Fracture toughness of Si3N4 measured with short bar chevron-notched specimens

The short bar chevron-notched specimen was used to measure the plane strain fracture toughness of hot-pressed Si₃N₄. Specimen proportions and chevron-notch angle were varied, thereby varying the amount of crack extension to maximum load (upon which K_ic was based). The measured toughness (4.68 ± 0.19 MN m^3/2) was independent of these variations, inferring that the material has a flat crack growth resistance curve.Nomenclature a crack length - a _A crack length at arrest of unstable crack advance - a ₁ length of chevron notch at specimen surface (distance from line of load application to point of chevron emergence at specimen surface) - a ₀ initial crack length (distance from line of load application to tip of chevron) - a _R crack length at ending of stable crack extension (conversely, crack length at onset of abrupt, unstable crack advance) - B specimen thickness - H specimen half-height - K _1A stress intensity factor at arrest of unstable crack advance - K _IR stress intensity factor at end of stable crack extension (crack growth resistance) - K _IC plane strain fracture toughness - P _max maximum applied load in fracture toughness test - W specimen width - Y ^* dimensionless stress intensity factor coefficient for chevron-notched specimen - Y ^* _m minimum value ofY ^* as a function of - a/W - ₀ a ₀/W - ₁ a ₁/W     

Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites

Microstructure and fracture mechanical behaviour of injection-moulded, longer glass fibrereinforced polypropylene (Verton* aspect ratio 320) were studied as a function of fibre volume fraction and compared to that of shorter fibre-filled polypropylene (aspect ratio 70). Toughness was measured using instrumented notched lzod and falling weight impact tests, as well as compact tension specimens. It was found that the addition of longer fibres generally increased the toughness of the material, although more significant increases were seen in the impact tests than were seen in the compact tension test. For the latter results, a correlation between toughness improvement and microstructural details was performed on the basis of the microstructural efficiency concept, a semi-empirical approach of the formK _c,C = (a* +nR)K _c,M, where,K _c,C andK _c,M are the fracture toughnesses of the composite and the matrix, respectively,_a* is a matrix stress correction factor,n is a scaling parameter andR is a fibre reinforcement effectiveness factor. The latter corrects for differences in the composite microstructures, and incorporates effective fibre orientation factors, layering of injection moulded parts, and fibre volumes in the different layers.Nomenclature a crack length - a ^* matrix toughness correction factor - A cross-sectional area - B thickness of the sample plaques - C thickness of the composite core regions - E _peak energy adsorbed up to the maximum force in the impact load-displacement curve - E _t tensile modulus - F _max maximum force in impact force-displacement curves - f _p fibre orientation factor - f _pe effective orientation factor - f _pe,C effective orientation parameter, core region - f _{pe, s} effective orientation parameter, surface region - F critical load in the tensile test load-displacement curves - K _c critical stress intensity factor/fracture toughness - K _L fracture toughness of the composite materials - K _d dynamic fracture toughness - K _L fracture toughness of the matrix - L test with crack parallel to the mould filling direction - M microstructural efficiency factor - n scaling parameter for reinforcement effectiveness factor (energy absorbtion ratio) - R reinforcement effectiveness factor - S thickness of the composite surface regions - T test with crack perpendicular to the mould filling direction - V _f fibre volume fraction - V _m matrix volume fraction (= 1 —V _f) - W specimen width - W _f fibre weight fraction - W _m matrix weight fraction (= 1 —W _f) - X _n number average fibre length - X _v volume average fibre length - Y(a/ W) polynomial correction for compact tension specimens - variable in effective orientation factor formula - variable in effective orientation factor formula - _B strain to break - _c density of the composite - _f fibre density - _m matrix density - _F fracture strength - fibre angle with respect to a reference direction     

Effects of precracked specimen geometry on local cleavage fracture stress σf of low alloy steel

An elastic-plastic finite element method (FEM) is used to analyze the stress distributions ahead of crack tips for three types of COD specimens with different precracked depth a/W and height W of a low alloy steel, and the tensile and COD tests are carried out at various temperatures. By accurately measuring the distances of the cleavage initiation sites from the blunted crack tips, the local cleavage fracture stresses _f are measured. With increasing precrack depth a/W, specimen height W and test temperatures in a certain range, it was found that the _f essentially does not change. The _f is a steady inherent parameter of the material whose value is independent of the precracked specimen geometry.     

The failure of fibre composites and adhesively bonded fibre composites under high rates of test

The dynamic effects which are commonly encountered during high-rate DCB tests with fibre composite and adhesively bonded fibre composite arms have been studied in detail. This paper, Part II of the series, follows Part I, which described the experimental aspects of the high-rate testing. Part III will report the results from mode II and mixed-mode I/II tests on the fibre-composite materials.Nomenclature a crack length - a ₀ initial crack length - a crack speed - ä crack acceleration - c longitudinal wave speed - h thickness of single arm of test specimen - p crack length perturbation (i.e. the measured value of the crack length minus the value predic ted by steady-state theory) - p crack velocity perturbation - crack acceleration perturbation - t time - t ₀ time taken for crack to initiate during the mode I test - u ₀ load-line vertical displacement of single arm of test specimen (/2 in Part I) - u(x) vertical displacement of specimen at distance x from the load-line - u(x) vertical displacement rate of specimen at distance x from the load-line - x distance along the test specimen from the load-line - A constant relating the steady state crack length to root time - B width of specimen - C compliance of the specimen (u ₀/P) - E ₁₁ axial modulus of the fibre-composite beam - G mode I energy release rate - G _Ic mode I critical energy release rate or fracture toughness - G ₁ half the value of G _Ic during steady-state propagation (i.e. calculated for half the beam as shown in Fig. 1) - G ₂ half the value of G _Ic at crack initiation - P end load applied to specimen - U _ext external work done - U _s strain energy - U _k kinetic energy - V velocity of a single arm of test specimen (i.e. half the measured test velocity) - dynamic term, governed by the ratio of the energy to initiate versus that to propagate a crack - _I mode I crack shear deflection and root rotation correction term - crack length correction term, evaluated by the negative intercept on the a versus t ^1/2 plot - dynamic term controlling the form of the computed perturbations - Poisson's ratio for the fibre-composite beams density of the fibre-composite beams - time, normalized by the initiation time, t ₀ and thus equivalent to (t/t ₀) - values of at which crack arrest occurs. n = 1,2,3... - ratio of distance along beam to crack length (x/a)     

Strength improvement of cemented carbides by hot isostatic pressing (HIP)

HIP treatment after sintering increases the strength of the investigated cemented carbide alloy by a factor of two whereas hardness, fracture toughness, and work of fracture remain unchanged. HIP does not affect the microstructural parameters of the carbide skeleton and the binder phase, but the residual pores are eliminated entirely. Failure of both the as-sintered and post-densified material occurs by a pure Griffith mechanism. The strength-flaw size relationship is established experimentally and is shown to obey exactly Griffith's basic strength equation. The strength is controlled by the largest microstructural defects, i.e. pores in the as-sintered material, and coarse WC grains and inclusions in the HIP-treated specimens.Nomenclature a size of the fracture initiating flaw - a _th theoretical flaw size - b sample thickness - c length of the pre-crack - C contiguity of the carbide phase - D _WC mean carbide grain size - E Young's modulus - F fracture surface - G _IC critical energy release rate - h sample height - H _V Vicker's hardness - K _IC critical stress intensity factor - l span length - l _Co mean Co layer thickness - m Weibull parameter - P load - r _p1 radius of the plastic zone - R crack resistance - S probability of failure - U fracture energy - X relative crack length - Y K-calibration - _F specific work of fracture - _I specific energy for fracture initiation - spread of grain size distribution - compliance of the pre-cracked specimen - ₀ compliance of the uncracked specimen - v Poisson's ratio - fracture stress - ₀ maximum stress - _B bend strength - _Y Yield strength - _eff maximum local stress     

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.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.     

