Fracture resistance of ceramics: Base diagram and R-line

Modern methods of determining crack resistance of ceramics are analyzed and it is shown that fracture of the specimens can be divided into the three stages: formation of a stress concentrator, nucleation and propagation of a crack. Note that standard methods provide determining at the second and third stages but the EF method effects measurements at all the three stages, with testing small-size specimens. The flaking resistance F_R was estimated by the Rockwell indentation of the specimens of oxide and nonoxide linear elastic and inelastic ceramics as well as particulate ceramic composites. It was established that FR values for homogeneous linear elastic ceramics were invariant (independent of flaking loads and chip scar sizes). It was demonstrated on the flaking resistance-critical stress intensity factor diagram that the values for ceramics with enhanced damage resistance were found to the left of the base line, while those of homogeneous linear elastic ceramics fell on this line. The values for ceramics with enhanced crack propagation resistance are to the right of this line. Crack propagation resistance diagrams (R-lines) are proposed, they are similar to known R-curves but they are plotted on the basis of results obtained with flaking off the edges of ceramic specimens. For homogeneous linear elastic ceramics these lines are flat, which is indicative of their surface energy invariance. __________ Translated from Problemy Prochnosti, No. 3, pp. 60–74, May–June, 2006.     

Glass fracture in edge flaking

Fracture resistance of technical quartz and normal window glasses was investigated in testing polished rectangular parallelepipeds by edge flaking their long edges with Rockwell and Vickers indenters (EF method) and by scratching the specimen surface with a Rockwell indenter followed by flaking its edge (S+EF method). It was established that the fracture of those glass specimens in their edge flaking with a Rockwell indenter was started with the formation of a Hertzian ring crack and their corresponding chip scars had the form of Hertzian “quasi-cones.” Fractographic data were used in analysis of test results. __________ Translated from Problemy Prochnosti, No. 6, pp. 103–112, November–December, 2007.     

Fracture toughness studies on V-notched ceramic specimens

The fracture toughness of silicon nitride, alumina, and zirconia ceramics was compared by the SEVNB method. This method, easily realized in practice both for compact and for composite ceramics, is shown to provide small scatter of data. The K_lc values determined by this method correspond to those obtained by the SEPB method. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 120–127, January–February, 2000.     

The Express Method of Determining the Fracture Toughness of Brittle Materials

This paper presents a novel method of fracture toughness determination, - a method that does not require introduction of an initial crack or notch-type defect in a sample. The corresponding formula for calculating fracture toughness, which does not depend on crack length is derived. This “express” test is useful for industrial applications because it economical and may be used for a wide range of brittle materials from ceramics to concrete and rocks. Test results are shown to be in good accord with the results obtained by ASTM methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture mechanics of oilseed rape pods

The basic theory of linear elastic fracture mechanics was applied to the fracture of pods from six genetic lines of oilseed rape (Brassica napus). An experiment was designed to allow the energetics of the fracture process to be accurately determined. The work of fracture, toughness and fracture toughness of five experimental varieties and one common commercial variety (Apex) were measured. The values for the toughness (0.006–0.271 kJ m-2) and fracture toughness (0.026–0.233 MN m-3/2) obtained from each line were distinct from each other but broadly similar to those of other brittle materials. The toughness and fracture toughness of Apex were approximately midway between the lowest and highest values measured. This result indicates that there is scope for improving the fracture resistance of oilseed rape crops so as to reduce seed loss before and during harvest. The approach described would be useful in selecting fracture-resistant genetic lines to help to develop such crops. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture toughness of acrylic bone cements

Clinical experience has shown that fracture of PMMA-based bone cements is a significant factor in the failure of orthopaedic joint replacements. Earlier studies of the fracture toughness properties of bone cement have been limited to relatively large test specimens — ASTM standard test methods require the use of specimens with dimensions considerably larger that those associated with bone cement in clinical use. In this study, a miniature short-rod specimen was used to measure the fracture toughness (K _IC) or two bone cements (Simplex-P and Zimmer LVC). The dimension of our mini specimens approaches the cross-section of bone cements as usedin vivo. The short-rod elastic-plastic fracture toughness test method introduced by Barker was utilized to ascertain the effect of specimen preparation and ageing in distilled water on fracture toughness. Our study indicated that slow hand-mixed specimens possess comparable fracture toughness to centrifuged specimens. After ageing in water, however, centrifuged and slow hand-mixed specimens are more fracture resistant than specimens prepared by mixing the cement quickly. An optimum void content for the bone cements studied was suggested by the experimental results; for Simplex-P bone cement it appeared to be less than 1.6% whereas it was between 1.6 and 3.6% for Zimmer LVC cement. Simplex-P bone cement also showed superior fracture toughness compared to Zimmer LVC cement after storage in water for 60 days at 37° C.     

