R-curve measurement of silicon nitride ceramics using single-edge notched beam specimens

R-curve behaviour of three kinds of silicon nitride-based ceramics has been studied using the single-edge notched beam (SENB) technique. If the notch is deep enough, the specimen shows stable fracture during the bending test, even when the sample is a brittle material. The conditions required to obtain stable fracture in the bending test are clarified by the analysis. The crack length of the specimen was also calculated from the changing load during the fracture test. In this study, coarse-grained silicon nitride shows a large increase of theR-curve. On the other hand, silicon nitride with silicon carbide whiskers shows noR-curve increase. The rise of theR-curve should be related to the microstructure of the ceramics, and especially to the grain size of the specimen, because silicon carbide whiskers are not large compared to the silicon nitride grains, and silicon carbide can reduce the grain growth of silicon nitride during sintering.     

The resistance to crack growth of asbestos cement

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

A microstructural approach to flaw size dependence of strength in engineering ceramics

In this work, microstructural effects on the flaw size dependence of ceramic strength were investigated from aspects of stress analysis in the grain just ahead of the crack tip and also R-curve behaviour. In the analysis, it was assumed that the stress averaged in one grain just ahead of the crack tip, in ceramics, might control the fracture from a flaw. A microstructurally modified fracture criterion using the averaged stress was established by introducing the R-curve due to the grain bridging effect for longer cracks. A new R-curve of an exponential type was proposed for the fracture criterion. The criterion could adequately express the central trend in the dispersal of experimental results in the strength versus flaw size relation. To explain the scatter of results, the size distribution and the crystallographic anisotropy of the grain ahead of the crack tip were examined as dominant factors. The lower bound of strength scatter was estimated from the largest grain size, and the strength dispersion was reduced by decreasing the range of grain size variation. In FEM simulations, each element was regarded as one grain with a different crystallographic orientation, which was randomly selected by using a series of quasi-uniform random numbers. It was revealed that the scatter of strength due to crystallographic variations was smaller than the strength dispersion caused by a distributed grain size.     

Subcritical interlaminar crack growth in fibre composites exhibiting a risingR-curve

Subcritical crack growth behaviour has been evaluated in composite laminates based on uniaxial carbon fibres in poly(ether-ether ketone) matrices. Double cantilever beam (DCB) specimens have been employed to give mode I loading and it is first shown that the materials exhibit a risingR-curve, i.e. the value of the interlaminar fracture energy,G _IC, increases as the crack propagates through the specimens. Secondly, when a DCB specimen is held at a constant displacement, subcritical crack growth is found to occur. The velocity of the subcritical crack growth,v, has been measured using a load-relaxation technique. Hence, values of the crack velocity,v, have been obtained as a function of the strain-energy release rate,G _I applied during subcritical crack growth. Owing to the presence of theR-curve, these data have been measured at various stages during the development of theR-curve. The relationships betweenv andG _I are modelled using power-law expressions. Finally, it is considered that theR-curve behaviour is most likely caused by the fibre bridging which develops behind the crack tip as the delamination propagates through the specimen. Fibre bridging allows stress to be transferred across the crack faces, behind the advancing crack tip, and so results in a shielding of the stress field at the crack tip from the applied stress. Therefore, the expression ascertained for the relationship between the velocity,v, of subcritical crack growth and the corresponding value ofG _I has been further refined and modelled to account for the presence of fibre bridging.     

Influence of the fracture softening behaviour of wood on load-COD curve and R-curve

A cohesive crack model is used to analyse failure of wood in mode I along the grain. Several configurations of the gradual fracture softening behaviour of an interface, meshed with joint-elements located on the potential crack path, are investigated. Different constitutive laws, obtained from a single normalized polynomial function, are tested in order to estimate the influence of parameters such as, the tensile strength, the fracture energy or the ultimate opening of the interface, on the macroscopic response of a fracture specimen. Numerical results are compared with experimental data obtained on DCB specimen. We argue that the fracture energy related to the constitutive law must correspond to the plateau value of the R-curve. Moreover, this study reveals that the peak load of a load-COD (Crack Opening Displacement) curve is strongly affected by the slope of the softening behaviour. Finally, we present a review of the influence of each parameter describing the softening function on: (1) the load-COD curve and (2) the corresponding R-curve.     

