorter primary frictional zone during the debonding process than the primary frictional zone during pull-out. Note that, if the elastic constants of the fibre are such that no radial contraction occurs over the load required to debond, then the entire length of fibre would contribute equally to interfacial friction. Fracture mechunics of the single-jibre pull-out test

Many theoretical models regarding the pull-out of fibres from a brittle matrix are in the literature (refs 7,10,17,24,44,50,52,62,69). These models are based on either fracture energy (refs 6,10,11,48) or stress analysis (refs 7,8,35,46), and have proven insightful. However, the wide use and application of these models to experimental data are at best limited. This is partially due to difficulties in developing micro-scale samples with good experimental reproducibility and the appropriate recording of the failure events, especially for small- and sometimes for large-scale samples. In spite of these

pull-out test. 1: C. DiFrancia et al.

problems, efforts to relate the experimental models to composite failure have been made. In 1969, Outwater and Murphy presented their work on the fracture energy of unidirectional laminates’. Their analysis detailed the instability and debonding of a filament within a matrix via ‘craze induced tension’, and the relationship between the debonding of this fibre, the tension in the fibre and the fracture energy of the laminate’. The basis of their work, and of many to follow, was the general compliance equation expressed as: G = (p/27rd)(dC/dLc)

(1)

where G is the opening mode fracture energy, P is the tensile load on the fibre, dis the fibre diameter and dC/da the compliance of the structure as a function of crack length. Here, the key assumption is the initial existence of an interfacial crack. It is recognised that the debonding event is mixed-mode and, after initiation of crack propagation from the resin end face, the failure is predominantly in the shear mode (mode II) and not the opening mode (mode I). The successful model for determination of the strain energy release rate for both the initiation of crack propagation and for the continuation of the crack front along the fibre length, will consider the physical constants of the materials, the response of these materials to a load and, ultimately, the thermo-mechanical history of the specimen for a given loading configuration. The efforts of some researchers and theoreticians have resulted in developing methods for the quantitative evaluation of the single-fibre pull-out test based on fracture mechanics.

The approach of Gao et al.

The most rigorous and useful mathematical description of the single-fibre pull-out test found in the literature at the time of this article, was reported by Gao et a1.33. In their paper a fracture mechanics based debonding criterion, which included friction, was reported. Rather than paraphrase their analysis, the reader is referred to their work and the following equations are referenced. For systems with relatively low fibre volume and fibre modulus, their equation for the strain energy release rate for crack initiation simplified to the compliance equation generated by Outwater and Murphy, equation (1). However, it was shown that the debonding criterion could be described by combining a debonding and frictional term to generate the strain energy release rate for the continuation of the interfacial crack: Gcontinue=

(1 - 2kq)[P-

(1 + S)QIZ

47&3Ef( 1 + Lv

(2)

where k=

auf

+ Y%l

CY(l--l/f)+l+V,+ZY

599

The single-fibre

pull-out

p =

test. 1: C. DiFrancia et al.

Table 1 Strain energy release rates (in Jmm2) for the initiation of crack propagation as reported in the literature

$1 - 2kvrn) (Y(1- 24

System

Strain energy release rate

Steel/cement Carbonlepoxf Glass/epoxy6 Glass/epoxy6 Glass/polyesterc Glass/polyesterc Stainless steel

2.49 f 50 50f 79 f 57 f 190 f 200d

Comments

Ref.

and Q = T,(l)

=

ri!‘+ GuL’ (exr - 1)

(5)

P is a constant which represents the load at the end of the primary frictional zone: j3=

(6)

where q0 is the normal pressure exerted on the fibre due to resin shrinkage during cure plus the difference between the thermal coefficients of expansion of the fibre and matrix. Finally,

x=2! r

(

avf

0.05 14 8 3 30

No heat 24hat 60°C No heat 6hatWC

35 30 31 31 31 31 33

’Not specified ’ Shell Epon 8 15 with Ancamine XT ‘Ashland Crystic 2-491-PA with MEK d Glniliate

+ Ym

a(l-v,)+1+vm+2y)

1

(7)

and a = Em/E yr2/(RL2)=

cf/cm - vo 1ume fraction of fibre in the matrix r = fibre radius R = matrix radius I = location of the crack front ,U= coefficient of friction, determined from the tail of the fibre pull-out trace Tf and T, are the tensile forces on the fibre and matrix cylinder P = T, + Tf

are the Young’s moduli and Poisson’s ratios for the fibre and matrix, respectively.

Ef, Em and vf,

urn

Equation (2) shows that the debonding load is a function of crack length, Poisson’s contraction, the coefficient of friction at the interface, the volume fraction of fibre and matrix and their Young’s moduli. This model, unfortunately, was not applied to experimental data which included debonding over the frictional region of the fibre. Instead, they addressed the point of crack initiation and the model reduced to equation (1). The evaluation of the single-fibre pull-out test has produced a variety of mechanistic models to describe the onset of fibre-matrix interfacial failure and the propagation of this event. While no values for the strain energy release rate during debonding could be found in the literature, the critical strain energy release rate associated with crack initiation, estimated by implementing various forms of Outwater and Murphy’s equation, are presented in Table 1. The variability of the physical parameters in the material systems in Table I, which are not accounted for with the strain energy release rate estimate, prevents any comparison of the data. Only a model that can account for the various experimental and material parameters as well as the interaction between the joined materials will allow for accurate quantification of the data generated by the single-fibre pull-out test.

600

Fiber Embedded Length, 1

Figure 1 Theoretical embedded fibre length versusload required to debond

Relationship between debonding stress and embedded length

With regard to the relationship between embedded fibre length and debonding load or stress, the following is presented. It is customary, though not necessarily appropriate, to report the maximum load as the value associated with fibre debonding from the matrix. For the case of catastrophic failure, this is accurate and this load, P catastrophic 9 is a function of embedded length up to a maximum fibre length beyond which catastrophic failure does not occur, /maxcatastrophic. If, however, the failure is not catastrophic, the maximum load on the trace may represent the load required to debond the fibre from the resin plus an amount of energy dissipated by frictional effects between the fibre and iesin over the debonded fibre length. As discussed earlier, this total length of fibre which shows friction is finite, call this Zmaxfc,-tion. If the embedded length of the fibre is somewhere between Imaxcatastrophic and lmaxftiction y then there is a different relationship between embedded length and maximum load. For embedded lengths greater than Zmaxfhction, Poisson’s forces come into play and the maximum load is independent of embedded length, see Figure 1. The high standard deviations associated with the load ver.sus embedded length relationship reported

The single-fibre

throughout the literature may in part be the result of the inappropriate measure or choice of the load data point. While it was thought that the maximum load in the pull-out trace represented the load at initiation, in reality, for fibre lengths greater than that at catastrophic failure, it may represent load during crack propagation which initially varies as a function of crack length and then levels off as the frictional contribution becomes constant. It is critical, therefore, to know the length debonded when the initiation of crack propagation occurs. To assume the debond length equals the embedded length may lead to erroneous quantification of the data and meaningless comparisons between model test methods. Stress transfer jiiom matrix toJibre

