Median-radial cracks, indentation

Lawn B. R., Evans A. G., Marshall D. B., 1980, Elastic-plastic indentation damage in ceramics. The median/radial crack system, J. Am. Ceram. Soc., 63, (9-10), 574-581. 

Fig. 6.2.9. Indentation /strength model system, (a) Vickers indenter, peak load P, generates median/radial crack, characteristic dimensions (value c0 at completion of contact cycle, with further post-indentation, supercritical extension to c0, if exposed to moisture), (b) Tensile field a in combination with residual ( ghost ) contact field, drives crack system to failure. (After Marshall and Lawn, 1980)...

The second indentation approach to measure fracture toughness is to break indented specimens. The median-radial cracks are loaded in mode I and the indentation strength is determined. In some cases, more than one indentation crack is introduced. In this case, failure will occur from one indentation and the other indentations can be used to determine the extent of the stable growth. Equation (8.65) can be re-arranged to the form... 

Figure 8.85 Median-radial crack formed at a Vickers indentation in soda-lime-silica glass the crack shape is semi-elliptical. (Optical micrograph courtesy of Vincenzo Sglavo.)...

The indentation fracture mechanics approach likens abrasive-workpiece interactions for grinding of ceramics to small-scale indentation events. The deformation and fracture patterns observed for normal contact with a Vickers pyramidal indentor under an applied load P are illustrated in Figure 3.1. A zone of plastic deformation is foimd directly imder the indentor. Two principal crack systems emanate from the plastic zone med-ian/radial and lateral cracks. Median/radial cracks are usually associated with strength degradation and lateral cracks with material removal. 

Plastic zone, median/radial cracks (R), and lateral cracks (L) for Vickers indentation. (From Lawn, B.R. and Swain, M.V., /. Mater. Sci., 10, 113, 1975. With permission.)... 

B.R. Lawn, A.G. Evans, and D.B. Marshall, Elastic/Plastic Indentation Damage in Ceramics The Median/Radial Crack System J. Amer. Cer. Soc., 63 574 581 (1980). 

Sakai and co-workers have investigated the GCs produced by different densifi-cation processes using a Vickers indenter. The indentation hysteresis behavior was found on curves of indentation load versus indentation depth for all indentation loads from 10 to 500 N. For GCs, it was also observed that ring/cone cracks were induced by Vickers indentation instead of the median/radial crack systems more usually observed in brittle materials under a sharp indenter. A superior feature of GCs compared to ordinary brittle ceramics is their resistance to strength degradation by contact with hard particles as demonstrated by anomalous ring/cone crack formation. 

Four microcrack morphologies may develop in a brittle solid after formation of the plastic zone beneath the indent median cracks, Fig. 9a, radial cracks (a halfpenny shaped elliptical crack Fig. 9b, much larger than the median crack), lateral cracks (in a plane normal to the median and radial cracks). Fig. 9c, and Palmqvist... 

Figure 9. Cracks formed during an indentation toughness test (a) median cracks (b) radial cracks (c) lateral cracks and (d) Palmqvist cracks. Reproduced with permission of.(3).

Finally, Palmqvist cracks are short, shallow cracks, initiated at the end of the indent diagonals at relatively low loads. Fig. 9d. The plane of a Palmqvist crack coincides with the plane of the radial cracks, and there is some evidence that the Palmqvist cracks may, in some ceramics, initiate before the radial cracks, at the same time as the median crack. 

Figure 5.2. (a) Normal form of median crack with P < critical load needed to cause "pop-in and P still applied, (b) After unloading, residual tensile stress causes pop-in and development of radial crack as well as development of shallow lateral cracks on planes parallel to specimen surface, (c) Plan view of indented surface after indentation cracking, (d) Palmqvist crack formed before the median pops in as radial. 

Also referred to as median vent cracks, these are caused to pop-in by exceeding a critical indenter load. It is the pop-in phenomenon that is important to the development of this subject in ceramic science because the halfpenny crack has the surface trace which allows opaque materials to be analyzed by recording the radial crack size as a function of increasing load. There is, however, the implication that the surface must be prepared carefully by polishing to an optical finish in order to see the radial cracks. If necessary, samples must be annealed to remove polishing stresses. Radial cracks are the result of surface tensile stresses, (Xyy in equation (1.29). Such stresses are at a maximum at the elastic-plastic boundary. 

In equation (5.80) y = fracture surface energy, G = shear modulus, i> = Poisson s ratio, and L is the slip length along which shear acts. When radial cracks are formed along with median cracks, L < 1.4a where a is, as usual, the half diagonal of the indent impression. Hagan s equations for critical load and the critical flaw length such a load produces are... 

These cracks are shown in Figure 5.2(d). They are shallow radial surface cracks lying within median planes (i.e., planes containing the axis of the indenter) extending out from the corners of an indentation. Clearly when the median crack pops in, the Palmqvist cracks become part of the median-radial system described in Section 5.2.I.2. 

STEP 4. Microcracks nucleated in Step 3 develop into a penny-shaped crack below the indenter and shallow Palmqvist cracks in the surface region. These are the median and radial cracks. STEP 5. In the surface the indenter causes compression, not tension ... 

Flaws of the size estimated from equation (5.82) are the median, radial, and lateral cracks caused by indentation, and the questions are where and why do they nucleate in a noncrystalline material Examination of the deformed zone beneath an indent or an impact shows that a series of intersecting flow lines is produced. Plastic strain is concentrated on the flow lines while the material between them is only strained elastically. Median cracks arise from the need to accommodate strains at the intersections of flow lines in a way analogous to crack nucleation from dislocations on intersecting slip planes in fully crystalline materials. 

Compressive stresses are found to subdue median and radial cracking at indentation sites, but the strain energy associated with the indentation leads to enhanced lateral cracking. 

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