Radial median crack

Figure 7. Optical micrograph of a Vickers hardness impression and the radial/median cracks generated on the corners of impression on the polished surface of a dental porcelain (a), and schematic image showing the dimensions a and c used to calculate the hardness, H V, and fracture toughness, by indentation fracture (IF) method...

Figure 9. Schematic images of radial/median cracks generated at the corners of Vickers impression (a) before ion exchange, without residual stresses and (b) after ion exchange, indicating the shortening of the cracks due to the residual compressive stress fields (indicated by arrows)...

Concerning the indentation fracture patterns, two different behaviors may be distinguished the so-called normal glasses tend to develop the radial-median crack... 

The method is illustrated in Figure 8.28 for Vickers-induced radial-median cracks in a glass beam under four-point bending. The Vickers mark is orientated so that the crack parallel to the smaller side of the beam develops imder the applied tensile stress um that is maximum at the indented surface and along the longer beam side. 

In a first step, a radial-median crack is introduced under a force F. Its extension is given by (supposing residual stresses are null)... 

Fig. 6.2.10. (a) A schematic diagram of the composite block illustrating the grain orientation and the indentations Q and R respectively, along and away from the bulk interface, a—a. (b) A schematic diagram of flow lines in the porous zone, pz, and radial, median and lateral cracks, rc, me and 1c respectively within the deformed zone. (After van der Zwaag et al., 1980)... 

Figure 8.86 Schematic illustration of radial and lateral crack formation a) and b) no median crack nucleated c) radial cracks (R) form during unloading and d) lateral cracks (L) form close to complete unload.

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. 

Table 5.2. Critical Loads for Generation of the Critical Sized Cracks on Radial, Median, and Lateral Systems...

Lawn, Marshall, and others have emphasized the fact that the residual stress term was not just a correction factor but played the important part in determining the final size of the radial crack system. However, like Evans and Charles, they developed the model of the plastic deformed zone acting to force open the penny-shaped median crack just beneath it, so that the basic equations to be used were still... 

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. 

There has been some discussion as to whether these cracks always precede the formation of the median crack in ceramics and therefore are evident before the penny median can become the halfpenny radial. An answer to this query is important because if they do always occur first, then surface flaws are important in their formation and subsequently in the mechanical failure, erosion, and wear of ceramic materials. Furthermore,... 

In equation (5.66), fl is a crack-geometry factor—that is, an experimental parameter which reflects the fact that the cracks are formed close to a free surface, that because of the demands of crystal structure the profile of the radian or median cracks may be noncircular, and that there is mutual interaction between radials and median cracks that are simultaneously formed. 

As stated in Section 5.2.1.4, when considering Palmqvist cracks, ceramics can produce shallow radials without prior formation of median cracks, and then a new stress distribution is used to anticipate this situation such that L in equation (5.80) becomes 1.577a the result is that equation (5.81) is rewritten as equation (5.83) while the critical flaw size is left as equation (5.82) describes... 

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. 

The cracks observed around the groove were mainly surface chips or radial(chevron) cracks. There was no median crack beneath the groove. Figure 12 shows the cross section of the scratch groove in soda-lime glass. For the other glasses, no median crack can be also observed in the cross sections. 

Sharp indenters like Vickers diamond pyramids produce two basic types of crack pattern (i) the radial-median system and (ii) the lateral one (Figures 8.15 and 8.16). 

Figure 8.1 S Radial median fracture under a iarge enough ioads are used, iaterai cracks...

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 three attrition mechanisms are in turn governed by different failure modes brittle, semibrittle, and ductile (Ghadiri, 1997). Brittle failure occurs when internal or surface cracks already exist and is dominant at low elastic deformation at the powder contact surface (Shipway and Hutchings, 1993). Semibrittle failure, at limited plastic deformation, is responsible for flaw initiation and occurs when the impact forces surpass the yield point. In fact, median and radial cracks cause particle fragmentation, and lateral cracks cause chipping. Soft materials are usually ductile and the mechanisms for particulate solids under ductile mode have not yet been elucidated (Ghadiri, 1997). 

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... 

---