The term critical fibre length 1, has been used to describe many phenomena. It has been applied to the weighted average fibre length resulting from fibre fragmentation (refs 18,23,24,51,65), to the primary frictional zone associated with debonding and pullout’4s9 and to the bimodal relationship between embedded length and load to debond28>69. The common denominator of this descriptor in these applications are the tensile properties of the fibre relative to those of the matrix, and the normal forces exerted by the resin on the fibre. The following is a brief discussion of the critical fibre length value relating to fibre pull-out. Here, the critical fibre length is the maximum embedded length which will catastrophically fail, 1, = /maxcatastrophic. The primary frictional zone which results during debonding and subsequent pull-out is an event related to the Poisson’s contraction of the fibre under a given load. Removal of the fibre from the surrounding matrix is realized when the load required for the radial contraction is less than the load required for steady-state debonding, which, in turn, is less than the ultimate strength of the fibre. The relationship between fibre length up to 1, and associated stress, and the relationship between fibre embedded length and load required to debond, is the same. This is the result of the load-carrying ability of a fibre with length less than 1,. The heavily documented embedding length versus load required to debond has been reported as a bimodal relationship based on catastrophic interfacial failure. Given the inherent scatter in the data, it was unclear to many if the relationship between debonding force and embedded length was a linear increase then a flat plateau, or a linear increase followed by another linear increase with a modestly different slope. As will be elaborated upon in this article, the initially rising portion of the curve does reflect catastrophic interfacial failure of embedded fibre lengths less than 1,. For fibre lengths greater than f,, the role of friction is seen as a second region displaying a new positive slope. Only when the various embedded fibre lengths are all greater than 1, will there be an initial positive slope followed by a plateau. In this case, the first region is the result of failure plus friction and the plateau

pull-out test. 1: C. DiFrancia et al.

the result of steady-state propagation beyond the primary frictional zone. Based on many of the previous arguments, the relationship between load to debond and embedded fibre length may be depicted and interpreted as follows, refer back to Figure I. As the embedded length I increases. the required load to catastrophically debond also increases. As the length of fibre increases beyond I,. the fibre will display some sliding against the surrounding cylinder of matrix. This frictional sliding will continue with increasing crack length and increasing load to propagate the crack front until the effect of Poisson’s contraction can overcome the effect of the normal pressure of the matrix on the fibre. These frictional contributions to energy dissipation result in an increase in load as a function of embedded fibre length-not a plateau. When the debond length from the crack front surpasses the length associated with catastrophic failure and the additional length required to overcome normal forces on the fibre, steady-state crack propagation will commence with a constant input of energy. Thus, if the elastic constants and strength of the fibre accommodate steady-state debonding loads that are less than the ultimate strength of the fibre, a constant debonding load will be realized at embedded lengths greater than the length affected by the primary frictional zone. Interfacial shear stress between ,$bre and resin

In the single-fibre pull-out test, the interfacial shear stress can be determined at three different experimental times to describe various events. Initially, at the onset of crack propagation, the interfacial bond shear stress is determined from P,, = Piit, where Piit represents crack initiation or catastrophic interfacial failure (refs 11,26,33,34,41, 57,61). Secondly, for P,,, > Pinit, i.e. propagation with friction, the debonding interfacial shear stress is determined from the change in load required for crack propagationt4. Thirdly. when debond is complete, a pull-out interfacial shear strength2’,” can also be determined. Researchers have used the different interfacial shear stress values, as well as the coefficient of friction (refs 22,25,27,40,47), as a means of quantitatively evaluating and comparing single-fibre pull-put data. Znterfacial bond shear stress. The determination of the interfacial bond shear stress, detailed and applied by Pitkethly and DobleSS, evolved from Cox’s shear lag analysis. Here, the fibre diameter. embedded length and load required for crack initiation were used to determine the maximum value of the interfacial bond shear stress, 7b0nd, equation (8). These authors argued that because load transfer from matrix to fibre occurred primarily over the ineffective length of the fibre, the shear strength calculated from a fibre system whose embedded length was greater than this value would be underestimated. This was because a length of fibre was included over which little stress transfer occurred. Pitkethly and Doble

601

The single-fibre

pull-out

test. 1: C. DiFrancia

et

al.

also stated that the maximum shear stress should be calculated as the embedded length became exceedingly small. Here, Pinit

birefringence data, load versus crack length a has a linear relationship-at least over the initial primary frictional zone of debonding. Therefore, from the slope dP/da, Td&,“,jcan be calculated from:

Tbond = -

rdl

Tdebond

where d is the fibre diameter and 1 the embedded length. Pitkethly and Doble’s approach was to calculate the average interfacial shear strength from the abovementioned parameters, and then To,,, was put into a series of equations to determine T,,,. The typical problem of scatter plagued their results. However, 7-max values were calculated and fairly good agreement between experiment and theory was reported55. debond shear stress. As regards the singlefibre pull-out test, once crack propagation begins there is a debonding interfacial shear stress which results in a frictional dissipation of energy. This is how the initial rise in the debonding portion of the pull-out trace was explained previously. If the simplifying assumption is made that this is the only cause of the increasing load with displacement, the interfacial shear stress of this region, ~&&,,,d,can be determined. However, it is not the load versus displacement relationship but the load versus crack-length relationship which must be implemented. As noted later via the Interfacial

Table 2

(Q/da)

( 1 l4

(9)

Znterfacial sliding shear stress. With the completion of fibre debonding, frictional sliding occurs as the fibre is removed. The interfacial shear stress of sliding can be calculated from the tail of the load versus extension trace27’51.Here, Tpull-out= (dPld4

(1 l4

(10)

where dP/dS is the slope of the pull-out tail from the load versus extension trace. Literature values for the interfacial shear stress as determined for the different events of the single-fibre pull-out test are compiled in Table 2. The materials and specific stresses determined are noted. Coeficient of friction. The coefficient of friction has been determined from both the slope of the debonding frictional region and the tail of the pull-out trace using63: r=pP

(11)

Experimentally determined values for the interfacial shear stress (in MPa) as reported in the literature

System Glass/poly(butylene terepthalate) Kevlar 29/DGEBA epoxy’ Kevlar 49/DGEBA epoxy” Celion/DGEBA epoxf Stainless steel/epoxyb Glass/DGEBA” Kevlar/DGEBA epoxf Kevlar/DGEBA epoxyC Copper/epoxyd Copperlepoxyd Carbon/DGEBA epoxy’ Steel/epoxyb Nickel/epoxyb Glass/epoxyd Glass/epoxyd Glass/polyester’ Glass/polyester’ Carbon/DGEBA epoxf Carbon/DGEBA epoxya Carbon/DGEBA epoxya Carbon/DGEBA epoxy” Carbon/DGEBA epoxy” Stainless/epoxyl AU carbon/DGEBA epoxy’ AS carbon/DGEBA epoxy’ AS (300) carbon/DGEBA epoxy AS (600) carbon/DGEBA epoxy’ AS (750) carbon/DGEBA epoxy’

h)bond

(T)pull-out

31.1 40 41.1 65.3 20 33.1 39.3 zt 7.8 21.6f0.51 1.4 0.13 27

Comments

With release agent

21.8 3.6 x 10” 21 is 34i 10 7f7 lOf5 21.2f4.5 40.6 f 7.8 30.0 f 9.0 58.4 f 12.8 66.6 Lt 10 1.13kgmmm2 24.1h 74h 71.7h 68h 65.58h

’ Shell Epon 828 ’ Not specified ’Ciba-Geigy 6010 and Aldrich triethylene tetramine d Ciba-Geigy Araldite 502 with hardener 956 e Shell Epon 8 15 with Ancamine XT / OGBA + BAS-A MY750 g Debond plateau h Interfacial shear stress measured by critical length tensile test

602

=

No heat 24 h at 60°C No heat 6 h at 80°C Tcure = r.t. TCUre= 60°C T c”re = 120°C T CUIe= 165°C T cure = 180°C

Ref. 34 41 41 41 33 26 26 57 57 57 61 27 14 51 51 51 51 56 56 56 56 56 11 18 18 18 18 18

The single-fibre

where P is the normal pressure on the fibre resulting from chemical shrinkage and thermal mismatch between resin and fibre during cure.

