Rising Crack-Growth-Resistance (R-Curve) Behavior of Toughened Alumina and Silicon Nitride

R -curves for a sinter/HIPed SiC(whisker)-reinforced alumina and a sintered silicon nitride were assessed by direct measurements of lengths of cracks associated with Vickers indentation flaws. The fracture toughness measurements based on (a) initial (as-indented) crack lengths, (b) equilibrium growth of cracks during increasing far-field loading, and (c) crack lengths corresponding to unstable fracture showed definitive trends of R -curves for both materials. The fracture mechanics analyses employed an indenter-material constant that was independently estimated using a physical model for the residual driving force and a free surface correction factor that accounted for the effects of size and shape of the cracks on stress intensity. It is shown that R -curve estimations based on crack length measurements have the intrinsic advantage that crack length dependence of fracture toughness is not assumed a priori as is done in conventional analysis based on strength. The measured fracture toughness of SiC(whisker)-reinforced alumina was in agreement with the prediction of a toughening model based on crack bridging by partially debonded whiskers.     

Reliability Analysis of Structural Ceramics Subjected to Biaxial Flexure

Sintered alumina and silicon nitride were tested in uniaxial (four-point and three-point bend) and biaxial (uniformpressure-on-disk) flexure tests in inert conditions. Fracture origins were identified to be surface flaws in alumina and subsurface pores in silicon nitride. Batdorf's statistical fracture theory and two different fracture criteria, the critical normal stress criterion and a noncoplanar strain energy release rate criterion, were used to examine size and stress-state effects on fracture strengths of the two ceramics. Size effects assessed in four-point and three-point bend tests were in good agreement with the theoretical predictions for both ceramics. Measured biaxial strengths of alumina were in good agreement with the prediction when a noncoplanar strain energy release rate criterion and random surface flaw orientations were assumed. On the other hand, biaxial fracture strength of the silicon nitride was consistent with a prediction based on preferred flaw orientation (i.e., normal to the principal stress in the disks) and the normal stress fracture criterion. Orientation distributions of the fracture planes assessed from the fracture patterns of the disks supported the assumptions of random flaw orientations (alumina) and the preferred flaw orientations (silicon nitride), respectively, for the two ceramics. The preferred flaw orientation in silicon nitride is suggested to originate at subsurface pores as a result of crack nucleation in the plane of maximum tensile stress concentration, i.e., a diametral plane normal to the maximum principal stress.     

Short-Crack Toughness and Abrasive Machining of Silicon Nitride

Hardness and toughness are often used to analyze the abrasive machining behavior of ceramic materials. However, toughness values of silicon nitride ceramics with microstructures containing elongated grains increase with crack extension. The present study investigates the effect of toughness on the process of abrasive machining to determine which value of toughness should be used in the analysis. The toughness curves (i.e., toughness as a function of crack length) of ten different silicon nitride materials are characterized by an indentation-strength technique and an indentation technique. The forces in surface grinding are measured as a function of the depth of cut. Examination of ground surfaces by scanning electron microscopy indicates that the material-removal processes in grinding follows the formation of short cracks (i.e., microcracks) and grain-scale material dislodgement. An indentation fracture model for material removal in abrasive machining is used to correlate the grinding forces with toughness and hardness of the materials. An agreement is obtained between the experimental results and the indentation model only when the toughness associated with short cracks is used. This study shows the importance of using appropriate toughness values corresponding to the microfracture processes in analyzing abrasive machining results for materials possessing rising toughness curves.     

Stresses developed in reaction-bonded ceramics

A physical model is presented that predicts the stress distribution created in a particle during its reaction with a surrounding reactant to form a uniform layer of reaction product on its surface, when the reaction involves a volume change. The results of the model are applied specifically to the case of silicon reacting with nitrogen to form Si₃N₄. The model predicts the generation of a high, tensile hydrostatic stress in the Si core as well as high tensile radial stress and compressive tangential stress in the nitride layer. Although the model is restricted to elastic deformation only and therefore predicts unrealistically high stresses in some cases, the results are anyway of relevance in the consideration of possible non-elastic processes such as creep and fracture and also in assessing the possible effect of stress on the reaction equilibrium. It is predicted that the nitride reaction layer would fracture during the nitridation process. A second model is also presented predicting the residual stresses arising during cooling of a partially reacted particle as a result of the difference in thermal expansion of the reactant core and the reaction product layer. In the case of the reaction of silicon to silicon nitride these thermal expansion mismatch stresses are significant but small compared to the stresses due to the chemical reaction. ©     

