Mixed-Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al₂O₃. Multiaxial fracture mechanics of the Al₂O₃ ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness K _Ic, the mode III fracture initiation toughness is 2.3 times higher than K _Ic. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.     

Fracture and Subcritical Crack Growth in Soda-Lime Glass under Combined Modes I and II Loading

Fracture and subcritical crack growth characteristics under combined modes I and II loading were studied using the compact tension shear specimens of soda–lime glass. The maximum normal stress criterion gives a good agreement with the experimental mode I–mode II fracture toughness envelope for initially straight cracks and kinked cracks. Subcritical crack growth characteristics were determined under sustained modes I and II loading in water. The values of K _I and K _II were calculated approximately by replacing the subcritical kinked crack with an assumed straight crack ā, and the K _Imax value based on the maximum normal stress criterion was used to describe this subcritical kinked crack growth. The experimental results show that subcritical crack growth under pure mode I, pure mode II, and various combined modes I and II loading can be well described by the K _Imax value based on the approximate maximum normal stress criterion.     

Combined Mode I-Mode III Fracture of Fatigue-Precracked Alumina

The mixed-mode fracture behavior of (cyclic) fatigue pre-cracked ceramic specimens was studied in combined tension-torsion loading. Circumferentially notched cylindrical rods of polycrystalline alumina were precracked in uniaxiai cyclic compression to introduce a concentric mode I fatigue crack. Subsequently, the rods were quasi-statically fractured in pure tension, pure torsion, and various combinations of tensile and torsional stresses to obtain the mode I-mode III fracture envelope. The introduction of torsional loads promotes severe abrasion between the crack faces. The critical stress intensity factor for fracture initiation increases by a factor of °2.3 as the loading mode is changed from pure tension to pure torsion. Fracture surface tortuosity and abrasion "shield" the crack-tip from the far-field tensile and torsional loads to cause an apparent toughening effect. The mechanisms of mixed-mode fracture in alumina are examined and consequences of the breakdown of the similitude concept implicit in the nominal use of fracture mechanics are discussed.     

Effects of Residual Stress and Loading Geometry on Single-Edge Precracked-Beam (SEPB) Fracture-Toughness Test Results

The single-edge precracked-beam (SEPB) specimen test, using the "bridge indentation" method, is one of the standard test methods in the new ASTM standard for the determination of the fracture toughness of ceramics. In support of this effort, the effect of several test parameters on the fracture-toughness ( K _{I C} ) values was established. The effect of the residual stress, because of the indent and the alignment in three- and four-point bending, on the K _{I C} values was determined using aluminum nitride specimens. The results show that indent loads should be kept below 10 kgf, and the crack-plane angle should be <5°, to prevent artificially high K _{I C} values.     

Polymorphism of Tricalcium Silicate and Its Solid Solutions

In tricalcium silicate and its solid solutions six modifications were established: one rhombohedral ( R ), two monoclinic ( M _I, M _II), and three triclinic ( T _I, T _II, T _III). All these forms are rhombohedral or pseudorhombohedral and extremely similar; the variations in the X-ray diagrams and the transformation enthalpies are minute. Only three of the five transitions were observed by both X rays and DTA: T _I- T _II (600°), T _III– M _I (980°), and M _I– M _II (990°); one was established by DTA ( T _II– T _III, 920°) and one by X rays only ( M _II– R , 1050°C). This scheme of polymorphism is compared critically with results of other authors, and the nature of the various displacive transformations is discussed. X-ray and DTA investigations of solid solutions of Ca₃SiO₅ with Al₂O₃ and ZnO established the phase relations as functions of temperature and composition. With Al₂O₃, two modifications ( T _I and T _II) were stabilized; and with ZnO, five polymorphs ( T _I T _II, M_I, M _II, and R ). With both pure C₃S and the solid solutions, the results are consistent and have a close bearing on the constitution of alites in portland cement clinker.     