EXPERIMENTAL In conducting the single-fibre pull-out test on polymercoated optical fibres embedded in a dogbone of neat resin, many of the features described in the literature have been observed. Complementing these supporting observations, further details enabling a more enhanced interpretation of the load WYSUS displacement trace are presented. The series of experiments was conducted to evaluate the single-fibre pull-out test method more thoroughly and to relate the role of material combination to the failure mechanism of the system. Experimental observations of loads at crack initiation and stress distributions are reported and the fibre pullout traces discussed. A series of three test matrices was conducted. The first matrix considered various polymeric coatings/surface treatments on the optical fibres. The coatings were acrylate, polyimide and a silane coupling agent. These fibres were embedded in two different resins: a butylglycidyl ether of bisphenol-A (BGEBA) with epichlorohydrin and a catalysed tetraglycidyl-4-4’diaminodiphenylmethane (TGDDM) with 4,4’-diaminodiphenylsulfone (DDS). The second test matrix varied the polyimide fibre coating while maintaining one embedding resin. There, polyimide-coated fibres from six different manufacturers were embedded in uncatalysed TGDDM/DDS epoxy resin to determine the various loads and apparent locus of failure expected from the given fibre/polyimide/epoxy system. The effect of the resin on the single-fibre pull-out test was then evaluated in the third matrix of experiments. To accomplish this, polyimide-coated optical fibres from one manufacturer were embedded in three different commercial resins as well as an in-house toughened bismaleimide diallyl of bisphenol-A. This series of resins accommodated a variety of different thermal histories with completion of the reaction chemistry. For the optimization of the single-fibre pull-out test, a new sample configuration was developed59. Fibres were embedded lengthwise in a neat resin dogbone. The sample was notched across its width, prior to loading, to allow for the load measurement to be of the fibre-matrix interface. This notched sample was mounted on a tensile load frame which in turn was mounted on a microscope stage fitted with cross-polarizers and a camera system, thereby enabling the samples, their birefringence patterns and interfacial crack lengths to be viewed in real time. Experiments were carried out at 2 mm min-’ . The experiments for characterization of the fibre/ coating/resin systems were conducted as described in the following text. Fibres were from the same manufacturing run, the particular resins from the same production lot and handling and preparation of samples were maintained as consistent as possible.

pull-out

test.

1: C. DiFrancia

et al.

Opticaljbres

All fibres were commercially available. glass-on-glass optical fibres. All fibres, except those that were treated with the coupling agent, were acetone-cleaned prior to embedding. For the determination of fibre coating choice, acrylate-coated fibres from SpecTran Corporation [50/125/500pm (core/clad/coating diameter)] and polyimide-coated fibres from Polymicro Technologies, Inc. (105/125/l 50pm) were used. For the constant resin experiments, the various polyimide-coated fibres were received from Polymicro Technologies. Inc., AT&T, SpecTran Corporation, Fiberguide Industries, Inc., General FiberOptics and CeramOptec, Inc. [UV (loo/ 110/125pm)]. For evaluation of resin chemistry and the related cure cycle on the single-fibre pull-out test, Polymicro polyimide fibres were employed. Unless otherwise specified, all test scenarios were repeated in sets of six or more.

Coupling

agent coating

The coupling agent, Dow Corning Z6040-a glycidoxypropyltrimethoxy silane, was applied to SpecTran fibres which had originally been coated with acrylate. The acrylate was removed by swelling with acetone and then stripped mechanically. After stripping the fibres were acetone wiped, heated to 60°C for 20 min, cooled to room temperature and dipped into the coupling agent. They were then dried at room temperature in a fume hood for 24 h.

Resin system

Different resins were used for the various experiments. For all samples cured at elevated temperatures, the resin was melted and degassed (125°C 100 torr, 1 h) prior to pouring into the preheated moulds. To evaluate the initial performance of coated optical fibres when embedded in neat resin and subjected to the fibre pull-out experiment, two resins were employed: Micromeasurement Group PLM-9, a BGEBA with epichlorohydrin, and Hercules 3501-6, a BF3MEA catalysed TGDDM/DDS epoxy. Their cure procedures were as follows: the PLM-9 epoxy components were mixed, then cured for 48 h in an oven at 25°C; the catalysed TGDDM/DDS epoxy was heated at a rate of 4”Cmin-’ to 177”C, held at 177°C for 2.5 h, then cooled via bench-top equilibration to room temperature. For the evaluation of fibres with different polyimide coatings in one resin, Fiberite 976. an uncatalysed TGDDM/DDS epoxy, was the resin of choice. The uncatalysed TGDDM/DDS epoxy was heated at 1°C min- ’ to 15O”C, held for 3 h, cooled at 3.3”Cmin-’ to 65”C, then cooled at 5°C min-’ to room temperature. In continuing the evaluation of the effects of embedding one manufacturer’s fibre in different resin systems, the resins were BGEBA, uncatalysed TGDDM/DDS.

603

The single-fibre

pull-out test. 1: C. DiFrancia et al.

catalysed TGDDM/DDS and an in-house toughened bismaleimide: 5’7% by weight of Matrimide 5292A (4,4’bismaleimidodiphenyl methane) and 43% by weight of Matrimide 5292B (O,O’-diallyl bisphenol A), toughened with 10% by weight of amine-terminated poly(arylene ether sulfone) (M,, = 15 760 g/mole)75. The toughened BMI/diallyl/bisphenol-A was heated at 20°C min-* to 2OO”C,held for 1 h, heated at 20°C min-’ to 25O”C, held for 2 hand then cooled at 1°C min-’ to room temperature. Sample preparation

Samples were prepared by placing a single, acetonecleaned, optical fibre in the centre of a dogbone-shaped mould with a 25.6 x 3.0 x 1.2 mm gauge section plus two 8.2 x 15.3 x 1.2 mm tabs, and preheated to 125°C. This mould was then overfilled with resin and covered with a Teflon sheet followed by preheated weights; the BGEBA resin samples did not require preheated mouldlweights and were left to cure in an oven at 25°C at this point. All samples were cured following the schedules detailed above. Cured samples were notched with a cold razor blade approximately 12mm from one end of the dogbone. Initial notching was to ensure crack propagation across the dogbone at minimal or no load, i.e. the fibre alone bridged the two pieces of the specimen. Fibre pull-out tests were performed on a Polymer Laboratories Miniature Materials Tester (Minimat) Tensile Stage. This stage was mounted on an Olympus SZH microscope to permit visual examination of the samples during the test. To perform the test, the samples were clamped on the tensile stage and the clamps displaced, thus supplying sufficient load to extract the optical fibre from the surrounding matrix. The stresses which developed during debonding and pull-out, as birefringence bands via crosspolarized light, were examined by optical microscopy. Data were collected in a load versus extension format. Since fibre diameters varied between manufacturers, the statistical evaluation of load was normalized to stress. Extension was not converted to strain because the length of fibre over which the load was dissipated changed as a function of clamp displacement.