Analysis of applicability of small-sized specimens to prediction of temperature dependence of fracture toughness

The paper addresses the use of small-sized specimens of various types, including those with deep (50%) side grooves, for the purpose of fracture toughness prediction. The experimental data for numerous (more than 500) small-sized specimens prepared from materials of various degrees of embrittlement are compared to the test results for full-sized specimens of C(T) type. The concepts of Master Curve and Unified Curve are applied for the processing of experimental data. To handle the test results for small-sized deep-grooved specimens a calculation procedure has been elaborated, which adjusts the calculation method specified in the ASTM Standard E 1921. We provide recommendations of how to use precracked Charpy type deep-grooved (50%) specimens for prediction of a representative temperature dependence of fracture toughness. Translated from Problemy Prochnosti, No. 2, pp. 5–26, March–April, 2009.     

Effect of annealing on the microstructure, room-temperature strength, and fracture toughness of Al2O3−ZrO2−TiN ceramics

The microstructure, phase composition, room-temperature flexural strength, and fracture toughness of Al₂O₃−ZrO₂−TiN (AZT) ceramics were studied on specimens annealed in air at 1000, 1200, and 1400°C. The strength of the ceramics decreased with annealing temperature. The degradation in strength was caused by defects formed on or near the surface of the ceramics during oxidation of TiN which started at 600–700°C. The surface defects after annealing are influenced by the formation of rutile (TiO₂) at 1000 and 1200°C, aluminum titanate (Al₂TiO₅), and titanium suboxide Ti₅O₉ at 1400°C as well as by diffusion processes associated with ZrO₂. If the annealing of smooth AZT specimens in air resulted in lower strength, specimens in the form of single-edge notched beam (SENB) exhibited a considerable increase in fracture toughness (K _Ic) with annealing temperature. Such behavior was caused by the formation of an oxide layer which hindered the propagation of the main crack from the notch base. Thermal treatment of the smooth AZT specimens and further edge notching and testing did not result in a change of K _Ic values. The Al₂O₃ and Al₂O₃−ZrO₂ ceramics were also tested for comparison. Translated from Problemy Prochnosti, No. 1, pp. 132–138, January–February, 1999.     

Comparative analysis of fracture toughness test methods for ceramics and crystals at room and lower temperatures

Flexural and indentation tests to estimate the fracture toughness of ceramics and crystals were compared. It was demonstrated that different methods can give reliable estimates in tests of homogeneous ceramics and quite ambiguous in tests of nonhomogeneous materials. Zirconia ceramics partially stabilized with magnesia were shown to exhibit a low-temperature inelastic-elastic transition in the temperature range of their fracture toughness variations. Translated from Problemy Prochnosti, No. 3, pp. 104–118, May–June, 1997.     

Fracture strength and adhesive strength of hydroxyapatite-filled polycaprolactone

Fracture toughness and tear strength of hydroxyapatite (HAP)-filled poly(ε-caprolactone) (PCL) with increasing HAP concentration were studied. The toughness was assessed in terms of essential work of fracture (EWF). Adhesive strength between HAP and PCL interfaces was evaluated using T-peel testing. The adhesion between the two components was found to be relatively strong. Double edge notched tension (DENT) and trousers test specimens were used for the EWF tests. The effect of HAP phase in PCL on the fracture and tearing toughness was investigated. The results obtained from the EWF tests for the HAP-filled PCL complied with the validity criteria of the EWF concept, namely, (1) geometric similarity for all ligament lengths; (2) fully yielded ligament and (3) plane-stress fracture condition. Values for specific essential work of fracture (w _e ) and specific plastic work of fracture (βw _p ) were found to decrease with increase in HAP concentration. The testing procedure showed promise in quantifying the tearing resistance and rising R-curve behavior common in natural materials and it can be extended to other biomaterials that exhibit post-yield deformation. A quantitative assessment based on fracture mechanics of the adhesive strength between the bioactive interfaces plays an important role for continued development of tissue replacement and tissue regeneration materials.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 4. Fracture toughness after plastic prestraining of materials with cracks

