Dynamic Strenth Measurements on Granite and Basalt

Small samples of rock, like those used in laboratory collision experiments, are known to be much stronger than bodies that are meters to hundreds of meters in size [1]. Specifically, the impactor energy per unit target mass needed to shatter the target decreases dramatically with increasing target size. This occurs because the strength of rock, like many other geological materials, depends strongly on the duration or rate of loading. In small impacts, where the loading rates are high, the material is quite strong and requires a high energy per unit mass to shatter it. In large impacts, the loading rates are low, the material is relatively weak and the energy per unit mass for shattering is correspondingly reduced. Thus, the interpretation and extrapolation of lab collision experiments to asteroid collisions is directly connected to the relationship between strength and strain rate. In fact, the scaling of collisional outcomes with event size is directly related to the rate-dependence of strength [1,2]. Therefore, one may gain insights into the scaling of collisional outcomes by studying the strain rate dependent strength of rock. Measurements of the dynamic strength of rock have been reported previously [3-5]. However, the materials used were generally not the same as those used in collision experiments. In the present study, strength measurements are made on the same granite [1] and basalt [6] used in previously documented collision experiments. Experiments: The dynamic tensile strength is measured here using a dynamic version of a conventional Brazilian, or splitting test, in which a cylindrical sample is compressed along a direction perpendicular to the cylinder axis. This loading condition produces a state of nearly uniform tension that splits the specimen across its diameter. The tensile strength is calculated as 2F/πDL, where F is the compressive force at failure, D is the specimen diameter and L is its length. The dynamic Brazilian test is performed in a Split Hopkinson Pressure Bar, schematically shown in Figure 1. An impactor strikes the input bar, generating a compressive wave that loads the specimen in the configuration of a standard Brazilian test. Part of the compression wave is transmitted through the specimen into the output bar. A strain gage on the output bar measures the compressive loading from which the load at failure is calculated using the standard Hopkinson Bar analysis methods. A strain gage on the specimen directly measures the loading strain rate, as the standard methods for calculating specimen strain in a Hopkinson Bar test do not apply in this case. Thus, each test produces a value of the tensile failure strength and the loading rate.