Determining the Toughness of Ceramics from Vickers Indentations Using the Crack-Opening Displacements: An Experimental Study

Recently, a method for evaluating the fracture toughness of ceramics has been proposed by Fett based on the computed crack-opening displacements of cracks emanating from Vickers hardness indentations. To verify this method, experiments have been conducted to determine the toughness of a commercial silicon carbide ceramic, Hexoloy SA, by measuring the crack-opening profiles of such Vickers indentation cracks. Although the obtained toughness value of K _o= 2.3 MPa·m^1/2 is within 10% of that measured using conventional fracture toughness testing, the computed crack-opening profiles corresponding to this toughness display poor agreement with those measured experimentally, raising concerns about the suitability of this method for determining the toughness of ceramics. The effects of subsurface cracking and cracking during loading are considered as possible causes of such discrepancies, with the former based on direct observations of lateral subsurface cracks below the indents.     

Cracking and the Indentation Size Effect for Knoop Hardness of Glasses

The Knoop hardnesses of five glasses decreased with increasing load in accordance with the classic indentation size effect (ISE). At moderate loads, cracking dramatically altered the indentation sizes and the ISE trends in three of the five glasses. Cracked indentations were as much as 10 μm longer than uncracked indentations made under identical conditions. Diagonal length readings must be corrected for optical resolution limitations if low power lenses are used.     

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.     

The effect of laser sintering on the microstructure,relative density,and cracking of sol-gel–derived silica thin films

Combining sol-gel processing and laser sintering is a promising way for fabricating functional ceramic deposition with high dimensional resolution. In this work, crack-free silica tracks on a silica substrate with a thickness from ~360 nm to ~950 nm, have been obtained by direct exposure to a CO₂ laser beam. At a fixed scanning speed, the density and microstructures of the silica deposition can be precisely controlled by varying the laser output power. The porosity of the laser-sintered silica tracks ranged from close to 0% to ~60%. When the thickness of the silica deposition exceeded the critical thickness (eg, ~2.2 µm before firing), cracks occurred in both laser-sintered and furnace-sintered samples. Cracks propagated along the edge of the laser-sintered track, resulting in the crack-free track. However, for the furnace heat-treated counterpart, the cracks spread randomly. To understand the laser sintering effect, we established a finite element model (FEM) to calculate the temperature profile of the substrate during laser scanning, which agreed well with the one-dimensional analytical model. The FEM model confirmed that laser sintering was the main thermal effect and the calculated temperature profile can be used to predict the microstructure of the laser-sintered tracks. Combining these results, we were able to fabricate, predesigned patterned (Clemson tiger paw) silica films with high density using a galvo scanner.     

Influence of Surface Residual Stress State on Crack Path Evolution in Polycrystalline Alumina

The residual stress distribution in polycrystalline alumina is estimated by an object-oriented finite element method. By combining the microstructural image, individual grain orientation, and the crystal elastic properties, the residual stress distribution under a plane stress assumption is obtained by an analysis cooling of the sample through 1000°C. Furthermore, the residual stresses associated with grain boundary areas are investigated and discussed in the context of the concomitant influence on the observed crack path.     

Strength of brittle materials in moderately corrosive environments

The strengths of four brittle materials―cordierite glass ceramic, fused silica, silicon, and polycrystalline alumina were measured after exposure to weakly corrosive water and moderately corrosive buffered HF (BHF) solution. Exposure to water did not alter the strengths in subsequent inert strength tests and decreased the strengths in reactive strength tests. Exposure to BHF increased the strengths in both tests, but only after an incubation exposure time. Prior to the incubation time, the BHF had the same effect as water, suggesting that the bond rupture kinetics were unaffected. Examination of strength‐controlling indentation flaws after the incubation time showed clear corrosive effects on the flaw geometry indicative of reductions in the indentation residual stress fields. The implication is that moderately corrosive environments increase the strength or lifetime of a brittle component by reducing the crack driving force via flaw alteration and do not, as perhaps expected, decrease the strength or lifetime through enhanced chemical reactivity.     