Hertzian crack propagation in graded glass/ceramic composites

In literature, the concept of material gradation is shown to inhibit surface crack initiation in glass/ceramic composites subjected to Hertzian indentation. However, surface cracks could yet initiate due to relatively higher loadings or in the presence of surface flaws/defects. Hence, characterization of graded composites concerning the resistance against Hertzian crack initiation and propagation manifests itself as a prominent matter. In this study, axisymmetric Hertzian cracks evolving in graded glass/ceramic composites propelled by a rigid cylindrical punch are investigated employing a novel recursive method, called the stacked-node propagation procedure. Crack trajectories and their propagation susceptibilities are predicted via the minimum strain energy density (MSED) criterion regarding the crack growth resistance (R-curve) of ceramics. The stress trajectory approach is also considered for a homogeneous glass to reveal the reliance and effectiveness of the MSED criterion in the present crack problems. The Mori–Tanaka relations are adopted to model the elastic modulus and Poisson's ratio variations through the composites, which are implemented on the simulations via the homogeneous finite element approach. Hertzian crack problem of a practically producible graded composite comprised of oxynitride glass and a fine-grained silicon nitride ceramics (Si₃N₄) is treated as a case study. The degree of material gradation is assessed for the mitigation of surface crack initiation and propagation risks.     

Simulation of crack propagation in fiber-reinforced concrete by fracture mechanics

Mode I crack propagation in fiber-reinforced concrete (FRC) is simulated by a fracture mechanics approach. A superposition method is applied to calculate the crack tip stress intensity factor. The model relies on the fracture toughness of hardened cement paste (K_IC) and the crack bridging law, so-called stress-crack width (σ-δ) relationship of the material, as the fundamental material parameters for model input. As two examples, experimental data from steel FRC beams under three-point bending load are analyzed with the present fracture mechanics model. A good agreement has been found between model predictions and experimental results in terms of flexural stress-crack mouth opening displacement (CMOD) diagrams. These analyses and comparisons confirm that the structural performance of concrete and FRC elements, such as beams in bending, can be predicted by the simple fracture mechanics model as long as the related material properties, K_IC and (σ-δ) relationship, are known.     

Thermal shock resistance of porous ceramic foams with temperature-dependent material properties

The impact of temperature dependence of material properties on thermal shock resistance of porous ceramic foams is studied in this paper. Two cases of thermal shock are carried out: sudden heating and sudden cooling. Finite difference method and weight function method are employed to get the thermal stress field at crack tip. The effects of time dependence and temperature dependence of material properties on thermal shock behavior are analyzed. The thermal shock resistance is acquired based on two different criteria: fracture mechanics criterion and stress criterion. By comparison analysis, results show that taking temperature dependence of the material properties into account is crucial in the assessment of thermal shock resistance of ceramic foams. Cold shock fracture experiments of Al₂O₃ foams with different relative densities are also made, and the obtained results are in coincidence with theoretical results very well.     

含表面裂纹群的PTA加压罐的安全评定

以断裂力学为方法，以“合乎使用”为原则，在对ＰＴＡ加压罐进行了外观检验、无损检测、应力分析及材料性能分析后，采用流变应力准则，对其焊缝热影响区附近的表面裂纹群进行了安全评定。评定结果表明，在现有的操作压力水平下，含表面裂纹群的在用加压罐可以继续安全使用，不必进行任何返修。     

Fatigue Threshold R‐curves Predict Fatigue Endurance Strength for Self‐Reinforced Silicon Nitride

There is a need for methods that can help predict and avoid fatigue failures of silicon nitride ceramic components. The fatigue threshold R‐curve has been proposed as potential solution to this problem. In this study, the fatigue threshold R‐curve for small, semielliptical surface cracks was calculated for a silicon nitride ceramic using the published bridging stress distribution developed from fatigue threshold tests on macroscopic crack specimens. To test the accuracy of the endurance strengths predicted using the fatigue threshold R‐curve, fatigue tests were conducted using four‐point bend beams of silicon nitride containing semielliptical surface cracks introduced by Knoop indentation. The effectiveness of the methodology was verified; indeed, 77% of the beams tested at stress levels above the predicted endurance strength failed within 10⁷ cycles and 0% of the beams tested below the predicted endurance strength failed within 10⁷ cycles. Furthermore, using the bridging stress distribution, which is thought to be a material property, the need for prohibitively difficult fatigue threshold experiments on small surface cracks is avoided. Accordingly, this methodology is potentially quite practical for use in the engineering design of ceramic mechanical components.     

Sensitivity of Scratch Resistance to Grinding-Induced Damage Anisotropy in Silicon Nitride

Single-grit scratch experiments were conducted on polished as well as on longitudinally and transversely ground silicon nitride specimens to investigate the influence of grinding direction on scratch resistance. It was found that the volume of material removed and the extent of cracking were the largest when the scratches were parallel to the grinding direction and were the least on the polished specimens. These results were rationalized based on the grinding-induced sub-surface damage anisotropy and were quantified using a scratch resistance measure. A linear elastic fracture mechanics analysis revealed that only cracks of certain length and orientation grow to cause the observed trends in the scratch resistance.     

