5.4.1 Introduction
The merits of Hertzian fracture studies were described earlier.
Briefly these were twofold. Firstly, because of the small amount of
material required to perform indentation studies it is possible to
perform a greater number of tests them using conventional 4 point
loading. Secondly because the stress field is inhomogeneous a wider
range of defect depths would be observed emd so the distribution of
flaws could more satisfactorily be studied.
In performing Hertzian fracture studies, the fracture event,
because it is a microscopic event,is less easily observed them in
conventional testing. The restrictions therefore on testing conditions
and testing technique are more severe and hence it was decided to
carry out Hertzian fracture studies under conditions of room temperature
and a relative humidity of 60% which is comparable to the conditions
used for 4 point bend studies.
5.4.2 Experimental
The apparatus initially available for Hertzian fracture testing
had previously been described by Chlebik, Adams and McMillan (1977).
The apparatus had been originally designed for testing opaque materials
and had used a transparent corundum indenter. However in carrying out
preliminary studies it was observed that the corundum indenters
themselves were damaged after approximately 150 indentations. Since
it was felt that using a single indenter for all the tests was an
important factor in minimising possible spurious effects, an indenter
of an alternative material was sought.
Tungsten carbide spheres were obtained in a range of sizes and
the test configuration was inverted such that a 4mm diameter sphere was
now mounted on the moveable loading system and the specimen was
stationary.
The Hertzian fracture testing apparatus in this "inverted"
configuration is shown in Figure 5.10. The important parts of the
test equipment are: the loading system, the indenter, the specimen
and its mountings and the optical system for observing the fracture
event.
The loading system consists of a piston and cylinder arrangement
constructed of aluminium with the indenter held on a brass support
plate above the central axis of the piston. Load is applied by
introducing nitrogen under pressure to one side of the piston whilst
Microscope
the other side is at atmospheric pressure. Pressure is supplied
from commercial gas cylinders containing nitrogen with a regulated
outlet pressure of 0.345 MPa (SO psig). This pressure is then
further regulated b y means of a constant pressure relief valve, which
is driven by a small electric motor which, was fitted with a dial
pressure gauge accurate to ± 0.003 MPa.
Calibration of the loading system was carried out by placing
the entire loading assembly onto the base of a 5 K N "Instron" tensile
testing machine. The load cell, whi c h was mounted in the base of the
crosshead, was then driven downwards until it was just above the
loading piston. Th e motor for the pressure valve drive was then
started, and a record of the load/time history was obtained. The
load/time history indicated that the rate of loading was 2.9 Ms 1
and linear up to a maximum load of 450 N.
The optical system used to obtain the indentation process consists
of a "Vickers" binocular microscope to which had been fitted a
10X vernier eyepiece and a 3X objective lens. The formation of a
Hertzian ring crack was observed through the base of the specimen
and through a piece of 6css thick plate glass. The image observed was
greatly improved b y the application of a thin film of silicon grease
between the plate glass and the base of the specimen. Calibration
of the optical system was carried out by placing an electron microscope
specimen—mounting grid between the indenter and the test specimen.
The spacing between five grid wires was then measured using the
vernier eyepiece. The spacing of the five grid wires was also measured
using a travelling microscope with an accuracy of ± 0.01mm, giving
a theoretical precision of ± O.00167mm per division of the vernier
eyepiece. However, in observing a ring crack the diameter could
not be accurately measured to better them ± 3 divisions on the
vernier eyepiece.
Specimens for Hertzian fracture studies were initially prepared
by cutting rectangular parallelepiped blocks, 5Ctam x 25mm x 8mm,
from a large block. The two large surfaces were then polished to
a 1 ym finish using the techniques previously described in Chapter 4,
Prior to abrasion, specimens were stored in an evacuated dessicator.
The technique used to abrade these specimens was very similar to that
described for four point bend test specimens. The two differences
in specimen preparation technique were: first, two specimens of
different glasses were glued to opposite side of the jar and abraded
simultaneously. The second difference in preparation technique was
that the Hertzian fracture test specimens were not etched in
hydroflouric acid because of the experimental difficulties introduced
when etching was attempted.
Etching of some Hertzian fracture specimens was tried, however
it introduced two experimental difficulties. Firstly the etching
process degraded the optical finish of both surfaces of the specimen
so making observation of the microscopic fracture event much more
difficult. Secondly the etching process introduced pits which were
significant in comparison to the indentation stress field, and
resulted in the formation of crescent shaped cracks which are
indicative of a misalignment between indenter and specimen surface.
C l e a r l y the fact that: It proved Impossible to use the same
abrasion process for Hertzian fracture and four point bend studies
can lead to difficulties in the analysis of the results obtained
and this point will be discussed In Chapter 3.
A f t e r abrasion the two specimens were removed from the glass
jar and washed In acetone. The unabraded face of each specimen was
then covered in a thin film of silicone grease and the specimens
pressed b y their edges onto the plate glass specimen support.
Indentations were then performed on alternate specimens at the loading
rate of 2.9 N * 1 and loading stopped the moment a fracture event
was observed. The pressure at fracture and the diameter of the
ring crack were then recorded. It should be noted however, that the
fracture "event" was not always a perfect ring crack which then
developed into a cone crack. Occasionally it was observed that the
crack,once originated, would propagate down into the bulk of glass
before slowly becoming a full circle in direct contradiction of the
theories proposed b y Langitan and Lawn C1969). This effect was
observed on all the glasses tested and the frequency of occurrence
of this type of event did not appear to have any systematic
relationship to glass composition. In all, approximately 25-35
indentations were performed on each specimen. Care was taken to
ensure that the test locations were at least 2smt apart which Is over
tbree times a typical diameter of contact, 0.5mm.
Humidity could not be controlled in the Hertzian fracture experiment because of the restrictions that atmospheric control
Imposed on the specimen handling. However atmospheric humidity
was measured using a horse-hair hygrometer and testing was only
carried out when the atmospheric humidity was 62 ± 3% R.H. Because
humidity could only be monitored rather than controlled two specimens
from different glasses were tested over the same time period by
performing indentations on alternative specimens.
In all, at least three specimens of each glass were tested resulting
in a minimum of 60 indentation results for each glass. The method
of analysis of the results and the results themselves will be 7
reported in Chapter 7.
CHAPTER 6
OTHER EXPERIMENTAL STUDIES
6. 1 INTRODUCTION
In this chapter the experimental studies other than the mechanical
strength studies are described. A necessary part of the evaluation
of Hertsian fracture strength is the definition of the stress
field. In order to use the equations given by Johnson et al (1973)
which describe the Hertzian stress field under no-slip and
complete slip conditions it is necessary to know the elastic
constants and the coefficient of static friction. In addition,
experiments to examine the structural role of hydroxyl ions are
described.