4716 KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS case, grey symbols represent failures from cone termined from previous(Vickers indentation)stu- cracks and black symbols from radial cracks dies [32-34], with just P, and a, as adjustable Section 4.2). Open boxes at left axis and associated parameters; for the other materials, N, PI and al horizontal dashed lines are strengths of unindented are all treated as adjustable parameters. The fitted pecimens. Solid curves through the data are theor- curves are consistent with the main data trends in etical fits the cone crack region, within the data scatter 4.1.1. Cyclic contact fatigue tests. Figure 2 shows 4.1.2. Cyclic vs static fatigue tests. Figure 4 com- lots of o(n) data for each material/environment pares a(n)data for cyclic and static tests, again for system, for indentations at specified sphere radius r, the same material/environment systems, with the at two selected loads P. In each case the two loads time scale for the cyclic data determined as are selected so as to straddle the single-cycle cone [= Gen/f according to equation(13). Chosen values crack threshold value, PI(see Table 1, later ). Gen- of n and P are such that degradation occurs within erally, at the higher of the two selected P values thethe first cycle. In the region of the first strength strength is substantially degraded within the first decrement the data overlap, within the scatter bars cycle--in this case, failures originate from indenta- However, in the region of the second strength tion sites at all n. At the lower of the P values the decrement the cyclic data diverge markedly below strength shows no degradation initially, correspond ing to failures away from the contact sites at natu- ral flaws (indicating that any initial flaw extension rior to ring-crack instability is too minor to a)Glass/water grade the strength); but beyond a critical number les (ne) the strength again declines above a 100 er of cycles(n>ne). Spec be made of the data for porcelain/water at the lower load P= 200N in Fig. 2(b)in this case P lies so close to Pi that the failures are stochastical distributed between cone crack and natural-faw gins. her n values the strength data show noticeable accelerating decline. This second region 200 (b) Porcelain/water =3.18mm becomes clearly evident after only a few hundred cycles at P= 500 N in the glass/water and porce- 2 150 lain/water systems; in the silicon nitrideair system it becomes apparent only after n10 cycles at the ases the glass and porcelain specimens fail during d the contact test itself (arrows). Figure 3 shows analogous o(P) results for the l material/environment systems, an 0 same specified sphere radius r, comparing data after longed cycling at specified numbers of cycles (e)Si3N4/air r=1.98mm (n>1)with those in single-cycle loading (n= 1) These results confirm a significant degradation in 1000 "乎“基”“T““““-“1 strength from the cycling. In the glass/water and porcelain/water systems the cyclic data fall withi the domain of the second strength decrement ove the entire range of P(cf. Fig. 2), and so tend to fall beneath the predicted curve; conversely, in the sili- con nitride/air system the cyclic data remain within 0001500 00 the bounds of the first strength decrement at all P. The solid curves in Figs 2 and 3 are best fits of Contact load, P(N) the initial degradation region corresponding to fail- indentation with WC spheres of radie of contact are from cone cracks (i.e. grey symbols), using N, water;(c) silicon nitride/ air. Data points are means and PI and a1 as parameters. Vertical solid lines indi- standard deviations, minimum five specimens per point cate critical ne or Pc values for cone crack initiation Filled symbols indicate failures from indentation sites- lequations(7a)and(7b)); the solid curves at ne >1 grey symbols from cone cracks, black symbols from radial nd Pe>I represent strength degradation functions cracks. Unfilled symbols indicate failures from natural faws-box at left axis and horizontal dashed line are for failure from these cone cracks [equations(12a)"laboratory"strengths (unindented specimens). Solid and(12b)] For soda-lime glass, N=17.9 is prede- urves are theoretical fits to datacase, grey symbols represent failures from cone cracks and black symbols from radial cracks (Section 4.2). Open boxes at left axis and associated horizontal dashed lines are strengths of unindented specimens. Solid curves through the data are theor￾etical ®ts. 4.1.1. Cyclic contact fatigue tests. Figure 2 shows plots of s(n) data for each material/environment system, for indentations at speci®ed sphere radius r, at two selected loads P. In each case the two loads are selected so as to straddle the single-cycle cone crack threshold value, P1 (see Table 1, later). Gen￾erally, at the higher of the two selected P values the strength is substantially degraded within the ®rst cycleÐin this case, failures originate from indenta￾tion sites at all n. At the lower of the P values the strength shows no degradation initially, correspond￾ing to failures away from the contact sites at natu￾ral ¯aws (indicating that any initial ¯aw extension prior to ring-crack instability is too minor to degrade the strength); but beyond a critical number of cycles (nc) the strength again declines above a critical number of cycles (n > nc). Special note may be made of the data for porcelain/water at the lower load P = 200 N in Fig. 2(b)Ðin this case P lies so close to P1 that the failures are stochastically distributed between cone crack and natural-¯aw failure origins. At higher n values the strength data show a noticeable accelerating decline. This second region becomes clearly evident after only a few hundred cycles at P = 500 N in the glass/water and porce￾lain/water systems; in the silicon nitride/air system it becomes apparent only after n1107 cycles at the comparatively high load P = 2200 N. In extreme cases the glass and porcelain specimens fail during the contact test itself (arrows). Figure 3 shows analogous s(P) results for the same material/environment systems, and at the same speci®ed sphere radius r, comparing data after prolonged cycling at speci®ed numbers of cycles (nw1) with those in single-cycle loading (n ˆ 1). These results con®rm a signi®cant degradation in strength from the cycling. In the glass/water and porcelain/water systems the cyclic data fall within the domain of the second strength decrement over the entire range of P (cf. Fig. 2), and so tend to fall beneath the predicted curve; conversely, in the sili￾con nitride/air system the cyclic data remain within the bounds of the ®rst strength decrement at all P. The solid curves in Figs 2 and 3 are best ®ts of equations (7a), (7b), (12a) and (12b) to the data in the initial degradation region corresponding to fail￾ure from cone cracks (i.e. grey symbols), using N, P1 and s1 as parameters. Vertical solid lines indi￾cate critical nc or Pc values for cone crack initiation [equations (7a) and (7b)]; the solid curves at nc > 1 and Pc > 1 represent strength degradation functions for failure from these cone cracks [equations (12a) and (12b)]. For soda-lime glass, N ˆ 17:9 is prede￾termined from previous (Vickers indentation) stu￾dies [32±34], with just P1 and s1 as adjustable parameters; for the other materials, N, P1 and s1 are all treated as adjustable parameters. The ®tted curves are consistent with the main data trends in the cone crack region, within the data scatter. 4.1.2. Cyclic vs static fatigue tests. Figure 4 com￾pares s(t) data for cyclic and static tests, again for the same material/environment systems, with the time scale for the cyclic data determined as t ˆ Gcn=f according to equation (13). Chosen values of n and P are such that degradation occurs within the ®rst cycle. In the region of the ®rst strength decrement the data overlap, within the scatter bars. However, in the region of the second strength decrement the cyclic data diverge markedly below Fig. 3. Inert strength s as a function of contact load P, indentation with WC spheres of radius r, at number of cycles n indicated: (a) soda-lime glass/water; (b) porcelain/ water; (c) silicon nitride/air. Data points are means and standard deviations, minimum ®ve specimens per point. Filled symbols indicate failures from indentation sitesÐ grey symbols from cone cracks, black symbols from radial cracks. Un®lled symbols indicate failures from natural ¯awsÐbox at left axis and horizontal dashed line are ``laboratory'' strengths (unindented specimens). Solid curves are theoretical ®ts to data. 4716 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS