Crack resistance curves of alumina at high temperatures

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (K _lc) were then measured as a function of sharp crack length in a fast-fracture, load-controlled test at 900, 1000 and 1100° C. By means of these fast fracture tests, crack resistance curves (K _lc against crack length) were determined for two commercially pure aluminas of different grain size and for a debased alumina containing a glassy phase. The crack resistance curve for the pure, fine grained alumina proved to be flat at 900° C, as was found for room temperature. A steeply rising crack resistance was, however, observed for the pure coarse-grained alumina at 1100° C and for the debased alumina at 1000 and 1100° C. This rise in KR curves is explained by friction effects of the cracked microstructure behind the crack front for the coarse grained alumina and by adhesive forces caused by the second phase behind the crack front for the debased alumina. These facts are proved by comparison to experiments on notched specimen and by annealing experiments. From the annealing experiments the size of the adhesive zone is estimated for the debased material.The death of Dr R. F. Pabst is sadly recorded. (On leave of absence from Max-Planck-Institut für Metallforschung, Seestraße 92, 7000 Stuttgart 1, Federal Republic of Germany).     

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.     

Single and multi-specimenR-curve methods forJ IC determination of toughened nylons

For characterization of the fracture resistance of materials used in the upper shelf toughness regime,J-R curves are widely considered the most promising candidates. However, there still remain problems concerning both the generation and measurement ofJ-R curves as material characterizing parameters and their application in ductile fracture analyses for failure prediction in polymeric materials. This paper reports the results of investigations conducted on two rubbertoughened nylons at room temperature. Two different methods ofJ-R curve determination are covered, namely multi-specimen and single specimen test methods. The resultingJ-R curves have also been evaluated to obtain values of the initiation toughness,J _IC, following the extrapolation and interpolation schemes prescribed by ASTM E813-81 and ASTM E813-87 test procedures, respectively. The results show that the multiple specimen unloading method and the single specimen partial unloading compliance method can be used to generate comparable crack growth resistanceJ-R curves of the toughened nylons. The value ofJ _IC for the crystalline rubber-toughened nylon was approximately twice the value obtained for the amorphous rubber-toughened nylon. The former material also exhibited a greater resistance to ductile crack growth.     

Application of artificial neural network for predicting plain strain fracture toughness using tensile test results

A back‐propagation neural network was applied to predicting the K_IC values using tensile material data and investigating the effects of crack plane orientation and temperature. The 595 K_IC data of structural steels were used for training and testing the neural network model. In the trained neural network model, yield stress has relatively the most effect on K_IC value among tensile material properties and K_IC value was more sensitive to K_IC test temperature than to crack plane orientation valid in the range of material data covered in this study. The performance of the trained artificial neural network (ANN) was evaluated by comparing output of the ANN with results of a conventional least squares fit to an assumed shape. The conventional linear or nonlinear least squares fitting methods gave very poor fitting results but the results predicted by the trained neural network were considerably satisfactory. This study shows that the neural network can be a good tool to predict K_IC values according to the variation of the temperature and the crack plane orientation using tensile test results.     

Ermittlung des Bruchwiderstands an Oxidkeramik und Hartmetallen mit verschiedenen Methoden

Fracture Toughness Determination of Alumina and Cemented Carbide with Different Testing Methods Fracture toughness of a sintered alumina and two tungsten carbidecobalt materials was determined using four-point-bend specimens with straight through and chevron notches and with the short rod specimen. With the specimens with a straight through notch a lower K_Ic was measured for Al₂O₃ and a higher for WC-Co compared to the chevron-notched specimens. This behavior was explained by the different shapes of the crack growth resistance curves and the different critical notch radii. For Al₂O₃ a steeply rising crack growth resistance curve was measured in a controlled fracture test, for WC-Co a flatter curve was obtained. The effect of the shape of the crack growth resistance curve and of notch width on the evaluated toughness is discussed.     

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     

Viscoelasticity of ceramics at high temperatures

The dependence of the fracture toughness, K _IC, on the loading rate has been calculated. On the basis of linear elastic fracture mechanics (LEFM) a strong dependence of the fracture toughness on the loading rate is obtained if subcritical crack growth is taken into account. If the subcritical crack growth parameters n and B are sufficiently small, which correspond to a high velocity of crack extension, the fracture toughness should decrease at lower loading rates. This behaviour is similar to the well-known decrease of bending strength. The experimental results for alumina containing glassy phase as a model material, however, show a maximum in a certain regime of loading rates. A model is established, which combines LEFM and the viscoelasticity, and leads to a maximum of K _IC at a certain loading rate dependent on the viscosity of the glassy phase.     

