Study on the subsurface damage mechanism of optical quartz glass during single grain scratching

The single grain scratching SPH simulation model was established to study the subsurface damage of optical quartz glass. Based on the analysis of the stress, strain and scratching force during scratching, the generation and propagation of subsurface cracks were studied by combining with the scratch elastic stress field model. The simulation results show that the cracks generate firstly at the elastic-plastic deformation boundary in front of the grain (φ = 28°) due to the influence of the maximum principal tensile stress. During the scratching process, the median crack closes to form the subsurface damage by extending downward, the lateral crack promotes the brittle removal of the material by extending upward to the free surface, and microcracks remain in the elastic-plastic boundary at the bottom of the scratch after scratching. The depth of subsurface crack and plastic deformation increases with rising scratching depth. The increase of scratching speed leads to the greater dynamic fracture toughness, accompanied by a significant decrease of the maximum depth of subsurface crack and the number of subsurface cracks. The subsurface residual stress is concentrated at the bottom of the scratch, and the residual stress on both sides of the scratch surface would generate and propogate the Hertz crack. When the scratching depth is less than 1.5 μm or the scratching speed is greater than 75 m/s, the residual stress value and the depth of residual stress are relatively small. Finally, the scratching experiment was carried out. The simulation analysis is verified to be correct, as the generation and propagation of the cracks in the scratching experiment are consistent with the simulation analysis and the experimental scratching force indicates the same variation tendency with the simulation scratching force. The research results in this paper could help to restrain the subsurface damage in grinding process.     

Lateral cracks during sliding indentation on various optical materials

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂–Al₂O₃–P₂O₅–Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅–Al₂O₃–K₂O–BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 µm conical, and 200 µm conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.     

Elastic stress field model and micro-crack evolution for isotropic brittle materials during single grit scratching

An analytical model for the elastic stress field in isotropic hard and brittle materials during scratching is presented. The model considers the entire elastic stress field and the effect of material densification that was ignored in past studies, and is developed under a cylindrical coordinate system to make the modeling process simpler. Based on the model's predictions, the location and sequence of crack nucleation are estimated and the associated mechanisms are discussed. A single grit scratching experiment with an increasing scratch depth up to 2 µm is conducted for two types of optical glasses representing isotropic brittle materials: fused silica and BK7 glasses. It is found that the model's predictions correlate well with experimental data. Median cracks are found to be formed first during scratching, and the corresponding depth of the scratch sets the basis for determining the critical depth for brittle to ductile machining. Lateral cracks are initiated in the plastic yielding region and deflect to the work surface to cause material removal, while Hertzian cracks interact with lateral cracks to help remove lateral-cracked material. Furthermore, it is found that, owing to its open network molecular structure, fused silica has a much worse ductile machinability than the BK7 glass.     

The fracture toughness of inorganic glasses

Measuring the fracture toughness (K_Ic) of glasses still remains a difficult task, raising experimental and theoretical problems as well. The available methods to estimate K_Ic are reviewed, with emphasis on their respective advantages and drawbacks. In view of our current understanding, this analysis gives precedence to the SEPB method. The ultimate glass strength, the critical flaw size, and the indentation load for the onset of crack initiation are discussed, in the light of the fundamentals of fracture mechanics and classical background regarding the mechanics of brittle materials. Analytical expressions were further proposed to predict the fracture energy and fracture toughness of glasses from different chemical systems from their nominal compositions. The theoretical values were compared with the experimental ones, as obtained by self‐consistent methods when available. The agreement observed in most cases suggests that measured K_Ic values correspond to the crack propagation regime (as opposed to the crack initiation threshold), and supports previous investigations in glasses and ceramics, which showed that a crack tip is nearly atomically sharp in these materials (but for metallic glasses). Some ideas to design tougher glasses are finally presented.     

