Dynamic Strength and Fragmentation Experiments on Brittle Materials Using Theta-Specimens
Characterization of the strength and fragmentation response of brittle materials poses unique challenges related to specimen gripping and alignment. These challenges are often exacerbated when the characterization is to be conducted at elevated strain rat
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Dynamic Strength and Fragmentation Experiments on Brittle Materials Using Theta-Specimens Jamie Kimberley and Antonio Garcia Abstract Characterization of the strength and fragmentation response of brittle materials poses unique challenges related to specimen gripping and alignment. These challenges are often exacerbated when the characterization is to be conducted at elevated strain rates. Tensile strength of brittle samples are often characterized using the Brazilian disk testing geometry. While this ameliorates issues related to specimen alignment, the stress field in the specimen is not uniform, complicating the analysis of the test results. The theta specimen geometry was designed specifically to provide a uniform state of uniaxial stress in the specimen gage section when the exterior of the sample is subjected to compressive loading. Here we evaluate the use of the theta specimen geometry with a compressive Kolsky bar to measure the dynamic tensile strength and fragmentation response of a brittle polymer, Poly(Methyl methacrylate). Finite element simulations are used to investigate the effect of geometry and loading pulse shape on the ability to establish a state of uniaxial stress in the gage section. Particular attention is given the excitation of lateral vibrations in the gage section, which would perturb the desired uniaxial stress state. Keywords Dynamic testing • High-rate • Tension • Kolsky bar • Split Hopkinson • Theta
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Introduction
Measurement of the tensile strength using “direct” testing methods (e.g. dog-bone pull tests) presents significant difficulties with regard to specimen gripping and alignment when applied to the testing of brittle materials. The very act of gripping the specimen may introduce stress concentrations leading to preferential failure at the grip, and invalid testing results. Minor amounts of misalignment of the test specimen with respect to the loading axis can also introduce non-uniform stress state in the specimen, introducing error into the measurements. In an effort to reduce the occurrence of these errors in testing, so called “indirect” tensile test methods have been developed for determining the tensile strength of brittle materials. Most of these methods use specimen geometry to convert a compressive load into tensile stress, relying on the fact that the compressive strength of the material to be tested is significantly greater than the tensile strength. One commonly used indirect tensile test method is the Brazilian disk test, in which a disk of material is subjected to compression by diametrically opposed forces. This configuration results in the development of a tensile state of stress acting normal to the compression axis. The value of tensile stress varies with distance from the center of the specimen, and achieves 2P a maximum value σ t ¼ πDt at the mid-plane of the sample, where P is the applied load (assumed positive in tension), D is the disk Diameter, and t is the thickness of the disk [1]. While the Brazilian disk test method eliminates issues with re
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