The orientation of the Hertzian cone crack in soda-lime glass formed by oblique dynamic and quasi-static loading with a hard sphere

Abstract

High speed photographic studies, made at a framing speed of 10 6 frames per second, of the oblique impact of 2 mm diameter tungsten carbide spheres on blocks of soda-lime glass are described. The oblique impact causes sliding, which has a very marked influence on the orientation of the Hertzian cone crack with respect to the surface normal. An explanation of this effect is also provided. Similar observations are made from oblique quasi-static loading experiments.

Dynamic fracture of inorganic glasses by hard spherical and conical projectiles

“…in the direction of the impact) of the skirt of the cone crack makes a considerably larger angle to the impacted surface than does the rear part of the skirt of the cone crack. This orientation has been found to be similar to the orientation of the Hertzian cone crack in a block of soda-lime glass when the latter is loaded at an oblique angle quasi-statically [34]. As explained in §4, this type of crack orientation is a result of the geometrical coverage of the front part of the surface ring crack with the contact disc and the uncovering of the rear part of the ring crack due to the sliding of the impacting sphere.…”

“…The high-speed photographic sequence presented in figure 8 shows the inclination of the Hertzian cone crack being opposite to the suggestion made in [33]. As suggested by us earlier [34], the orientation of the cone crack is controlled by the fact that, after the formation of the ring crack under the impacting sphere, the contact disc between the sphere and the glass surface covers more and more of the front part of the ring crack owing to the sliding and at the same time the rear part of the ring crack will be covered less and less by the contact disc. This means that the front part of the Hertzian cone crack will grow along steeper stress trajectories than the rear part of the cone.…”

Ballistic impact studies of a borosilicate glass

“…It is possible that a radiograph taken very early on in the process (say 3 s) might have shown cone crack formation as with the studies by Chaudhri & Chen [18] of oblique impact of glass blocks by spheres, but any such features have been obliterated by 40 s, if they ever existed.…”

“…For the case of a failure front propagating in a glass rod, Radford and coworkers found that for sufficiently high impact stresses the failure front propagated at a limiting velocity of 2c s [15] consistent with a suggestion by Rosakis and co-workers [16] that a single shear crack in an infinite medium could propagate at this velocity. However, in a later paper Willmott & Radford [17] found matters were more complex than this in that the velocity of failure fronts in glass rods above impact pressures of about 2 GPa were Instead, studies of the interaction of spherical impactors and indenters with glasses shed more light on the nature of the flattening behaviour of the failure front [9,11,14,18,19] . One phenomenon which is commonly seen is the Hertzian cone crack [18,20,21] .…”

“…However, in a later paper Willmott & Radford [17] found matters were more complex than this in that the velocity of failure fronts in glass rods above impact pressures of about 2 GPa were Instead, studies of the interaction of spherical impactors and indenters with glasses shed more light on the nature of the flattening behaviour of the failure front [9,11,14,18,19] . One phenomenon which is commonly seen is the Hertzian cone crack [18,20,21] . Hertz [22][23][24] first analysed the elastic stresses involved and found that the tensile stress has a maximum at the edge of the contact area and falls off with increasing radial distance.…”