The paper presents the results of an experimental investigation of the influence of warm prestressing (WPS) on fracture toughness characteristics of large-size specimens. The WPS has been found to be an efficient method for enhancing brittle fracture resistance of large-size bodies from the investigated materials and can be recommended for practical realization in nuclear reactors and other critical structures whose brittle fracture is impermissible both in the process of normal operation and in emergency situations. The optimum temperature-loading regime of the WPS is defined by both the properties of a given material and its thickness which governs the intensity of plastic deformation in the process of WPS. Based on the established mechanisms of the WPS effect, a physicomechanical model has been developed for the prediction of fracture toughness for pressure-vessel heat-resistant steels after WPS taking into account the influence of the stress state at the crack tip. The model makes it possible to predict fracture toughness for large-size bodies subjected to WPS with the given temperature and loading regimes from the results of testing small laboratory specimens. The most optimum regimes of the WPS can also be determined using this model and even those for several materials making up a structural component and subjected to the WPS. Translated from Problemy Prochnosti, No. 3, pp. 39–54, May–June, 1997.     

Fracture toughness of multilayer pipes

Multilayer pipes composed of various materials improve partially the properties of a pipe system and are frequently used in service. To estimate the lifetime of these pipes the basic fracture parameters have to be measured. In the contribution a new approach to this estimation is presented. Special type of a C-shaped inhomogeneous fracture mechanics specimen machined directly from a pipe has been proposed, numerically analyzed and tested. The corresponding K values are calculated by finite-element method and fracture toughness values of polyethylene pipes material are obtained. __________ Translated from Problemy Prochnosti, No. 1, pp. 146–149, January–February, 2008.     

Fracture Toughness Test with a Sharp Notch Introduced by Focussed Ion Beam

The validity of fracture toughness data obtained from tests with V-notched bending bars is affected by the notch root radius and the presence of R-curve behavior. A macroscopic test specimen has been developed that contains a notch introduced by focused ion beam machining. This produces a notch root radius of less than 0.1 μm, so that notch effects can be ignored for most ceramics. Also, due to the very small notch depths the influence of a rising R-curve should be very close to that of natural cracks. First tests, carried out on a Ce-doped zirconia ceramic resulted in a toughness of K _Ic ≈ 5.9 MPa√m.     

Experimental and Numerical Investigation of Mixed-Mode Interlaminar Fracture of Carbon-Polyester Laminated Woven Composite by Using Arcan Set-up

Composite materials are widely used in marine, aerospace and automobile industries. These materials are often subjected to defects and damages from both in-service and manufacturing process. Delamination is the most important of these defects. This paper reports investigation of mixed-mode fracture toughness in carbon–polyester composite by using numerical and experimental methods. All tests were performed by Arcan set-up. By changing the loading angle, α, from 0° to 90° at 15° intervals, mode-I, mixed-mode and mode-II fracture data were obtained. Correction factors for various conditions were obtained by using ABAQUS software. Effects of the crack length and the loading angle on fracture were also studied. The interaction j-integral method was used to separate the mixed–mode stress intensity factors at the crack tip under different loading conditions. As the result, it can be seen that the shearing mode interlaminar fracture toughness is larger than the opening mode interlaminar fracture toughness. This means that interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition.     

Fracture toughness diagrams of a notched body

To describe fracture toughness diagrams of notched bodies, a model of the cohesion zone near the notch root and an averaging criterion of stresses in this zone were employed. The geometric stress concentration factor and biaxiality coefficient affect greatly the shape of fracture toughness diagram. The notch root critical stress intensity factor is a decreasing function of geometric stress concentration factor. __________ Translated from Problemy Prochnosti, No. 5, pp. 142–148, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).     