Surface damage resistance and yielding of chemically strengthened silicate glasses: From normal indentation to scratch loading

We report on surface elasticity, plastic deformation and crack initiation of chemically strengthened soda-lime silicate and sodium aluminosilicate glasses during lateral indentation and scratch testing. Instrumented indentation using a normal indenter set-up corroborated previous findings on the effects of chemical strengthening on surface Young's modulus, hardness, and indentation cracking. Using lateral indentation in the elastic-plastic regime, we find a pronounced increase in the scratch hardness as a result of chemical strengthening, manifest in higher work of deformation required for creating the scratch groove. Thereby, the glass composition is found to play a stronger role than the absolute magnitude of surface compressive stress. Using a blunt conical stylus for instrumented scratch testing reveals three distinct modes of scratch-induced surface fracture, which occur during scratching or after unloading. Occasional micro-cracking caused by pre-existing surface flaws at low scratching load can be completely suppressed through chemical strengthening. The intrinsic defect resistance to microcracking is reduced as a result of ion stuffing, depending on the initial glass composition, whereas the resistance to abrasive yielding is enhanced by several hundred MPa.     

Relationship between fracture toughness determined by surface crack in flexure and fracture resistance measured by indentation fracture for silicon nitride ceramics with various microstructures

The reliability of the Vickers indentation fracture (IF) method for various types of silicon nitride (Si₃N₄) ceramics was assessed by comparing the fracture resistance, K_R obtained from the IF test with the fracture toughness, K_Ic from the surface crack in flexure (SCF) technique in the same crack depth region. The K_R of a fine-grained and equiaxed Si₃N₄ matched with the K_Ic from the SCF test when Miyoshi's equation was used, while the K_Ic of a bearing-grade Si₃N₄ was found to lie between K_R values calculated with Niihara's equation (higher side) and Miyoshi's equations (lower side). In the case of coarse Si₃N₄ with elongated grains, the K_R determined using Niihara's equation gave the best fit with K_Ic. The inconsistent outcomes were explained by the probable mechanisms, indicating that the K_R from the IF test cannot be correlated directly with the K_Ic unless the effective crack length for the IF test was clarified.     

Fracture toughness testing of biomedical ceramic-based materials using beams,plates and discs

The testing of fracture toughness becomes problematic when only limited amount of material is available that hinders the production of typical beam specimens to be tested in bending. Here we explore fracture toughness testing methodologies that allow for small discs and plates having surface cracks to be tested in biaxial flexure using the Ball-on-3-balls (B3B) set-up, or sawed notches as in the Compact Tension geometry. The B3B-K_Ic test has shown to be versatile and account for a very small overestimation of the K_Ic-value in the order of 0.8–1.25% due to in-plane crack mispositioning, and a maximum of 4% if a worst-case scenario of additional out-of-plane mispositioning is assumed. The geometrical factor in the standard SCF method, derived by Newman and Raju, resulted in an overestimation of ～8% of the K_Ic-value compared to the new calculation by Strobl et al. for materials with Poisson’s ratio <0.3.     

Elastic properties and fracture toughness of SiOC-based glass-ceramic nanocomposites

Four different SiOC glass ceramics were synthesized and their fracture toughness (K_Ic) and fracture surface energy (γ) were assessed by means of the single-edge precracked beam (SEPB) method. In addition, the elastic moduli were measured and the Vickers indentation behavior (hardness and microcracking) was characterized. In particular, the dependence of K_Ic on the free carbon content and on the fraction of crystallized nanoparticles (SiC, ZrO₂, HfO₂) was investigated. An increase in K_Ic, from about 0.73 to 0.99 MPa √m is observed as the free carbon content is increased from less than 1 to 12 vol%. The addition of Hf and Zr (resulting in 4.5 to 7.8 vol% HfO₂ and ZrO₂ nanoparticles) was found to increase K_Ic to an extent similar to the free carbon content. Moreover, predicted K_Ic values, assuming that the crack travels through all phases accounting for their respective volume fractions, disrupting the weakest links within the structural units, are in agreement with the experimental values.     

Indentation size effect–crack propagation model and finite element simulation verification for microhardness test of ceramic materials

In this study, an indentation size effect–crack propagation model for hard and brittle materials in microhardness testing was proposed on the basis of the relationship between the size effects in microhardness testing and the generation and propagation of cracks in an indentation area. Results showed that crack length and crack opening angle were the main factors that influenced the size effect. The longer the crack length, the larger the crack opening angle, and the more obvious the size effect. The generation and propagation of cracks in the indentation region of ultrafine-grained Si₂N₂O–Si₃N₄ ceramics during microhardness testing were simulated on ABAQUS finite element software. The distributions of displacement field, strain field, and stress field in the indentation area with the presence of cracks was analyzed, the influence of crack propagation on the elastic recovery of the indentation area was discussed, and the correctness of the size effect–crack propagation model was verified.     