OBSERVATIONS AND INTERPRETATION THE SINGLE-FIBRE PULL-OUT TEST

This first set of experiments was designed to evaluate the performance of the different optical fibre coatings when the fibre was subjected to the single-fibre pull-out test. Of interest were SpecTran’s acrylate-coated, Polymicro polyimide-coated and Dow Corning coupling-agent-treated optical fibres. The resins of interest were BGEBA (25°C for 48 h) and the catalysed TGDDM/DDS (177°C for 3 h). The results of the experiments where fibres were coated with coupling agent, acrylate and polyimide were very different from each other in a given resin and between resins as observed via birefringence patterns, loads of crack initiation, acoustic activity during debonding and loads associated with pull-out. Bisphenol-A based epoxy resin. The BGEBA resin was chosen since there would be minimal thermally induced stress seen by the embedded fibre. Three repetitions per fibre set were performed. The crack initiation stresses were 18.06 (single value), 696.0 f 336 and 901.5 f 101 MPa for the SpecTran acrylate, Polymicro polyimide and Dow Corning’s coupling-agent-coated fibres, respectively. These results, as well as those for the next section, are compared in Figure 2. Visually, the acrylate-coated fibre samples displayed minimal stress transfer via the birefringence pattern. With the onset of clamp displacement, debonding would begin almost immediately. There was migration of the interfacial crack along the fibre from both sides of the notch; this migration was immediate and with no hesitations. The system appeared to ‘unzip’. At crack completion, the fibre began to pull-out. In this resin, the removed, coated fibre surface was not damaged, i.e. failure appeared to take place at the coating-resin interface. Interestingly, when the fibre was removed from the resin, the coating extended beyond the glass fibre end. This probably resulted from slippage of the entire coating (rather than coating deformation) and the fibre end that was still embedded likely displayed a corresponding small region of uncoated glass fibre. This was not verified. The coupling-agent-treated fibres also displayed low Stress at crack initiation

OF

In conducting the single-fibre pull-out test on polymercoated optical fibres embedded in a dogbone of neat resin, many of the features described in the literature were observed. To determine both the model materials (fibre, coating and resin), as well as model cure conditions for subsequent work, an array of experiments were initially conducted. The results of this work not only defined the model materials for the research to follow, but also provided the experimental information to more fully interpret and describe the single-fibre pull-out test reported here.

604

Eflect ofJibre coating on the single-jibre pull-out test

? ?BGEBA

696+1-

(MPa)

1892+/36.:

[13 TGDDMIDDS

t

Spectran acrylate

Polymicro Polyimide

Fiber/coating

DOW Corning coupling agent

Figure 2 Fibers supporting various coatings embedded in BGEBA and TGDDM/DDS resin systems

The single-fibre

transfer stresses via the load frame data and the birefringence patterns. Here, there was a non-linear load response to extension of the sample, i.e. the interfacial crack displayed halts and hesitations while propagating to the end of the fibre. These fibres did pullout in an uneventful manner, i.e. with minimal stick-slip and a linear decrease in load with extension. The polyimide-coated fibres exhibited a comparatively large amount of stress transfer activity in the form of isochromatic bands which as a group migrated in a non-linear fashion along the fibre. As will be shown, the isochromatic bands seen here were minimal when compared with the samples cured at elevated temperatures. With the polyimide samples there was a pullout plateau at low loads of 225-550MPa. The locus of failure was at the polyimide-resin interface. Catalysed TGDDM/DDS epoxy resin. In this set of experiments acrylate- and polyimide-coated fibres were employed. The coupling-agent-coated fibres were not used because of the difficulty in prenotching the specimens without causing fibre failure. Fibres removed from the catalysed TGDDM/DDS epoxy resin responded in a more dramatic fashion than fibres embedded in the BGEBA system. Upon loading, the acrylate-coated samples exhibited crack initiation stresses of 27.2 f 0.74MPa. As with samples in the BGEBA system, these samples displayed minimal stress transfer via the birefringence pattern and interfacial crack propagation along the fibre from both sides of the notch. Again, the system unzipped. At crack completion the fibre began to pull-out and, visually, one could see that the integrity of the coating was compromised. Although some bare fibre was seen, it was observed that the locus of failure was primarily cohesive in the acrylate coating as it was severely torn. None of these samples displayed any stick-slip activity. In contrast to the acrylate in catalysed TGDDM/ DDS and to all fibres in BGEBA, the experiments conducted on the Polymicro polyimide-coated optical fibres in catalysed TGDDM/DDS revealed a significantly different behaviour. Here, there was substantial stress transfer from the fibre to the matrix via isochromatic bands of greater magnitude and higher order. Interfacial crack initiation stresses were 1892.2 3~67 MPa. For these samples, once the interfacial crack began to migrate, there was a great deal of acoustic activity and, correspondingly, the moving isochromatic bands showed substantial hesitations. These observations appear to represent the effect of increased normal pressures on the fibre resulting from the embedding resin. This will be expanded upon in a later section. For all of these samples, the locus of failure appeared visually to be at the glass-polyimide coating interface. Of these, half resulted in fibre failure with the exposed fibre showing no polyimide intact. Stick-slip activity was prevalent for these samples with increased magnitude at the end of the run which may have been due to the locus of failure.

Eflect ofjbre

pull-out test. 1: C. DiFrancia et al.

manufacture on the single-fibre pull-out test

To determine the most appropriate polyimide-coated optical fibre for embedding in the uncatalysed TGDDM/ DDS epoxy resin for the later evaluation of the cure cycle7’, fibres supplied by six different manufacturers were examined. Some significant differences between sample sets were found. For specimens obtained from Polymicro Technologies, the dominant mode of failure was polyimide-epoxy debonding with a few cases of glass-polyimide debonding. Data depicted in Figure 3 were typical for this sample set in that all previously described regions were present. For fibres obtained from AT&T, General FiberOptics and SpecTran, there was an inconsistent mixed failure, i.e. glass-polyimide, polyimide-matrix and fibre failure. Of the samples which did not result in fibre failure, a typical load versus extension plot did not show a pull-out plateau region. Instead, a maximum load was reached and the fibre pulled out in a consistent manner, i.e. decreasing load with extension, as in Figure 4. For the AT&T and SpecTran samples, stickslip activity was minimal. General FiberOptics fibres, however, displayed a failure locus of matrix microcracking. This corresponded to excellent interfacial adhesion

100

80

g 60 D c” -1 40

~

_~__

0.2

04

0.6

08

20

0

4

2

8

IO

Extension

(mm)

6

12

,416

Figure 3 Experimental load versus extension traces showing all described debonding and pull-out regions as well as stick-slip activity

85 7s 65 55 iz 45 ‘CJ z 35 a 2s 15

-5

Figure plateau

1 0

2

4 Experimental regions

6

8

Extension

(mm)

