The Transfer of Matrix Toughness to Composite Mode I Interlaminar Fracture Toughness in Glass-Fibre/vinyl Ester Composites

The transfer of matrix toughness to composite mode I interlaminar fracture toughness (G _Ic ) has been investigated in unidirectional glass-fibre reinforced composites with brittle and rubber-toughened vinyl ester matrices. Single-edge-notch bend (SENB) and double cantilever beam (DCB) specimens were used for matrix and composite G _Ic characteristion, respectively. The initial crack opening displacement rate was used as the parameter for comparison of G _Ic results. Matrix G _Ic was completely transferred to composite G _Ic for crack initiation (G _Ic-init) in the brittle-matrix composites, but in the toughened composites transfer was only partial due to the presence of fibres. The conclusion is that the maximum contribution to energy absorption by the matrix is more accurately reflected by G _Ic-init, and should be used for further assessment of the enhancing effect of fibre bridging during steady-state crack propagation, instead of matrix G _Ic . A plot of composite G _Ic for steady-state crack propagation, G _Ic-prop versus G _Ic-init indicates that the enhancing effect of fibre bridging is greater in the toughened composites. This enhancement is related to a larger deformation zone size in the toughened matrices.     

Determination of valid R-curves for materials with large fracture toughness to yield strength ratios

Crack growth resistance curves are derived from a generalised theory of quasi-static crack propagation due to Gurney and Hunt. Both the subcritical and continuous cracking regions are investigated, where the fracture toughness of the material may depend on the cracking rate, the reacting environment at the crack tip and the mode of fracture. Precise conditions for stability of the spreading crack relative to chosen constraints of either a displacement- or load-controlled machine are formulated. Cracking of sheet materials with high fracture toughness and low yield stress, (e.g. (K/ _y )² > 200 mm), which do not satisfy certain size requirements, is often complicated by generalised yielding at regions remote from the crack tip. Complete R-curves for such materials cannot be established with conventional testpieces in the laboratory. The present paper adopts a new experimental technique [1] where a laboratory size reinforcement rig attached to the testpiece eliminates all irreversibilities caused by generalised yielding. Valid fracture toughness values and crack growth resistance curves are thereby determined, irrespective of the amount of elastic and plastic deformations occurring at the crack tip. Successful R-curve experiments are described for fracture in a few ductile and tough materials such as 7075-T3. and 1100-0 aluminium alloys, and a low carbon steel. Comparison is made with other published R-curves, and the influence of sheet thickness and (K _1c / _y ) ratio on the geometry of R-curves is investigated. A simple relationship for R-curves is suggested, viz.: R = R ₀ + (L) ^p , where, it seems, R ₀can be identified with the plane strain toughness (i.e. R ₀ = G _1c = K _1c ² /E(1 - v ²)1/2). A possible reason for this unexpected result is given in the paper. Useful estimates of K _lcmay thus be available from thin sheet tests.Paper presented in part at the 11th Annual Meeting of the Society of Engineering Science, November 11–13, 1974, Duke University, Durham, N.C., USA.     

Gc versus crack velocity in single groove double cantilever beam specimens of polycarbonate

The dependence of G _c on crack velocity in single-groove double cantilever beams (SG DCB) is negligible over the range of crack velocities from 0.2 to 1100 in. min^–1. The constancy of G _c appears to reflect a counterbalancing of the rise in yield stress by a decrease in crack opening displacement. The latter occurs through a decrease in the gauge length of material engulfed by yielding rather than by a decrease in the ultimate plastic strain in the crack tip plastic zone. The energy of shear lip formation at any crack velocity appears to be accurately estimated from G _c's for SG DCB specimens fractured at low velocity.     

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.     

