Microstructure-Strength Properties in Ceramics: II, Fatigue Relations

The study of crack-size effects in aluminas and other selected ceramics in Part I is here extended to dynamic fatigue properties. Controlled flaws are used to measure the fatigue response in the large-crack (indentation-controlled) and small-crack (microstructure-controlled) regions. It is demonstrated that the "microstructural driving forces" responsible for the R-curve behavior are readily accommodated into existing indentation fracture theories of fatigue strengths. The modified theory provides well-defined solutions for the strengths in terms of stressing rate and indentation load. Two load-invariant quantities, relating to the exponent and coefficient in an assumed power-law crack velocity function, are sufficient to define the entire data set for a given material, at all stressing rates and loads. This is demonstrated graphically by reducing such data sets onto universal fatigue diagrams. The data for sapphire do not coincide with those for the poly crystalline aluminas, suggesting again that it is the grain-boundary structure which holds the key to the fracture properties in the latter. From the standpoint of reliability, the study emphasizes the need to account for microstructural effects when extrapolating to the domain of naturally occurring flaws. In this context, the adjustable quantities obtained from the dynamic fatigue data fits emerge as appropriate design parameters.     

Multi‐Scale Effects in the Strength of Ceramics

Multiple length‐scale effects are demonstrated in indentation‐strength measurements of a range of ceramic materials under inert and reactive conditions. Meso‐scale effects associated with flaw disruption by lateral cracking at large indentation loads are shown to increase strengths above the ideal indentation response. Micro‐scale effects associated with toughening by microstructural restraints at small indentation loads are shown to decrease strengths below the ideal response. A combined meso‐micro‐scale analysis is developed that describes ceramic inert strength behaviors over the complete indentation flaw size range. Nano‐scale effects associated with chemical equilibria and crack velocity thresholds are shown to lead to invariant minimum strengths at slow applied stressing rates under reactive conditions. A combined meso‐micro‐nano‐scale analysis is developed that describes the full range of reactive and inert strength behaviors as a function of indentation load and applied stressing rate. Applications of the multi‐scale analysis are demonstrated for materials design, materials selection, toughness determination, crack velocity determination, bond rupture parameter determination, and prediction of reactive strengths. The measurements and analysis provide strong support for the existence of sharp crack tips in ceramics such that the nano‐scale mechanisms of discrete bond rupture are separate from the larger scale crack driving force mechanics characterized by continuum‐based stress‐intensity factors.     

Study of Microstructural Effects in the Strength of Alumina Using Controlled Flaws

Strength characteristics were studied as a function ofVickers indentation Load for aluminas with two grain sizes. At low loads the strengths tend to well-defined plateaus, the levels of which bear an inverse relation to grain size. These trends are consistent with a trunsition from indentation-controlled to microstructure-controlled behavior as flaw size diminishes. The conventional indentation fracture formalism was modified to account for this transition.     

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.     

Strength Degradation in Polycrystalline Alumina Due to Sharp-Particle Impact Damage

Sharp-particle impact damage in five aluminas, varying in purity, grain size, and porosity, was studied, and postimpact strengths were determined. Target specimens were subjected to single-particle impacts using a gas gun and multiparticle impacts using a slinger-type apparatus. For comparison, static indentation damage in the same aluminas was studied using a Vickers microhardness indenter. For the fine-grained materials the impact damage morphology was characterized by severe radial cracking and lateral chipping; the coarse-grained materials exhibited chipping and grain fall-out and very irregular radial crack patterns. The postimpact and postindentation fracture strength was modeled by assuming that the materials exhibited crack resistance toughening. Based on these results, fracture resistance curves ( R curves) for each of the five aluminas were predicted and compared. The large-grained aluminas exhibited the strongest R -curve behavior and the greatest impact resistance; i.e., strength degradation was least sensitive to impacting energy.     

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.     

