Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

Fibre-matrix adhesion and its relationship to composite mechanical properties

Two major areas of enquiry exist in the field of fibre-matrix adhesion in composite materials. One is the fundamental role that fibre-matrix adhesion plays on composite mechanical properties. The other is what is the best method used to measure fibre-matrix adhesion in composite materials. Results of an attempt to provide an experimental foundation for both areas are reported here. A well-characterized experimental system consisting of an epoxy matrix and carbon fibres was selected in which only the fibre surface chemistry was altered to produce three different degrees of adhesion. Embedded single-fibre fragmentation tests were conducted to quantify the level of fibre-matrix adhesion. Observation of the events occurring at the fibre breaks led to the documentation of three distinct failure modes coincident with the three levels of adhesion. The lowest level produced a frictional debonding, the intermediate level produced interfacial crack growth and the highest level produced radial matrix fracture. High fibre volume fraction composites made from the same material were tested for on- and off-axis, as well as fracture, properties. Results indicate that composite results can be explained if both differences in adhesion and failure mode are considered. It will be further demonstrated that fibre-matrix adhesion is an optimum condition which has to be selected for the stress state that the interface will experience. The embedded single-fibre fragmentation test is both a valuable measurement tool for quantifying fibre-matrix adhesion as well as the one method which provides fundamental information about the failure mode necessary for understanding the role of adhesion on composite mechanical properties.     

Mechanical properties of alkaline earth-doped lanthanum gallate

Lanthanum gallate doped with alkaline earths was prepared from combustion-synthesized powders. Mechanical properties of the doped gallates were evaluated as a function of composition and temperature. The indentation fracture toughness of Sr-substituted gallates was significantly better than the Ca- and Ba-substituted materials, but the toughness of all the doped gallates was significantly lower than yttria-stabilized zirconia, a typical electrolyte material. Small improvements in room temperature toughness and strength were measured in (La_0.9Sr_0.1)_xGa_0.8Mg_0.2O_3–, (LSGM-1020) samples with significant A-site cation non-stoichiometry (x = 0.9). The flexural strength of stoichiometric LSGM-1020 decreased from 150 MPa at room temperature, to 100 MPa at higher temperatures (600–1000°C). The notched-beam fracture toughness of LSGM-1020 decreased from 2.0–2.2 MPam at room temperature, to 1.0 MPam at 600°C. The decrease in mechanical properties over this temperature range was correlated to changes in crystal structure that have been identified by neutron diffraction. These crystallographic changes were also accompanied by significant changes in the thermal expansion behavior and elastic modulus. For off-stoichiometric LSGM-1020 with A/B cation stoichiometry of 0.90, strength and toughness also decreased with temperature, but the retained toughness (1.5 MPam) at elevated temperatures was higher than the toughness of the stoichiometric LSGM material.     

Axial compressive behaviour of reinforcing fibres and interphase in glass/epoxy composite materials

Axial compressive behaviour of reinforcing fibres and interphase in glass fibre/epoxy resin composites were examined. Axial compressive strengths of glass fibres were evaluated by the tensile recoil method. The effects of silane-based coupling surface treatment agent on the fibre compressive strengths were investigated. The glass fibres showed higher compressive strengths when coated by the surface treatment. Interphase behaviour was also investigated by means of the single-fibre embedded compressive test. The particular stress and strain distributions inside the specimen were examined by a three-dimensional finite element analysis. The parameter interfacial transmissibility instead of the conventional critical fibre length theory was introduced as an index of interfacial properties. This parameter was useful to estimate the interfacial properties at the elastic state apart from the complicated critical state. It was confirmed that the surface treatment improved the glass/epoxy interphase under axial compressive load.     

Interfacial cracking of a composite

Interfacial failure as a result of bending has been observed in a beam containing an interface along its mid-plane. The energy balance theory of fracture was applied to this system and a debonding criterion deduced. This was experimentally supported by studies of interface fracture in polymethylmethacrylate laminates. Results showed that interfacial crack propagation due to bending could be predicted from a knowledge of beam geometry, elastic properties, and interface fracture energy. There was no need to introduce interlaminar shear strength in this model situation.     

