JOURNAL OF MATERIALS SCIENCE 19 (1984) 254_258 Hertzian ndentation f sintered lumina M . T . LAUG E R Sandvik Limited, Hard Materials Research Centre, PO Box 109, Coventry, JK Hertzian ndentation xperiments ave ee n performed n sintered -Alro, using WC-Co spheres ith radii n the range .5 o 6.5 m m . The critical oad P * t o cause i n g cracking as proportional o indenter adius 9 which s consistent ith Auerbach's a w. Values f room emperature racture urface nergy, , a n d racture oughness, 16 , w€r€ derived sing he heories f Frank and Lawn and Warren. 1 . Introduction Early work on Hertzian indentation-induced fracture of brittle materials ended to focus on th e empirical result known as Auerbach's Law [1 which states hat the ratio of the critical oad to produce a ring crack to the radius of the in - denter is constant. In conjunction with Hertz's [ 2 ] equations t o b e presented ater), Auerbach's la w implies that the maximum tensile stress at fracture is not constant but increases s R-1/3 where R is the indenter adius. Developments n Hertzian ndentation theory, based on the Griffith [3 ] energy balance riterion, have ed to improved understanding f ring crack formation in brittle materials and this has ed to a convenient method for the determination of fracture surface energy, 7, and racture oughness, Krc. A brief account of these esults s provided below. When a spherical ndenter s loaded against he flat surface of an elastic solid, a symmetrical tress distribution s se t up in which th e principal stresses ar e compressive n a tear-drop shaped region beneath he indenter o a depth of the order o f the contact diameter. Outside he contact region, th e greatest tress omponent s tensile an d reaches it s maximum value on the surface of the solid on the circle of contact. This tensile stress ecreases rapidly in magnitude with both pistance z from th e surface an d with distance along he surface. Along the surface he stress s radial an d may be wrilten f2,41: o(Y,z:o) +2P'PY zTa- I 1 ' where . 4kPR u- 3E and s | trl k: _ l(l_/r)+(1 _v")+l 1 6 L ' ' E ' l where P is the normal load, a is the radius of the circle of contact, R the radius of the indenter, E, E and v,vr are the Young's moduli and Poisson's ratios of the sample and indenter, respectively. Th e loading geometry is illustrated in Fig. . Ring cracks ar e ormed at a critical oa d P* an d generally t is found that the ring crack radius is slightly greater ha n th e contact radius a. Initially th e crack is almost normal to th e sample surr%ce, bu t under increased oading it extends along a conical surface in a stable fashion remaining almost normal to the traiectorv of maximum tensile stress. Th e basis fo r a fracture mechanics reatment of Hertzian ring cracking has been the use of an expression or the stress ntensity factor of an internal crack of lengLh 2c in an infinite plate subjected o a variable normal tensile stress long its length. A general expression educed by Warren [ 5 ] fo r th e critical load P" to form a ring crack from pre-existing laws o f size is: pkRT a D- tc - lo(.)l-' (l-v2)c where O(c) represents n integral of the variable applied stress over th e crack length c, and p is a 254 0022-2461184 03.00 , 1 2 @ 1984 Chopman nd Hall Lrd.
