Fracture toughness of glasses and hydroxyapatite: A comparative study of 7 methods by using Vickers indenter

Numerous methods have been proposed to estimate the indentation fracture toughness Kic for brittle materials. These methods generally uses formulæ established from empirical correlations between critical applied force, or average crack length, and classical fracture mechanics tests. This study compares several models of fracture toughness calculation obtained by using Vickers indenters. Two optical glasses (Crown and Flint), one vitroceramic (Zerodur) and one ceramic (hydroxyapatite) are tested. Fracture toughness and hardness are obtained by using instrumented Vickers indentation at micrometer scale. Young's moduli are obtained by instrumented Berkovich indentation at nanometer scale. Fracture toughness is calculated with models involving crack length measurements, and by models free of crack length measurements by considering critical force, chipping, pop-in. Finally, method based on the cracking energy, commonly employed for coated materials is also used.The aim of this work is to compare seven methods, which enable the facture toughness determination, on four brittle materials. To do so, it was necessary to determine some specific constant in the case of Vickers tip use.On the one hand, results show that methods using crack length, critical force, edge chipping or pop-in lead to comparable results, and the advantages and drawbacks are highlighted. On the other hand, the indentation energy method leads to underestimated results of about 20%.     

Measurement of the Fracture Toughness of Ceramic Materials Using a Miniaturized Disk-Bend Test

The fracture toughness of several ceramic materials has been measured using a miniaturized disk-bend test apparatus and methodology based on small disk-shaped samples 3 mm in diameter. The method involves the Vickers indentation of specimens ranging in thickness from 300 to 700 μm, and testing them in a ring-on-ring bending mode. New experiments on a glass-ceramic (GC) and Si₃N₄ have been performed to demonstrate the validity of the technique, supplementing the original work on ZnS. The fracture resistances of these materials increase with increasing crack length ( R -curve behavior). The data are analyzed using a specific model for the relationship between fracture resistance and crack length; this model enables the R -curve behavior to be treated analytically, and the fracture resistance at "infinite" crack length to be evaluated using a straightforward graphical procedure. The resulting values of the fracture toughness for ZnS, GC, and Si₃N₄ are 0.74 ± 0.02, 2.18 ± 0.09, and 4.97 ± 0.07 MPa-m^1/2, respectively, which are all in very good agreement with values obtained from conventional fracture toughness tests on large specimens. The results verify the utility of the miniaturized diskbend method for measuring the fracture toughness of brittle materials.     

New method for extracting fracture toughness of ceramic materials by instrumented indentation test with Berkovich indenter

Applying finite element analysis, a method is proposed for evaluating fracture toughness of ceramic materials by instrumented indentation with Berkovich indenter. The crack-tip K_I (Stress intensity factor) of Berkovich-produced crack is numerically calculated by using virtual crack closure technique, in particular, three kinds of crack pattern, i.e., radial crack, transition crack and half-penny crack are identified and their crack fronts meet the equi-K_I requirement. The validity of the proposed method is verified by instrumented indentation tests on standard SRM2100 (Si₃N₄) and CRM156 (Fused Silica) samples. Comparison with six representative conventional indentation methods indicates that the proposed method has advantages including wide application range, high accuracy and applicability to different crack patterns. Additionally, it’s revealed that the conventional indentation fracture toughness formulae derived from Lawn-Evans-Marshall formula tend to exhibit larger test error when applied to materials of relatively high indentation work ratio W_e/W_t.     

A critical evaluation of indentation crack lengths in air

An extensive overview is presented of Vickers indentation crack lengths in ceramics in air. Measurement of such crack lengths is one of the most common and powerful assessments of the fracture properties of ceramics and the overview provides a critical evaluation of observed behavior as functions of material type and indentation load, and an extensive basis for comparison of results from new materials and analyses. The overview considers single crystals, polycrystals, transforming materials, glasses, and multiphase materials, including cermets, glass-ceramics, and tooth enamel. The coverage extends over structural and electronic ceramics, including oxides, carbides, nitrides, and titanates. The data are presented in a single format for ease of interpretation in terms of idealized indentation fracture and for inter-material comparisons; most data are unique to this work, but the results of selected studies from the published literature are included. The overview considers the precision and accuracy of crack length measurements and demonstrates a simple quantitative evaluation and ranking scheme for ceramic fracture based on load-adjusted crack length and cracking susceptibility. Indentation hardness and cracking threshold are also determined and related to the susceptibility. Material toughness is related to cracking susceptibility by fracture mechanics analyses: typical crack length measurements in air are shown to provide estimates of inert toughness with a relative uncertainty of ±50%.     

