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.     

Effect of Strain Rate and Preloading on the Fracture Toughness of ZrO2-Based Ceramics

We study the variation of the fracture toughness K_Ic ofZrO₂ - Y₂ O₃ ceramics (density 98%) as a function of the testing machine crosshead speed (0.005–50 mm/min) and preloading at K_I < K_c. The fracture toughness is shown to be practically constant in the speed range from 0.05 to 5 mm/min. At a loading rate of 50 mm/min, the quantity K_Ic substantially decreases (by a factor of more than two), whereas at a rate of 0.005 mm/min it slightly increases. Preloading leads to a 1.5-fold increase in K_Ic. Variation of the fracture toughness is associated with structural transformations.     

Cracked Brazilian disc specimen subjected to mode II deformation

The centrally cracked Brazilian disc specimen has been used by many researchers to study mode I and mode II brittle fracture in different materials. However, the experimental results obtained in the past from this specimen indicate that the fracture toughness ratio (K_IIc/K_Ic) is always significantly higher than the theoretical predictions. It is shown in this paper that the increase in the ratio K_IIc/K_Ic can be predicted if a modified maximum tangential stress (MTS) criterion is used. The modified criterion takes into account the effect of T-stress in addition to the conventional singular stresses. The fracture toughness ratio K_IIc/K_Ic is calculated for two brittle materials using the modified criterion and is compared with the relevant published experimental results obtained from fracture tests on the cracked Brazilian disc specimen. A very good agreement is shown to exist between the theoretical predictions and the experimental results.     

High strain rate behavior, transformation-induced plasticity and fracture toughness characterization of cast and additionally tempered Fe85Cr4Mo8V2C1 alloy manufactured using a rapid solidification technique

This study focuses on the characterization of the microstructures of an FeCrMoVC alloy in two states (an as-cast and a heat-treated state) as well as the compressive strain rate-dependent material and fracture toughness behavior. Both microstructures consist of martensite, retained austenite and complex carbides. Tempering results in a transformation of retained austenite into martensite, the precipitation of fine alloy carbides, and diffusion processes. High yield stresses, flow and ultimate compressive strength values at a relatively good deformability were measured. The yield and flow stresses at the onset of deformation are higher for the heat-treated state due to higher martensitic phase fractions and fine precipitations of alloy carbides respectively. Compressive deformation causes a strain-induced transformation of retained austenite to α′-martensite. Hence, both high-strength alloys are TRIP-assisted steels (TRansformation-Induced Plasticity). However, the martensitic transformation is more pronounced in the as-cast state due to higher phase fractions of retained austenite already in the initial state. Examinations of strained microstructures showed decreased crystallite sizes with increasing deformation. It is assumed that, during plastic deformation, the amount of low angle grain boundaries increases while the incremental formation of α′-martensite leads to decreased crystallite size. In general, lower microstrains were determined in the heat-treated state as a consequence of stress relaxation during tempering. In comparison to commercially available tool steels, the determined fracture toughness K _Ic of both variants revealed relatively high fracture toughness values. It was found that the lower shelf of K _Ic is already reached at room temperature. Higher loading rates $ \dot{K} $ resulted in lower dynamic fracture toughness K _Id values. Notch fracture toughness K _A measurements indicate that the critical notch tip radii of the examined materials are slightly smaller than 0.09?mm.     

Fracture parameters for sintered steels

Measurements of the plane strain fracture toughness K _Ic of sintered steels have frequently been invalid because the requirement that P _max/P _Q<1.1 (where P _max = maximum load and P _Q=load used to calculate K _Ic) has not been met. We show that the reason for the criterion not being met is that sintered steels have a considerable crack growth resistance K _R. Values obtained in the past for K _Ic probably have been over-estimates of the initiation value of the crack growth resistance K _i and under-estimates of the maximum crack growth resistance K . The important point is that the assessment of the toughness of sintered steels by a single parameter is not appropriate. Test methods to determine the crack growth resistance of sintered steels are discussed. Crack growth, which is difficult to detect by visual observation, can be determined by compliance techniques. Because of the porous nature of sintered steel, fatigue cracks are unnecessary at the tip of the notch and indeed are undesirable as they can easily cause errors in toughness measurements through inadvertent overloading. The thickness requirement for plane strain measurements can also be relaxed.     

Fracture toughness and evaluation of coating strength with an initial residual stress field

The effect of residual elastic stresses on the geometry of cracks which arise with contact and spontaneous failure of brittle coatings made of high-strength compounds is studied. Conditions are established for the correctness of fracture toughness K_Ic tests with indentation of a standard Vickers pyramid as applied to surface layers with an inhomogeneous structure and an initial residual stress field. Taking account of the anisotropy of fracture toughness established by experiment a reliable approach is suggested for evaluating the brittle strength of coatings in the presence of residual stresses.Translated from Problemy Prochnosti, No. 1, pp. 51–61, January, 1994.     

