Controlled Crack Shapes for Indentation Fracture of Soda–Lime Glass

Radial cracks for indented soda–lime glass aged in distilled water were highly elliptical because of truncation by lateral cracks. Indentation in silicone oil minimized radial/lateral crack interaction but still produced cracks having nominally constant ellipticity during bend testing. Analysis of applied stress/indentation crack length data using stress intensity factors based on half-penny crack shape resulted in apparent R -curve behavior and/or overestimation of the fracture toughness. Incorporation of elliptical shape factors eliminated the R -curve behavior and reduced measured toughness to near the accepted value for soda–lime glass.     

Crack profiles under a Vickers indent in silicon nitride ceramics with various microstructures

The effect of microstructure on crack morphology under a Vickers indentation was studied using 20 various silicon nitride ceramics including bearing-grade silicon nitrides. The indentation load was decreased from 98 N to 9.8 N and a transition of the crack types from half-penny crack to radial one was observed with both decoration method and serial sectioning technique. All of the indented samples possessed the half-penny cracks at the load of 98 N. The transition of crack profiles in the samples with coarse microstructure occurred when the load decreased from 49 N to 19.6 N, whereas the transition load for the sample with fine microstructure was ～9.8 N. Half-penny cracks were formed regardless of the microstructures when the ratio of the half of crack length to the half of diagonal size of an indentation, c/a, was above ～2. The dependence of the transition load on both Vickers hardness and fracture resistances was analyzed using Pajares's equation.     

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.     

Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics

A review of the observations of indentation-induced fracture suggests that there is no simple generalization which may be made concerning crack initiation sequences. Here, we investigate the material dependence of the initiation sequence of indentation cracks (cone, radial, median, half-penny, and lateral) using an inverted tester allowing simultaneous viewing of the fracture process and measurement of the indeter load and displacement during contact. Two normal glasses, two anomalous glasses, and seven crystalline materials are examined. Key results include (i) direct evidence that the surface traces of cracks observed at indentation contacts are those of radial cracks, rather than median-nucleated half-penny cracks (at least for peak contact loads <40 N) and (ii) that, in crystalline materials, radial cracks form almost immediately on loading of the indenter, in anomalous glasses at somewhat greater loads, but in normal glasses during unloading. A detailed consideration of the stress fields arising during indentation contact predicts material-dependent initiation sequences, in agreement with observations, particularly those of radial crack formation on loading for materials with large modulus-to-hardness ratios. In addition, a new, unexplored crack system is demonstrated, the shallow lateral cracks, which appear to be responsible for material removal at sharp contacts.     

Indentation Studies on Y2O2-Stabilized ZrO2: I, Development of Indentation-Induced Cracks

The development of Vickers indent-induced tracks with increasing indent load has been studied in two Y₂O₃-stabilizel ZrO₂ ceramics. Such cracks form as radial or Palmqvist cracks at low loads, assume "kidney" shapes at intermediate loads, and finally form median (half-penny) cracks at high loads. The plastic zone directly beneath the indent is uncracked; a significant portion of the plasticity induced by indentation occurs by martensitic transformation.     

Revealing crack profiles in polycrystalline tetragonal zirconia by ageing

Exposure to hot water vapour is shown to be useful for staining indentation crack profiles in doped zirconia polycrystals. This is illustrated here in 3Y-TZP with two different grain sizes, for which Vickers indentation cracks are of Palmqvist type, as well as in 3Y-TZP with 2.5 wt.% cerium oxide, for which indentation cracks are half-penny. The crack profile is clearly revealed on the fracture surface after biaxial flexural testing in all the specimens previously exposed to hot water vapour. The contrast in 3Y-TZP is induced by t–m transformation caused by hydrothermal degradation, which induces an intergranular fracture zone in front of the initial position of the indentation crack tip. The biaxial strength and apparent fracture toughness of 3Y-TZP increase substantially with the time of exposure at a rate that depends on the grain size. On the contrary, in 3Y-TZP doped with ceria no signal of t–m transformation is found and the flexure biaxial stress remains practically constant, but the initial position of the indentation crack is also clearly revealed by an intergranular fracture zone in front of the initial position of the crack tip. In this case, this is associated to environmentally assisted slow crack growth under the indentation residual stress during exposure to hot water vapour in autoclave.     