Fracture toughness of glasses as measured by the SCF and SEPB methods

The fracture toughness, K_Ic, of six glasses was measured by the surface crack in flexure (SCF) and single-edged precracked beam (SEPB) methods. Results depended upon the loading rate as well as the test environment. Environmentally-assisted slow crack growth affects the results for tests done in air. Dry nitrogen testing is preferred. Crack healing may be a severe complicating factor with precracked flexure bar type specimens if the specimens are unloaded between the precracking and final fracture test. Success in K_Ic testing depends to a large degree on upon the ability to make good precracks.     

Crack resistance and other characteristics of ceramics of partially stabilized zirconia with an iron oxide additive

The strength, toughness, hardness, and crack resistance of ceramics based on zirconia stabilized by yttrium oxide and having iron oxide as a reinforcing component are investigated. Certain features of this material are studied in detail at low and high temperatures. It is established that the ultimate strength in three-point bending is 977 MPa, and the critical coefficient of stress intensityK _Ic for a notched beam can attain 16.7 MPa · m^1/2. Different testing methods are used and analyzed in the investigation of crack resistance. For example, it is shown that in bending a beam indented under a load of 500 N the value ofK _Ic at room temperature is 9.5 MPa · m^1/2 and after cooling to – 140°CK _Ic is 12.3 MPa · m^1/2. For this testing method the dependence ofK _Ic on the length of a radial crackc _av is established. The results are analyzed with the use of additional data and a fractographic investigation.Translated from Ogneupory, No. 2, pp. 2 – 9, February, 1996.     

Comparison of fracture resistance as measured by the indentation fracture method and fracture toughness determined by the single-edge-precracked beam technique using silicon nitrides with different microstructures

Because of the industrial need for an assessment of fracture resistance, K_R from small ceramic parts, K_R of Si₃N₄ ceramics has been measured by the indentation fracture (IF) method using representative formulae to evaluate the compatibility with the fracture toughness, K_Ic determined from the single-edge-precracked beam (SEPB) technique. K_R of the fine Si₃N₄ showed little dependence on the crack length, whereas the samples with coarse microstructures exhibited a rising R-curve behavior. The IF equation which gave the nearest value to K_Ic from SEPB was different depending on the microstructures. The assessment of fracture resistance with Miyoshi's equation was considered to be preferable for the flat R-curve behavior. By contrast, in the case of the rising R-curve behavior, it was revealed that the relationship between the IF and SEPB values was difficult to explain unless the effective crack extension against K_Ic for SEPB was clarified.     

Characterisation of subcritical crack growth in ceramics using indentation cracks

Abstract

The introduction of indentation cracks into brittle materials has proved to be a useful tool in characterising subcritical crack growth, notably in efficiently measuring the kinetic growth parameters and in defining whether the material exhibits a fatigue threshold. The accuracy of the subcritical crack growth parameters obtained using indentation mechanics can be excellent, provided the stress intensity factor associated with the indentation cracks is well characterised. Indentation cracks can also be used to measure crack velocity as a function of the applied stress intensity factor by direct observation. In such testing, it is critical that the changes in crack shape as the crack extends are known or accurately predicted. Numerical simulations suggest that the shape changes can be influenced not only by the testing geometry but also the growth kinetics. Finally, it is shown that the fatigue threshold can be determined by allowing median cracks to extend subcritically during indentation.     

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.     

Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with vickers indenter

Virtual crack closure technique and elastoplastic finite element method were employed to calculate the stress intensity factors (SIF) of ceramic materials on the tip of both half‐penny crack (HPC) and radial crack (RC) induced by Vickers indenter and the value of fracture toughness (K_IC) was extracted by the design of equi‐SIF contour of HPC and RC crack front. Through dimensional theorem and regressive analysis, a functional relationship between instrumented indentation parameters, crack length of Vickers impression and fracture toughness of ceramic materials was established, thus a novel methodology has been presented for measuring fracture toughness of ceramic materials by instrumented Vickers indentation. Both numerical analysis and experiments have indicated that this methodology enjoys higher measurement precision compared with other available indentation methods. The methodology is universally suitable for HPC, RC as well as transition cracks and capable of determining fracture toughness and elastic modulus in a single indentation test. In addition, it saves the effort of measuring the diagonal length of Vickers impression in case that the impression remains unclear.     