Relationships between fracture parameters and fracture surface roughness of brittle polymers

Fracture parameters such as crack velocity à, stress intensity factor K _d and a specific crack extension resistance R ^* were measured for Homalite-100, PMMA and epoxy in the course of fast crack propagation using a Cranz-Schardin type high speed camera. Fracture surface roughness was evaluated as a function of crack length a so that it could be correlated with the fracture parameters above. The results showed that none of those parameters could be uniquely related to . Instead, there was a good correlation between and a product R ^* à.     

Size effects and ductile-brittle transition of polypropylene

The influence of specimen width on fracture parameters has been investigated. The range examined was sufficiently large to obtain ductile and brittle fractures. With reference to previously published work, the phenomenology has been analysed by combining BCS model and Carpinteri's brittleness number approach.Nomenclature a crack length - f(a/W) shape function according to ASTM specification [16] - F(a/W) shape function according to Tada Paris notation [21] - E elastic modulus - K _IC plane strain fracture toughness - K _IC ^f fictitious plane strain fracture toughness - K _IC2 plane stress fracture toughness - J _IC ^f J-integral at maximum load - L span - weight average molecular weight - number average molecular weight - polydispersity - P _M maximum load - P _F load of brittle fracture - p _P load of plastic collapse - s brittleness number - V machine cross speed - W specimen width - _y yield stress - strain rate     

An evaluation of the short rod technique to measure the fracture toughness of polymers

The investigation of the fundamental variables which influence the fracture toughness of structural plastics is greatly hampered by a large amount of scatter and uncertainty associated with the fracture toughness measurement. A major part of the problem is due to a lack of adherence to ASTM Standard E399, mainly with regard to the requirement for a fatigue crack. A razor-blade arrested crack, which is often blunted, is common practice in the plastics field. It is also common to ignore size (plane strain) and precise machining requirements. The short rod (SR) method was evaluated as a potentially more precise and simpler fracture toughness measurement. This toughness measurement is made on a slowly moving and presumably sharp crack, and the geometry of the sample enforces plane strain conditions. Toughness measurements on compact tension (CT) specimens via ASTM E399 were performed on one-inch (25 mm) samples of poly(methyl methacrylate) (PMMA), polystyrene (PS), polycarbonate (PC) and polysulphone (PSO). Also, a constant compliance method using a contoured double cantilever beam (CDCB) was used to evaluate the toughness of PS, PC, and PSO, but in general we did not achieve stable crack growth. The used samples were then fabricated into SR specimens and their toughness measured. The CT and CDCB methods agreed with each other for PSO and PC, but for PS the CDCB method gave high values. It is argued that the SR method should be compared to the other methods without using a plasticity correction. Then the SR method agrees well with the CT method for PSO and PS and is 15% higher for PC. The PMMA SR results were invalid. Differences between the methods are explained in terms of crack blunting, rate effects, non-homogeneity, residual stresses and the global nature of the crack front. The SR method has promise for polymer evaluation but more experience and evaluation is needed. The method is unique in the ability to study the effects of thermal history and of the environment on fracture toughness.Nomenclature a Distance from load line in the crack plane to the crack tip - a ₀ Distance from load line in the crack plane to the chevron tip. Equal to 10.11 + 0.287 mm - A Calibration constant:A = 22 atr = 0.555,A = 50.9r ² - 56.25r + 37.58 forr > 0.555,A = 77.87r ² -86.05r + 45.77 forr < 0.555. These relationships for A, supplied to us by Terra Tek, were found to be valid forr = 0.4 to 0.75 - B SR specimen diameter, equal to 19.1 ± 0.23 mm in this study or to specimen thickness for CT and CDCB specimens - C Correction for SR specimen sizes which do not exactly meet specifications of compliance calibration - C _a,C _b,C _w,C C corrections fora, B, W and , respectively - F SR load atr = 0.555 - K Stress intensity factor (MPam^1/2). - K _c Critical value of K at point of instability - K _1c K _c, in opening mode - K _1A Arrest toughness - K _sr (=K _Isr) Short-rod determined toughness. When used in conjunction withK _srp, refers to toughness value without thep correction - K _srp (=K _isrp) K _sr withp correction. A prime (as used inK_srp) is used to differentiate between toughness atr _c and at the downloadings - m Constant-compliance constant for CDCB specimen derived from specimen geometry and beam theory - m Correction tom obtained from experimental compliance calibration. Corrects for side grooves - p Ratio of difference in strain for two SR downloading curves at load = 0 to that at load =F. Must be less than 0.2. See Fig. 3 - p p correction due to plasticity alone - r SR initial compliance divided by     

