Short crack fracture toughness in (1−x)(Na1/2Bi1/2)TiO3–xBaTiO3 relaxor ferroelectrics

The fracture toughness in the lead‐free relaxor ferroelectric (1?x)(Na_1/2Bi_1/2)TiO₃–xBaTiO₃ was investigated utilizing the surface crack in flexure method. To allow a comprehensive assessment, unpoled, and poled samples from the rhombohedral, the tetragonal, and the morphotropic phase regime were considered. It was found that the fracture toughness is up to 23% higher for the poled state. In order to cover the transition from ferroelectric to relaxor phase, the temperature dependence of 0.97(Na_1/2Bi_1/2)TiO₃–0.03BaTiO₃ was studied as well. Fracture toughness values of up to 2 MPam^1/2 were determined, which are considerably above data for lead zirconate titanate materials. The results are rationalized using a simple transformation toughening‐type model in conjunction with investigations into the ferroelastic behavior. The presented model can be applied without fitting parameters but utilizes measurements of the coercive stress and remanent strain as well as the elastic modulus.     

In-Plane Fracture Resistance of a Crossply Fibrous Monolith

The in-plane fracture resistance of a crossply Si₃N₄/BN fibrous monolith in the 0°/90° and ±45° orientations is examined through tests on notched flexure specimens. The measurements and observations demonstrate the importance of fiber pullout following fiber fracture. The mechanical response is modeled using a crack-bridging approach. Two complementary approaches to evaluating the bridging law are developed: one based on a micromechanical model of fiber pullout and the other based on the load versus crack mouth opening displacement response of the flexure specimens following fracture of all fibers. Both approaches indicate that the bridging law follows an exponential form, characterized by a bridging strength and an effective pullout length. An assessment of the bridging model is made through comparisons of simulations of the load–displacement response with those measured experimentally.     

Crack Growth along Interfaces in Porous Ceramic Layers

Crack growth along porous ceramic layers was studied experimentally. Double cantilever beam sandwich specimens were loaded with pure bending moments to obtain stable crack growth. The experiments were conducted in an environmental scanning electron microscope enabling in situ observations of various mechanisms associated with crack growth. The macroscopic fracture energy of the interface between dense lanthanum strontium chromite and a porous lanthanum strontium manganite was measured to lie in the range of 1.4–3.8 J/m². Several micromechanisms were observed ahead of, or in the wake of, the crack tip. The measured variation of the fracture energy along the crack length may be attributed to such phenomena.     

Mode I interlaminar fracture behavior of 2D woven ceramic matrix composites

Interlaminar fracture properties of melt-infiltrated woven SiC/SiC ceramic matrix composites were investigated using traditional and wedge-loaded double cantilever beam methods. The two methods produced comparable G_IC results for some specimens. The difference in boundary conditions between the two methods appeared to influence the crack propagation path. The DCB method, having free-end boundary condition, allowed more interaction between the crack and the composite microstructure than the wedge method did. The effect of fiber tow layout sequence had an effect on the interlaminar properties. Higher toughness was observed for the orientation where crack propagation occurs between planes with more transverse tows. Jump-arrest phenomenon was found to have higher significance on the rising R-curve behavior than fiber bridging.     