Mechanical properties of injection moulded styrene maleic anhydride (SMA) Part II Influence of short glass fibres and weldlines

The dependence of the various mechanical and fracture properties on the volume fraction ofshort glass fibres in the styrene maleic anhydride (SMA) polymer was investigated. Special attention has been given to describing the dependence of various mechanical properties on the volume fraction of the glass fibres, f by way of the rule of mixtures. It was found that, strength, elastic modulus and fracture toughness, all follow a simple rule-of-mixtures of the form Qc=Qff+Qm(1–f), where Qc is the measured quantity for the composite, Qm and Qf are the corresponding values for the matrix and the fibre, respectively, and is the overall efficiency of the fibres, taking into account the orientation and the length of the fibres in the composite. It was also found that, while the presence of the weldline had no significant effect upon elastic modulus, its presence significantly reduced tensile strength and the fracture toughness of SMA and its composites. © 1998 Kluwer Academic Publishers     

Effects of pre-existent crack in double and gradient coatings on the crack extension into fibre and interfacial debonding

When a crack is formed on a fibre surface by the premature fracture of the coating, crack extension into the fibre or interfacial debonding between fibre and coating occurs, affecting the strength of the coated fibre. In the present work, the influence of pre-existent crack in double and gradient coating layers on the crack extension and interfacial debonding was studied to find the condition to improve the strength of the coated fibre. It is shown that, in both types of coating, (i) the energy release rates for crack extension into the fibre and for interfacial debonding become low when the inner coating portion adjacent to the fibre has low Youngs modulus, while they become high when the inner portion has a high Youngs modulus, and (ii) the ratio of the energy release rate for debonding to that for crack extension into the fibre is approximately 0.3. These results suggest that the reduced fibre strength by crack extension into the fibre in the case of strong interfacial bonding can be raised by double and gradient coatings with reduced Youngs modulus of the inner coating portion. Alternatively it can be increased by weakening the interface so that the critical energy release rate for debonding is less than 0.3 times the critical energy release rate for crack extension into the fibre.     

Microstructure and crystallographic texture of rolled polycrystalline Fe3Al

An imperfectly B₂ ordered Fe₃Al aggregate was cast, thermomechanically hot rolled and finally annealed at 870 K. Subsequently, the specimen was rolled at 800–830 K to a strain of 80%. The microstructure and the crystallographic texture of the rolled polycrystalline sample was investigated within the range =20–80%. The microstructure consisted of flat, elongated grains. In numerous grains straight slip lines were detected. Even after =80% recrystallization was not observed. The rolling texture of Fe₃Al considerably deviates from that of non-ordered body centered cubic (b.c.c.) alloys and pure b.c.c. metals. The {111}uvw texture fibre (7-fibre) was very pronounced, while the {hkl}110 fibre (-fibre) was very weak. The {112}110 orientation which represents the strongest texture component in non-ordered b.c.c. alloys did not occur at all. The textures are discussed in terms of the {110}111, {112}111, {112}111 and {123}111 slip systems. The contribution of crystallographic slip of the various types of potential slip systems was simulated by means of the Taylor theory.     

New evaluation technique of interfacial properties in GFRP

A new method was proposed to evaluate the mechanical properties at the interface between the fibres and the matrix in composites using an embedded single fibre coupon test. A mechanical parameter at the interface (called the interfacial transmissibility, ) was derived from the fibre strength and the apparent stress of the fibre immediately before the first fracture of embedded fibre, _fa. This parameter indicated the degree of the mechanical transmission from the matrix to the fibre through the interface. This avoided some complicated problems such as the stress distribution along fibre fragments and the critical fragment state in a typical single-fibre test. This new method was tried to determine the -values for a fibre glass/epoxy resin with different amounts of a coupling agent at the interface. In order to measure the stress at the first fracture, the fracture process was monitored with a video camera during the single fibre test. The stress values at the first fracture for many coupons were analysed as a function of the three-parameter Weibull distribution. The resulting average stress and its coefficient of variation indicated that the reliability of the measurement for the stress at the first fracture was not less than that obtained by the usual single-fibre test. The change of interfacial transmissibility with amount of the coupling agent revealed the existence of an optimal interface.     