Sigmoidal Indentation–Strength Characteristics of Polycrystalline Alumina

The fracture properties of a series of three polycrystailine aluminas are examined using indentationstrength and double cantilever beam techniques. The indentation-strength response is shown to be sigmoidal with concave-down behavior at small indentation loads and concave-up behavior at large indentation loads. A model is developed for the general response, combining increasing toughening by ligamentary bridging at small crack lengths and increasing residual-stress relief by lateral cracking at large indentation loads. The model is fit to the strength data and used to deconvolute the underlying toughness variation and predict the intrinsic strength of the materials. Direct measurements of toughness using the "long-crack" double cantilever beam geometry are shown to overestimate the toughness variations effective during "short-crack" strength tests.     

Modeling of Grain-Size-Dependent Microfracture-Controlled Sliding Wear in Polycrystalline Alumina

To quantify grain-size-dependent sliding wear of polycrystalline alumina induced by grain-boundary microfracture, an attempt is made to extend and combine Cho et al. 's fracture mechanics analysis and Fu and Evans' simple micro-cracking theory. An analytical equation is derived to relate wear with microstructural parameters. Wear by intergranular microfracture occurs, provided that the combined stresses are greater than a threshold value. The critical sliding time to the wear transition decreases with increasing grain size, and the wear rate after the threshold is proportional to the grain size. The theoretical predictions are correlated with the lubricated sliding wear data of aluminas with different grain sizes reported by Cho et al.     

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.     

Role of Crack-Bridging Ligaments in the Cyclic Fatigue Behavior of Alumina

The cyclic fatigue crack growth behavior in two aluminas with different grain sizes and purities has been investigated using tapered cantilever beam specimens. The curves of load–crack opening displacement revealed a hysteretic loss behavior, in both aluminas, produced by frictional forces generated in the crack wake. From measurements of the specimen complinces it is concluded that the fatigue cracks in these materials were strongly bridged by both "frictional" and "elastic" load-bearing ligaments. It is shown that the "elastic" contribution to the total crack-bridging force is far greater than that produced by fristional sliding ligaments. The results support the view that cyclic loads produce degradation of the strength of the bridging ligaments. The effect of grain size and compressive loads on the magnitude of the bridging forces is discussed.     

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.     

Objective Evaluation of Short-Crack Toughness Curves Using Indentation Flaws: Case Study on Alumina-Based Ceramics

An objective methodology is developed for evaluating toughness curves ( T -curves) of ceramics using indentation flaws. Two experimental routes are considered: (i) conventional measurement of inert strength as a function of indentation load; (ii) in situ measurement of crack size as a function of applied stress. Central to the procedure is a proper calibration of the indentation coefficients that determine the K -field of indentation cracks in combined residual-contact and applied-stress loading, using data on an appropriate base material with single-valued toughness. Tests on a fine-grain alumina serve to demonstrate the approach. A key constraint in the coefficient evaluation is an observed satisfaction of the classical indentation strength–(load)^−1/3 relation for such materials, implying an essential geometrical similarity in the crack configurations at failure. T -curves for any alumina-based ceramic without single-valued toughness can then be generated objectively from inert-strength or in situ crack-size data. The methodology thereby circumvents the need for any preconceived model of toughening, or for any prescribed analytical representation of the T -curve function. Data on coarse-grained aluminas and alumina-matrix material with aluminum titanate second-phase particles are used in an illustrative case study.     

Strength Degradation of Brittle Surfaces: Blunt Indenters

Indentation fracture mechanics is used to develop a theoretical basis for predetermining the strength properties of brittle surfaces in prospective contact situations. Indenters are classified as blunt or sharp; only the first is considered in the present work. The classical Hertzian cone crack conveniently models the fracture damage incurred by the surface in this class of indentation event. Significant degradation is predicted at a critical contact load; when the load is increased beyond this critical level, further degradation occurs at a relatively slight rate. Bend tests on abraded glass slabs confirm the essential features of the theoretical predictions. The controlling variables in the degradation process, notably starting flaw size and in-denter radius, are investigated systematically. An indication is also given as to optimization of material parameters.     