Microstructure,mechanical properties and toughening mechanisms of graphene reinforced Al2O3-WC-TiC composite ceramic tool material

The low fracture toughness of Al₂O₃-based ceramics limited their practical application in cutting tools. In this work, graphene was chosen to reinforce Al₂O₃-WC-TiC composite ceramic tool materials by hot pressing. Microstructure, mechanical properties and toughening mechanisms of the composite ceramic tool materials were investigated. The results indicated that the more refined and denser composite microstructures were obtained with the introduction of graphene. The optimal flexural strength, Vickers hardness, indentation fracture toughness were 646.31?±?20.78?MPa, 24.64?±?0.42?GPa, 9.42?±?0.40?MPa?m^1/2, respectively, at 0.5?vol% of graphene content, which were significantly improved compared to ceramic tool material without graphene. The main toughening mechanisms originated from weak interfaces induced by graphene, and rugged fractured surface, grain refinement, graphene pull-out, crack deflection, crack bridging, micro-crack and surface peeling were responsible for the increase of fracture toughness values.     

多孔Si3N4-SiO2复相陶瓷及其性能

采用近净尺寸成型制备工艺-氧化烧结结合溶胶浸渍再烧结法,制备了多孔Si3N4-SiO2复相陶瓷.讨论了制各工艺对材料的成分、微结构和性能的影响规律.研究表明:随着硅溶胶浸渍量的增加,材料的抗弯强度、硬度、断裂韧性、密度和介电常数均增大.分别采用压痕法和单边切口梁法对材料的断裂韧性进行了测定和比较.结果表明:采用压痕法测定断裂韧性时,多孔Si3N4-SiO2复相陶瓷的增韧机理有裂纹偏转、裂纹分叉、裂纹桥接以及孔的钝化.采用单边切口梁法测定断裂韧性时,多孔Si3N4-SiO2复相陶瓷的增韧机理只有裂纹偏转.     

Anisotropy of Mechanical Properties of Zirconia-Based Ceramics Tested for Bending

The effect of bending stress s of different magnitudes and signs on the fracture toughness K _1c of polycrystalline specimens of partially stabilized zirconia (PSZ) is considered. A method for testing pre-stressed PSZ specimens by Vickers indentation using a four-point bending scheme is proposed. The dimensions of the impression from a diamond pyramid and the length of the radial cracks generated thereby are determined. An anisotropy of strength properties is revealed in the specimens tested, which is explained by the involvement of two mechanisms: forcing action of an external stress on the crack opening and activation of the tetragonal- monoclinic phase transition in the tensile stress field.     

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.     

Instrumented indentation study of materials edge chipping

The resistance to local fracture of brittle materials is currently characterized by the value of edge toughness. An “instrumented micro-edge chipping” (IMEC) is proposed and tested. This test was carried out on various brittle materials: light krone glass LK-5, polycrystalline silicon Si, partially stabilized dioxide zirconium ceramic TS and tetragonal dioxide zirconium ceramic Y-TZP. IMEC test provides a closer correlation between the edge toughness Fr values at different values of the distance L between the test specimen edge and the indentation point than with the macro-EF test. Comparison of the macro-EF and IMEC tests for studied materials showed the almost identical trend in the ratio of the edge toughness values for all the studied materials. It was found that there is a significant time from the moment of crack formation to the full realization of the edge chip. The duration of the chip process is different for the studied materials.     

Fracture Toughness of Porous Material of LSCF in Bulk and Film Forms

Fracture toughness of La_0.6Sr_0.4Co_0.2Fe_0.8O_3‐δ (LSCF) in both bulk and film forms after sintering at 900°C to 1200°C was measured using both single‐edge V‐notched beam (SEVNB) 3‐point bending and Berkovich indentation. FIB/SEM slice‐and‐view observation after indentation revealed the presence of Palmqvist radial crack systems after indentation of the bulk materials. Based on crack length measurements, the fracture toughness of bulk LSCF specimens was determined to be in the range 0.54–0.99 MPa·m^1/2 (depending on sintering temperature), in good agreement with the SEVNB measurements (0.57–1.13 MPa·m^1/2). The fracture toughness was approximately linearly dependent on porosity over the range studied. However, experiments on films showed that the generation of observable indentation‐induced cracks was very difficult for films sintered at temperatures below 1200°C. This was interpreted as being the result of the substrate having much higher modulus than these films. Cracks were only detectable in the films sintered at 1200°C and gave an apparent toughness of 0.17 MPa·m^1/2 using the same analysis as for bulk specimens. This value is much smaller than that for bulk material with the same porosity. The residual thermal expansion mismatch stress measured using XRD was found to be responsible for such a low apparent toughness.     