Tensile fracture of centre-notched angle ply (0/±45/0)S and (0/90)2S graphite — epoxy composites

The fracture behaviour of centre-notched (0/± 45/0)_S and (0/90)_2S laminates with increasing notch length has been studied. Two test series have been investigated: specimens of constant width (W=20 mm) and small notch length (2a 12 mm), and specimens with various notch lengths (5 2a 35 mm) and a constant relative notch length (2a/W=0.5). An X-ray technique showed that the damage at the notch tip, which is formed at increasing load, consists mainly of subcracks parallel to the fibres of the constituent layers. The damage zone causes the crack opening displacement (COD) to deviate from the original linearity. TheK _R curve concept has been applied assuming that the COD deviation from linearity is completely the result of original crack extension. This approach fails to describe the notch length effect, because a tangent point between theK _R andK curves was not found and because of a strong dependency of the maximum fracture resistanceK _Rmax on notch length. The fracture behaviour of 20 mm wide specimens could be explained with the point and average stress criteria, based on characteristic lengths which are independent of notch length. At various notch lengths at a constant 2a/W=0.5, however, the characteristic lengths increased with increasing notch length.     

Fracture toughness behaviour of ferritic ductile cast iron

The static rate fracture toughness of a series of eight heats of ductile cast iron has been measured. Samples from each heat were tested in a heat treated condition which produced a fully ferritic matrix. The dominant influence of carbide (primarily in e pearlitic form) in controling the fracture toughness was thus eliminated in this study. The chemical composition and the microstructural feature size has also been measured directly from each specimen tested. A multiple linear regression method was used to establish a simple mathematical relationship between fracture toughness and the composition and microstructure. Fracture toughness was found to be strongly associated with the spacing (or size) of the graphite nodules in these fully ferritic ductile cast irons. Other features, including the composition, the ferrite grain size, or the amount of graphite (over the ranges examined), did not strongly influence the fracture toughness. Fracture toughness also did not correlate with tensile properties (i.e. strength or ductility) in these alloys. The results of this work can be used to develop an appropriate quality control program for applications which require assurance against fracture toughness related failures.Nomenclature YS 0.2% offset yield strength (MPa) - UTS Ultimate tensile strength (MPa) - %El % tensile elongation - %RA % reduction in area - E Young's modulus (MPa) - J _Ic Elastic-plastic fracture toughness (fromJ-integral test) (kJ m^–2) - K _Ic Linear-elastic fracture toughness, (MPa m^1/2) - V _v ^graphite Volume fraction graphite - d ^ferrite Ferrite grain size - N _A Nodule count on a random plane (number mm^–2) - D _v Three-dimensional nodule diameter (mm) - _v Three-dimensional mean free nodule spacing (centre-to-centre) (mm) - D _A Average nodule diameter on a random plane (two-dimensional size) (mm) - _A Average nearest neighbour spacing (centre-to-centre) on a random plane (two-dimensional spacing) (mm) - a tog Constants in the multiple linear regression analysis     

Statistical analysis of the brittle fracture of sintered tungsten

A Weibull analysis was applied to the fracture data of sintered tungsten round bar specimens. Fracture data were obtained by performing flexural and tensile tests on these components. Two quantities were obtained which characterized the material variability and strength for each test method. The correlation between these quantities for the two test methods was found to be close.Nomenclature C least square line intercept - P _f failure probability - P _f ⁱ experimental failure probability - V specimen volume - W applied load - X horizontal coordinate of least square line - Y vertical coordinate of least square line - d specimen diameter - L distance between supporting knife edges - m Weibull modulus - v unit volume - stress - ₀ normalizing stress - _fV failure stress of specimen - _fv unit volume failure stress of specimen - _fv ^B unit volume failure stress in bending - ⁱ experimental stress - gamma function     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Crack propagation studies in brittle materials