Stoichiometry Effects on the Fracture of TiO2−x

Fracture characteristics of TiO_{2− x} were studied as a function of Stoichiometry. With increasing x , the fracture toughness K _{I e} and the fracture surface energy γ _f decrease and the amount of transgranular cleavage increases, corresponding to the increased concentration of planar defects within the grains. Increasing nonstoichiometry also shifted the ( K _I- V ) diagram to lower K _I values, commensurate with the K_{I e} decrease. Water accelerated stress corrosion by promoting intergranular failure during subcritical crack growth.     

Subcritical Crack Growth in Soda-Lime Glass under Combined Modes I and III Loading

Fracture and subcritical crack-growth characteristics under combined Modes I and III loading were studied using the modified compact tension (CT) specimens of soda-lime glass. The combined mode load was applied to the specimen in the direction β with respect to the initial crack. By superposition of Mode III, the advancing crack begins to rotate at an angle Ψ to the initial crack plane, which nearly maximizes the Mode I stress intensity factor K _I(Ψ), and the crack continues to propagate in the same direction. In this case, unlike combined Modes I and II, the crack breaks into multiple partial fronts, and ligamentary bridging forms fracture lances when these segmented cracks are held together. The crack velocity d a /d t was plotted versus the maximum Mode I stress intensity factor K _I(Ψ) for combined Modes I and III loading. The d a /d t values are initially high, and the crack growth tends to be discontinuous compared with the result for pure Mode I. The subcritical crack growth seems to occur when the K _I value for the initial crack reaches a certain value. The d a /d t - K _I(Ψ) curves for combined Modes I and III lie roughly on the same curve as that for pure Mode I as the crack growth increases.     

Mixed-Mode Fracture of Ceramics in Diametral Compression

Mixed-mode fracture of a glass-ceramic and an alumina ceramic from inclined Knoop indenter flaws was studied in diametral compression and four-point-bend tests. In annealed specimens the directions of extension of the cracks and mode I and mode II stress-intensity factors at fracture were analyzed and compared to the predictions of a maximum crack-tip hoop stress theory. Knoop flaws in all cases extended in directions normal to the principal maximum tension rather than in the direction of maximum hoop stress near the crack tip. Mixed-mode fracture envelopes assessed in experiments, particularly with the diametral-compression test, showed significant deviation to higher K_II values relative to the fracture-mechanics predictions. As a consequence, an apparent K _IIc value assessed in the diametral-compression test was approximately twice the value of K _Ic.     

Method to Estimate Crack-Tip Toughness from Bending Tests on Prenotched Bars

A strain-gauge procedure that enables determination of the crack-tip toughness ( K _I0) from bending-strength tests is described. The procedure is applied to coarse-grained alumina and yields an average K _I0 value of 2.51 MPa·m^1/2, with a standard deviation of 0.16 MPa·m^1/2.     

Fracture Toughness of Polycrystalline Ceramics in Combined Mode I and Mode II Loading

Fracture of Polycrystalline alumina and zirconia ceramics in combined mode I and mode II loading was studied using precracked disk specimens in diametral compression. Fracture toughness was assessed in different stress states (including pure mode I, combined mode I and mode II, and pure mode II) by aligning the center crack at specific angles relative to the loading diameter. The resulting mixed-mode fracture-toughness envelope showed significant deviation to higher fracture toughness in mode II relative to the predictions of the linear elastic fracture mechanics theory. Critical comparison with corresponding results on soda–lime glass and fracture-surface observations showed that crack-surface resistances arising from grain interlocking and abrasion were the main sources of the increased fracture resistance in mode II loading of the polycrystalline ceramics. Quantitative fractography confirmed an increased percentage of transgranular fracture of the grains in mode II loading.     

