Abstract
Specimens of Salem limestone were loaded cyclically at a frequency of 2 cycles/sec in uniaxial cyclic compression, tension, and compression-tension. The number of cycles to failure, maximum deformation for each cycle, and load-deformation hysteresis loops were recorded. The fatigue life and fatigue limit values under cyclic compressive loading are comparable with those under cyclic tensile loading, whereas under cyclic compressive-tensile loading they are considerably lower.
Introduction
The study of rock behavior in cyclic loading has been relatively ignored in the past, even though certain problems in rock mechanics are closely related to cyclic loading. These problems include the effects of percussive drilling and the vibrations generated by blasting. An understanding of the mechanisms of fatigue failure in rock can be expected to help improve drilling efficiency and prevent vibration damage caused by blasting.
Because of the lack of bask information on rock behavior under cyclic loading, the Federal Bureau of Mines, Twin Cities Mining Research Center began in 1968 an extensive program for studying cyclic loading effects. This program included the investigation of the behavior of rock loaded cyclically at different frequencies under varying test geometries, loading configurations, and environments. In the high-frequency range, sonic power transducers are being used to apply cyclic loading at a frequency of 10,000 Hz, and an electromagnetic shaker is being used at frequencies from 100 to 1,000 Hz. In the low-frequency range, cyclic loading of 2 to 10 Hz is applied by a closed-loop servocontrolled electrohydraulic testing machine. In each frequency range, experiments are conducted to provide the following information: fatigue limits, fatigue life, energy dissipation, temperature induced in the specimen, and the time history of load and deformation. This paper presents the first phase of be results obtained on specimens of Salem limestone loaded in the low-frequency range. The early findings on the high-frequency effects were reported separately. Recently, the effect of cyclic loading on rock behavior has been receiving more attention and considerable information is being generated.
General Loading Concept in Cyclic Loading
In conventional strength tests the monotonic loading program is specified by the loading rate and control mode. For cyclic loading, where the load is a periodic function of time, the problem is more complex. To evaluate such material properties as fatigue life, the load must be described systematically and concisely in terms of physically significant parameters. parameters. For a general case, one approach is to divide the cyclic stress into time-independent and time-dependent components. The time-independent component (or mean stress) is the time average of the stress. A cyclic stress with an amplitude A and zero mean can be superimposed on this loading. For the usual case of cyclic loading with steady loading conditions, the stress can be described as follows.(1)= + (t),
where f(t) is a periodic function of time, t, and can be represented by a sine or sawtooth wave. Other ways of describing the stress are available such as using the maximum and minimum stresses, which are related to the mean and amplitude:(2)max = .
and(3)min = .
The key issue is to describe the loading in terms that will correlate with the material properties of interest. The use of amplitude and mean stress to describe cyclic loading separates the time-dependent bona the time-independent portion of the stress because the effect of each portion of the loading should be investigated separately. In analyzing the effect of cyclic loading on rock, another significant factor is the large difference between the tensile strength and the compressive strength.
P. 19
Application of the method of asymptotic homogenization to an acoustic metafluid