An analysis was made of cantilever beam specimens used for crack propagation studies, Included in this analysis were the effects of a plastic zone at the crack tip, beam rotation, and the viscoelastic response of the material. This analysis showed that application of a constant bending moment to the specimen rather than a constant load provides a test in which the strain energy release rate,G, is independent of crack length. Other advantages of this test configuration are that corrections for shear or beam rotation effects are not necessary. Results of this test on both glass and ceramics are reported.List of symbols a crack length - A cross-sectional area of beam - b total thickness of specimen - d deflection of loading arm - E elastic modulus of material - E ₁ dynamic modulus - E ₂ transient response modulus - G shear modulus of material - G strain energy release rate - G _vE strain energy release rate of viscoelastic material - h half height of specimen - I moment of inertia of cantilever beam =bh ^/12 - k modulus of elastic foundation - K stress intensity factor - L distance from point of load application to fulcrum of loading arm - L distance from point at which arm deflection is measured to fulcrum - M applied bending moment - P force applied to beam - r length of plastic zone - t thickness of specimen at groove - T force applied to loading arm - u displacement of beam - V crack velocity - w half height of groove - W stored elastic energy - characteristic length of beam on elastic foundation - reciprocal of the characteristic length of beam - rotation of beam - X viscoelastic creep compliance function - time - inherent opening distance as defined by Wnuk [10] - _y yield strength of material - Poisson's ratio     

Developing combined convection of non-Newtonian fluids in an eccentric annulus

Summary Laminar combined convection of non-Newtonian fluids in vertical eccentric annuli, in which the inner and outer walls are held at different constant temperatures is considered and a new economical method of solution for the three-dimensional flow in the annulus is developed. Assuming that the ratio of the radial to the vertical scale, , is small, as occurs frequently in many industrial applications, then the governing equations can be simplified by expanding all the variables in terms of . This simplification gives rise to the presence of a dominant cross-stream plane in which all the physical quantities change more rapidly than in the vertical direction. The solution trechnique consists of marching in the vertical streamwise direction using a finite-difference scheme and solving the resulting equations at each streamwise step by a novel technique incorporating the Finite Element Method. The process is continued until the velocity, pressure and temperature fields are fully developed, and results are presented for a range of the governing non-dimensional parameters, namely the Grashof, Prandtl, Reynolds and Bingham numbers.List of symbols Bn Bingham number, - d ^* difference between the radii of the outer and inner cylinders,r _o ^*–r_i ^* - e ^* distance between the axes of the inner and outer cylinders - e eccentricity,e ^*/d^* - F ^* external force acting on the fluid - g ^* acceleration due to gravity - g ^* gravitational vector, (0,0,g ^*) - Gr Grashof number, _m *² g**(T ₀*–T _e*)d*³/ _m *² - K ^* consistency of the fluid - L ^* height of the cylinders of the annulus - n flow behaviour index - p ^* dimensional pressure - P dimensionless pressure gradient - Pr Prandtl number, _m */ _m ** - r _i ^* radius of the inner cylinder of the annulus - r _o ^* radius of the outer cylinder of the annulus - r _T wall temperature difference ratio,(T _i ^*–T_e ^*)/(T_o ^*–T_e ^*) - Re Reynolds number, _m d*w _m */ _m * - T dimensionless temperature of the fluid,(T ^*–T_e ^*)/(T_o ^*–T_e ^*) - T _dif ^* temperature difference between the walls of the annulus - T _e ^* temperature at the fluid at the entrance of the annulus - T _i ^* temperature at the inner cylinder of the annulus - T _o ^* temperature at the outer cylinder of the annulus - u dimensionless transverse velocity in thex direction,u ^*/(w_m ^*) - U dimensionless transverse velocity in the annulus,Reu - u ^* fluid velocity vector, (u ^*, v^*, w^*) - v dimensionless transverse velocity in they direction,v ^*/(w_m ^*) - V dimensionless transverse velocity in the annulus,Rev - w dimensionless vertical velocity,w ^*/w_m ^* - w _m scaling used to non-dimensionalise the vertical velocity - x dimensionless transverse coordinate,x ^*/d^* - y dimensionless transverse coordinate,y ^*/d^* - z dimensionless vertical coordinate,z ^*/L^* - Z dimensionless vertical coordinate,z/Re - Z _r dimensionless distance in the vertical direction where the final wall temperatures are attained,Z _r ^*/L^* - * dimensional molecular thermal diffusivity - * coefficient of thermal expansion, - dimensional rate of strain tensor - dimensionless ratio of the length scales in the annulus,d ^*/L^* - * dimensional apparent non-Newtonian viscosity - _m * mean viscosity, - * dimensional fluid density - _m * dimensional reference fluid density - * dimensional stress tensor - yield stress     