4

load

versus

extension

10

traces

12

showing

14

no

605

The single-fibre pull-out

test. 1: C. DiFrancia et al.

at both the glass-polyimide and polyimide-epoxy interfaces. For these sample, ultimate failure took place between the polyimide and matrix and stick-slip did occur. Visually, the stick-slip activity did not necessarily coincide with the sites of microcracked matrix. Fibre specimens obtained from Fiberguide generally failed at the polyimide-epoxy interface and typically showed a great deal of stick-slip activity. CeramOptec fibres primarily displayed failure at the glass-polyimide coating interface. While the loads seen during the runs were unimpressive, there was substantial stick-slip activity which occurred in the last third of the plot after minimal stick-slip occurred in the pull-out

40

30

2

20

-z s

10

0

t -2 0

2

4

6

8

Extension

10

12

14

(mm)

Figure 5 Typical load versus extension trace for glass-coating interface failure. Example from the CeramOptec set

plateau region. This is shown in Figure 5. This was possibly due to micro-scale build-up of coating material resulting in a decreased area from which the fibre was being withdrawn, i.e. plowing. Note that this was typical of specimens failing at the glass-coating interface. Efect of resin choice on the single-jibre pull-out test

To evaluate the effect of cure cycle and resin chemistry on the single-fibre pull-out test, polyimide-coated fibres were embedded in four different resins. Here, the choice of polyimide-coated fibre was based upon the results of the previous section via the loads associated with debonding and the locus of failure. Polymicro’s polyimide-coated optical fibres were embedded in BGEBA (cure schedule: 25°C for 48 h), uncatalysed TGDDM/ DDS (15O’C for 3 h), catalysed TGDDM/DDS (177°C for 3 h) and toughened BMI/diallyl/bisphenol-A resin (200°C for 1 h and 250°C for 2 h). The data for all experiments conducted to evaluate the tensile performance of Polymicro fibres in various resins are presented in Figure 6. The data include resin, locus of failure, stress at crack initiation ginitiation,and interfacial shear stress for final pull-out (7)pull_out. These experiments are detailed in the following text. The first set of experiments examined BGEBA (room temperature cure, 24h). The average initiation was 696 f 336MPa and the observations were detailed earlier.

Temperature, Temperature,

‘C

“C

Figure 6 Bar chart of Polymicro polyimide-coated fibres embedded in various resins: (a) average stress at initiation; (b) average interfacial shear stress for pull-out

606

The single-fibre

The next two sets of experiments implemented uncatalysed and catalysed TGDDM/DDS epoxy systems which required elevated temperatures for cure. As the specimen cure cycle temperature increased, the load required for initial debond increased, indicative of resin shrinkage or clamping. There was substantial stress transfer from the fibre to the matrix via isochromatic bands of greater magnitude and higher order. For the uncatalysed TGDDM/DDS and catalysed TGDDM/ DDS epoxy resin systems, the average crack initiation loads were 1596.6 f 469 and 1892 * 367 MPa, respectively. For these samples, once the interfacial crack began to migrate, there was a great deal of acoustic activity and, correspondingly, the moving isochromatic bands showed substantial hesitations. At crack completion, the fibre began pull-out. For the uncatalysed samples, the locus of failure was at the coating-resin interface. Figure 3 presents a typical load versus extension trace for this set of samples. For the catalysed sample set, the primary locus of failure was at the glasscoating interface. Unfortunately this set included some fibres from a different lot, therefore this result was probably due to varied fibres rather than the embedding resin. A typical load versus extension trace was described in Figure 5. Indicative of the glass-coating failure is the substantial stick-slip behaviour at the tail end of the trace. For fibres embedded in toughened BMI/diallyl/ bisphenol-A, the final set of experiments, the average load required for crack initiation was 3830.9 f 523 MPa. For these samples, the stick-slip load differential was often as high as 1130 MPa. While the coating-resin interface was the primary locus of failure, the fibre would often fail at some time during the run. This series of experiments has shown that the combined chemistry and thermal cure cycle of the embedding resin substantially affect the results of the single-fibre pull-out test. Not only were the stresses associated with crack initiation a function of resin properties, but crack propagation associated with fibre sliding properties were affected as well. Based on these varied material combinations, an enhanced interpretation of the load-extension trace evolved as parameters such as cure conditions were considered. The experimental observations are shown in Figure 7. The stress field isochromatics were present to a greater or lesser extent depending on the material combination, as was the speed of their migration along the fibre-resin interface during debonding. Typical experimental observations corresponding to Figure 7 are detailed as follows. Upon notching and clamping the dogbone specimen, it was loaded at a constant rate of displacement. (A small interfacial crack is assumed to exist initially as a result of the notching process via the high stress concentration where the fibre emerges from the end face of the resin.) As the load increased, isochromatic bands, radiating out from the notch and along the fibre, grew and intensified. This continued through the linear elastic region of the

pull-out

test.

1: C. Difrancia

et al.

material system. At a critical load, which was dependent on fibre/coating/resin and thermal history, an interfacial crack between the fibre coating and the resin would begin to propagate. This crack would propagate along the fibre with clamp displacement. Depending on the fibre/ coating/resin system this crack would either flash quickly to the fibre end or migrate slowly with periodic halts. Visually, a small degree of pulsing or micro-movement would sometimes be seen prior to the more dramatic migrations of the crack front. This may have been the result of circumferential progression of the crack around the fibre. Also, a constant stress redistribution was seen as changes in the birefringence pattern. Once the interfacial crack had completely debonded the fibre from the resin, the fibre began pull-out and stick-slip activity was generally observed. This activity would continue until the fibre end exited the resin or the fibre fractured. Upon inspection, failure was found to take place at either the glass-coating or coating-resin interface, or in the case of good interfacial adhesion, there was matrix microcracking and fibre failure. The stick-slip phenomenon is the result of interfacial frictional sliding. The relationship of this phenomenon to the length of the fibre affected may be of significant importance when considering the performance of a given composite. This is because the energy absorbed by friction during the fibre pull-out process contributes a substantial portion of the resistance to fracture”. Here, the sticking phenomenon represents the mechanical hold on the fibre which must be overcome for sliding to proceed. The slip displacement represents the recovery of the fibre to an equilibrium status for a particular load. It has been found here and by other researchers4 that the stick slope nearly replicates the slope related to elastic loading of the system. This means that the mechanical clamping associated with the embedding process provides for the absorption of energy before and after the integrity of the interface is compromised. Upon embedding the optical fibre, notching and loading the samples, a load versus extension trace was generated. A model load-extension trace is presented in Figure 8. Here, the linear elastic region began with initial loading and ended at a point depicted as (Sinit, Pinit). Point (Sinit, Pi,,) indicates the initiation of propagation of the interfacial crack. The location of this crack initiation in the rising portion of the trace was first reported by Kelly’ and more recently by Jiang and Penn67. However, the use of this value for reporting debonding loads or numerical representations had not been forthcoming. From point (c$,,,~,P;,,t) to point (&ion > f’ftiction) and then to (&omp~ete~ f’comp~ete)7the interfacial crack travelled along the fibre length until the fibre was debonded through to one end of the specimen. During the debonding process from Pinit to Pfhction,there was a significant effect of interfacial friction on the dissipation of energy, as evidenced by the positive slope. However, for fibre lengths which exceeded (Sfriction,Pfriction)lengths, there was a constant frictional force due to Poisson’s contraction of the fibre providing

