Abstract
It is well established that measurements of the dynamic mechanical response of materials are susceptible to errors due to the inertia of the specimen, which causes stresses in addition to the intrinsic material strength. A number of authors have derived equations for these stresses in compression experiments; these equations can be used as a guideline for good specimen design. However, no such equations have been presented in the literature for the equivalent effects in tensile experiments. This paper begins by considering and rationalising the equations available for compression, before producing a set of equations which can be used in design of specimens for, e.g., tensile Hopkinson bar experiments.
Highlights
It has long been known in the high rate testing community [1, 2] that the apparent strength of any test specimen is a combination of the intrinsic material strength, and any effects due to specimen inertia
Because the shoulders deform less than the specimen, it is likely that the inertial stress in the shoulders is less than σi, and there is potential for the shoulders themselves to yield if the reduction in σi is not sufficiently countered by an increase in radius
Equations have been derived for the effects of specimen inertia on the observed mechanical response of dog-bone specimens under dynamic tensile loading
Summary
It has long been known in the high rate testing community [1, 2] that the apparent strength of any test specimen is a combination of the intrinsic material strength, and any effects due to specimen inertia. The calculations can be divided into two categories: those which use an energy based approach, and those which use calculations of the stress-field in the specimen. Both approaches require some approximations to the behaviour of a real specimen. This paper will begin by examining the different equations derived for compressive inertia, reconciling the different expressions obtained by the energy and stress based approaches. Extending the energy based analysis, expressions will be derived for the effects of inertia in a tensile experiment. Point masses will be added to mimic the ends of a dog-bone tensile specimen, before moving to an analysis which considers a more realistic specimen geometry
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