Palmqvist Crack Extension and the Center-Loaded Penny Crack Analogy

Palmqvist crack extension in WC-Co can be described using the center-loaded penny crack analogy. When Palmqvist cracks are represented by semicircles of diameter l (l=crack length measured from an impression corner), the stress intensity factor which controls crack extension differs from that of a half-penny crack of radius l+a (2a = impression size) by only a slowly varying factor m=2^1/2 (l/a)^1/2; m≅1.0 to 2.4 for WC-Co and m≅0.8 to 1.4 for ceramics.     

3D characterisation of indentation induced sub-surface cracking in silicon nitride using FIB tomography

In this study, a combination of 3D FIB tomography and incremental surface polishing has been used to characterize cracking beneath 0.5 kg and 1 kg Vickers indentations on silicon nitride. It is shown that a half-penny cracking regime exists even for low indentation loads with c/a ratios < 2 indicating that the c/a ratio cannot reliably be used to predict sub-surface crack morphology. For the first time, the presence of deep lateral cracks interconnected with radial cracks was also observed surrounding indentations of low loads on silicon nitride, and it is likely that these could contribute to material removal via spalling.     

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.     

A technique for measuring stresses in small spatial regions using cube-corner indentation: Application to tempered glass plates

Vickers indentation cracks have been used to estimate residual stress in materials; however, a high threshold load for cracking limits the smallest spatial region for stress measurement. Cube-corner indenters have a lower included angle, and their sharpness leads to lowered cracking thresholds enabling stress measurement in small spatial regions. Cube-corner indentations on tempered glass plate and on annealed soda-lime-silica glass revealed that crack surface traces on the tempered material were significantly smaller. Cracks were found to be quarter-penny shaped as opposed to half-penny/radial for Vickers indentation. Using an appropriate stress-intensity factor and a stress-intensity factor superposition approach, surface stresses in the tempered plate were calculated. The stresses were in good agreement with those determined using well-established Vickers indentation approach; however, the spatial region sampled is 6–10 times smaller. An estimate of the smallest spatial region at which a particular stress may be measured using this technique is presented.     

Cone Crack Nucleation at Sharp Contacts

The distribution of initiation loads for cone cracking during Vickers indentation is studied by direct experimental observation of the indentation process and by simulation. Observations on three different glasses show that cone cracks initiate at the edge of the contact impression and yield distributions of initiation loads with nonzero minima. The simulations, based on a model of an expanding indentation impression in a random array of active crack nuclei, yield distributions of initiation loads with minima of zero. Cone cracks at sharp contacts are concluded to be initiated from nuclei generated by the contact process itself, rather than by nuclei preexisting on the contact surface.     

Measurement of Indentation Residual Stresses in Materials Susceptible to Slow Crack Growth

Knowledge of the size and distribution of the indentation residual stress field is important when interpreting slow crack growth data for indented ceramic materials. A technique based on compressively loading indentation cracks has been used to measure the wedging residual stresses at radial indentation cracks. The method also gives information on the fatigue limit and can be applied on any ceramic material susceptible to slow crack growth. Soda–lime glass specimens were indented and the resulting residual stresses, wedging the radial cracks, were measured as a function of indentation load. Calculations of K ₀, the fatigue limit, were made for both virgin indentation cracks and cracks aged until saturation. The magnitude of closing stress needed to prevent slow crack growth was found to depend linearly on the indentation load. For example, for indentation loads of 20 and 60 N, the corresponding closing stresses were 14 and 26 MPa, respectively.     

Determining indentation toughness by incorporating true hardness into fracture mechanics equations

The Lawn–Evans–Marshall (LEM) indentation fracture mechanics model for the well-developed half-penny crack is reexamined theoretically, with a particular emphasis on the physical meaning of the hardness parameter in this model. It is shown that there may be some confusion arising from the use of the hardness definition. A modified indentation toughness equation is then proposed, in which a true hardness number, rather than the apparent hardness, is incorporated. This modified equation predicts that it is the quantity a²/c^3/2, rather than P/c^3/2, that would keep constant in the half-penny crack regime. This prediction is verified by analyzing the previously published indentation data. It is also confirmed that a comparable value of indentation toughness can be deduced with this modified equation.     