Water-assisted sub-critical crack growth along an interface between polyimide passivation and epoxy underfill

Direct chip attach (DCA) microelectronic packaging technology is gaining prominence due to its numerous advantages. Delamination (debonding) of the underfill epoxy/ polyimide passivation interface of a DCA during hydro-thermal reliability testing has always been one of the salient problems. We have studied the water-assisted sub-critical crack growth along this interface and our measurement offers important clues as to the origins of the poor hydro-thermal testing results for these interfaces. A modified asymmetric double cantilever beam (ADCB) testing technique has been used to measure the sub-critical crack growth velocity v at various relative humidities and temperatures as a function of the crack driving force (strain energy release rate) G ^*. The presence of a significant partial pressure of water p _H2O produces a marked decrease (by up to a factor of 12) in the threshold G ^* for crack growth at measurable velocities. Above the threshold log v rises linearly with but then enters a regime where the crack velocity (v=v ^*) is almost independent of . Finally, at the values of G ^* corresponding to rapid crack propagation in the absence of water, log v increases very rapidly with G ^*. By analogy to the classic work on water-assisted sub-critical crack growth in silica-based glasses, where very similar features are observed, we believe that the sub-critical crack growth along the polyimide-epoxy interface results from stress-assisted hydrolysis of primary covalent bonds, in our case ester bonds across the interface. The regime of just above the threshold corresponds to a physicochemical situation where the water activity (p _{H 2O} ) at the crack tip is the same as that of the gaseous environment. In the regime where v=v ^* constant, the water activity at the crack tip is below that in the environment and the crack growth velocity is limited by the transport of water vapor to the bonds ahead of the crack tip. We develop a model of this crack growth following Wiederhorn 1967 that allows us to predict the sub-critical crack growth as a function of G ^* for arbitrary relative humidity and temperature conditions.     

Interlaminar fracture analysis of composite DCB specimens

Mode I interlaminar fracture was studies using double cantilever beam (DCB) specimens of unidirectional carbon fiber/epoxy composites. An improved analytical model was introduced to study the crack opening displacement (COD), compliance (C) and fracture toughness (G _I) as a function of the material stiffness () ahead of the crack front. The COD expression was derived and compared with the COD profiles near the crack tip measured by moiré interferometry. Results showed that the COD expression can predict all the important qualitative features of the measured COD profiles; also, the quantitative agreement at the loading point was very good. It was found that plays an important role in evaluating the values of COD, C and GI.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Fracture behaviour of a TiB2-based ceramic composite material

The fracture behaviour of a multicomponent TiB₂/BN/AlN material was studied in both the double cantilever beam (DCB) and single-edge-notched beam (SENB) geometries. Crack growth in the SENB geometry at various stages of the test was monitored using optical and electron microscopes. R-curve behaviour was found in both specimen geometries for this material. Evidence of crack-interface tractions were found in the form of (i) ligamentary bridges and (ii) frictional interlocks, along with evidence for microcracking about the crack tip. Measurements of crack-opening displacement with distance back from the crack tip were made. The inflection point of such data is in agreement with the range of the measuredR-curve.     

Subcritical crack growth,surface energy,fracture toughness,stick-slip and embrittlement

It is proposed that the difficulties encountered with the meaning of subcritical crack growth arose from a misunderstanding of the Griffith equation. This equation is G=2γ for an equilibrium crack (stable or unstable) where γ is the intrinsic surface energy. When G>2γ the crack has a velocity v depending on the crack extension force G−2γ, even in a vacuum, and the following equation, well verified for adherence of elastomers, G−2γ=2γφ _T(v) where φ _T(v) is related to viscoelastic losses or internal friction at the crack tip, is generalized to other materials. At a critical speed v _c, dφ/dv becomes negative; as a negative branch cannot be observed the velocity jumps to high values on a second positive branch, so that G=G _c is a criterion for crack speed discontinuity, not the Griffith criterion. The multiplicative factor 2γ on the right-hand side accounts for the shift of the v-K curves with environment. No stress corrosion is needed to explain subcritical crack growth. Subcritical crack growth in glasses and ceramics and velocity jump in brittle polymers are shown to agree with this proposal. This model can also explain stick-slip motion when a mean velocity is imposed in the negative branch. Occurrence of velocity jump or stick-slip depends on the geometry tested and the stiffness of the apparatus. A second kind of stick-slip associated with cavitation in liquid-filled cracks is discussed. When the surrounding medium can reach the crack tip and reduce the surface energy, even at the critical speed v _c, the critical strain energy release rate G _c is reduced in the same proportion as γ, and a loading which would have given subcritical growth will give a catastrophic failure. Reduction of surface energy in the Rehbinder effect and in embrittlement by segregation is discussed. Finally, the evolution of ideas concerning the Irwin-Orowan formula and fracture toughness is examined.     