Influence ofR-curve behaviour on strength degradation due to Hertzian indentation

The influence ofR-curve behaviour on the post-indentation strength of two types of alumina was studied using Hertzian indentation. Soda-lime glass was included in the study to represent a material which does not exhibitR-curve behaviour. Specimens were indented with a spherical indentor with increasing loads. Post-indentation strength was measured in a mineral-oil environment using a ring-on-ring biaxial fixture. Indentation of the two aluminas produced the typical Hertzian crack pattern with a somewhat greater statistical variability than that found in soda-lime glass. The strength of the two aluminas fell into four different regimes that were separated by the onset of ring, cone, and radial crack formation, respectively.R-curve behaviour did not appreciably influence the results, undoubtedly due to the relatively narrow range of indentation loads where failure was controlled by ring and cone cracks. These strength results contrast to those obtained for soda-lime glass. In soda-lime glass, ring and cone crack nucleation occurred simultaneously with a sudden drop in strength followed by a gradual decline in strength with increasing indentation load, in accordance with the prediction of Hertzian cone-crack theory.     

Viscoelastic effects in testing of an Al2O3 ceramic containing a glassy phase

An alumina with 3 wt% glassy phase was tested at different loading rates at two temperatures (900 and 1000 °C). It was found that an increase in fracture toughness was accompanied by a decrease of the bending strength at the same loading rates. A model is given, which describes the experimental results by linear viscoelasticity of the second phase. Whereas the bulk properties are mainly due to the alumina grains and, therefore, remain nearly unchanged, the crack growth and the fracture behaviour in the intergranular regions is dominated by the viscosity of the glassy phase. This leads to a non-unique value ofK _Ic, which is dependent on the temperature and the loading rate.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

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

The temperature dependence of the fracture toughness and acoustic emission of polycrystalline alumina

The technique of acoustic emission has been shown to be suitable for the monitoring of fracture-toughness tests over a range of temperatures. Commercial polycrystalline alumina has been tested at temperatures up to 1000° C to determine the effect of microstructure and impurity content on fracture toughness and acoustic emission. For a given alumina there was no significant variation in acoustic response or fracture toughness up to 650° C. The emissions observed prior to fracture in this temperature range were attributed to subcritical crack growth. The number of emissions depended on the amount of subcritical crack growth, the grain size, and the presence and amount of porosity. Above 650° C the fracture behaviour changed due to the flow of a grain-boundary glassy phase. This was associated with a peak in the temperature dependence of the apparentK _IC and was accompanied by a large number of acoustic events of low amplitude and low pulse width. At these elevated temperatures the extent of grain-boundary glassy flow, and hence the acoustic response, increased with decreasing grain size and increasing impurity content.     

A load-cycling technique for R-curve behaviour: application to a low cement refractory

The data presented below for a low cement refractory shows that the material has strong R-curve behaviour for certain specimen sizes. The superposition method proposed by Sakai and Bradt [1] was coupled with the effective crack model developed by Karihaloo and Nallathambi [2] and used to investigate this R-curve behaviour. The technique that was developed involves load cycling on one specimen to evaluate K _IC values with crack extension, and was shown to give favourable results for this material.     

The effect of grain-boundary devitrification on the wear of glass-bonded alumina ceramics

The steady-state wear behaviour of a 94 wt% alumina was investigated in the as-fired condition and after a post-sintering heat treatment. The post-sintering heat treatment yielded devitrification of the 6 wt% calcia-magnesia-alumino-silicate (CaO · MgO · Al₂O₃ · SiO₂) glass grain-boundary phase. In addition, the effect of surface finishing on the wear behaviour of as-fired and heat-treated samples was studied. Steady-state wear rates were determined using a single-pin-on-disc tribometer. The results indicated that heat treated, unfinished samples exhibit a higher steady-state wear rate than as-fired, unfinished samples. The differences observed may arise in response to one or more of the following mechanisms: (i) creation of intergranular thermoelastic stresses due to thermal-expansion mismatch among intergranular species, (ii) elimination of the lubricative glass phase in devitrified specimens, and (iii) elimination of the advantageous effects of viscoplastic deformation of the intergranular glassy phase on stress relaxation. Surface finishing further increased the steady-state wear rate of the heat-treated samples only, and it correlated with an increase in subsurface microcracking and grain pull-out. A lubricative glass film was found to persist on all sample wear tracks, suggesting that the differences in wear behaviour are dominated by intergranular fracture and grain pull-out.     

