4712 KIM et al: CYCLIC FATIGUE OF BRITTLE CERAMICS test procedure. This procedure involves two steps: single-cycle contacts falls off abruptly beyond a cyclic contacts on specimen surfaces using a hard critical load for cone crack formation, and there sphere of given radius, at prescribed frequency and after declines continuously and slowly with increas- maximum load; ( ii) inert strength measurement of ing contact load, in accordance with traditional the contact-damaged specimens. The first step indentation equilibrium fracture mechanics. One allows characterization of the actual damage pro- study with spheres in sustained static loading over cess-the second step enables quantification of the prescribed contact durations (static fatigue")on damage severity. Glass is an ideal model brittle ma- glass in water [31] reported a rate-dependent re- terial because of its well-documented indentation duction of the critical load for initiation of cone strength properties in single-cycle sphere loading cracks and subsequent propagation of the cone [28-31( see Section 2.1), as well as its availability cracks, with corresponding steady depression in the of essential crack velocity parameters for data ensuing strength levels. Those rate effects were analysis (from Vickers indentation fracture studies found to be entirely consistent with time-integrated [32-34]). Moreover, the transparency of glass allows chemically-enhanced slow crack growth, in accord- for direct observations of the fracture damage from ance with expectation for brittle solids. Another the contact tests and the response of this damage in study with impacting spheres [30 reported strength subsequent strength tests. Other brittle ceramics degradation characteristics similar to those in static selected for study include: a translucent dental por- loading. In that case the main features of the degra lain, because of its brittleness and its amenability dation could be accounted for by introducing a to limited subsurface observation [25, 26]; and a simple relation between impact velocity and impul- relatively strong bearing-grade silicon nitride [35], sive load into the indentation fracture mechanics included to expand the range of toughness values. However, in this latter study some irregularities in The bulk of the contact fatigue tests are conducted the detailed strength response were noted. particu n moist environments, to highlight any chemical larly with smaller and denser spheres-these irregu- effect larities were correlated with the appearance of Using an indentation fracture analysis, we con- plasticity-induced radial cracks from sphere pen- firm that the initial stages of strength degradation etration into the impact surface, in a manner first are indeed consistent with chemically-enhanced observed by Phillips (cited in Ref. [38] and later low growth of classical cone cracks, integrated quantified by Swain and Hagan [39 over the duration of the fatigue test (brittle" Later, strength degradation studies from single region). The analysis provides simple power-law re- cycle sphere contacts were extended to relatively lations for evaluating cyclic lifetimes in this region. homogeneous polycrystalline ceramics [35, 40-44 However, beyond a critical number of cycles, a Again, cone cracking was identified as the principa more deleterious mechanism of degradation comes mode of damage, with similar abrupt strength into play, signaling the imminent demise of the ma- decrements at critical contact loading. In more het terial. This second mode is shown to be associated erogeneous ceramics, quasi-plastic damage also with the onset of distributed subsurface microdam- degraded the strength, initially without the abrupt age, with attendant development of more dangerous falloff [27]however, in these materials the pro- radial cracks (quasi-plastic region). Comparison spect of microcrack coalescence within the damage of the cyclic fatigue data with static fatigue data zone was identified as a potential source of ultimate confirms a strong mechanical component in the cyc- rapid strength decline in more severe indentation lic damage buildup in the latter region. These events [27], e.g. in single-cycle overload, multi-cycle results highlight both the strengths and limitations contacts [21], or high-velocity impact [45]. of traditional fracture mechanics concepts in fatigue analysis, especially in the context of lifetime design, 2.2. Fracture mechanics analysis and foreshadow a totally dominant quasi-plastic Consider the application of indentation fracture mode of failure in tougher, more heterogeneous cer- mechanics to the analysis of strength degradation from cyclic contacts with spheres, Fig. 1. Begin with the assumption that the material is ideally brittle, so that the degradation is caused exclusively by failure from cone cracks. The cone fracture is 2. CONTACT FATIG assumed to be subject to slow crack growth during DEGRADATION he cyclic contact loading according to a power- law velocity function, as previously considered in static 2. 