Controlled Crack Propagation Experiments with a Novel Alumina‐Based Refractory

Innovative, carbon‐reduced and carbon‐free refractory materials are currently under development within the framework of the DFG priority program “FIRE”. Among various novel material solutions an alumina‐based refractory with titania and zirconia additives (AZT) has gained special interest for application in high temperature processes under thermal shock conditions. The resistance against fracture of the AZT material and, for comparison, of a pure alumina refractory was examined by controlled crack propagation experiments. Wedge splitting and compact tension tests with in situ crack growth observation, partially on microstructural level, have been performed for both materials. Based on the measured room temperature values of dissipated energy, refractory stiffness and fracture stress, the Hasselman thermal shock parameter R″″ was determined. The results allow to predict that AZT is less prone to scale thermal shock damage than pure alumina. The microstructural observations reveal that growth and opening displacement of the main crack is accompanied in AZT by pronounced microcracking, branching and bridging processes. First efforts are also directed towards a mechanical quantification of this fracture behavior in terms of an R‐curve representation (fracture resistance as a function of apparent crack length). The specific problems of R‐curve evaluation that exist in AZT due to nonlinear deformation behavior are addressed and the influence of the observed crack growth mechanisms is discussed.     

A fractographic criterion for subcritical crack-growth boundaries in hot-pressed alumina

The percent intergranular fracture (PIF) was measured along radii extending from fracture origins in hot-pressed alumina specimens, fractured at various loading rates and temperatures, and plotted versus estimates of stress intensity factors (K _I) at the various crack lengths. Minima in PIF occur at values ofK _I that are close to the critical stress intensity factors (K _IC) for cleavage on various crystal lattice planes in sapphire. The subcritical crack-growth boundary (K _I=K _IC of the polycrystalline material) occurs near the primary minimum in PIF suggesting that this minimum can be used as a criterion for locating this boundary. In addition, it was noted that the polycrystallineK _IC (4.2 MPa m^1/2) is very close to theK _IC for fracture on {¯1 ¯1 2 6} planes which is 4.3 MPa m^1/2. These observations suggest that critical crack growth begins when increased fracture energy can no longer be absorbed by cleavage on these planes. There is a secondary minimum atK _I>K _IC that appears to be associated with theK _IC necessary for fracture on combinations of planes selected by the fracture as alternatives to the high fracture-toughness basal plane.     

Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings

For massive brittle materials, the fracture toughness in mode I, K_IC, can be determined using various reliable techniques. Besides, Vickers Indentation Fracture (VIF) technique has been developed to locally determine fracture toughness. However, since the indentation test generates a complex three-dimensional crack system around the indent, fracture toughness, K_C, is calculated instead of K_IC. Consequently some authors rightly reject the VIF technique to determine standard fracture toughness by arguing that the literature counts numerous VIF crack equations thus revealing discrepancies of this technique. Nevertheless in some cases (e.g. brittle ceramic coatings) inclusive material techniques are not applicable since presence of the substrate and/or multi-crack network can modify the crack propagation into the coating.In this work, we employed VIF technique to study multi-cracking behavior of titania, alumina and zirconia ceramic oxide coatings obtained by plasma spraying. To calculate VIF toughness, we propose (i) to select two crack equations for radial-median and Palmqvist cracking modes respectively, (ii) to adjust the crack equation of Miranzo and Moya for intermediate cracking mode, (iii) to develop a mathematical approach to determine the cracking mode, (iv) to take into account the multi-crack network by defining an equivalent four-crack system and (v) to propose a universal crack equation applicable independently of the cracking mode.     

Subcritical crack growth in partially stabilized ZrO2(MgO)

The room temperature slow crack growth resistance in air ( 50% relative humidity) and in water for large cracks in MgO-partially stabilized zircoba (PSZ) improves with increase in critical fracture toughness,K _lc. Ageing the as-fired PSZ at 1400° C for 8 h results in decreasing K_lc from 8.5 MPa m^1/2 to 6 M Pa M^1/2. The ageing treatment also promotes the growth of eutectoid decomposition products on grain boundaries that is accompanied by a decrease in the dependence (A the change in Region I crack velocity with a change in the applied stress intensity. Calculated times to failures are markedly decreased in the aged as compared to the as-fired PSZ ceramic.     