607

The single-fibre pull-out

test. 1: C. DiFrancia et al.

a constant length of fibre experiencing frictional sliding. This contraction of fibre resulted in the removal of a portion of fibre length greater than the critical fibre length, i.e. Bowling and Groves’ plug. Here, when the crack front reached the end of the critical length, which was a function of the elastic properties of the fibre and the cure cycle of the resin as well as the thermal mismatch between fibre and resin, the entire frictional region would migrate along the length of the fibre as the crack front propagated. Behind the crack front, then, was a critical length of fibre experiencing frictional sliding and behind this length was a length or zone of no friction. For a nonductile fibre it is most probable that the radius of the fibre is a function of location relative to the crack front and the forces associated with interfacial friction are a function of location with the maximum value behind the crack front. It is suggested here that there is a critical fibre length over which the majority of the frictional dissipation of energy occurs. This portion of the fibre, (binit, PiGit) to (brcction,Z’rhction),is thus considered the primary frictional zone and the remainder of the fibre, (&ction, Pftiction) to (&ompiete,Complete), as the secondary frictional zone. It should be noted that the point

Figure 7

608

Fibre debonding

and pull-out

sequence

showing

the photoelastic

&ompkte, &omp~ete) may or may not represent the maximum load the fibre carried during crack propagation, but, physically, it does correspond to the crack front reaching the end of the fibre. Once the interfacial crack completely debonded the fibre from the resin, the fibre was pulled out and, depending on the system, stick-slip behaviour was observed. Also, depending on the length of fibre debonded from the resin and the degree of interfacial friction over that length, there may have been a drop in load following completion (Figure 3) or, alternatively, a steady decrease in load until fibre removal (Figure 4). For the situation where there was minimal or no drop in load, this was thought to correspond to the entire length of debonded fibre significantly contributing to interfacial friction. In most systems, however, there was a drop in load after Pcompleteand a relatively small load-extension slope was observed until some critical point. At this critical point, x, the beginning of a more substantial linear decrease in load with resident fibre length began. The change in slope at x defines the length of fibre corresponding to the primary frictional zone of sliding. Note that for a non-ductile fibre the primary frictional

birefringence

patterns

as load increases

The single-fibre

Figure 7

pull-out

test. 1: C. DiFrancia

et al.

Continued

zone is over a greater length of fibre during pull-out than during debonding. This is the result of a lower load required to pull-out with friction than to propagate a crack in the presence of friction. It has been found that the linear elastic region of the fibre/resin system, and the debonding of the primary frictional zone, are not readily resolved in the load versus extension trace, i.e. to realize the difference in the slopes requires sufficient data collection. Regarding many of the experimental results reported to date, this similarity in slope may be one of the reasons for the extent of experimental scatter associated with the single-fibre or microdebond test data. While the visual observation of crack initiation was certainly accommodated in many of the large samples described in the literature, small sample sizes are a problem. Penn and Lee46 reported the following visual observations [with loading]: ‘a circumferential crack appears at the interface where the fiber enters the matrix. Loading is continued with no apparent visible event, and then suddenly an upward displacement of the fiber with respect to the matrix occurs’. The initial crack was not recorded on the load-extension trace. This

Load, N

t

Figure 8 test

Model load versus extension

trace for the single-fibre

pull-out

609

The single-fibre pull-out

test. 1: C. DiFrancia et al.

Table 3 Values for the load (in N) on the fibre at various times during the single-fibre pull-out test Experiment

pinit

Pfriction

15OJ 150K 177B 1771 1775 230D 2301 2305 230K 250F 250H 250K

32.9 29.9 78.72 39.14 47.44 65.98 12.38 54.36 60.46 51.58 50.3 68.48

_ 81.96 69.64 72.72 86.22 87.96 66.96 62.42 78.22 79.1 68.92

P compktc

Pdrop

55.78 89.16 73.32 73.12 69.84 89.3 66.68 64.86 61.3 85.06 91.5 105.44

37.3 62.6 59 51.6 58.3 69.5 60 58 53.8 60 61.5 47

was not unique to Penn and Lee. Many researchers have reported the same results of a linear slope to a maximum in the trace followed by a precipitous drop. Unless the time scale of the experiment is increased via longer embedded fibre lengths or the data collection rate is increased, the crack initiation event may be missed as perhaps it has been in the past. Table 3 shows a series of data generated from singlefibre pull-out tests. Listed are the loads associated with crack initiation Pinit, the crack reaching the end of the primary frictional zone Prection, the crack reaching the end of the fibre, Pcomplete,and the drop in load at the transition from debonding to sliding Pdrop. Clearly, there are significant differences in the loads or stresses associated with the various events of fibre-matrix interfacial failure and fibre pull-out. Information regarding the extent of load transfer from fibre to resin is not only obtained from the debonding of the fibre and matrix, but from the removal of the fibre from the matrix as well. With removal of the debonded fibre from the resin matrix, the resulting change in load with fibre removal gives direct information on the sliding interfacial shear stress of the system as well as on the effect of Poisson’s contraction. This interfacial shear stress reflects the normal pressure exerted on the fibre, and the length over which this pressure acts. This length can be used as a guide for determination of the load-carrying ability of the fibre in the debonding and fibre bridging process.

SUMMARY The interpretation of the load versus extension trace obtained from the single-fibre pull-out test has varied from researcher to researcher. It is reported here that with debond initiation, the interfacial crack initially propagated with a significant amount of friction. As the applied load increased, the effects of friction began to diminish due to Poisson’s contraction of the fibre. At some fibre length, which was dependent on the fibre, resin and thermal history, the debonding became a steady-state event and thus the load required for crack propagation a constant. This steady-state debonding

610

continued until the end of the fibre was reached, at which time sliding commenced. Here, remove secondary then primary frictional zones were typically observed. This type of fibre-matrix interaction reflected the effect of the residual stresses on the fibre via the coefficient of friction. Based on this interpretation of the single-fibre pullout test, the use of values from the load-extension trace can be evaluated quantitatively. Quantitative interpretation of the single-fibre pull-out test can be accomplished from both the data associated with fibre debond and fibre pull-out. With regard to the debonding process, the various events can be characterized numerically in the following way. The stress associated with the initiation of crack propagation can be interpreted via the critical strain energy release rate assuming a stressfree edge and no friction, equation (l), and/or the interfacial shear stress of the interface, equation (8). The strain energy release rate can be determined during the propagation of the crack front along some known debonded length with the consideration of the frictional forces via equation (2); the interfacial debond shear stress can be calculated from equation (9). At sufficiently long debond lengths, steady-state crack propagation occurs such that frictional forces are relatively constant and maximum for the critical length of fibre. The strain energy release rate for propagation beyond the primary frictional zone could be approximated using 1,. In the case of the fibre pull-out data, the stress associated with frictional sliding combined with the stick-slip activity describe the residual mechanical interaction between the debonded fibre and the surrounding matrix. With final removal of the fibre, the critical length of fibre associated with the primary frictional zone of sliding can be estimated, and the interfacial shear stress of sliding, equation (lo), and thus the coefficient of friction, equation (1 l), determined. All of the above-mentioned calculations have been made on experimental data and are reported in ref. 71. To date, the quantitative evaluation of the single-fibre pull-out test has been primarily reported as the maximum load required to debond the fibre from the resin. Previous interpretations of the single-fibre pull-out test have primarily evolved around the use of this maximum point in the load-extension trace. If this maximum was the result of a catastrophic interfacial failure, the embedded length of fibre was less than or equal to the length that would otherwise be the crack initiation length. Use of this data point for comparisons between samples requires specific consideration of the embedded length. Extensive work has been presented in this area by researchers implementing the microdebond test. However, if the maximum in the load-extension trace was not the result of catastrophic interfacial failure, the same data handling should not be implemented; the frictional effect of the debonded region of the fibre must be considered. In order to build a data base of information regarding the removal of fibres from neat resins, data reductions such as those employed here should be

The single-fibre pull-out test. 7: C. Difrancia

implemented rather than analysis.

and the load associated the maximum recorded

with initiation for numerical

2s

26

REFERENCES 1

2

3

4

5

6

1

12

13 14 15

16

17

18

19

20

21

22

23 24

Chambers, R.E. and McGarry, F.J. Paper presented at ‘14th Annual Technology and Management Conf.‘, Reinforced Plastics Division, SPI, February 1957, Section 12-B Haslett, W.H. and McGarry, F.J. Paper presented at ‘17th Annual Technology and Management Conf.‘, Reinforced Plastics Division, SPI, February 1962, Section 14-D Kellv. A. and Tvson. W.R. Tensile nronerties of fibre-reinforced metals: copperitungsten and copperjmolybdenum. J. Mech. Phys. Solids 1965, 13, 329 Broutman, L.J. Glass-resin joint strengths and their effect on failure mechanisms in reinforced plastics. Polym. Eng. Sci. 1966, 263 Broutman, L.J. Measurement of the fiber-polymer matrix interfacial strength. In ‘Interfaces in Composites’, ASTM STP 452, American Society for Testing and Materials, Philadelphia, PA, 1969, p. 2741 Greszczuk, L.B. Theoretical studies of the mechanics of the fiber-matrix interface in composites. In ‘Interfaces in ComSociety for Testing and posites’, ASTM STP 452, American Materials, Philadelphia, PA, 1969, pp. 42-58 Outwater, J.O. and Murphy, M.C. On the fracture energy of unidirectional laminates. Paper presented at ‘24th Annual Techical Conf.‘. Reinforced PlasticsiComnosites Division. The Society of the Plastics Industry, Inc., i969, Section 11-C pp. I-8 Kelly, A. Interfacial effects and the work of fracture of a fibrous composite. Proc. Roy. Sot. 1970, A319,95 Favre J.P. and Perrin J. Carbon fibre adhesion to organic matrices. J. Mater. SC.. 1972, 7, 1113 Lawrence, P. Some theoretical considerations of fibre pull-out from an elastic matrix. J. Marer. Sci. 1972, 7, 1 Takaku, A. and Arridge, R.G.C. The effect of interfacial radial and shear stress on fibre pull-out in composite material. J. Phys. D: Appl. Phys. 1973, 6, 2038 Morton, J. and Groves, G.W. The effect of metal wires on the fracture of a brittle-matrix composite. J. Mater. Sci. 1976, 11, 617 Hadjis, N. and Piggott, M.R. The effect of matrix stresses on fibre pull-out forces. J. Muter. Sci. 1977, 12, 358 Bowling, J. and Groves, G.W. The debonding and pull-out of ductile wires from a brittle matrix. J. Muter. Sci. 1979, 14, 431 Bowling, J. and Groves, G.W. The propagation of cracks in composites consisting of ductile wires in a brittle matrix. J. Mater. Sci. 1979, 14, 443 Drzal, L.T., Rich, M.J. and Lloyd, P.F. Adhesion of graphite fibers to epoxy matrices: I. The role of fiber surface treatment. J. Adhes. 1982, 16, 1 Emadipour, H., Chiang, P. and Koenig, J. L. Interfacial strength Res. Mechanica 1982, 5, studies of fibre-reinforced composites. 165 Drzal, L.T., Rich, M.J., Koenig, M.F. and Lloyd, P.F. Adhesion of graphite fibers to epoxy matrices: II. The effect of fiber finish. J. Adhes. 1983, 16, 133 Bascom, W.D., Boll, D.J., Fuller, B. and Phillips, P.J. Fractography of the interlaminar fracture of carbon fibre epoxy composites. J. Mater. Sci. 1985, 20, 3184 Chua, P.S. and Piggott, M.R. The glass fibre-polymer interface: I-Theoretical considerations for single fiber pull-out tests. Compos. Sc,i. Technol. 1985, 22, 33 Chua, P.S. and Piggott, M.R. The glass fibre-polymer interface: II---Work of fracture and shear stress. Compos. Sci. Technol. 1985. 22, 107 Chua, P.S. and Piggott, M.R. The glass fibre-polymer interface: III---Pressure and the coefficient of friction. Compos. Sci. Technol. 1985, 22, 185 Bascom, W.D. and Jensen, R.M. Stress transfer in single fiber/ resin tensile tests. J. Adhes. 1986, 19, 219 DiBenedetto, A.T., Nicolais, L. Ambrosio, L. and Groeger, J. Stress transfer and fracture in single fiber/epoxy composites.

27

28

29 30 31 32

33

34

35

36

37

38 39 40 41

42

43

44

45 46

47

48

49

50

51

et al.

