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TECHNICAL PAPER COLLECTOR’S EDITION

where r and θ are polar co-ordinates with an origin crack tip. If the specimen is large enough then the
at the crack tip. zone of stress disturbance can be considered to be
surrounded by an area in which the stresses are
An important aspect of this equation is that substantially in accordance with the ideal stress
the function f(θ) depends only on the material distribution of the type given by equation (1).
properties and not on the specimen or loading Under these conditions, linear fracture mechanics
geometry. Consequently it is reasonable to will apply. In other words, the crack propagation
formulate the failure criterion for crack propagation load can be based on linear fracture mechanics if
in terms of the load- and geometry-dependent the specimen is sufficiently large.
term K , the stress intensity factor. This failure
I
criterion may be written simply as CONCRETE FRACTURE TESTS

Various investigators have carried out tests
intended to evaluate the fracture toughness
of plain concrete, i.e., K or G IC l,2,3 . The results
IC
where K , the critical stress intensity factor, is of these tests have generally been somewhat
IC
a material property much the same as modulus disappointing. Kaplan reported flexural tests on
of rupture or crushing strength are material 3-in (75-mm) and 6-in (150-mm) prisms containing
properties. pre-formed cracks of various depths. The values of
fracture toughness determined from these tests
An alternative, but mathematically equivalent, were found to vary markedly with specimen size
failure criterion can be expressed in terms of the and the method of evaluation. Welch encountered
strain energy release rate G as similar difficulties with flexural tests on 4-in (100-
I
mm) prisms and used refined experimental
techniques to determine the amount of ‘slow crack
growth’ during the experiments. In the discussion
of Kaplan’s paper, Blakey and Beresford observed
where for plane stress
that the failure stress based on the net section was
consistent with the expected modulus of rupture
for the concrete, thus casting doubt on the validity
of the fracture mechanics approach. In this paper,
or for plane strain it is shown that the difficulties encountered in
previous tests were simply a consequence of
testing specimens that were too small.

In this study the stress intensity factor is preferred The specimens used in this investigation were of
because of the difficulties in assessing the the geometry shown in Fig 1. For such a specimen
appropriate values of modulus of elasticity to be the stress intensity factor is given by the equation
used in equations (4) and (5).

The validity of the failure criterion in equation
(2) depends upon the extent of microcracking or The function g was evaluated specifically for the
inelastic behaviour, or non-homogeneity near the geometry of the specimen and loading by means

34 The Indian Concrete Journal | November 2018