Anisotropic Fracture Behavior in Ferroelectric Relaxor PZN–4.5%PT Single Crystals

The anisotropic fracture behavior in unpoled and poled (1− x )Pb(Zn_2/3Nb_1/3)− x PbTiO₃ ( x =0.045) (PZN–4.5%PT) single-crystal relaxor ferroelectrics cut along the crystal planes, [010] and [001], was characterized. The crack tip toughness ( K _tip) determined from Vickers indentations was compared with the R -curve behavior measured using the single-edge V-notch beam (SEVNB) method. Several of the SEVNB fracture experiments resulted in cracks forming and propagating under mixed mode loading ( K _I and K _II) along the [110] crystal plane. Other specimens formed cracks at 0° along the [010] plane. To assess the anisotropic fracture behavior, the local and global critical energy release rates were determined using Stroh's formalism.     

Fracture Toughness Evaluation of Small Thin Ceramic Specimens

A test method to evaluate the fracture toughness, K_IC, of thin, small, precracked ceramic specimens is described. The method is applicable for thin plates, wafers, self-supported layers, etc., especially when a large amount of material is not available for testing. The method consists of bonding a small, thin single-edge notched beam on one side of a metallic beam. A stress-free precrack with a square root singularity is achieved when the assembly is deformed in three-point bending.
The fracture toughness of a thin, alumina single-edge precracked beam was evaluated experimentally using this method, and compared with that obtained for similar specimens having a 0.3-mm-wide machined notch. Comparison with previously reported fracture toughness values suggests that even a very sharp machined notch overestimates the evaluated fracture toughness.     

Mechanical Behavior of a Borosilicate Glass Under Aqueous Corrosion

In France, fission products are being vitrified for a possible final geological disposal. Under disposal conditions, corrosion of the glass by groundwater as well as stress corrosion because of stresses occurring at surface flaws cannot be excluded. Within this framework, the mechanical behavior of the French simulated nuclear waste glass SON68 was studied by Vickers indentation and fracture experiments in air and in a corrosive solution. The glass was corroded at 90°C in a solution enriched with Si, B, and Na. The results showed that the glass corrosion enhances the cracks propagation relative to experiments in air. The indentation fracture toughness ( K _{I C} ) obtained using a four-point bending test showed that the K _{I C} of the glass decreased with increasing corrosion time.     

Mode I Fracture Toughness of a Small-Grained Silicon Nitride: Orientation, Temperature, and Crack Length Effects

The Mode I fracture toughness ( K _{I C} ) of a small-grained Si₃N₄ was determined as a function of hot-pressing orientation, temperature, testing atmosphere, and crack length using the single-edge precracked beam method. The diameter of the Si₃N₄ grains was <0.4 µm, with aspect ratios of 2–8. K _{I C} at 25°C was 6.6 ± 0.2 and 5.9 ± 0.1 MPa·m^1/2 for the T–S and T–L orientations, respectively. This difference was attributed to the amount of elongated grains in the plane of crack growth. For both orientations, a continual decrease in K _IC was observed through 1200°C, to ∼4.1 MPa·m^1/2, before increasing rapidly to 7.5–8 MPa·m^1/2 at 1300°C. The decrease in K _IC through 1200°C was a result of grain-boundary glassy phase softening. At 1300°C, reorientation of elongated grains in the direction of the applied load was suggested to explain the large increase in K _IC. Crack healing was observed in specimens annealed in air. No R -curve behavior was observed for crack lengths as short as 300 µm at either 25° or 1000°C.     

Mixed-Mode Fracture of Hot-Pressed Si3N4

The mixed-mode fracture of hot-pressed Si₃N₄ was investigated using inclined indentation surface flaws in bending and large crack geometries in combined tension/torsion. Non-coplanar fracture was observed in all cases. Values of K_Ic, K_IIc, and K_IIIc stress intensity factors were obtained, with ratios K_IIc/K_Ic= 0.79 and K_IIIc/K_Ic= 1.55 observed. For large cracks, mode II conditions had more of an effect on mode I fracture than mode III conditions. The mixed-mode I-II fracture of surface flaws was significantly different from that for large cracks, suggesting surface flaw shear resistance effects. A model describing these effects was derived, based on the ratio of the crack-opening displacement to the crack surface asperity height.     