Fracture indentation beneath flat and spherical punches

The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy , and that the critical strain energy release rateG _c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2<G<G _c. The 1971 experimental results of Mikosza and Lawn are easily interpreted by this model. Finally, experiments performed on a borosilicate glass give results that agree satisfactorily with the theory. Due to kinetic effects, an apparent surface energy of about 4.5 J m^–2 is obtained, larger than the intrinsic surface energy and slightly lower than the fracture energy derived from high-speed experiments.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

Determination of da/dN-ΔK 1 curves for small cracks in alumina in alternating bending tests

Crack-growth relations under cyclic fatigue conditions are mostly determined for long cracks. In order to determine da/dN-K curves for small cracks from lifetimes under cyclic load a procedure has been derived which is based on a method usually applied to subcritical crack growth. To prove the cyclic effect and to demonstrate the procedure in detail, measurements were carried out on an Al₂O₃-ceramic in bending with anR-ratio ofR=–1 and two types of relatively small cracks, namely natural cracks and Knoop-cracks. It was found that both crack types exhibit the same da/dN-K relation. The exponent of the Paris law for fatigue crack growth is significantly different from the exponent of the power law for subcritical crack growth.     

The resistance to crack growth of asbestos cement

The crack resistance of sheet asbestos cement has been characterized in terms of anR-curve which can accomodate effects which often influence the measurement of the critical stress intensity factorK _c. The detection and location of the acoustic emission (AE) obtained from the asbestos cement has shown that it originates from microcracks in a zone just in front of the crack. The size of this zone increases to a maximum during slow propagation of the major crack and afterwards remains of constant size during the final crack growth. The form of theR-curve has been explained in terms of the mechanisms of fracture with the aid of AE and fractography studies. An analytical study has related the experimentalR-curve to a theoreticalR-curve and, hence, to the volume fraction, fibre aspect ratio and the strength of the fibre—matrix interface. It has been shown that the microcracking zone can be considered as a theoretical extension, of about one third of the zone length, to the real crack length.     

Fracture resistance of 8 mol% yttria stabilized zirconia

Anin situ technique for the assessment of fracture resistance employing double cantilever beam (DCB) specimens was developed in the present study. The side-grooved DCB specimens were loaded with pure bending moments in a specially designed and fabricated test fixture which went inside the specimen chamber of a scanning electron microscope. The study as conducted on a 8 mol% fully stabilized cubic phase yttria (Y₂O₃) stabilized zirconia (YSZ) ceramic. The powder processed sheets were sintered at 1600°C for 2 h in a zirconia tube furnace. The mode I applied energy release rate, G_I was determined for both pure YSZ and treated YSZ. Two sets of experiments were conducted for the complete characterization of the ceramics. Three fracture toughness values were determined for the pure and treated ceramics, viz. (i) at the onset of the crack initiation,G _ic, (ii) at the arrest of a subcritical crack, G_ia and (iii) at the onset of the fast fracture,G _if. Two analyses of the experimental data were carried out, viz. method of extrapolation and statistical analysis. In case of the pure YSZ, a transgranular mode of the stable crack growth was identified to be predominant. The porous coating treatment appeared to have positive effects as the crack initiation resistance increased due to electrode layers. The stable crack growth behaviours of the ceramics were investigated by monitoring the crack growth velocity as a function of appliedG values. The results obtained were of direct significance in designing and fabrication of SOFC stacks.     

Fracture load predictions and measurements for highly toughened epoxy adhesive joints

A method to predict the ultimate strength of adhesive joints has been evaluated for the quasi-static loading of a variety of cracked-lap shear (CLS) and single-lap shear (SLS) joints bonded with a high-strength, toughened epoxy adhesive. The adhesive strength was experimentally characterized in terms of the steady-state critical strain energy release rate, , as a function of the loading phase angle, using double cantilever beam (DCB) joints. Comparing the calculated energy release rate using the J-integral with the at the corresponding phase angle, the ultimate failure load in the fracture joint was predicted and compared with experimental results. When the toughening of the adhesive during subcritical crack growth (i.e. its R-curve behavior) was considered in the analysis, good agreement between the predicted and experimental failure loads was achieved, both for joints made with aluminum or steel adherends. The initial condition at the end of joint overlap (fillet or precrack) did not affect the ultimate joint strength because of the significant amount of subcritical crack growth.     