Analysis of the effect of embedded fibre length on fibre debonding and pull-out from an elastic matrix

The nature and properties of the resistance to fibre-matrix interfacial debonding in composites composed of ductile fibres in a brittle or elastic matrix can be determined using the single-fibre pull-out test. The results of such tests on cementitious matrix specimens indicate a non-linear relationship between the debonding and/or pull-out load and the embedded length of the fibre. Several of the theories developed to explain the debonding process and enable estimation of the parameters representing the debonding resistance through an analysis of pull-out test results are reviewed in this first of a two-part paper. The application of these theories to experimental data for steel fibre-cementitious matrix pull-out specimens is examined in the second part.Nomenclature b _i effective thickness of the fibre—matrix interface - d _f diameter of the fibre - l _c embedded fibre length at which fibre fracture rather than pull-out occurs - l _d debonded fibre length - l _e embedded length of the fibre in a pull-out specimen - l _{e, min} a minimum embedded fibre length which equals (1/₂cosh^–1 (_ib,max/_ib,f)^1/2 - l _k minimum embedded fibre length required to support the debonding stress in the fibre - l _p maximum embedded fibre length at which complete debonding occurs instantaneously - q _{ib, max} elastic shear flow resistance to fibre-matrix interfacial debonding - q _{ib, f} frictional shear flow resistance to slipping at the fibre-matrix interface after the elastic bond has broken - r _f radius of the fibre - r _m effective radius of the matrix block in a pull-out test specimen - A _f cross-sectional area of the fibre - A _m cross-sectional area of the matrix block in a pull-out test specimen - C ₁ a constant representing the normal compressive stress at the fibre-matrix interface - C ₂ a constant representing the coefficient of friction between the fibre and the matrix at the interface - D length of the debonding plateau (see Fig. 5a) - E _m modulus of elasticity of the matrix - E _f modulus of elasticity of the fibre - G _i shear modulus of the fibre-matrix interface - G _m shear modulus of the matrix - P _f load applied to the fibre in a pull-out test - P _{f, max} maximum load applied to the fibre in a pull-out test - P _{f, ult} applied load at which fibre fracture occurs - P _{f, edb} load required to break the adhesional or elastic fibre-matrix interfacial bond in a pull-out test specimen - P _{f, edb} maximum value of P _{f, edb} (see Fig. 7) - P _{f, d} instantaneous decrease in applied fibre load when debonding is complete - P _f,r residual fibre load required to overcome initial frictional resistance to fibre pull-out - P _f, applied fibre load required to debond an infinitely long fibre with no frictional resistance to slipping at the fibre-matrix interface - an elastic constant ₁ = (2G _i/b _i r _f E _f)^1/2 ₂ = [(2 G _m/ln(r _m r _f))(1/A _f E _f–1/A _m E _m)]^1/2 ₃=[4 G _m/ln(r _m/r _f)r _f E _f]^1/2 ₄=[G _m(A _f E _f + A _m E _m/A _f E _f A _m E _m)]^1/2 - _i surface energy of the fibre-matrix interface - _f fibre extension or displacement in a pull-out test - slope of the linear portion of the P _{f, max} against ₂ l _e curve and is equal to _ib,fd _f/₂ - fibre-matrix misfit - coefficient of friction between the fibre and matrix at the interface - _f Poisson's ratio of the fibre - _m Poisson's ratio of the matrix - _{f, max} stress in the fibre at which interfacial debonding occurs in a pull-out test specimen, i.e. debonding stress - _{f, max} plateau debonding stress (see Fig. 5b) - _{f, po} stress in the fibre when fibre pull-out begins, i.e. immediately following the completion of interfacial debonding - _{f, ult} ultimate tensile strength of the fibre - _{i, n} normal compressive stress exerted by the matrix on the fibre across the interface - _{i, av} average shear stress at the fibre-matrix interface - _{i, max} maximum shear stress at the fibre-matrix interface - _{ib, av} average shear strength of the fibre-matrix interfacial bond - _{ib, max} maximum or adhesional shear strength of the fibre-matrix interfacial bond - _{ib, f} frictional resistance to slipping at the fibre-matrix interface after the elastic bond has broken     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

Transverse properties of a Ti-6-4 matrix/SiC fibre-reinforced composite under monotonic and cyclic loading

The transverse response of a Ti-6-4/SM1140+ fibre-reinforced composite to both monotonic and cyclic loading has been investigated. Five distinct regions were found in the monotonic stress versus strain curve: (I) elastic deformation of the composite, (II) failure of the fibre/matrix interfaces, (III) elastic deformation of the remaining matrix ligaments, (IV) yielding of the matrix ligaments, and (V) gross plastic deformation, which ultimately leads to specimen failure. The stresses at which interface debonding, matrix yield and final failure occurred rose with increased displacement rate. Stressing to levels above the interface failure stress caused significant damage and limited (0.025%) plastic deformation. A non-linear stress-strain response was observed on unloading/reloading, because the presence within the specimen of constrained holes (containing debonded fibres) resulted in non-homogeneous elastic straining of the matrix. The transverse low-cycle fatigue lives of Ti-6-4/SM1140+composite specimens were strongly dependent on maximum stress for values up to the interfacial failure stress, but less so for maximum stresses greater than 260–265 MPa, where full fibre/matrix debonding had occurred. Fatigue life was also dependent on the uniformity of fibre spacings within the composite.     

