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.     

The energy of crack propagation in carbon fibre-reinforced resin systems

The energy expended during controlled crack propagation in unidirectionally reinforced composites of carbon fibre in a brittle resin matrix has been evaluated in terms of the energy dissipated during fibre-snapping, matrix-cracking and fibre pull-out. The work of fracture, _F, is found to depend principally on the frictional shear stress at the fibre/resin interface opposing pulling out of broken fibres. Differences in _F for carbon fibre/resin composites exhibiting a range of interfacial shear strengths and void contents have been explained with reference to variations in fracture surface topography of the fibrous composites. The effect of environment on properties of the interface and work of fracture was also investigated. The energy required to propagate a crack has been compared with the energy for fracture initiation, _I, using a linear elastic fracture mechanics approach. It was found that fibre pull-out energy is the principal contribution to _F, and _I is similar to the elastic strain energy release rate at the initiation of fracture of a brittle, orthotropic solid. For crack propagation parallel to fibres, _F and _I are similar and not unlike the fracture surface energy of the resin alone. The strength of the interface is important only in so far as it affects the value of _I.     

Fracture behavior of ultra-fine grained steel bar under dynamic loading

Ultra-fine grained steel bars were recently developed by thermo-mechanical controlled rolling with rapid cooling for increasing the strength of low carbon and low alloy steels. The developed steels are characterized by fine ferrite grains of less than 1 m and high strength as a result of grain refinement. However, their correlations between tensile properties and impact behavior are not well understood. In this paper, impact absorbed energy (E _p) and dynamic fracture toughness (J _Id) were used to evaluate the dynamic fracture behavior of the ultra-fine grained steels, and the fracture mechanisms were also investigated. For the ultra-fine grained steels, tensile stress-strain curve was shown to be correlated with the impact curve of load vs. time, and to be related to the dynamic fracture toughness. The steel with large ferrite grains, small ferrite grain colony and martensite was found to have a good combination of strength and toughness.     

Temperature and porosity effects on the fracture of fine grain size MgO

The strength of three fine grain size magnesias (<0.8m) has been studied as a function of porosity and temperature from 20 to 1200° C. In the low-temperature region (T800°C) fracture occurs by the extension of flaws introduced during the specimen machining. In this case the fracture stress can be related to porosity by an exponential law. In the high-temperature region (T>800° C) plasticity increases the size of pre-existing flaws, but this effect is partially annihilated by a rapid increase with temperature in the effective surface energy for fracture initiation. This entails only a slow decrease in fracture stress with temperature. These results are correlated with observations of fracture surfaces by scanning and transmission electron microscopy.     

The mechanical behaviour of high-impact polystyrene under pressure

High-impact polystyrene [HIPS], a two-phase polymeric system, has been investigated studying the pressure dependence of stress-elongation behaviour in tension over the range from atmospheric pressure to 4 kbar at room temperature and constant strain-rate. A comparative study of polystyrene [PS] was also undertaken. HIPS sealed from the environment exhibited ductile behaviour at all pressures. Surprisingly, specimens exposed to silicone oil environment exhibited two transitions as the applied hydrostatic pressure was raised: a ductile-to-brittle followed by a brittle-to-ductile transition. Stress-whitening was suppressed at relatively low pressures. The dilational requirement for profuse crazing was restrained by the combined effect of fluid under pressure resulting in the suppression of the energy absorption mechanism.Analysis of the stress-elongation curves for sealed specimens indicated that the pressure dependency of craze-initiation stress differs from that of shear band initiation stress. The brittle-to-ductile transition occurred when the initiation stresses of both processes became equal. The principal stress for craze initiation showed almost no pressure dependency, suggesting that crazes initiate when the principal stress level of the tensile specimen reaches a critical value irrespective of the applied hydrostatic pressure. A value for the proposed triaxial tension around the rubber particles was determined from the experimental results and found to be in good agreement with a calculated value. A general mechanics argument was used to explain the existence of the ductile-to-brittle and the brittle-to-ductile transition in HIPS, and also to predict the pressure dependencies of brittle-fracture stress and craze-initiation stress for sealed and non-sealed specimens.Nomenclature P hydrostatic pressure, here taken as always positive - BD brittle-to-ductile transition - CS craze-to-shear band transition - _T observed tensile stress - ¹ the first principal stress - _f ^s fracture stress for sealed specimens - _f ^ns fracture stress for non-sealed specimens - _y yield stress - _f fracture stress - _ci craze initiation stress     

