Abstract
This work presents a methodology to calibrate a strength model for ductile metals, based on dynamic tension tests of relatively long Dog-Bone specimens conducted on a Split Hopkinson Tension Bar (SHTB). We address the main difficulties involved in conducting and interpreting such tests, namely the duration of the loading pulse needed to deform long specimens and the non-uniform stress and strain distributions along the specimen due to neck formation. The first issue is addressed by using the waves‘ reflections within the output bar, as explained below. When the first loading (tension) wave does not cause failure of the specimen, a reflected compression wave travels from the specimen‘s bar end to the free bar‘s end. Upon reaching the free end this latter compression wave is reflected again as a second tension wave, which travels back along the bar until it reaches the specimen and loads it the second time. This enables further deformation of the specimen, practically doubling the loading pulse duration without changing the striker‘s length. The second issue is addresses by using full numerical simulations of the experimental setup, including the striker, the bars and the specimen. This way, the full dynamic behaviour of the specimen is taken into account, eliminating the need to consider specimen equilibrium and taking into account the current strain rate in the specimen as it deforms. Hence, model calibration can be done from the very start of plastic deformation and without the need to keep the strain rate constant during deformation. As a result, it is possible to reliably calibrate the strength model considering necking and neck location, as well as plastic heating which is a significant factor in the plastic deformation of ductile metals.
Highlights
The Split Hopkinson Tension Bar (SHTB) is a wellknown technique to characterize plastic flow and failure in uniaxial tension [1, 2]
Rodriguez et al [8], using finite element computations, suggest using an 'effective length' as a representative length, for which uniform strain can be assumed in a specimen, enabling the use of the classical analysis
Assuming that the strength model parameters hold approximately in tension as well, we conduct simulations to determine the setup for the tension tests
Summary
The Split Hopkinson Tension Bar (SHTB) is a wellknown technique to characterize plastic flow and failure in uniaxial tension [1, 2] With these modifications to the classical Split Hopkinson Pressure Bar (SHPB) [3], applying the classical analysis may become questionable, as the onset of necking creates a nonuniform distribution of stress and strain [4, 5]. Rajendran and Bless [6] use Bridgman's approximation [7] to obtain a stress-strain curve in dynamic tension beyond the point of necking To this end, they measure the geometry of the neck, using high speed photography. Rotbaum et al [9] suggest using long specimens, to keep the stress and strain distribution constant in a large part of the specimen prior to necking In this way they are able to use the classical analysis with minimal error, but only for plastic strains of up to 3%. Mirone [10] uses a correction to the classical analysis, which enables reconstruction of the stressstrain curve until failure, but within an error of 15-25%
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