Fracture strength of ion-exchange silicate-containing dental glass ceramics

Dental glass ceramics with the composition of (0.2K, 0.8Na)₂O–xAl₂O₃–ySiO₂ (x = 0.4–0.8, y = 4–6) were studied for their mechanical properties. Different ion-exchange practices were used to modify the sub-surface concentration distributions of K⁺, Na⁺, and H⁺ of these glass ceramics. Specimens were heat-treated in molten KNO₃, and NaNO₃ + KNO₃ salt baths at 350–450 °C for the ion exchanges of K⁺ and Na⁺, or in the 4% acetic aqueous solution at 85 °C for a hydration treatment. Some glass ceramics contained a feldspar crystalline phase, which was not affected by different ion-exchange practices. Specimens with a single ion-exchange process or with the hydration treatment had higher flexural strength than those without either of these two treatments. For double ion-exchange specimens, the flexural strength increased with decreasing ion-exchange temperature. The double ion-exchange specimens had flexural strength up to 280 MPa, which was slightly lower than that of the single ion-exchange specimens, but much higher than that of the as-annealed specimens. However, the Weibull modulus of these double ion-exchange specimens was 5–8 because of the presence of large defects. For further increasing mechanical reliability, silicate-containing dental glass ceramics were required to have appropriate flaw controls and ion-exchange processes.     

Fracture toughness of a high-strength beryllium at room temperature and 300° C

The fracture toughness of a high yield strength grade of hot-pressed beryllium block was determined at room temperature and 300° C. Fatigue cracks were generated in doublecantilever beam specimens by a reversed loading method. Room temperature fracture toughness values from specimens with electric discharge machined notches fell within the scatter band of values from specimens with fatigued precracks. Load—displacement records generated from test on specimens with machined notches exhibited the expected linearity. However, the records were nonlinear from tests on specimens with long cracks formed by repeated propagation and arrest. Evidence points to a crack-closure phenomenon rather than plasticity as the source of the nonlinearity. The fracture toughness data show that specimen orientation or test temperature have little effect. By contrast, reported ductility values for this material are very sensitive to both these variables. The mean value of the fracture toughness ranged from 9.0 MPa m^1/2 (8.1 ksi in. ^1/2) at 23° C to 10.8 MPa m^1/2 (9.7 ksi in. ^1/2) at 300° C. These values are among the lowest ever reported for beryllium.     

Determination of Fracture Toughness of Bone Cement by Nano-Indentation Test

The nano-indentation test was used to measure fracture toughness of the bone cement. The cement sample was prepared using two different mixing methods i.e., hand mixing and vacuum mixing. For this purpose, some cubic specimens, each of the size 10×10×5?mm³ were produced and then the nano-indentation test was performed on both the hand-mixed and the vacuum-mixed specimens by nano-indenter setup and atomic force microscopy observation. The fracture toughness values obtained from the hand-mixed and vacuum-mixed cements were compared. The results indicate that the vacuum-mixed cement has significantly higher fracture toughness compared with the hand-mixed ones. Since the nano-indentation test method needs less sample material, decreases costs and obtains reliable results, it can be considered as a suitable technique for determination of the mechanical properties of bone cements instead of the macroscale test methods.     

Effect of Pore Distribution on Elastic Stiffness and Fracture Toughness of Porous Materials

The paper focuses on experimental study of the effect of pore distribution on the mechanical properties of aluminum sheets containing multiple holes. Mechanical behavior of materials of uniform microstructure is compared with that of materials containing pore clusters of circular and elliptical shapes. The overall porosity of all specimens was 0.2. All the experiments were repeated 10 times. Our work demonstrates that overall elastic properties are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters. In contrast, fracture toughness of the specimens is strongly affected by the mutual positions of individual pores. Explicit connection between the fracture stress and minimum pore separation is obtained.     

Fracture toughness testing of materials by the EF method

Experimental evidence is presented that fracture toughness testing of ceramics by the EF method (fracture of the edge of a rectangular specimen as a result of indentation), which does not rely on modern fracture mechanics concepts, in contrast to its conventional analogs, is easy to implement and can be used under standard laboratory conditions. Testing results for yttria, alumina, zirconia, and silicon nitride ceramics confirm that this method is suitable for practical application. The EF method is well suited for testing nanostructured, dental, and other ceramics, as well as semiconductors, and is capable of providing reliable fracture toughness data even if the amount of material for testing is limited.