KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS 4717 Note that whereas the as(n) function extrapolates (a)Glass/water =3.l8m P=500N through the data over the complete time range, con- firming a predominantly chemical fatigue com- ponent in the static fatigue, the ac(o) function again declines to lower values beyond the second decre- ment 4.2. Damage morphology Cyclic Figure 5 shows surface and section optical micro- graphs of indentation damage sites in the three test (n= 1)and multi-cycle (n>1)loading. The glass P=500N [Fig. 5(a) and porcelain [Fig. 5(b)] are viewed in 习150 transmitted light, the latter after back-thinning: the silicon nitride is viewed in reflected light [Fig. 5(c) Static The loads and sphere radii chosen here highlight he transformation in damage mode(cf. Figs 2 and from simple, well-defined cone cracks just out- ide the contact in the single-cycle state to accumu- lated damage below the contact, with attendant 103 106 radial cracks as well as incipient material removal in the multi-cycle state. 1500s;N/r P-2200N failure origins at indentation damage sites in (a) 1000 glass and (b) porcelain strength specimens, in sequences of increasing n. The loads and sphere radii are again chosen to highlight the transform- ation in damage mode. At n= l the fracture path occur well outside the contact circle. consistent with failure from cone cracks. At intermediate n the frac- ture paths tend to move closer to the contact circle 00 ( more evident here in the Effective contact time, t(s) builds up within the contact area and begins to compete with the cone crack for dominance as a indentation. wC spheres of radius r, at maximum glass the fracture origin occurred outside and inside loads p indicated. Inert strength as a function of num be lain/water:(c)silicon nitride/air. Equivalent time axis for ability at P= 500 N and n= 105-cf. Fig. 3(a). At yclic test data computed as Gcnf. Data points are means large n the fracture paths intersect the indentation nd standard deviations, minimum five specimens per indicative of failures from radial cracks. Similar ob- oint. Circles are cyclic data, triangles static data-grey ymbols from cone cracks, black symbols from radial servations have been reported previously for the cracks. Box at left axis and horizontal dashed line are silicon nitride [44] and are not reproduced here: suf- ""laboratory" strengths (unindented specimens). Solid fice it to say that in this material the failure initiates curves are theoretical predictions from cone crack model. from cone cracks over the data range except at the highest value of n and P in Fig. 2 the static data, indicating the onset of a significant In situ observations of the indentation damage mechanical degradation component in the fatigue. sites during the strength tests provided more defini Equation (12a)is used to generate the solid tive confirmation of the failure origins in the trans- curves odn and os() in Fig. 4, using the calibrated parent glass specimens. In specimens with light parameters in Table I along with appropriate evalu- damage the failure initiated at the base of the cone tions of Gc(N)(Appendix).t Using equation(13) cracks and spread laterally and upward, forming to plot the time axis for the static data reduces the the characteristic inward-pointing cusp-like trace ado and os(n data to universal curves in the outside the contact on the upper surface seen in region just beyond the first strength decrement. Fig. 6 at n=l. This kind of failure occurred rapidly, with little extension before instability. In specimens with heavy damage, the failure was con- fActually, including the factor Gc() in equation (13) firmed to initiate from the edge of a favorably muscule shifts of the cyclic fatigue curves oriented radial crack (relative to the tension axis) uld still result in almost indistinguishable cyclic and The radial cracks extended outward 20%in dimension prior to failure, indicating a stabilizingthe static data, indicating the onset of a signi®cant mechanical degradation component in the fatigue. Equation (12a) is used to generate the solid curves sC(t) and sS(t) in Fig. 4, using the calibrated parameters in Table 1 along with appropriate evalu￾ations of GC(N) (Appendix).{ Using equation (13) to plot the time axis for the static data reduces the sC(t) and sS(t) data to universal curves in the region just beyond the ®rst strength decrement. Note that whereas the sS(t) function extrapolates through the data over the complete time range, con- ®rming a predominantly chemical fatigue com￾ponent in the static fatigue, the sC(t) function again declines to lower values beyond the second decre￾ment. 4.2. Damage morphology Figure 5 shows surface and section optical micro￾graphs of indentation damage sites in the three test materials, comparing damage after single-cycle (n ˆ 1) and multi-cycle (nw1) loading. The glass [Fig. 5(a)] and porcelain [Fig. 5(b)] are viewed in transmitted light, the latter after back-thinning; the silicon nitride is viewed in re¯ected light [Fig. 5(c)]. The loads and sphere radii chosen here highlight the transformation in damage mode (cf. Figs 2 and 3): from simple, well-de®ned cone cracks just out￾side the contact in the single-cycle state to accumu￾lated damage below the contact, with attendant radial cracks as well as incipient material removal, in the multi-cycle state. Figure 6 shows re¯ection optical micrographs of failure origins at indentation damage sites in (a) glass and (b) porcelain strength specimens, in sequences of increasing n. The loads and sphere radii are again chosen to highlight the transform￾ation in damage mode. At n ˆ 1 the fracture paths occur well outside the contact circle, consistent with failure from cone cracks. At intermediate n the frac￾ture paths tend to move closer to the contact circle (more evident here in the porcelain), as damage builds up within the contact area and begins to compete with the cone crack for dominance as a starting ¯aw in the ¯exural ®eld. [In the case of glass the fracture origin occurred outside and inside the contact circle with approximately equal prob￾ability at P = 500 N and n ˆ 103Ðcf. Fig. 3(a).] At large n the fracture paths intersect the indentation, indicative of failures from radial cracks. Similar ob￾servations have been reported previously for the silicon nitride [44] and are not reproduced here: suf- ®ce it to say that in this material the failure initiates from cone cracks over the data range except at the highest value of n and P in Fig. 2. In situ observations of the indentation damage sites during the strength tests provided more de®ni￾tive con®rmation of the failure origins in the trans￾parent glass specimens. In specimens with light damage the failure initiated at the base of the cone cracks and spread laterally and upward, forming the characteristic inward-pointing cusp-like trace outside the contact on the upper surface seen in Fig. 6 at n ˆ 1. This kind of failure occurred rapidly, with little extension before instability. In specimens with heavy damage, the failure was con- ®rmed to initiate from the edge of a favorably oriented radial crack (relative to the tension axis). The radial cracks extended outward 120% in dimension prior to failure, indicating a stabilizing Fig. 4. Comparison of cyclic and static contact fatigue, indentation with WC spheres of radius r, at maximum loads P indicated. Inert strength as a function of number of contact cycles for: (a) soda-lime glass/water; (b) porce￾lain/water; (c) silicon nitride/air. Equivalent time axis for cyclic test data computed as GCn/f. Data points are means and standard deviations, minimum ®ve specimens per point. Circles are cyclic data, triangles static dataÐgrey symbols from cone cracks, black symbols from radial cracks. Box at left axis and horizontal dashed line are ``laboratory'' strengths (unindented specimens). Solid curves are theoretical predictions from cone crack model. {Actually, including the factor GC(N) in equation (13) causes only minuscule shifts of the cyclic fatigue curves along the logarithmic time axis in Fig. 4, so that omitting it would still result in almost indistinguishable cyclic and static functions. KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS 4717