In ‘Composite Interfaces’ (Eds H. Ishida and J.L. Koenig), Elsevier Science Publishing Co. Inc., 1986, pp. 47-54 Piggott, M.R., Sanadi, A., Chua, P.S. and Andison, D. Mechanical interactions in the interphasial region of fibre reinforced thermosets. In ‘Composite Interfaces’ (Eds H. Ishida and J.L. Koenig), Elsevier SciencePublishing Co. Inc., 1986, pp. 1099121 Miller, B., Muri, P. and Rebenfeld, L. A microbond method for determination of the shear strength of a fiber/resin interface. Compos. Sci. Technol. 1987, 28, 17 Parry, T.V., Wilson, J.M. and Leek, D.C. Pull-out of steel fasteners from a laminated composite subjected to external pressure. Compos. Sci. Technol. 1987, 28, 279 Piggott, M.R. Debonding and friction at fibre-polymer interfaces, I. Criteria for failure and sliding. Compos. Sci. Technol. 1987,30,295 Piggott, M.R. The effect of the interface/interphase on fiber composite properties. Polym. Compos. 1987. 8, 291 Piggott, M.R. and Andison, D. The carbon fibreeepoxy interface. J. Reinf. Plast. Compos. 1987, 6, 290 Piggott, M.R. and Chua, P.S. Recent studies of the glass fiberpolymer interphase. Ind. Eng. Chem. Res. 1987, 26, 672 Desio, G.P., Miller, B. and Rebenfeld, L. The microbond method for the evaluation of interfacial shear strengths of composites. Paper presented at ‘AIChE Annual Meeting’, Washington, DC, 28 November, 1988 Gao, Y-C., Mai, Y-W and Cotterell, B. Fracture of fiberreinforced materials. J. Appli. Math. Phys. (ZAMP) 1988, 39, 550 McAlea, K.P. and Besio, G.J. Adhesion between PBT and Eglass measured with a microdebond technique. Polym. Compos. 1988,9,285 Morrison, J.K., Shah, S.P. and Jeng, Y.S. Analysis of fiber debonding and pull-out in composites. J. Eng. Mech. 1988. 114, 271 Narkis, M., Chen, J.H. and Pipes, R.B. Review of methods for Polvm. characterization of interfacial fiber-matrix interaction. Compos. 1988,9, 245 Piggott, M.R. Debonding and friction at fibreepolymer interfaces, II. Macroscopic model experiments. Compos. Sci. Technol. 1988, 31, 15 Waite, S.R. and Sage, G.N. The failure of optical fibers embedded in composite materials. Composites. 1988, 19, 288 Argawal, R.K. and Drzal, L.T. Effects of microwave processing on fiber-matrix adhesion in composites. J. Adhes. 1989, 29, 63 Cook, R.F., Thouless, M.D., Clarke, D.R. and Kroll, M.C. Stick-slip during fiber pull-out. Scripra MeraN. 1989, 23, 1725 Guar, U. and Miller, B. Microdebond method for determination of the shear strength of a fiber resin interface: evaluation of experimental parameters. Compos. Sci. Technol. 1989, 34, 35 Latour. R.A.. Black, J. and Miller, R. Fatigue behavior characterization of the fiber-matrix interface. J. Muter. Sci. 1989. 24, 477 Overton, B.J. and Taylor, C.R. Time temperature dependence of dual coated lightguide pull-out measurements. P+m. Eng. Sci. 1989. 29, 1169 Palley, 1. and Stevens, D. A fracture mechanics approach to the single fiber pull-out problem as applied to the evaluation of the adhesion strength between the fiber and the matrix. J. Adhes. Sci. Technol. 1989, 3, 141 Penn, L.S. and Jutis, B. The effect of pendent groups at the fiber surface on interfacial adhesion. J. Adhes. 1989. 30, 67 Penn, L.S. and Lee, SM. Interpretation of experimental results in the single pull-out filament test. .I. Compos. Technol. Rrs. 1989, 11,23 Piggott, M.R. and Roberedo, M.M. The properties of the interface between fibers and polymers. In ‘Proc. 34th lnt. SAMPE Symp. 881 I May 1989, p. 1913 Sigl, L.S. and Evans, A.G. Effects of residual stress and frictional sliding on cracking and pull-out in brittle matrix composites. Mech. Muter. 1989, 8, 1 Gaur, U. and Miller, B. Effects of environmental exposure on fiber/epoxy interfacial shear strength. Polvm. Compos. 1990, 11,217 Hutchinson, J.W. and Jensen, H.M. Model of fiber debonding and pull-out in brittle composites with friction. Mech. Mater. 1990,9, 139 Lee, SM. and Holguin, S. A new single fiber/resin interface test for high crosslinked resin systems. J. Adhe.r. 1990, 31, 91

611

The single-fibre pull-out test. I: C. DiFrancia et al.

52

Leung, C.K.Y. and Li, V.C. Applications of a two-way debonding theory to short fibre composites. Composites 1990, 65

21,305

53 54

55

56

57

58 59

60 61 62

63

Mlder, E. and Freitag, K.-H. Interface properties and their influence on short fibre composites. Composites 1990, 21, 397 Penn, L.S. and Chou, C.T. Identification of factors affecting single filament pull-out test results. J. Compos. Technol. Res. 1990, 12, 164 Pitkethly, M.J. and Doble, J.B. Characterizing the fiber/matrix interface of carbon fibre-reinforced composites using a single fiber pull-out test. Composites 1990, 21, 389 Biro, D.A., McLean, P. and Deslandes, Y. Application of the microbond technique: characterization of carbon-epoxy interfaces, Polym. Eng. Sci. 1991, 37, 1250 Chou, C.T. and Penn, L.S. Chemical bonding and physical interaction by attached chains at the fiber-matrix interface. J. Adhes. 1991, 36, 1125 Dtsarmot, G. and Favre, J.-P. Advances in pull-out testing and data analysis. Compos. Sci. Technol. 1991, 42, 151 DiFrancia, C.D., Claus, R.O., Hellgeth, J.W. and Ward, T.C. Characterization of polyimide-coated optical fibers for embedding in epoxy resin for the development of smart composite structures. In ‘Proc. Adhesion Society Fourteenth Annual Meeting’, Clearwater, FL, 1991 Hughs, J.D.-H. The carbon fibre/epoxy interface-a review. Compos. Sci. Technol. 1991,41, 13 Marshall, P. and Price, J. Fibre/matrix interface property determination. Composites 1991, 22, 53 Miller, B., Gaur, U. and Hirt, D. Measurement and mechanical aspects of the microbond pull-out technique for obtaining fiber/ resin interfacial strength. Compos. Sci. Technol. 1991,42, 207 Piggott, M.R. Failure processes in the fibre-polymer interphase. Compos. Sci. Technol. 1991,42,

64

612

57

Qui, Y. and Schwartz, P. A new method for study of the fiber-

66

67

matrix interface in composites: single fiber pull-out from a microcomposite. J. Adhes. Sci. Technol. 1991, 5, 741 Rao, V. and Drzal, L.T. The dependence of internal shear strength on matrix and interphase properties. Polymer Composites 199 1, 12,48 Wang, S.J., Baptiste, D., Bompard, P. and Francois, D. Microscopic failure mechanism of a unidirectional glass fiber composite. Fatigue Fract. Eng. Mater. 1991, 14, 391 Jiang, K.R. and Penn, L.S. Improved analysis and experimental evalution of the single filament pull-out test. Compos. Sci. Technol. 1992,45,

68

69

70 71

89

Moon, C.K., Lee, J.O., Cho, H.H. and Kim, K.S. Effect of diameter and surface treatment of fiber on ISS in glass fiber/epoxy and HDPE. J. Appl. Polym. Sci. 1992,45,443 Piggott, M.R. Interfaces properties and their influence of fiberreinforced polymers. In ‘Composite Applications The Role of Matrix. Fiber. and Interface’ (Eds T. Vieo and B. Kinzia._I VCH Publishers, Inc., 1992, pp.‘221-265 Personal communication with L.S. Penn DiFrancia, C., Ward, T.C. and Claus, R.O. The single-fiber pullout test. 2: The quantitative evaluation of an uncatalysed TGDDM/DDS epoxy cure study. Composites Part A: Appl. Sci. Manuf. 1996, 27A,

72

73 74

75

DiFrancia, C. The single fiber pull-out test: a study of fiber/ matrix interactions. Dissertation, Virginia Polytechnic Insitute and State University, 1992 Hampe, A. and Marotzke, C. Adhesion of polymers to reinforcing fibers. Polym. Int. 1992, 28, 313 Marshall, P. and Leonard, J. The dependence of data from single fiber pull-out tests on the loading direction. J. Mater. Sci. Lett. 1992, 11, 1401 Jurek, M.J. and McGrath, J.E. Synthesis and characterization of amine terminated poly(arylene ether sulfone) oligomers. Polymer 1989,30, 1551