Variation of mechanical properties of WC-Co alloys with microstructure

K_Ic values of various grades of WC-Co alloys seem to correlate with the single microstructural parameter, thickness of the binder phase. The correlation holds well for cobalt-layer thicknesses ranging from 0.02 to 1.0 μm, which covers almost all commercial grades. The K_Ic values reported by some other researchers fit this curve just as well. Hence K_Ic may be predicted from the thickness of the binder phase in the final product, irrespective of grain size and cobalt content. The correlation between cobalt-layer thickness and hardness, however, is not unique, and there are different curves for different grain sizes or cobalt contents.     

Nature of scatter of fracture toughness in static loading

The previously proposed model of unstable fatigue crack growth is used to explain a large (in comparison with other mechanical characteristics) scatter of static fracture toughness for 15Kh2MFA and 15Kh2NMFA steels at temperatures below the tactile-brittle transition temperature. The results show that for the materials for which K_fc ¹ < K_Ic the critical stress intensity factor K_Ic depends on the specific energy of inelastic strain W at the tip of the initial fatigue crack in its formation stage. The value of W is a function of the number of load cycles (in the conditions with a constant range of the stress intensity factor K) as a result of irregular fatigue crack growth. Here K_fc ¹ is the minimum cyclic fracture toughness. A method is proposed of evaluating the minimum fracture toughness of the material in static loading based on inspection of the process of irregular fatigue crack growth in the stage of crack initiation.Translated from Problemy Prochnosti, No. 2, pp. 10–16, February, 1990.     

Fracture surface formation of ceramics in the precritical crack growth range

A model is suggested for forming ceramic fracture geometry based on ideas about the failure process as a number mutally independent events of intra- and intergranular tensile failure, and the fraction of areas of intergranular cleavage inclined at an angle of less than to the average plane of a macrocrack is determined as the probability of a random plane intersecting an elementary cell of the material at an less than to one of the crystallographic planes along which cleavage is possible at a given load. It is established that fracture surface geometry changes with an increase in stress intensity factor from a maximum developed with an SIF less than K_Ic for the plane of simplest cleavage for a single crystal of a given material to an almost plane geometry with K_Ic for polycrystalline material. The fracture toughness for A1₂O₃ ceramics is estimated by calculation from values of K_Ic for crystallographic planes of simplest cleavage for sapphire.Translated from Problemy Prochnosti, No. 1, pp. 37–43, January, 1990.     

Temperature dependence of fracture toughness of epoxy resins cured with diamines

The fracture toughness (critical stress intensity factor, K _Ic) of epoxy resins cured with four diamines has been measured as a function of temperature over the range from –35° C to above T _g. It was found that K _Ic for each epoxy-diamine system did not vary below room temperature, and in the higher temperature range K _Ic increased with increasing temperature to a maximum and then decreased. The temperature which maximized K _Ic, agreed with the temperature at which the flexural modulus of the epoxy resins abruptly dropped. This temperature was therefore considered as T _g. This temperature was found to be about 20° C lower than the heat deflection temperature under load (1.82 M Pa) of the resins.     

Fracture-induced photon emission of aluminium oxide and its application to fracture mechanical investigations

Mechanically-stimulated luminescence is generated during sub-critical crack growth prior to macroscopic bending fracture of sintered alumina, fusion-cast Al₂O₃, sapphire, and ruby. At similar toughness, K _Ic, the measured intensity increases with the hardness of the tested specimens, it does not depend on the macroscopic fracture strength.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Fracture toughness of concretes at high temperature

The fracture toughness of ordinary and refractory concretes in the range of 20–1300C was investigated, and the stress intensity factor, K _Ic, on three-point bent specimens (according to ASTM E-399 recommendation) determined. With an increase in testing temperature, the stress intensity factor decreases for both concretes. The values of K _Ic at 20C for both concretes are comparable, being equal to 0.64 MNm^–3/2 for ordinary concrete, and 0.72 MNm^–3/2 for refractory concrete, respectively. At 1100C, K _Ic has a value of 0.043 MNm^–3/2 for ordinary concrete, and for the refractory concrete at 1300C, K _Ic=0.34 MNm^–3/2. The method presented for predicting the behaviour of concrete at high temperature may be used in engineering practice.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.     