Determination of structural and mechanical properties of multilayer graphene added silicon nitride-based composites

Silicon nitride based nanocomposites have been prepared with different amount (1 and 3 wt%) of multilayer graphene (MLG) as well as exfoliated graphite nanoplatelets (xGnP) and nano graphene platelets (Angstron) in comparison. The microstructure and mechanical properties of the graphene reinforced silicon nitride based composite materials have been investigated. Homogeneous distribution of the MLG additives have been observed on the fracture surface of the sintered material. The scanning electron microscopy examinations showed that graphene platelets are inducing porosity in matrix. The bending strength and elastic modulus of MLG/Si₃N₄ composites showed enhanced values compared to the other graphene added silicon nitride ceramic composites. These observations may be explained by the different type and quality of the starting materials and by the dispersion grade of graphene platelets having direct impact to the resulting density of the sintered samples.     

Controlled material removal mode and depth of micro cracks in precision grinding of fused silica – A theoretical model and experimental verification

A critical function for crack propagation for the single grit scratching of fused silica is developed based on the fracture mechanics. The effects of original crack density on the surface, strain rate and grinding coolant are considered in the function. A theoretical model for controlled material removal mode and depth of micro cracks precision grinding is presented based on the critical function for crack propagation. It can be predicted by the model that the material removal mode in the grinding of fused silica with original cracks damage will change from a ductile mode to a semi-brittle mode, a full-brittle mode and a semi-brittle mode in sequence with the increasing single grit scratching depth. It was found that the micro crack damage depth of fused silica does not increase with the single grit scratching depth after a full brittle mode grinding and it is always smaller than that after a semi brittle mode grinding even with a smaller single grit scratching depth. These interesting results are explained by the fracture mechanics. The ductile mode grinding is a recognized desirable process of fabricating fused silica while the full-brittle grinding is also a feasible process for its shallow subsurface damage, high efficiency, low grinding force and energy consumption. Therefore, the depth of micro cracks after grinding can be controlled by choosing suitable grinding parameters. Grinding experiments are conducted on fused silica. The undeformed chip thickness of randomly distributed effective grits is simulated based on 3D reconstruction of wheel topography to reveal the relationship between the grinding parameters and the single grit scratching depth. Ground surface roughness, sub-surface damage (SSD) depth and grinding force are measured and discussed. It is shown that the model predictions correlate well with the experimental trend of grinding modes.     

Residual static strength and the fracture initiation path in adhesively bonded joints weakened with interfacial edge pre-crack

This paper deals with the application of fracture mechanics approaches for predicting the residual static strength and the crack kinking angle of adhesively bonded joints containing interfacial edge pre-cracks. The interfacial cracks are created due to different factors such as inappropriate surface preparation which cause a significant reduction of the joint strength. To investigate the residual strength of interfacial cracked adhesive joints and predict the crack kinking angle, three different approaches including the maximum tangential stress (MTS), the minimum strain energy density (SED) and the maximum tangential strain energy density (MTSED) were assessed. To this end, single lap joints (SLJs) containing a brittle adhesive material and with different pre-crack sizes and various substrate thicknesses were manufactured and tested. The results were also verified by applying fracture mechanics approaches on previously published experimental data. According to the results, it was concluded that in mode II dominant cases, the predictions of kinking angle using the MTS method was in good agreement with the experimental observations, while in mode I dominant cases the mentioned approach provided poor predictions. It was also found that the SED criterion could be a precise model for predicting the crack extension angle in mode I dominant conditions. The results also showed that the MTS criterion predicts the residual static strength of interfacial cracked adhesive joints very well.     

High strain rate indentation-induced deformation in alumina ceramics measured by Cr fluorescence mapping

Alumina materials with a range of grain sizes and purities were subjected to small-scale dynamic impact by sharpened tungsten carbide projectiles at sub-ballistic velocities. The resistance of the materials to fracture was recorded by visual examination of the cracking on the impacted surface and the damage in the subsurface region. The residual stress and plastic deformation induced in each material were examined using Cr³⁺ fluorescence mapping. A modified Hertzian indentation model of the stress state in the material with the addition of a blister field representing the stress induced by the presence of the subsurface plastic zone was found accurately describe the observed cracks beneath the surface of the material, as well as the radial cracks on the surface.     