Hertzian indentation of thorium dioxide,ThO2

The Hertzian indentation technique was used to study the fracture properties of ThO₂ and to measure the fracture surface energy, , of sintered ThO₂. Optical microscopy and acoustic emission were employed to detect ring crack formation. Perfect cracks were always formed and no indication of permanent plastic deformation was observed. From the observed crack behaviour, a fracture surface energy, , of 2.5±0.2 J m^–2 at room temperature and a fracture toughness, K _Ic, of 1.07 MN m^–3/2 were deduced.     

Polymer/metal interfacial crack growth characterized by C*

This paper establishes a simple testing scheme to simultaneously measure the linear elastic strain energy release rate G, the non-linear J-integral, and the rate-dependent C ^*-integral for a growing crack at a polymer/metal interface. The test is applicable to fracture of adhesive bonds. A criterion governing C ^*-controlled fracturing is derived, analogous to the Hutchinson-Paris -criterion for J-controlled growth. The interfacial toughness of an adhesive commonly used for bonding metal plates is characterized at room temperature, and is shown to fracture in a C ^*-controlled manner. A relationship between C ^* and the crack growth rate is observed. The nature of this relationship warrants further exploration.     

An asymptotic approach to size effect on fracture toughness and fracture energy of composites

Size effect on fracture toughness and fracture energy of composites is investigated by a simple asymptotic approach. This asymptotic analysis based on the elastic/plastic fracture transition of a large plate with a small edge crack is extended to study fracture of composite. A reference crack length, a^*, is used in the model, which indicates an ideal elastic/plastic fracture transition defined by the yield strength and plane strain fracture toughness criteria. Experimental results of cementitious materials available in literature are analyzed and compared. It is shown that the common K_R-curves can also be obtained by the current asymptotic model. Furthermore, a local fracture energy distribution concept is also discussed and compared with the present asymptotic approach.     

Carbon fibre-reinforced cement

This review describes fabrication processes for aligned fibre and random fibre carbonreinforced cement and links important process parameters with composite theory. The way in which the material fits into the general framework of crack constraint and matrix cracking theories is discussed. A broad survey is made of the mechanical properties, durability and dimensional stability of a variety of carbon-reinforced cement composites, and economic constraints on potential applications are considered.List of symbols b breadth of three-point bend specimen - d depth of three-point bend specimen - E _c composite Young's modulus - E _f fibre Young's modulus - E _m matrix Young's modulus - l fibre length - l _c fibre critical transfer length - l _s specimen span in three-point bend test - m Weibull modulus - r fibre radius - P applied load - V _f fibre volume fraction - V _m matrix volume fraction - x length of fibre needed to transfer load _mu V _m - x _d crack spacing in a composite with short, aligned fibres - _fu fibre ultimate strain - _mu matrix ultimate strain - _fu fibre ultimate strength - _mu matrix ultimate strength - _cu composite ultimate strength - _MOR modulus of rupture - _T tensile strength - interlaminar shear strength - _i interfacial shear strength - _m matrix work of fracture - _F work of fracture