The application of fracture mechanics to the testing of wood

The problem of a mode I fracture toughness of wood is considered. After a short discussion of relevant literature the test results concerning mode I fracture on three types of wood and the obtained values of stress intensity factor, K _Ic, are discussed. The compressive and tensile strength of the wood fibres and flexural strength are also presented. A considerable variation of the stress intensity factor, K _Ic, has been found to depend on the wood species and the direction of taking specimens for tests. The character of a failure process and the obtained values of the stress intensity factor, K _Ic, were determined by interrelations of cohesion forces existing between particular components of the wood structure, and by anisotropy of the wood. Both the compressive and tensile strength tests performed along the fibres and the bending strength tests crosswise to the fibres have not confirmed the tendencies observed in the fracture toughness tests. The investigations performed show the usefulness of fracture mechanics for evaluation of the strength properties of wood. It is concluded that materials science must consider wood as a valuable and rewarding material upon which to focus research efforts.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Thermoplastic-toughened epoxy polymers

The microstructure and properties of two epoxy-resin systems which have been modified with varying amounts of a thermoplastic to improve the toughness of the thermosetting epoxy polymers, have been studied. The curing agent was 4,4 diaminodiphenylsulphone and the thermoplastic was a reactively terminated poly (ether sulphone) copolymer. Different microstructures were found to occur as the concentration of the thermoplastic component was steadily increased. In particular, the relationships between the microstructures and values of stress-intensity factor, K_Ic, and fracture energy, G_Ic, were explored.     

Residual stresses in particle-reinforced ceramic composites using synchrotron radiation

Residual stresses were determined in particle-reinforced ceramic composites using synchrotron based x-ray diffraction. The baseline Si₃N₄ and the Si₃N₄-TiN composites were processed by turbomilling, pressure casting, and isopressing. They were then continuously sintered to full density, under a pressureless, flowing nitrogen atmosphere. The flexural strength, fracture toughness, and residual stress were measured for as-machined samples and following quenching in water from 1000°C, 1100°C, and 1200°C. The residual stresses for both the baseline Si₃N₄ and the Si₃N₄-TiN composites were determined from the (441) and (531) reflections, by applying the 2-sin² method. The measured residual stresses were compared with the flexural strength and fracture toughness results to determine the effects of residual stress and thermal shocking on the mechanical properties of each material. In both the baseline Si₃N₄ and Si₃N₄-TiN composites, after thermal shocking, the compressive residual stresses were developed in directions both parallel and perpendicular to the sample surface. The residual compressive stresses for the Si₃N₄-TiN composites were much higher than the baseline Si₃N₄. As a result, both fracture toughness and flexural strength of the Si₃N₄-TiN composites were improved. In addition, the addition of the TiN appears to improve both the strength and toughness of the baseline Si₃N₄.     

Mixed-mode high temperature toughness of silicon nitride

Both opening-mode and mixed-mode fracture toughness tests were carried out at 1200 and 1300 °C on a sinter/HIP grade of silicon nitride. Data for pure opening loading (K _Ic) agree well with other experiments on the same material, which showed that the toughness was lower at 1000 °C than at room temperature, but increased as temperature increased above 1000 °C. The ratio of K _IIc/K _Ic was sufficiently insensitive to temperature that it can be considered to be constant. Results are discussed in the context of mechanisms that have been proposed to explain fracture toughness in silicon nitride.     

Correlation of fracture toughness with microstructural features for ultrafine‐grained 6082 Al alloy

In the present work, cryorolling (CR) and room temperature rolling (RTR) followed by annealing (AN) at 200°C were carried out to investigate the effects of grain size, precipitates (Mg‐Si‐phases), and AlFeMnSi‐phases on the fracture toughness of 6082 Al alloy. Using the values of the conditional fracture toughness, (K_Q), in the critical fracture toughness (K_IC) validation criteria, it was found that the sample size is inappropriate, which implies that the conditional fracture toughness obtained cannot be considered as the critical fracture toughness. Therefore, to establish the relative improvement in fracture toughness, the equivalent energy fracture toughness (K_ee) and J‐integral were calculated and used. The results show that the values of K_ee (89.91 MPa √m) and J (89.86 kJ/m²) obtained for the sample processed via CR followed by AN (CR + AN) are the highest when compared with the other samples processed through CR, RTR, and RTR followed by AN, RTR + AN. Microstructural features such as high fraction of low Taylor factor, high fraction of kernel average misorientation, Si‐rich particles, small size AlFeMnSi‐phases, and mixed mode of failure (transgranular shear and micro‐void coalescence) also support the high fracture toughness in the CR + AN sample. It was also observed that the effect of residual stresses on the fracture toughness of CR and RTR samples is minimal. Therefore, the correlation between microstructure and residual stresses is not considered in the present work due to very small values of the residual stresses for CR and RTR samples and the absence of residual stress from the heat‐treated samples.