Slow stable crack growth in high density polyethylenes

The phenomenon of slow stable crack growth in polyethylene is investigated using notched specimens subject to constant load and the concepts of fracture mechanics. The effect of specimen geometry and dimension, the loading and the mode of loading on the applied stress intensity factor versus crack speed ($\text{K}{}_{\mathrm{c}}\text{-}\text{a}\text{?}$) curves has been studied to demonstrate that K_c is the controlling stress parameter for crack growth under suitable conditions. $\text{K}{}_{\mathrm{c}}\text{-}\text{a}\text{?}$ curves are obtained for a high density polyethylene homopolymer in distilled water and in a diluted detergent solution at four different temperatures. Results are also obtained for a much tougher medium density polyethylene copolymer whenever possible. Several mechanisms can be identified from the form of the $\text{K}{}_{\mathrm{c}}\text{-}\text{a}\text{?}$ curves. Two, in particular, have been observed but not explained before: (i) crack growth with a time dependence of 0.25, and (ii) the high $\text{K}{}_{\mathrm{c}}\text{-}\text{a}\text{?}$ slopes for crack growth in a tough copolymer. With the help of scanning electron microscopic studies of the fracture surfaces, (i) is postulated to be due to diffusion controlled void growth process and (ii) is considered to be the result of crack tip blunting effects. From the temperature dependence of crack growth, the activation energy of the diffusion controlled crack growth process is found to coincide with that of the x-relaxation process in polyethylene implying that diffusion controlled crack growth may be related to the motion of main chains in the polymer.     

Anisotropy free energy contribution of the ferroelectric domain dynamics in PMN-PT and PIN-PMN-PT relaxor ferroelectrics

A direct correlation between the materials property behavior with its associated ferroelectric domain mechanisms and the anisotropic component of the Landau free energy is established for binary PMN-PT (generation I) and ternary PIN-PMN-PT (generation II) relaxor ferroelectric single crystal material systems. In addition to their trade-off in material properties, the observed ferroelectric domain dynamic and the determined free energy anisotropies, especially as approaching phase transition, provide direct insights into the materials field-dependent behavior between the binary and ternary ferroelectric systems. Domain configuration features such as lamellar structures in binary PMN-PT and concentric oval-like structures in ternary PIN-PMN-PT result in different material responses to external stimuli. Compared to binary PMN-PT, the concentric oval-like domain structures of ternary PIN-PMN-PT result in a 20°C higher temperature range of field-dependent linear behavior, 40% increase in coercive electric field $E_C,$ higher elastic stiffness during ferroelectric domain switching, and lower electromechanical energy losses. Separation of the isotropic and anisotropic components in the Landau free energy reveals a higher anisotropic free energy contribution from the ternary system, especially at temperature for practical applications. The high anisotropic free energy found in the ternary PIN-PMN-PT system implies that the concentric oval-like domain structure contributes to reduced electromechanical energy losses and enhanced stability under external applied fields.     

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%.     

Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, K_o, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.     

Notch Sensitivity of Ceramic Composites with Rising Fracture Resistance

A theoretical framework is developed for the notched strength of ceramic composites that exhibit rising fracture resistance. It is based on established concepts of crack stability under stress-controlled loadings. On using a linear representation of the resistance curve (expressed in terms of an energy release rate), straightforward analytical solutions are obtained for the strength as well the amount of stable crack growth preceding fracture and the associated fracture resistance. Calculations are performed for several test configurations commonly used for material characterization, including single- and double-edge-notched tension, center-notched tension, and single-edge-notched bending. The results reveal salient trends in strength with notch length and specimen geometry. An assessment of the theory is made through comparison with experimental measurements on an all-oxide fiber composite. Transitions in the degree of notch sensitivity with notch length are identified and explored. The utility of the theoretical results both for rationalizing the trends in measured notched strength and for guiding experimental studies of notch sensitivity is demonstrated.     

Fracture Toughness of Amorphous Precursor-Derived Ceramics in the Silicon-Carbon-Nitrogen System

The toughness of amorphous precursor-derived ceramics in the Si-C-N system is investigated. Crack-growth data are obtained from DCB specimens, whereas the crack-tip toughness is determined from the crack-tip profile of indentation cracks. For amorphous Si-C-N ceramics that have been fabricated via the powder route, an R -curve effect is observed. The initial values of the rising R -curve are consistent with the estimated crack-tip toughness.     

Effects of Methane Concentration in the Deposition Process on the Crystal Structure and the Adhesive Fracture Toughness of CVD Diamond

Crystal structures of CVD diamond particles were observed in detail by transmission electron microscopy. The particles were deposited on silicon substrates under various conditions and had different levels of adhesion. An interlayer of SiC was found along the interface obtained with low methane concentration in the source gas, but it disappeared when deposited with higher methane concentrations. On the other hand, the size of crystal grains became smaller with increasing methane concentrations. From the correspondence between the structures and the adhesive toughness of these particles, it was suggested that the effect of both the SiC interlayer and the variation of grain size resulted in the complicated trend of adhesion with respect to methane concentration.     