Effect of ion exchange on <Emphasis Type="Italic">R</Emphasis>-curve behavior of a dental porcelain

The objective of this study was to evaluate the effect of the ion exchange treatment on the R-curve behavior of a leucite-reinforced dental porcelain, testing the hypothesis that the ion exchange is able to improve the R-curve behavior of the porcelain studied. Porcelain disks were sintered, finely polished, and submitted to an ion exchange treatment with a KNO₃ paste. The R-curve behavior was assessed by fracturing the specimens in a biaxial flexure design after making Vickers indentations in the center of the polished surface with loads of 1.8, 3.1, 4.9, 9.8, 31.4, and 49.0 N. The results showed that the ion exchange process resulted in significant improvements in terms of fracture toughness and flexural strength as compared to the untreated material. Nevertheless, the rising R-curve behavior previously observed in the control group disappeared after the ion exchange treatment, i.e., fracture toughness did not increase with the increase in crack size for the treated group.     

R-curve modeling of rate and size effects in quasibrittle fracture

The equivalent linear elastic fracture model based on an R-curve (a curve characterizing the variation of the critical energy release rate with the crack propagation length) is generalized to describe both the rate effect and size effect observed in concrete, rock or other quasibrittle materials. It is assumed that the crack propagation velocity depends on the ratio of the stress intensity factor to its critical value based on the R-curve and that this dependence has the form of a power function with an exponent much larger than 1. The shape of the R-curve is determined as the envelope of the fracture equilibrium curves corresponding to the maximum load values for geometrically similar specimens of different sizes. The creep in the bulk of a concrete specimen must be taken into account, which is done by replacing the elastic constants in the linear elastic fracture mechanics (LEFM) formulas with a linear viscoelastic operator in time (for rocks, which do not creep, this is omitted). The experimental observation that the brittleness of concrete increases as the loading rate decreases (i.e. the response shifts in the size effect plot closer to LEFM) can be approximately described by assuming that stress relaxation causes the effective process zone lenght in the R-curve expression to decrease with a decreasing loading rate. Another power function is used to describe this. Good fits of test data for which the times to peak range from 1 sec to 250000 sec are demonstrated. Furthermore, the theory also describes the recently conducted relaxation tests, as well as the recently observed response to a sudden change of loading rate (both increase and decrease), and particularly the fact that a sufficient rate increase in the post-peak range can produce a load-displacement response of positive slope leading to a second peak.     

Flaw tolerance in ceramics with rising crack resistance characteristics

The stabilizing influence of increasing toughness with crack size associated with a cumulative closure-stress process (R-curve, orT-curve) on the strength properties of brittle ceramic materials is analysed. Three strength-controlling flaw types are examined in quantitative detail: microcracks with closure-stress history through both the initial formation and the extension in subsequent strength testing; microcracks with closure stresses active only during the subsequent extension; spherical pores. Using a polycrystalline alumina with pronouncedT-curve behaviour as a case study, it is demonstrated that the strength is insensitive to a greater or lesser extent on the initial size of the flaw, i.e. the material exhibits the quality of flaw tolerance. This insensitivity is particularly striking for the flaws with full closure-stress history, with virtually total independence on initial size up to some 100m; for the flaws with only post-evolutionary exposure to the closure elements the effect is less dramatic, but the strength characteristics are nevertheless significantly more insensitive to initial flaw size than their counterparts for materials with single-value toughnesses. The implications of these results to engineering design methodologies, as expressed in conventionalR-curve constructions, and to processing strategies for tailoring materials with optimal crack resistance properties, are discussed.     

