Energy balance of brittle fracture under bulk stress state conditions

Abstract

The energy balance of brittle fracture of rock specimens is investigated in [1-3] under uniaxial compression conditions and empirical relationships are established that connect all the parameters involved. In particular, it is shown that the ratio of the energy H d expended in scattering fragments of the fractured material to the energy H k of the vibratory motions that the loading unit exhibits after fracture of the specimen is determined by the ratio of the mass m d of the fractured material to vibrating mass of the loading unit ms i.e., Hd/H k = md/ms It is established experimentally that the energy H e stored in the specimen at the strengtP limit is expended completely in irreversible processes of deformation and destruction of the specimen material and does not go over into other kinds of energy associated with the dynamics of scattering fragments or vibratory processes in the loading unit. A source of the dynamic effects during destruction is the energy Hs stored in the loading unit. The amount of the thermal energy HT in the total balance is less than one percent. For a deeper comprehension of the brittle fracture process it is necessary to study the influence oft he stress state, particularly because the rock under natural conditions is in a complicated stress state during which deformation and fracture occur. Earthquakes and rock burst are examples of such fractures. INVESTIGATION OF THE ENERGY BALANCE Before proceeding directly to an examination of the energy balance of the dynamic uncontrolled fracture process under bulk stress, attention must be turned to the difference between the deformation and fracture mechanisms of rock specimens tested at different hydrostatic pressure levels. This difference induces certain features in the process of energy exchange between the loading system and the material being fractured. Figure 1 shows diagrams of the stress AG I = a z -- ~2, the relative longitudinal El and transverse r stains of the specimen for different lateral pressures o 2 . The tests were performed on 60 mm long and 30 nml diameter cylindrical specimens. The longitudinal strain on the whole specimen was measured during the test. The transverse strain was measured using several extensometers oriented in different directions along the central part of the specimen. Graphs of Ao I - r constructed using the extensometer readings that recorded the greatesl (solid line) and least (dashed line) change in the transverse strain are shown together in Fig. i. For low lateral pressure (a 2 = 0, 10, 25 MPa), the limiting branch of the diagram is shallower than for high pressures (a 2 = 50, 100, 150 MPa) although an increase in the lateral pressure should increase the plastic properties of the material and result in a "reduction in the modulus of the drop M = dAoz/dr I. The deviation from the standard dependence in the behavior of the drop modulus in this a 2 range is explained as follows. At low lateral pressures, including o 2 = 0, a set of cracks forms in the specimen beyond the strength limit that traverse the whole specimen and which are approximately uniformly distributed over its volume resulting in great disintegration of the material (up to 10%) along with an identical strain ~2 in all the directions being measured.