Interfacial characterization of catalyst coating on electrolyte polymer through microscratch analysis in DMFC

This study combined scratch testing and fracture-mechanical analysis to characterize the interfacial adhesion of catalyst coating on electrolyte polymer in microfuel cell. Scratch testing was used to determine the critical load for interfacial failure, while fracture-mechanical analysis was used to quantify the adhesion between Nafion (the electrolyte polymer substrate) and Pt/Ru alloy (the catalyst coating). Especially, it is appropriate to establish a relationship between interfacial toughness and adhesion failure by scratching because the failure mechanism by electrochemically induced swelling and shrinking at this interface is very similar to that of scratch testing. We also proposed a key of solving ambiguous problems in indentation crack testing by determining geometric information from crack propagation and critical points, as for a hard porous coating on a soft substrate. Finally, three kinds of process manufacturing the catalyst layer for anode were compared to verify our new test algorithm qualitatively.     

Crack propagation during Vickers indentation of zirconia ceramics

A quarter finite element model of 3 mol% yttria stabilized tetragonal zirconia polycrystal (3Y-TZP) ceramics undergoing Vickers indentation was established to simulate the evolution of stress and the propagation of cracks inside a sample. The indentation experiment was carried out on the Micro Vickers Hardness Tester. The results of the geometric characteristic parameters, such as the indentation diagonal half-length a, the crack length c and the maximum indent depth h_m, from the indentation simulation and experiment were similar. The types of indentation cracks under various loads were determined according to the Lawn-Evan model, which exactly correspond to the simulation results. In addition, the propagation of indentation cracks was discussed based on the maximum principal stress contour plots at various stages, and the conclusions were verified by the indentation analysis model proposed by Yoffe. As a result, the model developed in this paper can be used in indentation studies to solve the related problem.     

Toughness measurement on ball specimens. Part II: Experimental procedure and measurement uncertainties

The “Surface Crack in Flexure” method is widely used for fracture toughness (K_Ic) determination of ceramics. In part I of the paper we developed the theoretical fundamentals to apply this procedure to ceramic balls by using the stress application as developed for the so-called “Notched ball test”. The new test (SCF-NB) can be used to test spherical components without the need to cut out special specimens such as bending bars. In this work the practical part is presented including suggestions for crack introduction and specimen preparation and possible measurement errors are discussed. It is concluded that a measurement error less than ±5% is possible.Experiments on balls and bars made from the same silicon nitride ceramic indicate that SCF-NB delivers the same K_Ic-values as standardised measurements on bars. Additionally, K_Ic-values obtained for silicon carbide, alumina and zirconia ceramics are presented. They coincide with K_Ic-data from the literature.     

Fracture mechanics studies on concrete compounds

An experimental and analytical investigation was conducted to determine fracture mechanics characteristics of hardened cement paste, aggregates and aggregate-cement paste interfaces. For this the fracture toughness K_Ic was determined on wedge loaded CT-specimens. It was found that hardened cement paste, aggregates and interfaces exhibit unique K_Ic values which are independent of the initial crack length. In additional test series the ductility of various model concretes tested in flexure was determined. The ductility depends primarily on the fracture toughness toughness of the aggregate-hardened cement paste interfaces and is less affected by the fracture toughness of the hardened cement paste.     

Engineering dislocation-rich plastic zones in ceramics via room-temperature scratching

In this communication, we demonstrate a simple but powerful method to engineer dislocations into large plastic zones in various single-crystal ceramic materials via room-temperature scratching. By using a Brinell indenter with a diameter of 2.5 mm, we successfully produced plastic zones with a width and depth of ∼150 µm in a single scratch track, while the length of the scratch track can be arbitrarily long depending on the sample size. Increasing the number of repetitive scratching cycles increases the dislocation density up to ∼10¹³ m⁻² without visible crack formation. The outlined experimental procedure is showcased on single-crystal SrTiO₃, MgO, ZnS, and CaF₂ to demonstrate the general applicability of this technique. In light of the increasing research interest in dislocation-tuned functional and mechanical properties in ceramics, our method will serve as a simple, fast, and robust technique to pave the road for scaling up the required large plastic zones for dislocation engineering in ceramics.