The effect of microstructure on the morphology of fatigue cracks in UDIMET® 720

The low cycle fatigue (LCF) behaviour of four variants of UDIMET^® 720 was investigated. The materials comprised a fine grained (approximately 10 μm), powder processed material with a fine bimodal distribution (～20 and 80 nm) of secondary γ′; the same material, but with enlarged secondary γ′ (～480 nm); a coarse grained powder processed material (grain size ～62 μm) and finally a cast and wrought material with a similar microstructural scale to the fine grained powder processed alloy, but with reduced interstitial element content. LCF testing was undertaken on corner notched square section specimens at 20, 300 and 600 °C with a frequency of 0.25 Hz, a cyclic stress range of 500 MPa and an R ratio of +0.1. At 20 and 600 °C fracture was found to be macroscopically flat for all materials. However, at 300 °C, significant shear fracture was observed in the two materials that had a fine grain size and a fine secondary γ′ size, leading to a characteristic ‘tear‐drop’ appearance. Only minor shear fracture was observed in the coarse grained and enlarged secondary γ′ materials. Tensile tests indicated that weak dynamic strain ageing occurred in all materials at 300 °C. The fine grained powder processed U720 also exhibited dynamic strain ageing at 600 °C, but this was not the case for the coarse grained or cast and wrought materials. The origin of the shear fracture are discussed and related to the microstructure.     

Effects of rate,temperature and absorption of organic solvents on the fracture of plain and glass-filled polystyrene

The rate/temperature dependent fracture behaviour of plain and glass-filled polystyrene has been investigated over the crack speed (a) range of 10^–6 to 10^–2 m sec^–1 and in the temperature (T) range of 296 to 363 K. TheK _c (a, T) relationships obtained, whereK _c is the stress intensity factor at fracture, are shown to follow those given by the Williams/Marshall relaxation crack growth model and the toughness-biased rate theory. Crack propagation in both materials is shown to be controlled by a-relaxation molecular process associated with crazing. Crack instabilities observed in plain polystyrene are analysed successfully in terms of isothermal-adiabatic transitions at the crack tip. Fracture initiation experiments are also conducted in which the effects of organic liquids on the fracture resistances of both plain/glass-filled polystyrene have been determined. Good correlations betweenK _i ² (K _i being the crack initiation stress intensity factor) and _s, solvent solubility parameter, of various liquid environments have been obtained, which give a minimumK _i ² value at _{s p}, where _p is the solubility parameter of the polymer. For a given temperature, liquid environment and crack speed, the glass-filled polystyrene is shown to possess greater resistances to crack propagation than plain polystyrene.     

Branching of a fast crack in polymers

Crack branching in Araldited and Homalite-911 was studied using a modified Cranz-Schardin type high speed camera which provided simultaneously taken shadow patterns and specimen-focussed images. Fracture parameters including crack velocity a, stress intensity factorK _d and specific crack extension resistanceR were measured in the course of crack propagation. No definite critical values could be determined with one of those fracture parameters for the onset of crack branching. Instead, the productR a, i.e., energy per unit crack width per unit time, was found to have a critical value for the branching.     

Evaluation of Fracture Parameters by Double-G,Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (K_Ic^c), unstable fracture toughness (K_Ic^un) and initiation fracture toughness (K_Icⁱⁿⁱ) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K_Ic^un of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.     

Micro‐indentation fracture from flat‐ended cylindrical indenter

Unlike a Hertzian ring crack induced by a spherical indenter in absence of a singular stress field, a ring crack generated by a rigid flat cylindrical indenter can be explicitly linked to a K‐dominant singular stress field at the perimeter of the flat indenter. This means microcrack initiation induced by a flat indenter and relevant properties such as the critical indentation load and fracture toughness can be formulated explicitly using the fracture mechanics approach. It is shown in this paper that the indentation stress intensity factor, , for such a stress field is similar to that of a mode I crack. Based on the energy‐releasing rate and the Griffith's theorem, a flat indentation cracking model has been proposed; the critical load and critical cracking angle for crack initiation are derived. A new concept of fracture toughness for negative mode I singular stress field,, has been defined and a relationship between and the traditional K_IC has been derived. The experimental investigation validates the existence of such , from which the K_IC value of the glass had been determined to be 0.772 ± 0.003 MPa m^1/2, agreeing well with the literature data. This analysis for indentation fracture or crack initiation due to surface contact of a flat indenter is particularly useful in determining K_IC of brittle materials with dimensions in micro/nanoscales, e.g. thin films and other microstructures as flat micro/nano‐indenters are available and can be used on various nano‐indentation machines.     