Fractography of biaxial tested Si3N4-specimens

The strength of ceramic materials is limited by flaws which are distributed in the volume or on the surface of the material. Commonly, fractographic investigations are performed after the strength tests to interpret the strength values.The relatively new Ball-on-Three Balls (B3B)-bending test applies a biaxial stress state (which is more searching for cracks than a uniaxial stress state) on the specimen. To identify typical fracture initiating flaws and to get a better understanding of the fracture behaviour of B3B-specimens a systematic fractographic investigation was performed on 260 silicon nitride specimens divided into batches with different surface qualities. It could be shown that in most cases (at least those in which origins could be clearly identified) surface or near surface located defects were responsible for failure. On specimens with poor surface qualities, surface defects were introduced through machining. On specimens with a better surface quality, volume defects, which were exposed on the surface by polishing, could be identified as fracture origins. In only a few cases defects in the bulk were fracture origins.     

Temperature dependent first matrix cracking stress model for the unidirectional fiber reinforced ceramic composites

Based on a kind of equivalence between heat energy and fracture energy, assuming that there is a constant maximum storage of energy that includes both heat energy and fracture energy, a new temperature dependent fracture surface energy model is developed. Using the new model and the classical ACK theory, a temperature dependent first matrix cracking stress model is obtained for the fiber reinforced ceramic composites. According to the model, the temperature dependent first matrix cracking stress of materials can be easily predicted using some basic material parameters such as matrix fracture surface energy and Young’s modulus. The model is verified by comparison with experimental data of SiC fiber reinforced reaction-bonded Si₃N₄ composites at different temperatures. Good agreement is obtained between predicted and experimental data of first matrix cracking stress. The dependency of first matrix cracking stress on fracture surface energy and interfacial shear strength is systematically analyzed.     

Substrate constraint and adhesive thickness effects on fracture toughness of adhesive joints

The adhesive thickness effect on fracture behaviour of adhesive joints has been studied using the boundary effect model recently developed for specimen size effect on fracture properties of concrete, and the essential work of fracture model for ligament (uncracked region) effect on largescale yield of bulk metals and polymers. The leading common mechanism responsible for the nonlinear elastic fracture mechanics behaviours, such as adhesive thickness effect of adhesive joints, specimen size effect of brittle heterogeneous materials and notch dependence of deeply notched metal and polymer specimens, is discussed. These two fracture mechanics models show that the height variation of a fracture process zone (FPZ) or a plastic zone is directly responsible for any change in fracture energy measurements such as the specific fracture energy G _f and the critical strain energy release rate G _c. Both models show that G _f is rapidly reduced when the crack-tip approaches the back-face boundary of a specimen because only a limited FPZ or plastic zone height h _FPZ can be developed in the boundary region. In the case of a thin adhesive joint, the development of a plastic zone height is limited by the thickness of the adhesive sandwiched between the upper and lower adherends or substrates. Consequently, a linear relationship between the adhesive joint toughness and adhesive thickness is established. Test results on adhesive joints from the literature are analysed and compared with the new adhesive joint failure model based on the two well-established fracture mechanics models developed for other material systems.     

Oblique Impact of Spherical Particles onto Silicon Nitride

Oblique impact damage to gas-pressure-sintered silicon nitride is investigated by examining changes in the stress field beneath the impact site of the silicon nitride. Varying the impact angle changes the morphologies of the initiated cracks from Hertzian cone crack to surface ring crack as the impact angle decreases. Moreover, impact at greater angles (90° and 60°) creates Hertizian cone cracks that drastically decrease the strength of the target materials; impact at smaller angles (45° and 30°), on the other hand, creates surface ring cracks that cause only moderate strength degradation.     

Mechanical properties of structural ceramic materials based on silicon nitride

The creation of structural ceramic materials based on silicon nitride is considered. The results of a study of the properties of these materials in a wide temperature range are presented, including data on the short-term strength, elastic characteristics, and parameters of fracture mechanics and results of long-term static and dynamic tests of some silicon nitride materials.Translated from Ogneupory i Tekhnicheskaya Keramika, No. 11, pp. 14–17, November, 1996.     

Crack-location-dependent R-curve behavior in Si3N4

The rising crack resistance (R-curve) behavior in a hot-pressed Si₃N₄ with an elongated grain structure was studied by observing the stable growth of annealed indentation-induced cracks during the bending test. The experimental data corresponding to each individual crack were analyzed according to an exponential function proposed by Ramachandran and Shetty. [Ramachandran, N. and Shetty D. K., Rising crack growth-resistance (R-curve) behaviour of toughened alumina and silicon nitride. J. Am. Ceram. Soc., 1991, 74, 2634–2641]. It was found that the measured R-curve is strongly dependent on the crack location. Due mainly to the existence of a microstructural driving force for crack growth, all cracks may start to propagate at nearly the same level of the applied stress intensity. During the subsequent stable growth, however, the variations of crack resistance with crack extension may be different for different cracks located in different sites of the surface of material. The effect of the random orientation of the elongated grains within the material on the interaction between the bridging grain and the propagating crack was suggested to be the main cause of the crack-location-dependence of the measured R-curve behavior.