Effect of Lateral Cracks on Fracture Toughness Determined by the Surface-Crack-in-Flexure Method

The surface-crack-in-flexure (SCF) method uses a Knoop indenter to create small, semielliptical surface precracks in beam specimens. Lateral cracks may interfere with the primary median crack and cause errors of up to 10% in determination of fracture toughness, particularly for materials for which the fracture toughness is ∼3 MPa·m^1/2 or less. Although the residual-stress-damage zone is ground or polished away by hand by removing 4.5–5 times the indentation depth, this amount may not be sufficient to completely remove the lateral cracks in low-fracture-toughness materials. A series of tests were conducted on sintered alpha silicon carbide with different amounts of material removed after indentation. Once the lateral cracks were fully removed, the SCF results concurred with single-edged-precracked-beam and chevron-notched-beam data collected in accordance with ASTM Designation C1421. A simple remedy for the SCF method is to examine the outer ground surface for remnants of lateral cracks before fracture and to remove more material if necessary.     

Controlled Precracking of Fracture Mechanics Specimens Using Contact Stresses

A simple method is proposed for introducing precracks into thin-plate fracture mechanics specimens, i.e., compact-tension and double-cantilever-beam specimens, using standard testing equipment and without performing complicated machining operations on the specimens. The surface of the specimen is first scored to a known length, using a scribe, and the specimen is then compressed between polymer blocks. Mismatch between the elastic properties of the polymer and the specimen results in an in-plane tensile stress in the vicinity of the scratch that causes a crack to initiate from the scratch and propagate through the specimen thickness. Provided that certain conditions are met, the crack arrests without significant growth beyond the initial scratch length. The result is a straight, through-thickness precrack of controllable length. Fracture toughness measurements made on glass specimens precracked using the proposed method are in good agreement with literature values for this material.     

Lateral Cracks and Microstructural Effects in the Indentation Fracture of Yttria

The fracture properties of three polycrystalline Y₂O₃ materials: one fully cubic phase, one containing an Al₂O₃ grain-boundary phase, and one containing hexagonal phase, were examined by indentation over a wide range of contact loads. The two former microstructures displayed tendencies at large indentation loads to radial crack lengths shorter than those extrapolated from the ideal response at low loads. The deviations correlated with the development of lateral cracks at the larger contacts, rather than with any observable change in the interaction between the cracks and the microstructure. After taking the lateral crack influence into account, the toughness of all three materials was estimated to be constant over the range of crack lengths studied, in contrast to the phenomena observed in similar grain size noncubic materials and inferred from earlier fractographic studies. The toughness of the partially hexagonal material was estimated to be 50% greater than the cubic materials. The general phenomenon of partitioning energy into lateral cracks at the expense of radial cracks at large indentation loads has been characterized by a lateral crack development parameter, L_D , which varies from 0 to 1 as lateral cracks progressively develop and remove material.     

Fracture Toughness of a Toughened Silicon Nitride by ASTM C 1421

The fracture toughness of a sintered reaction-bonded silicon nitride was measured by the single-edge precracked beam and surface crack in flexure methods, which are two of the three complementary test methods in ASTM C 1421. Results were compared with chevron-notched beam results that were available from another source. Precracks ranged from tiny artificial flaws introduced by Knoop indentation to millimeter-long precracks in single-edge precracked beams. The fracture toughness values from the three methods were in good agreement at 5.6 MPa·m^1/2.     

Measurement of Stresses Using Fluorescence in an Optical Microprobe: Stresses around Indentations in a Chromium-Doped Sapphire

A technique for measuring stress (positive and negative) with a lateral spatial extent of approximately 2 μm is introduced. The technique, implemented using a Raman microprobe, is demonstrated with measurements of the frequency shift of the sharp, R-luminescence lines (2Ā and Ē to ⁴A₂ radiative transitions) in, and around, a hardness indentation in a 0.06-wt%-chromium doped sapphire. From the observed frequency shifts the stresses in regions sampled in the hardness impression, in the complex stress field surrounding it, and at the tip of a crack are measured.     

Criterion for the Avoidance of Edge Cracking in Layered Systems

When fabricating multilayers with brittle constituents, a prevalent design strategy is to choose fabrication conditions and thermal expansion coefficients that impose in-plane compression on the brittle layers. In such designs, a small zone of out-of-plane tension is induced at the edges that can cause cracks to form and extend, especially along the midplane. The associated stresses and energy release rates have been analyzed, revealing a fail-safe criterion , attributed to the existence of a maximum possible energy release rate, G _max. Equating this maximum to the toughness defines a fail-safe parameter expressing the influence of the layer thickness, the misfit stress, and the toughness. When fail-safe designs cannot be realized, thin interlayers can be interposed in a manner that diminishes G _max, broadening accessibility. The roles of misfit stress and interlayer thickness in attaining this condition are derived.