Stacking fault energy and planar defects on the basal plane in the beta-alumina system

Commercial forms of beta alumina have been examined using transmission electron microscopy. Measurements of the stacking fault energy on the basal plane have been made from the separation of partial dislocations and the equilibrium separation of partials at dislocation nodes, and estimated as 0.6 to 1.65×10^–3 Jm^–2. The structure of two- and three-block beta-alumina has been discussed and their relationship and transformation examined. It has been shown that transformation from two- to three-block beta-alumina cannot be accomplished by a simple shear. Structures generated by the passage of partial dislocations on the glide plane are discussed, and simple twining on the basal plane is examined and shown to be possible in the three-block, but not in the two-block material.     

Fracture resistance of paper

An attempt has been made to apply the concepts of fracture mechanics to describe the behaviour of a paper sheet with a crack. Considering paper as an orthotropic homogeneous continuum, the critical strain energy release rate, G _c, for eight different papers has been measured using linear elastic fracture mechanics. Also, a direct measurement of work of fracture, R, has been made for these samples by using the quasi-static crack propagation technique. For both techniques, results independent of specimen dimensions were obtained. G _c and R were found to be experimentally equivalent. The fracture toughness of paper has been compared with that of other engineering materials.Nomenclature a Initial crack length (cm) - a _ij Elements of compliance matrix (cm² dyn^–1) - A Area of fractured surface (cm²) - b Specimen width (cm) - E Young's modulus (dyn cm^–2) - E ₁ Young's modulus in the machine direction (dyn cm^–2) - E ₂ Young's modulus in the cross direction (dyn cm^–2) - E Young's modulus at angle to the machine direction (dyn cm^–2) - F Finite-width correction factor - G Strain energy release rate (erg cm^–2) - G _c Critical strain energy release rate (erg cm^–2) - K Stress intensity factor (dyn cm^–3/2) - K _c Critical stress intensity factor (dyn cm^–3/2) - l Specimen length (cm) - r _y Size of plastic zone (cm) - R Work of fracture (erg cm^–2) - t Specimen thickness (cm) - U Strain energy (erg) - Angle in the plane of the sheet measured from the machine direction - Specimen density (g cm^–3) - _c Gross tensile stress at fracture (dyn cm^–2) - _N Net tensile stress at fracture (dyn cm^–2) - _ys Tensile yield stress (dyn cm^–2)     

Fracture toughness and absorbed energy measurements in impact tests on brittle materials

Previous work on impact testing has shown that the energy/unit area (w) normally measured in notched impact tests is dependent on specimen geometry. A fracture mechanical analysis has now been developed to account for the observed dependence ofw on notch size. A correction factor () has been derived to accommodate notch effects and this allows for the calculation of the strain energy release-rateG directly from the measured fracture energies.Tests on PMMA have shown that corrected results are independent of specimen geometry and theG _c for PMMA has been evaluated as 1.04 × 10³ J m^–2. The experimental results show that there is an additional energy term which must be accounted for and this has been interpreted here as being due to kinetic energy losses in the specimens. A conservation of momentum analysis has allowed a realistic correction term to be calculated to include kinetic energy effects and the normalized experimental results show complete consistency between all the geometries used in the test series.It is concluded that the analysis resolves many of the difficulties associated with notched impact testing and provides for the calculation of realistic fracture toughness parameters.     

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.     

Observations on the effect of calcium segregation on the fracture behaviour of polycrystalline alumina

The influence of calcium segregation to the grain boundaries of polycrystalline alumina on room temperature fracture behaviour has been investigated. In a commercial high-density single-phase alumina containing less than 5 ppm calcium by weight, thermal treatments were employed to achieve equilibrium segregation from 0.6 to 1.6 at % calcium without detectable changes in grain size (18m) or porosity distribution. Room temperature SENB test results revealed an inverse dependence of K _IC on calcium segregation levels in the range examined. Fractures were primarily intergranular in all specimens. Qualitatively, the relationship between K _IC and calcium segregation would be predicted from a consideration of the effect of such an ion on the interatomic spacing at the boundary. However, quantitative agreement with the model is poor, the measured effect being much greater than predicted. A relatively high K _IC value was achieved in a fine grained (2m) hot-pressed alumina containing very low levels of segregated impurities. This material exhibited substantial amounts of cleavage fracture. The higher fracture toughness of this alumina is discussed in terms of both increased intergranular and transgranular fracture stresses promoted by the relatively clean grain boundaries and small grain size, respectively.     

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.     