Classification of environmentally assisted fatigue crack growth behavior

Fatigue crack growth is represented using fracture mechanics parameters, ΔK and K_max. Environmental effects that depend on time and stress affect the fatigue behavior predominantly through K_max parameter. The superimposed effects of environment and stress are seemingly complex. We have developed a methodology for classifying and separating the effects of environment on fatigue crack growth. A “crack growth trajectory map” is constructed from the behavior of ΔK versus K_max for various constant crack growth rate curves. A “pure fatigue” behavior is defined, in terms of environment-free behavior, such as in high vacuum. Deviation from this “pure fatigue” reference of the trajectory map is associated with either monotonic mode of fracture or to the superimposed environmental effects on crack growth. Using such an approach, called “Unified Damage Approach”, we classify the environmental effects in almost all materials into only five types. Each of these types shows the combination of time and stress affecting the crack tip driving force, and thus ΔK and K_max. The trajectory map depicts the changing material resistance due to the changing crack growth mechanisms with increasing crack growth rate, as reflected in terms of the applied stress intensities, ΔK and K_max. Thus the trajectory map provides a useful tool to separate the contributions from pure fatigue and superimposed monotonic modes and the governing crack growth mechanisms as a function of load-ratio, crack growth rate and environment. Understanding and quantification of the governing mechanisms would help in developing a more fundamental and reliable life prediction method.     

CYCLIC FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR IN ALUMINA CERAMICS

Cyclic fatigue crack growth behaviour in alumina ceramics is investigated and the effect of grain size discussed. Special attention is given to crack closure effects. Cyclic fatigue tests were carried out using four-point bend specimens, and the load–strain and load–differential strain curves were monitored. These curves show hysteretic behaviour probably related to frictional sliding of bridging grains, and also include non-linearities due to crack closure. The crack opening load is determined from the load–differential strain curve by using a method introduced in this study. Growth rates can be successfully described by the relationship da/dN = C[ΔK_{eff /(1 ? Kmax /KIC )]m} which is proposed in this study to account for the effects of crack closure and the maximum stress intensity factor. Irrespective of grain size, growth rates can be well represented by the above relationship, implying that the grain size exerts an influence on growth rates not only because of crack closure behaviour but also the material fracture toughness. The growth rate curve based on the proposed relationship shows a sigmoidal form for ceramic materials, which is similar to metals.     

Short-rod elastic-plastic fracture toughness test using miniature specimens

The standard ASTM-E399 plane-strain fracture toughness (K _IC) test requires (1) the test specimen dimensions to be greater than a minimum size and, (2) fatigue precracking of the specimen. These criteria render many materials impractical to test. The short-rod elastic-plastic plane-strain fracture toughness test proposed by Barker offers a method of testing not requiring fatigue precracking and furthermore, it appears that test specimens smaller than that stipulated by ASTM can be used to obtain validK _IC values. In this study, the use of a modified miniature short-rod fracture toughness test specimen was investigated. Our miniature short-rod specimen is approximately 7 mm long and 4 mm diameter. These mini specimens are well suited for the purpose of testing biomaterials. The value of the minimum stress intensity factor coefficient (Y _m ^* ) for the mini short-rod specimens was determined experimentally using specimens machined from extruded acrylic rod stock. An elastic-plastic fracture toughness analysis using the mini specimens gave values ofK _IC for extruded acrylic (nominally PMMA) equal to 0.67 ± 0.06 MPa m^1/2. The problem of testing non-flat crack growth resistance curve materials (such as PMMA) using the short-rod fracture toughness test method is discussed. A modification to the test procedure involving the use of aY ^* value corresponding to a short crack length is suggested as a method of overcoming this difficulty.Nomenclature a crack length - a ₀ initial crack length - a ₁ length of the chevron notch on the mini short-rod specimen - a _m critical crack length — crack length atY _m ^* - C specimen compliance - C dimensionless specimen compliance = CED - D mini short-rod specimen diameter - E Young's modulus - K ₁ stress intensity factor - K _1C plane-strain fracture toughness - K _max fracture toughness calculated usingP _max - P load applied to the test specimen during a short-rod fracture toughness test - P _c load applied to the test specimen atY _m ^* - P _max maximum load applied to the specimen during a short-rod fracture toughness test - p plasticity factor - W mini short-rod specimen width - Y ^* stress intensity factor coefficient - Y _m ^* minimum of the stress intensity factor coefficient - dimensionless crack length =a/W - ₀ dimensionless initial crack length = ₀/W - ₁ dimensionless chevron notch length =a ₁/W - _m dimensionless critical crack length =a _m/W     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