Fracture Energy of an Aligned Porous Silicon Nitride

The fracture energy of a porous silicon nitride with aligned fibrous grains was investigated, using a chevron-notched-beam technique. A crack was constrained to propagate normal to the grain alignment. The obtained fracture energy was ∼500 J/m², which was ∼7 times larger than that of a dense silicon nitride with randomly oriented fibrous grains. The large fracture energy was attributable primarily to the sliding resistance associated with interlocking grains.     

Surface Integrity Effects on the Fracture Resistance of Electrical-Discharge-Machined WC–Co Cemented Carbides

The flexural strength evolution for two WC–16 vol% Co cemented carbides, with different mean carbide size, subjected to sequential and upgrading electrical-discharge machining (EDM) is studied. It is compared with the fracture behavior exhibited by a reference surface finish condition, attained through conventional mechanical grinding and polishing using diamond as abrasive. Considering that rupture is related to existing defects, either introduced during sample elaboration or induced by machining, a detailed fractographic examination by scanning electron microscopy is conducted to discern fracture origins. The experimental findings indicate that the flexural strength of WC–Co hardmetals may be strongly affected by EDM, depending on the correlation existing between natural defects, as given by particular microstructural parameters, and EDM-induced flaws. An analysis of the results using a linear–elastic fracture mechanics approach permits one to establish a clear connection between surface integrity and fracture resistance. Quantitative discrepancies between the estimated and the experimentally measured critical flaw sizes for all the EDM-related grades are rationalized through the existence of local residual tensile stresses of considerable magnitude at the shaped surface. Release of these stresses through final mechanical and annealing treatments is pointed out as a quite effective alternative for improving the fracture behavior of WC–Co cemented carbides shaped by EDM.     

Fracture Resistance of Highly Textured Alumina

Textured alumina has been fabricated previously by either hot-deformation processing, to produce moderate texture, or templating with aligned platelets, to produce stronger texture. Fracture-toughness measurements on ceramics fabricated by hot deformation have indicated only a modest improvement in toughness compared with that of untextured ceramics, while measurements on more strongly textured ceramics have been very limited. In this work, a simplified process for fabricating highly textured alumina was developed, using a solvent-based slurry, tape casting, and liquid-phase sintering. Grain size was tailored to maximize the likelihood of grain bridging and crack deflection. Image analysis was used to characterize morphologic texture, and X-ray pole-figure analysis was used to measure crystallographic texture. Fracture tests revealed significant changes to the crack path as a result of the texture. However, the apparent fracture resistances measured using single-edge notched-beam samples were similar for textured and untextured ceramics. The lack of apparent toughening resulting from texturing is discussed in light of previous results.     

Fracture Toughness of Spray-Dried Powder Compacts

The strengths and fracture toughness values were measured for alumina powder compacts containing two different binder systems. Diametral compression was used to measure both the tensile strength and the fracture toughness (through-thickness notch). This methodology was very useful in linking processing parameters, such as binder choice and compaction stress, to the quality of the green bodies. Observations of the compact structure before and after fracture showed that the binders segregated to the region between the spray-dried granules. The presence of the excess binder in this region was linked to both the failure mode and the creation of secondary cracks.     

Hardness and Fracture Toughness of Pressureless-Sintered Boron Carbide (B4C)

This is a companion work to our previous study on the pressureless sintering of boron carbide (B₄C). The Vickers hardness and indentation fracture toughness of B₄C compacts were measured after various sintering heat treatments. Increases in hardness and decreases in indentation fracture toughness as the grain size decreased in sintered B₄C were attributed to the effects of more rapid strain hardening associated with dislocation pileups at grain boundaries.     

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.     

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.     

Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.