Fabrication and mechanical properties of Al2O3-SiCw-TiCnp ceramic tool material

Whiskers and nanoparticles are usually used as reinforcing additives of ceramic composite materials due to the synergistically toughening and strengthening mechanisms. In this paper, the effects of TiC nanoparticle content, particle size and preparation process on the mechanical properties of hot pressed Al₂O₃-SiC_w ceramic tool materials were investigated. The results showed that the Vickers hardness and fracture toughness of the materials increased with the increasing of TiC content. The optimized flexural strength was obtained with TiC content of 4 vol% and particle size of 40 nm. The particle size has been found to have a great influence on flexural strength and small influence on hardness and fracture toughness. It was concluded that the flexural strength increased remarkably with the decreasing of the TiC particle size, which was resulted from the improved density and refined grain size of the composite material due to the dispersion of the smaller TiC particle size. SEM micrographs of fracture surface showed the whiskers to be mainly distributed along the direction perpendicular to the hot-pressing direction. The fracture toughness was improved by whisker crack bridging, crack deflection and whisker pullout; the TiC nanoparticles in Al₂O₃ grains caused transgranular fracture and crack deflection, which improved the flexural strength and fracture toughness with whiskers synergistically. Uniaxial hot-pressing of SiC whisker reinforced Al₂O₃ ceramic composites resulted in the anisotropy of whiskers’ distribution, which led to crack propagation differences between lateral crack and radical crack.     

陶瓷材料断裂韧性测试新技术：静态爆破剂预制裂纹的研究

准确测试陶瓷材料断裂韧性Ｋ１Ｃ的关键是预制具有原生裂纹的试样。本文以单边切口梁法测试Ｋ１Ｃ为基础，提出了一种简便而有效的陶瓷材料原生裂纹的预制方法－静态膨胀法。研究结果表明：静态膨胀法中裂纹的扩展是稳态的；通过调节影响微裂纹产生与扩展的多种因素，可以准确地控制裂纹扩展的深度，预制出合适的原生裂纹，为准确评价结构陶瓷的断裂韧性提供了一种有效可行的方法。     

Rate‐Dependent Mechanical Behavior and Amorphization of Ultrafine‐Grained Boron Carbide

An investigation into mechanical properties and amorphization behavior of ultrafine‐grained (0.3 μm) boron carbide (B₄C) is conducted and compared to a baseline coarse‐grained (10 μm) boron carbide. Static and dynamic uniaxial compressive strength, and static and dynamic Vickers indentation hardness were determined, and Raman spectroscopy was then conducted on indented regions to quantify and compare the intensity of amorphization. In relation to coarse‐grained B₄C the ultrafine‐grained material exhibited, on average, a 33% higher static compressive strength, 20% higher dynamic compressive strength, 10% higher static Vickers hardness, and 23% higher dynamic Vickers hardness. In addition, there was an 18% reduction in indentation‐induced radial crack length in ultrafine‐grained B₄C, which corresponded to an increase in estimated fracture toughness. Although traditional coarse‐grained B₄C exhibits an 8.6% decrease in hardness from the static to dynamic regimes, ultrafine‐grained B₄C showed only negligible change under similar conditions, suggesting a reduced propensity for amorphization. Raman spectroscopic analysis confirmed this result by revealing significantly lower amorphization intensity in ultrafine‐B₄C compared to coarse‐grained B₄C. These results may have significant positive implications in the implementation of ultrafine‐grained boron carbide as a material for improved performance in impact and other high‐pressure applications.     

On the Vickers Indentation Fracture Toughness Test

The Vickers indentation fracture toughness test, or VIF, is addressed by considering its origins and the numerous equations that have been applied along with the technique to estimate the fracture resistance, or the K _{I c} of ceramics. Initiation and propagation of cracks during the VIF test are described and contrasted with the pre-cracking and crack growth for internationally standardized fracture toughness tests. It is concluded that the VIF test technique is fundamentally different than standard fracture toughness tests. The VIF test has a complex three-dimensional crack system with substantial deformation residual stresses and damage around the cracks. The VIF test relates to an ill-defined crack arrest condition as opposed to the rapid crack propagation of the standardized fracture toughness tests.
Previously published fracture toughness results employing the VIF technique are reviewed. These reveal serious discrepancies in reported VIF fracture toughness values. Finally, recent fracture resistance measurements by the VIF technique for the Standard Reference Material SRM 2100 are presented. These are compared with standardized test results for the same material. It is concluded that the VIF technique is not reliable as a fracture toughness test for ceramics or for other brittle materials. What the VIF actually measures in terms of fracture resistance cannot be readily defined. It is recommended that the VIF technique no longer be acceptable for the fracture toughness testing of ceramic materials.     