Influence of grain size and degree of crystallization of intergranular glassy phase on the mechanical behaviour of a debased alumina

The influence of microstructure on the crack resistance (R-curve) behaviour of a commercial debased alumina containing large amounts of glassy phase (28 vol%) has been studied by strength measurements at controlled flaw sizes produced by indentation. Both the individual and combined effects of (a) grain size, and (b) intergranular second phase (glassy or crystalline) were evaluated. Enhancement of theR-curve behaviour was observed when the average grain size was increased from 3–18 μm by thermal treatment. However, no effect of the degree of crystallinity of the intergranular second phase on theR-curve behaviour, in either small or large-grained materials, was observed. These results are discussed with reference to the influence of grain-boundary residual stresses on grain bridging across the crack interface.     

Subcritical crack growth in partially stabilized zirconia(PSZ)

Studies on the subcritical crack growth behaviour of partially stabilized zirconia (ZrO₂-I, 5 to 10 vol% tetragonal phase; ZrO₂-II, 35%) were carried out using the double-torsion technique and data from the dynamic fatigue of unnotched bend specimens. The results of subcritical crack growth support the model of stress induced transformation from the tetragonal to monoclinic modification. Differences in the crack growth parameter n (as-received condition) using the double-torsion technique or bend specimens may be explained by the special nature of subcritical crack extension at stressed surfaces for these different specimen types. The log v-log K _i plot of ZrO₂-I using the double torsion technique shows a plateau of constant velocity, which has to be attributed to a tetragonal-monoclinic transformation. After annealing (1500° C, 5 h) the plateau has vanished and the n value is comparable to bend test in an as-received condition.     

Correlation between resin material variables and transverse cracking in composites

In this paper, the correlation between the resin material variables and the transverse cracking in composites is established. A theoretical model based on the fracture mechanics principle is built to describe thein situ failure process of transverse cracking. The central concept of the model is that the fracture is controlled by the plastic zone developed at the crack tip. Based on an approximate crack tip stress distribution, a quantitative representation is found to relate the laminate transverse cracking fracture toughness,G _c(comp), to certain resin properties: fracture toughness,G _c(resin), yield stress, _y, Young's modulus,E, and residual stress build-up, _R.G _c(comp) values of several fibre-glass/epoxy laminate systems were measured using the double torsion technique. The experimental results are found to be interpreted reasonably well by the theory. As a result, a clear picture of transverse cracking emerges. It seems that _y ²/E plays a more dominant role thanG _c(resin) in controllingG _c(comp). The residual stress _R can weaken the laminate significantly when its level is high. It is also shown that the failure model discussed here can be readily applied to laminate delamination failure as well as adhesive bond fracture.     

Boundary element study on the optical method of caustic for measuring fast crack propagation toughness K ID

The dynamic stress field near the tip of a crack tip which is accelerated and decelerated in an elastic plate with finite width under impact loading is analyzed by the boundary element method, and a simulation of measuring fast crack propagation toughness K _ID by the caustic method is performed. The results of the simulation agree qualitatively with the experimental results by Arakawa and Takahashi, and indicate the dependence of the measured K _ID not only on crack acceleration but also plate width. The dependence of measured K _ID on crack acceleration may result from the fact that under the condition of high loading rate or abrupt change in crack velocity, the transient stress field near the initial curve of caustic can not be represented fully by the dynamic stress intensity factor K _I(t, v), as suggested by Rosakis et al. The dependence of measured K _ID on plate width may be attributable to the fact that the transient stress field near the initial curve is affected directly by the reflected stess wave and also indirectly through crack acceleration which depends on the reflected stress wave. The possible dependence of the measured K _ID on loading rate, loading history, crack propagation history is also discussed.