Why K? High order singularities and small scale yielding

Singular terms in the crack tip elastic stress field of order r ^-3/2, r ^-5/2, ... are often neglected, thus rationalizing the use of the K field, r ^-1/2, as the dominant term for fracture mechanics. We find the common explanation for neglecting the more singular terms in the series solution for the crack tip stress field unsatisfying. Further, the more singular terms are non-zero and are needed to understand the energetics of fracture, i.e., J and {ie97-1}. Given that the singular terms are generally present, the rationale for the validity of the small scale yielding assumption (the basis of linear elastic fracture) is more subtle than any argument which depends on the elimination of terms with stress r ^-3/2, r ^-5/2, ... Our explanation for the validity of small scale yielding is as follows. First, with or without small scale yielding, the stress field outside of the nonlinear zone does contain more singular terms. In the limit as the nonlinear zone at the crack tip shrinks to zero size (SSY) we show that the r ^-1/2 term in the Williams expansion dominates both the more singular and the non-singular terms in an annular region somewhat removed from this zone. Further, in this limit the magnitude of the r ^-1/2 term is almost entirely determined by tractions on the outer boundary. Our theory and examples are for representative problems in mode III anti-plane shear fracture. We expect, however, that the general results also apply to mode I and mode II fracture.     

The effect of molecular weight on slow crack growth in linear polyethylene homopolymers

The rate of initiation and growth of cracks in linear high-density polyethylene with different molecular weights was observed in single-edge-notched tensile specimens under plane strain condition as a function of applied stress, notch depth and temperature. The initial rates of crack initiation all have the form of C ^m a ₀ ⁿ exp (–Q/RT) or AK ^pexp (–Q/RT) where = stress, a ₀ = notch depth and K= stress intensity factor. For the different molecular weights, m, n, P and Q are almost the same where m=5, n=2, P=4.7 and Q=115 kJ mol^–1, but the constants C and A varied as (¯M _w–¯M _c)^–1 where ¯M_c is a limiting molecular weight for sudden fracture. A molecular model based on tie-molecules has been used to explain the dependence on ¯M _w. The effect of ¯M _w on the fast-fracture strength at low temperature and the relationship to tie-molecules have also been investigated. Quantitative relationships between the concentration of tie-molecules and the fracture behaviour have been obtained.     

The toughening of cyanate-ester polymers Part I Physical modification using particles, fibres and woven-mats

A fracture mechanics approach has been used to investigate the effects of the addition of physical modifiers on the fracture energy, G _c, of brittle cyanate-ester polymers. Tests were performed using adhesive joint specimens at –55, 21 and 150°C, with all the specimens exhibiting cohesive failure in the cyanate-ester adhesive layer. The fracture energies of systems modified using a range of inorganic and thermoplastic particles, fibres and woven-mats have been measured, and scanning electron microscopy has been used to determine the toughening micromechanisms involved. Firstly, it is shown that the addition of 10% by weight of particulate modifiers can increase the fracture energy of the cyanate-ester polymer by 100%, due to a combination of toughening micromechanisms such as crack deflection, pinning and matrix cavitation around the second-phase particles. These experimental data have been compared to predictions from an analytical model. Secondly, it is demonstrated that the use of long fibres or woven-mats can give an a major increase in the value of the fracture energy, G _c, at initiation, and a further increase with increasing crack length, i.e. a significant R-curve effect is observed. At relatively long crack lengths, the measured fracture energy may be six times greater than that of the unmodified polymer value, due to fibres debonding and bridging across the fracture surfaces. Finally, it is shown that several of the physically-modified polymers developed in the present work have fracture energies that are greater than a typical commercially-available cyanate-ester film adhesive.     

Fracture mechanism in coarse grained HAZ of HSLA steel welds

• 1.1. The effects of M-A constituent on the micromechanism of fracture processes in the coarse grained HAZ of HSLA steel welds were investigated by examining the initiation of voids and microcracks in sectioned tensile specimens.
• 2.2. The coarse grained HAZ includes two locally brittle microstructures, whose toughness values are strongly affected by the amount of M-A constituents.
• 3.3. Voids and microcracks are observed to initiate at the M-A constituents by the shear cracking process, i.e., cracking or decohesion of the M-A constituents at the orientation of 40– 50 degree to the tensile axis when the M-A constituents are approximately parallel to the tensile axis.
• 4.4. The void initiation strain in the coarse grained HAZ are very low because of premature void nucleation or brittle fracture at M-A constituents, confirming that the M-A constituents is the main metallurgical factor which governs the toughness of the coarse grained HAZ.