Anisotropy in the hardness and friction of calcium fluoride crystals

Anisotropy in the Knoop indentation hardness and the friction of diamond cones on calcium fluoride crystals has been investigated at experimental temperatures from 20 to 300° C. It is shown that the directions of minimum and maximum indentation hardness, on the (001) plane, are 110 and 100 respectively whilst the 1¯10 are harder than the 11¯2 directions on the (111) plane. Also, the sliding friction in the (001) plane is greatest in the 110 directions and least in the 100 and, on the (111) cleavage plane, [¯1¯12] sliding leads to higher friction than [11¯2]. The nature of anisotropy, for both hardness and friction measurements, does not change over the experimental temperature range covered in this work. Observations on the resultant deformation are made and these anisotropic properties are explained in terms of the effective resolved shear stresses developed on the {100} 011 primary slip systems at all experimental temperatures.     

Interlaminar Fracture Toughness of CF/PEI and GF/PEI Composites at Elevated Temperatures

An experimental study has been conducted to assess temperature effects on mode-I and mode-II interlaminar fracture toughness of carbon fibre/polyetherimide (CF/PEI) and glass fibre/polyetherimide (GF/PEI) thermoplastic composites. Mode-I double cantilever beam (DCB) and mode-II end notched flexure (ENF) tests were carried out in a temperature range from 25 to 130°C. For both composite systems, the initiation toughness, G _IC,ini and G _IIC,ini, of mode-I and mode-II interlaminar fracture decreased with an increase in temperature, while the propagation toughness, G _IC,prop and G _IIC,prop, displayed a reverse trend. Three main mechanisms were identified to contribute to the interlaminar fracture toughness, namely matrix deformation, fibre/matrix interfacial failure and fibre bridging during the delamination process. At delamination initiation, the weakened fibre/matrix interface at elevated temperatures plays an overriding role with the delamination growth initiating at the fibre/matrix interface, rather than from a blunt crack tip introduced by the insert film, leading to low values of G _IC,ini and G _IIC,ini. On the other hand, during delamination propagation, enhanced matrix deformation at elevated temperatures and fibre bridging promoted by weakened fibre/matrix interface result in greater G _IC,prop values. Meanwhile enhanced matrix toughness and ductility at elevated temperatures also increase the stability of mode-II crack growth.     

Fibre orientation effects on the fracture of short fibre polymer composites: on the existence of a critical fibre orientation on varying internal material variables

The dependence of fracture toughness on fibre orientation, in short fibre reinforced polymers, was investigated using materials with different polymer matrix (polyamide 6.6, polyarylamide and polyoxymethylene), fibre sizing, fibre content, mean fibre length and fibre length distribution.To assess the dependence on fibre orientation, plates with unidirectionally oriented fibres were prepared and cut at various angles with respect to the direction of the aligned fibres. The fracture behaviour was investigated by single-edge notch three-point bending tests. In addition the stress-strain behaviour was examined by performing uniaxial tension and compression tests.Both the critical stress intensity factor K _C and the fracture energy G _C measured at fracture initiation were found to present a bi-linear relationship to the factor characterizing fibre orientation, with different slopes over different ranges of the orientation factor. This suggested the occurrence of a transition between different failure mechanisms with varying fibre orientation, namely matrix fracture and fibre debonding at low values of the fibre orientation factor, fibre breakage and pull-out at high values of the fibre orientation factor. This interpretation is supported by the observation of the crack growth direction (which varies with varying fibre orientation) and the analysis of the fracture surfaces. The slopes of the two linear branches of the toughness vs. fibre-orientation-factor plot and the critical fibre orientation angle depend on all internal variables investigated: constituent polymer matrix, degree of fibre-matrix adhesion, fibre content, mean fibre length and fibre length distribution.     