Anrißerzeugung in WC-Co-Hartmetall-Proben für die Messung des kritischen Spannungsintensitätsfaktors KIC

Precracking of WC-Co-Hardmetal-Specimens for Fracture-Toughness Testing The determination of a valid critical stress intensity factor K_IC requires an extremely sharp, well defined initial crack. Methods producing such a crack are well known for metallic materials, but they often can not be used with brittle materials, like cemented carbides or ceramics. Their low fracture toughness makes a controlled crack growth under pure tensile stress nearly impossible. More useful are precracking methods, utilizing a stress gradient to stop the crack at defined depth. A very simple methods uses the indentation of a hardness tester to produce a semi-elliptical surface crack, interfered with residual stresses. For different areas of application and specimen geometries, bridge indentation, wedge indentation and composite bending method produce cracks with a straight front. Also under cyclic loading, under tensile as well as under compressive stress, the creation of a sharp precrack, applicable in K_IC measurement, is possible.     

R-curve evaluation with ceramic materials at elevated temperatures by an energy approach using direct observation and compliance calculation of the crack length

An experimental procedure is presented which allows the direct visual observation and measurement of crack extension in ceramic materials at high temperatures. The directly measured crack lengths, gained from displacement-controlled three-point bend tests, are compared to those calculated from the compliance. An energy approach is presented to calculateR-values from the load-displacement curves. TheseR-values for a pure alumina and an alumina containing a glassy phase, for which the load-displacement curves show non-linearity at high temperatures, are compared toK-values andJ-values. The stress intensity approach, based on traction-free surfaces, gives unrealistic data for the nonlinear behaving material owing to adhesive effects behind the actual crack front. TheJ-values, calculated by two methods developed for investigations with moving cracks, are identical to those from the energy approach.     

Evaluation by indentation of fracture toughness of ceramic materials

A transition fracture mode from Palmqvist to median has been observed in a number of ceramic materials. A new expression to determine the fracture toughness (K _IC) by indentation is presented. The K _IC values calculated by this formula are independent of the crack profile (median or Palmqvist) and of the applied load. This formula has been obtained by modifying the universal curve of Evans and Charles to incorporate Palmqvist and median cracks over a wide range of loads in the case of brittle materials with different mechanical properties (elastic properties: E, v, K _IC).     

CRACK EXTENSION UNDER MIXED-MODE LOADING IN AN ANISOTROPIC MODE–ASYMMETRIC MATERIAL IN RESPECT OF RESISTANCE TO FRACTURE

Abstract— Recently, a crack path fracture criterion was proposed by Kfouri and Brown, based on maximum energy release rates at the tip of short kinks emanating from an existing crack when the main crack is subjected to mixed-mode loading. Assuming a ‘mode asymmetry’ in respect of the fracture resistances of the material, K_Ir, and K_IIr, for pure mode I and pure mode II, respectively, i.e., K_IIr, differing from K_Ir, generally, the modified criterion proposed that the resistance to fracture is a function of the ratio q (=k₂/k₁) of the mode II to the mode I stress intensity factors at the tip of the kink. The aim of the present paper is to extend the modified criterion by presenting it in a form that takes into account material fracture resistance anisotropy in addition to the fracture resistance mode asymmetry previously described. Note however that the material's elastic properties are still assumed to be isotropic. A short FORTRAN computer program has been written to predict the kink angle under mixed-mode loading for cracks in materials with mode asymmetry and material anisotropy with respect to their fracture resistance properties, and the inclination angle, θ, defining the direction of the main crack in the material. The values of four parameters, r₀, r₉₀, s and θ, described in the text, characterising the material fracture resistance asymmetrical and anisotropic properties and the orientation of the main crack, are prompted by the program, which provides, almost instantaneously, the kink angles under various loading modes and much additional relevant information. The effects of the variation of these parameters, treated singly or in combination, and the discontinuous “catastrophic” character of many of the responses at certain “transition” values of the parameters, are illustrated further. In the discussion it is recognised that the translation of the results of the analysis of a highly idealised situation to actual practical problems on real materials encountered in practice, is not straightforward but, notwithstanding, since material fracture resistance anisotropy and fracture resistance mode asymmetry may well be present in the real world, the possible influence of these factors perhaps needs to be taken into account in studies on crack paths.