Indentation Crack Length Anisotropy in Silicon Nitride with Aligned Reinforcing Grains

Vickers indentation was performed on surfaces of silicon nitride with an aligned microstructure in order to study the interaction between cracks and the microstructure. Although there was not much evidence of crack bridging, the transverse radial cracks were very short, resulting in high fracture toughness values. The longitudinal radial cracks tended to propagate along the grain boundary of the reinforcements and were much longer than the transverse cracks. As the sintering temperature increased, the lateral cracks on the casting surface led to spalling and consumed more energy for the crack formation, making the longitudinal cracks shorter. On the surface normal to the alignment direction, there was no spalling and the indentation cracks became longer as the sintering temperature increased.     

Measurement of Crack Tip Toughness in Alumina as a Function of Grain Size

Crack profile measurements near the crack tip in the SEM were used to measure crack tip toughness of alumina as a function of grain size (average grain size 0.9–16 μm). For comparative tests, two crack configurations were included in the present study: straight cracks (CT specimen) loaded with an in situ device; and radial indentation cracks. The measured crack tip toughness values were independent of crack geometry, and no grain size dependence could be discerned. A mean crack tip toughness of 2.3 MPam^1/2 was evaluated. The crack tip toughness determined from crack profile measurements is significantly lower than the toughness evaluated with conventional indentation techniques (e.g., indentation strength bending).     

Low-Temperature Crack Closure in Fluoride Glass

Radial cracks generated in heavy-metal fluoride glass (HMFG) by Vickers indentation were found to decrease in length as a function of time when exposed to humid environments in the temperature range of 22° to 80°C. Inspection by optical and electron microscopy indicated that the cracks appear to be closing, leaving little or no evidence of the original crack aperture. The effect was observed to increase with time, temperature, and humidity levels for all conditions studied. Possible explanations for this behavior include viscous relaxation of glass in the region of the crack tip, or the generation and transport of a fluoride gel phase to the crack aperture.     

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.     

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected "reference" materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.     

Creep Cavitation in a Siliconized Silicon Carbide Tested in Tension and Flexure

Cavity formation was quantified in a grade of siliconized silicon carbide containing 33 vol% silicon. The type, size, and density of cavities were determined for smooth-bar specimens tested in both tension and bending, and for indented specimens tested in tension. In both tension and bending, the volume fraction of cavities was found to be proportional to the tensile creep strain. Cavities nucleated at random locations throughout the test specimen, eventually coalescing into cracks that were the source of failure at high temperatures. In tension, the strain to failure was about 1%. In flexure, stress relaxation at the tensile surface of test specimens helped stabilize cracks that formed during creep. As a consequence, strains to failure were about twice as large in bending as in tension. In tensile specimens containing large, >300 μm, indentation cracks, cavitation was profuse near the crack tips. At a volume fraction of about 3%, cavities coalesced to form secondary cracks near the tip of the indentation crack. Cracks advanced by linkage of cavitation cracks with the indentation crack. Crack growth was intermittent, requiring the buildup of cavities in front of the crack tip before crack advance could occur. If the indentation crack length was less than about 200 μm, cavity formation at the tip of the crack was not sufficient for crack advance. In such case, failure would have to occur by cavity coalescence and crack formation at some other location in the test specimen.     

Comparison of High-Temperature Crack Growth in SiC-Whisker-Reinforced Mullite and Si3N4

Crack growth behavior under creep conditions was studied in SiC-whisker-reinforced mullite and silicon nitride. Tests of four-point bend specimens with indentation cracks were periodically interrupted to observe the creep behavior. At each interruption the bulk creep strain of the specimen, the growth of the indentation cracks, and the nucleation and growth of creep-induced cracks were measured. A strong linear correlation was observed in both materials between the crack growth rate and the creep strain rate. For a given strain rate, cracks in the silicon nitride composite propagated at velocities about an order of magnitude greater than those in the mullite composite. On the other hand, for similar nominal stresses, creep rates in the silicon nitride composites were about an order of magnitude less than with the mullite composite.