Effects of grain size and specimen geometry on the transformation and R-curve behaviour of 9Ce-TZP ceramics

Transformation and R-curve behaviour have been investigated in 9 mol% Ce-TZP ceramics with different grain sizes. Both single-edge notched beam and short double-cantilever beam specimens were tested to measure the crack-resistance curves. The size and shape of the transformation zone not only depend on grain size, but are also strongly influenced by the specimen geometry. This different transformation behaviour has led to different crack-resistance curves. These experimental results are discussed in terms of the thermodynamics of transformation, the effect of autocatalytic transformation, and fracture mechanics.     

Science of zirconia-related engineering ceramics

In this paper, we comprehensively review the physical principles behind the improvement of mechanical properties of zirconia (ZrO₂) related ceramics. First, the transformation behaviour of different phases in zirconia is discussed. We next present an overview of two zirconia-related commercially important systems e.g. ZrO₂-MgO and ZrO₂-Y₂O₃. The commercial engineering ceramic materials, generated from these systems, are known as partially stabilized zirconia and tetragonal zirconia polycrystal respectively. The third important material is called zirconia toughened alumina. The evolution, characterization and importance of the microstructure in relation to the basic systems are also presented. Attention is then focussed on to three toughening mechanisms e.g. phase transformation toughening, microcrack toughening and crack deflection toughening. We carefully assess the roles they play in improving toughness. We discussR-curve behaviour arising out of these toughening mechanisms and the implications ofR-curve behaviour in engineering applications. Finally, the subcritical crack growth and tribological behaviour of these materials are discussed.     

SOME IMPLICATIONS OF THE USE OF THE PD6493 LEVEL 3 FAILURE ASSESSMENT PROCEDURE

Abstract— Under a natural mapping between the standard R-curve analysis diagram and the failure assessment diagrams of R6 and PD6493 Level 3 the R-curve becomes the RCI (R-curve image). It follows that whenever the assessment point moves along the failure assessment line during ductile crack growth, the implication is that the failure assessment line is the RCI. This result is used to test the conservatism of a specific PD6493 Level 3 analysis by two methods. The first calculates the variation during crack growth of the applied elastic-plastic crack tip opening displacement (CTOD) parameter (or‘driving force') which is implied by the PD6493 analysis and then compares this variation with an independent estimate of it. The second uses an assumed driving force to deduce the CTOD resistance curve implied by the failure assessment line. It is shown by both methods and also by a direct R-curve analysis that this particular PD6493 analysis is conservative relative to an R-curve analysis which uses a crack driving force estimated by the EPRI (Electric Power Research Institute) procedures. However there is inconsistency between standard R-curve analysis and PD6493 Level 3 analysis in that the latter implies a material resistance which, for a given material, depends on the geometry of the structure. A similar inconsistency arises in any failure assessment procedures like the Options 1 and 2 with Category 3 of R6, which require the assessment point to move on a geometry independent failure assessment line during crack growth; indeed, even when the failure assessment line is geometry dependent there is full agreement with R-curve analysis only if the correct RCI is used as the failure assessment line. In a brief discussion it is noted that the new failure assessment diagram studies involving multi-parameter fracture mechanics may help to ameliorate these problems.     

Fracture resistance determination of freshwater ice using a chevron notched tension specimen

Crack growth resistance (R-curve behavior) measurements on large grained S1 type freshwater ice were conducted in the Ice Mechanics Research Laboratory at Clarkson University. To overcome previous difficulties in obtaining stable cracking in freshwater ice, a new crack geometry was developed. The short rod Chevron Notched Tension (CNT) specimen was found to be extremely favorable in the sense of promoting stable,stick-slip, crack growth over a large portion of the uncracked ligament. A negative fracture resistanceK _R -curve was evaluated for this ice at -16°C.     

Effect of crack deflection and branching on the R-curve behaviour of an Al-Li alloy 2090 sheet

The methodology to predict the increase in crack growth resistance due to crack deflection and branching is described. These procedures are discussed with respect to an Al-Li alloy 2090 sheet in T6 condition, the R-curve tests on which revealed that the crack path in L-T orientation was deflected and branched while it remained nominally straight in T-L orientation. The resistance to slow stable crack extension in L-T orientation was found to be significantly higher as compared to that in T-L orientation. Such behaviour is rationalized in terms of crack deflection and branching. The observed variation in the crack path morphology and the resulting R-curves in L-T and T-L orientations can be understood in terms of the microstructural features of the alloy.