Mechanical properties of the solid electrolyte Al-substituted Li7La3Zr2O12 (LLZO) by utilizing micro-pillar indentation splitting test

Garnet structured Al-substituted Li₇La₃Zr₂O₁₂ (Al:LLZO) is a promising candidate as electrolyte in all-solid-state Li-ion batteries due to its chemical stability against Li-metal and high voltage cathode materials. In order to ensure long-term stable operation, electrolyte crack growth induced and/or the volume change of the active material on the cathode side needs to be avoided, requiring in particular knowledge of local and global mechanical properties of the electrolyte material. Micro-pillar splitting test was used for the first time on this material to determine the microscopic fracture toughness of single grains and compare it with conventional Vickers indentation fracture toughness (VIF), which represents macroscopic fracture toughness. Both methods yielded comparative results. In conclusion, the micro-pillar splitting test can be used as an advanced locally resolved characterization method that can open up new experimental directions for characterizing and understanding battery materials and enable a targeted approach for material improvements.     

Indenter Flaw Geometry and Fracture Toughness Estimates for a Glass-Ceramic

Shapes of cracks associated with Vickers indenter flaws in a glass-ceramic were assessed by stepwise polishing and measuring surface traces as a function of depth. The cracks were of the Palmqvist type even at200-N indentation load. The toad dependence of crack lengths and fracture toughness estimates were examined in terms of relations proposed for Palmqvist and half-penny cracks. Estimates based on the half-penny crack analogy were in closer agreement with bulk fracture toughness measurements despite the Palmqvist nature of the cracks.     

Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams

The analytical function of crack extension to a fractional power is used to represent the fracture resistance of a vitreous-bonded 96% alumina ceramic. A varying flaw size, controlled by Vickers indentation loading between 3 and 300 N, was placed on the prospective tensile surfaces of four-point bend specimens, previously polished and annealed. The lengths of surface cracks were measured by optical microscopy. Straight lines were fitted to the logarithmic functions of observed bending strength versus indentation load in two series of experiments: (I) including the residual stress due to indentation and (II) having the residual stress annealed out at an elevated temperature. Within the precision of measurement these lines have the same slope, being about 32% less than the -1/3 slope which a fracture toughness independent of crack extension would indicate. Considering the criteria for crack extension and specimen failure, the fracture mechanics equations were solved for the conditions of the two series of experiments. Approximately the same values of fracture toughness, rising as a function of indentation flaw size, were obtained from both series of experiments.     

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.     

Effect of the t–m transformation morphology and stress distribution around the crack path on the measured toughness of zirconia ceramics: A case study on Ce-TZP/alumina nanocomposite

The t–m transformation zone and related residual stress fields around two types of crack used for toughness measurements, i.e. SEVNB (arrested crack induced by a V-notch) and IF methods (indentation crack induced by a Vickers impression), are reported for a Ce-TZP/Al₂O₃ nanocomposite, in comparison with 3Y-TZP. The fact that Ce-TZP/Al₂O₃ exhibits significant high toughness value on occasions when evaluated by the IF method was determined to be clearly linked to the presence of wide ranged three-dimensional transformation configuration and resulting substantial compressive residual stress fields. In contrast, for 3Y-TZP, transformation behaviors around the two types of crack were quite similar, which proves that 3Y-TZP shows near toughness values for both SEVNB and IF methods.     

Contact-Induced Failure of Prestressed Glass Plates

An indentation fracture technique was used to determine critical contact conditions under which prestressed brittle surfaces are subject to catastrophic failure. A theoretical model based on the growth of a well-developed, contact-induced half-penny crack leads to a simple inverse-cube power relation between indentation load and tensile prestress. The analysis is developed in terms of fracture parameters which are readily calibrated in routine indentation/strength tests. Experiments on glass disks loaded simultaneously in biaxial flexure and Vickers indentation confirm the essential failure predictions of the theory; toughness is the key material parameter controlling resistance to failure. The results emphasize the danger of spurious tensile stresses in ceramic systems exposed to severe contact events.