The fracture energy and acoustic emission of a boron-epoxy composite

The fracture surface energy () of a boron fibre-epoxy resin composite has been measured by three different techniques: work of fracture, linear elastic fracture mechanics, and compliance variation. Significant differences were obtained by the different methods. The compliance data were analysed to give at different stages of crack propagation. It was observed that decreased as the crack entered the material and that this variation of could be correlated with the pull-out length of fibres and acoustic emission generated during fracture. The fracture surface energy is explained in terms of a debonding model.     

Synthesis of aluminum infiltrated boron suboxide drag cutters and drill bits

Synthesis of boron suboxide (B₆O) was made by reactive sintering of crystalline boron and zinc oxide powders at 1450 °C, in argon, for 12 h. After sintering, Vickers microhardness testing was performed on the material synthesized and an average hardness value of 34 GPa was obtained. Sintered suboxide (in crushed and ground powder form) was then analyzed through optical and scanning electron microscopies and X-ray diffraction. Following the completion of the analyses, consolidation of the powder was performed. Two different routes were carried out: (1) explosive consolidation which was performed in double tube (with a density value of 2.22 g/cm³) and single tube (with a density value of 2.12 g/cm³) canister design arrangements and (2) hot pressing which was performed in a graphite die assembly, at 1600 °C, in vacuum, for 2 and 4 h (with density values of 2.15 and 2.18 g/cm³ respectively). Consolidated samples of both routes showed different levels of mechanical attachment, agglomeration, porosity, fracture toughness and fracture strength values, whereas microhardness values and X-ray diffraction plots (as shown in Table I and Figs 6 and 8 respectively) were determined to be similar. Following characterizations, compacts of both routes were then given a high temperature sintering treatment (pressureless sintering) at 1800 °C, in vacuum, for full densification. Both in the as consolidated and densification sintered stages test results revealed the most desirable and well-established properties for the explosively consolidated double tube design compacts (with densification sintered density, microhardness and fracture toughness values of 2.46 g/cm³, 38 GPa and 7.05 MPa m^1/2 respectively). Consolidation and desification sintering steps were then followed by a pressureless infiltration step. Aluminum was infiltrated into densification sintered double tube design consolidated and 4 h of pressed samples (better-compacted and better-sintered compacts) in the temperature range 1100–1250 °C, in argon, for 10 h. During infiltrations, the optimum temperature of the infiltration process was determined to be 1200 °C. Characterization results revealed the most uniform and well established properties once more for the double tube design explosively consolidated compact (with aluminum infiltrated density, microhardness and fracture toughness values of 2.55 g/cm³, 41 GPa and 8.70 MPa m^1/2 respectively).     

The fracture energy of carbon-fibre reinforced glass

The fracture energy of carbon-fibre reinforced glass has been measured by the work of fracture technique, using specimens of varied geometry, Meaningful material properties were obtained only when crack propagation was controlled throughout failure. The work of fracture ( _F) depended on strain-rate and fibre volume fraction, and was typically 3 kJm^–2 for a 40 vol % specimen. Variations of work of fracture due to strain-rates have been related to the microstructure of the fracture surfaces and estimates have been obtained of the fibre-matrix interfacial shear stress during pull-out. Approximate estimates have been made of the fracture initiation energy ( _I) by fracture mechanics analyses, _I was less than _F and no strain-rate sensitivity was detected. An attempt has been made to explain _I in terms of the initial rate of release of strain energy during fibre fracture.     

Theoretical estimation of the effect of interfacial energy on the mechanical strength of spinodally decomposed alloys

New interfaces are produced on the slip plane when a crystal with continuous composition fluctuation arising from spinodal decomposition is deformed by slip. In this work, the energy of such interfaces is evaluated for both modulated and mottled structures, and their effects on slip behaviour are discussed. It is concluded that the contribution of this interfacial energy is large enough to account for the age-hardening concomitant with spinodal decomposition.     

The fracture energy of a glass fibre composite

The fracture energy of a glass fibre-polyester composite has been measured by work of fracture ( _f) measurements on bending beams, and by linear elastic fracture mechanics analyses ( _i) of the bending beams and edge-notched tensile plates. It was found that for the bend specimens _i< _f. The work of fracture, _f, displayed a strain rate dependence, but there was no such dependence of _i. It is postulated that _i is determined by a debonding mechanism while _f is the sum of a debonding mechanism plus a pull-out contribution. The edge-notched tensile plate experiments showed that _i obtained from thick plates was less than that obtained from side-grooved plates, and that in each case there was a dependence of _i on crack size.