Tensile Fracture Toughness Measurements in Ceramics

A novel procedure is outlined whereby fracture toughness values for ceramics can be measured under uniaxial tension (mode I) in specimens containing a fatigue crack. Circumferentially notched rods of rapolycrystalline aluminum oxide were precracked in cyclic compression to introduce a fatigue crack at room temperature, following the technique proposed by Suresh and co-workers.^7,10,11 Subsequently, the precracked rods were fractured in pure tension. Highly reproducible values of fracture toughness were obtained using this method.     

Combined Mode I and Mode II Fracture of Monolithic Ceramics

The mode I, mode II, and combined mode I–mode II fracture behaviors of a coarse-grained silicon nitride, a fine-grained silicon nitride, and an alumina were investigated. These ceramics were fractured from two types of fracture initiating flaws: small surface flaws and large single edge precracks. The small surface flaws were introduced by Knoop indentation in flexural samples at various angles to the tensile stress direction and fractured in four-point bending. The samples with large precracks were fractured in the asymmetric four-point-bend geometry. The mixed-mode fracture toughness values obtained from the two flaw configurations were in good agreement with each other. All three ceramics displayed very similar mixed-mode fracture behavior, although their microstructures were not similar. Comparison of experimental data to mixed-mode fracture theories revealed that the minimum strain energy density theory best described the mixed-mode fracture behavior of all three ceramics.     

Combined Mode I–Mode II Fracture of 12-mol%-Ceria-Doped Tetragonal Zirconia Polycrystalline Ceramic

The mode I, mode II, and combined mode Imode II fracture behavior of ceria-doped tetragonal zirconia polycrystalline (Ce-TZP) ceramic was studied. The single-edge-precracked-beam (SEPB) samples were fractured using the asymmetric four-point-bend geometry. The ratio of mode I to mode II loading was varied by varying the degree of asymmetry in the four-point-bend geometry. The minimum strain energy density theory best described the mixed-mode fracture behavior of Ce-TZP with the mode I fracture toughness, K _IC= 8.2 ± 0.6 MPa·m^1/2, and the mode II fracture toughness, K_IIC= 8.6± 1.3 MPa·m^1/2.     

Advances in the Grinding Efficiency of Sintered Alumina Abrasives

The study relates the grinding power of different grades of sintered alumina abrasives to their microstructures and to basic mechanical properties in comparison with conventionally fused electrocorundum and with an electrofused alumina/ zirconia eutectic. Contrary to the traditional approach of the Battelle test, the fracture toughness K _{I c} of individual grains is measured by a quantitative indentation analysis. Compared with fused corundum, sintered alumina grits exhibit an increased toughness and grinding efficiency, but the further increase of K _{I c} in the eutectic does not improve the grinding performance. The key parameter for grinding is the inherent hardness of the abrasive. The elimination of flaws by a new approach results in a strong increase in the grinding power of sintered alumina abrasives.     

Fracture Toughness Determination of A12O3 Using Four-Point-Bend Specimens with Straight-Through and Chevron Notches

Fracture toughness of a sintered A1₂O₃ was determined with four-point-bend specimens having either straight-through or chevron notches. For the straight-through notched specimens, measured K _Ic decreased with decreasing notch width. For the smallest notch width (66 μm) K _Ic= 3.42±0.13 MN m^−¾. For specimens with chevron notches, a crack initiates and extends from the tip of the notch under increasing load. K _Ic is calculated from the maximum load without measuring crack length, under the assumption that the derivative of the compliance is the same as that for a specimen with a straight-through crack. A refined calculation accounts for the truncated chevron crack shape at maximum load using Bluhm's slice model. For the chevronnotch configuration, a value of K _Ic= 3.49±0.11 MN m^−¾ was measured, which appears to be independent of the initial notch length a ₀ (distance from the crack mouth to the tip of the triangular notch). An effect of a ₁ (length of the chevron notch at the surface) on K _Ic was observed, independent of whether the calculation of K _Ic was based on the straight-through crack assumption or on the slice model.