Controlled Flaws in Ceramics: A Comparison of Knoop and Vickers Indentation

Application of indentation fracture analysis to Knoop and Vickers indentation is examined, with particular emphasis on determining the limitations of the point force representation for the residual stress field. Deviation from the point force approximation is insignificant for crack-size/plastic-zone-size ratios 1.3. The Vickers deformation/fracture configuration in brittle materials invariably conforms to this requirement, whereas the Knoop configuration does not (except at very high indentation loads). However, stable crack growth during a failure test extends the crack sufficiently that the strength degradation for both types of indentation is well described by the point force approximation.     

Strength Variability of Indented Soda-Lime Glass

Studies of annealed indentation flaws show that specimen strength is inversely proportional to the square root of the surface trace dimension of the strength-controlling radial crack over a range of indentation loads. Using the surface trace as the characteristic dimension in the appropriate fracture mechanics equations, however, underestimates the measured strengths by about 30%. There is also a lack of correlation between the individual strengths and the surface traces at a given indentation load. Despite the complex nature of indentation flaws, strength predictions of individual indentation cracks based on the radial crack depth (not the surface trace) are in agreement with measured strengths. Strength variability of indented glass specimens at a given indentation load is due mainly to the spectrum of crack depths.     

钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

针对钢化真空玻璃球形支撑物对玻璃压痕的应力场分布问题,采用接触力学,对Hertzian压痕方程进行了修正,推导了三维应力场方程,同时,对完全发展的锥形裂纹的应力强度因子进行了数值求解。结果表明,在球体与玻璃接触区域内,所有的主应力都是压应力,主应力σ₁导致了裂纹的萌生,而主应力σ₂形成了环形裂纹。与玻璃表面正交的最小主应力从接触边缘向外偏离,形成的近似平行的曲线即为锥形裂纹的形状,而最大拉应力总是垂直于这些曲线。因此,在最大主拉应力的作用下,球体加载后裂纹遵循最小主应力的轨迹。裂纹尖端的应力强度因子决定了断裂韧性,随着裂纹的扩展,应力强度因子减小,在离表面一定距离后,应力强度因子达到临界值,裂纹停止。不同压痕载荷下的归一化应力强度因子是一组具有相似形状的曲线。     

Fracture toughness of (Ce) stabilized ZrO2/Al2O3 composites

Three techniques for the determination of K_Ic in Ce-stabilized ZrO₂/Al₂O₃ composites have been evaluated: the single-edge-notched beam (SENB); the indentation strength in bending (ISB) and the indentation fracture (IF). Comparative measurements, performed on samples prepared by sintering uniaxially pressed powders obtained by a chemical route, showed that whatever the technique used, K_Ic increased as the Al₂O₃ grain size decreased.

The three methods give similar results if some procedural improvements are introduced, namely: (i) the polished samples are annealed prior to testing: (ii) a more reproducible notching technique would be developed for the SENB method; and (iii) the crack shape and length are known exactly in the IF technique.

In the IF test, the crack shape profile is of Palmquist type at low indentation loads while a transition to a half-penny-shaped crack occurs at higher loads.     

Effect of Grain Size on Hertzian Contact Damage in Alumina

The role of microstructural scale on deformation-micro fracture damage induced by contact with spheres is investigated in monophase alumina ceramics over a range 3–48 μ in grain size. Measurement of a universal indentation stress–strain curve indicates a critical contact pressure ≅5 GPa, above which irreversible deformation occurs in alumina. A novel sectioning technique identifies the deformation elements as intragrain shear faults, predominantly crystallographic twins, within a confining subsurface zone of intense compression-shear stress. The twins concentrate the shear stresses at the grain boundaries and, above a threshold grain size, initiate tensile intergranular microcracks. Below this threshold size, classical Hertzian cone fractures initiate outside the contact circle. Above the threshold, the density and scale of subsurface-zone microcracks increase dramatically with increasing grain size, ultimately dominating the cone fractures. The damage process is stochastic, highlighting the microstructural discreteness of the initial deformation field; those grains which lie in the upper tail of the grain-size distribution and which have favorable crystallographic orientation relative to local shear stresses in the contact field are preferentially activated. Initial flaw state is not an important factor, because the contact process creates its own flaw population. These and other generic features of the damage process will be discussed in relation to microstructural design of polycrystalline ceramics.     

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.