1. Background loading [31 but now with the time integral taken The first indentation-strength studies with over a periodic contact history. We defer, until cal indenters were carried out on soda-lime later, consideration of failure from any secondary glass, the quintessential brittle material, in mode of damage ycle indentation [28, 29, 36, 37]. Generall Thus. assume that the crack extends trength of surface- damaged glass specimens from cordance with a basic power-law crack velocitytest procedure. This procedure involves two steps: (i) cyclic contacts on specimen surfaces using a hard sphere of given radius, at prescribed frequency and maximum load; (ii) inert strength measurement of the contact-damaged specimens. The ®rst step allows characterization of the actual damage pro￾cessÐthe second step enables quanti®cation of the damage severity. Glass is an ideal model brittle ma￾terial because of its well-documented indentation± strength properties in single-cycle sphere loading [28±31] (see Section 2.1), as well as its availability of essential crack velocity parameters for data analysis (from Vickers indentation fracture studies [32±34]). Moreover, the transparency of glass allows for direct observations of the fracture damage from the contact tests and the response of this damage in subsequent strength tests. Other brittle ceramics selected for study include: a translucent dental por￾celain, because of its brittleness and its amenability to limited subsurface observation [25, 26]; and a relatively strong bearing-grade silicon nitride [35], included to expand the range of toughness values. The bulk of the contact fatigue tests are conducted in moist environments, to highlight any chemical e€ect. Using an indentation fracture analysis, we con- ®rm that the initial stages of strength degradation are indeed consistent with chemically-enhanced slow growth of classical cone cracks, integrated over the duration of the fatigue test (``brittle`` region). The analysis provides simple power-law re￾lations for evaluating cyclic lifetimes in this region. However, beyond a critical number of cycles, a more deleterious mechanism of degradation comes into play, signaling the imminent demise of the ma￾terial. This second mode is shown to be associated with the onset of distributed subsurface microdam￾age, with attendant development of more dangerous radial cracks (``quasi-plastic'' region). Comparison of the cyclic fatigue data with static fatigue data con®rms a strong mechanical component in the cyc￾lic damage buildup in the latter region. These results highlight both the strengths and limitations of traditional fracture mechanics concepts in fatigue analysis, especially in the context of lifetime design, and foreshadow a totally dominant quasi-plastic mode of failure in tougher, more heterogeneous cer￾amics. 2. CONTACT FATIGUE AND STRENGTH DEGRADATION 2.1. Background The ®rst indentation±strength studies with spheri￾cal indenters were carried out on soda-lime silicate glass, the quintessential brittle material, in single￾cycle indentation [28, 29, 36, 37]. Generally, the strength of surface-damaged glass specimens from single-cycle contacts falls o€ abruptly beyond a critical load for cone crack formation, and there￾after declines continuously and slowly with increas￾ing contact load, in accordance with traditional indentation equilibrium fracture mechanics. One study with spheres in sustained static loading over prescribed contact durations (``static fatigue'') on glass in water [31] reported a rate-dependent re￾duction of the critical load for initiation of cone cracks and subsequent propagation of the cone cracks, with corresponding steady depression in the ensuing strength levels. Those rate e€ects were found to be entirely consistent with time-integrated chemically-enhanced slow crack growth, in accord￾ance with expectation for brittle solids. Another study with impacting spheres [30] reported strength degradation characteristics similar to those in static loading. In that case the main features of the degra￾dation could be accounted for by introducing a simple relation between impact velocity and impul￾sive load into the indentation fracture mechanics. However, in this latter study some irregularities in the detailed strength response were noted, particu￾larly with smaller and denser spheresÐthese irregu￾larities were correlated with the appearance of plasticity-induced radial cracks from sphere pen￾etration into the impact surface, in a manner ®rst observed by Phillips (cited in Ref. [38]) and later quanti®ed by Swain and Hagan [39]. Later, strength degradation studies from single￾cycle sphere contacts were extended to relatively homogeneous polycrystalline ceramics [35, 40±44]. Again, cone cracking was identi®ed as the principal mode of damage, with similar abrupt strength decrements at critical contact loading. In more het￾erogeneous ceramics, quasi-plastic damage also degraded the strength, initially without the abrupt fallo€ [27]Ðhowever, in these materials the pro￾spect of microcrack coalescence within the damage zone was identi®ed as a potential source of ultimate rapid strength decline in more severe indentation events [27], e.g. in single-cycle overload, multi-cycle contacts [21], or high-velocity impact [45]. 2.2. Fracture mechanics analysis Consider the application of indentation fracture mechanics to the analysis of strength degradation from cyclic contacts with spheres, Fig. 1. Begin with the assumption that the material is ideally brittle, so that the degradation is caused exclusively by failure from cone cracks. The cone fracture is assumed to be subject to slow crack growth during the cyclic contact loading according to a power-law velocity function, as previously considered in static loading [31] but now with the time integral taken over a periodic contact history. We defer, until later, consideration of failure from any secondary mode of damage. Thus, assume that the cone crack extends in ac￾cordance with a basic power-law crack velocity 4712 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS