Analysis of Dynamic Bending Using DIC and Virtual Fields Method
The present work is aimed to analyze the dynamic bending response of a copper specimen. The specimen is impacted in a three point bending configuration using a Hopkinson bar apparatus. The impact force is measured by the use of two piezoelectric load-cell
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Analysis of Dynamic Bending Using DIC and Virtual Fields Method Behrad Koohbor, Addis Kidane, Michael A. Sutton, and Xing Zhao
Abstract The present work is aimed to analyze the dynamic bending response of a copper specimen. The specimen is impacted in a three point bending configuration using a Hopkinson bar apparatus. The impact force is measured by the use of two piezoelectric load-cells located behind the supports of the three point bending fixture. Dynamic deformation response of the specimen is studied and analyzed through the use of ultra-high speed photography in conjunction with digital image correlation. To do this, an ultra-high speed HPV-X camera is utilized to capture images of the specimen during deformation time at a frame rate of 106 frames per second. Full-field distributions of in-plane displacement and strain components are studied and used to calculate the strain rate and acceleration distributions in the specimen. An analytical approach based on the Virtual Fields Method (VFM) is then implemented which allows for the calculation of inertia forces developed in the specimen. In addition, the method of virtual fields is used in this work to identify the rate-dependent constitutive response of the material at plastic deformation regime. Keywords Digital image correlation • Hopkinson bar • Ultra-high speed camera • Virtual fields method • Dynamic bending
17.1
Introduction
Several mechanical testing procedures have been devised over the past century to enable the study and characterization of the mechanical behavior of materials at high strain rate loading conditions. Kolsky or split Hopkinson pressure bar (SHPB) is one of the most common apparatuses in this area. However, there are certain limitations associated with the use of SHPB. Such limitations are basically the results of simplifying assumptions in extracting the dynamic constitutive response of the specimens tested in SHPB [1]. The most significant of these limitations are the restriction of the test procedure to uniaxial loading conditions, as well as the assumption of stress equilibrium within the specimen. The latter becomes even more important as the applied strain rates are increased and/or the dynamic response of a low impedance material is to be investigated [2–4]. In such cases, the accuracy of the results obtained from conventional test procedure may not be assured unless “inertia effects” are incorporated in the analysis [5]. Direct measurement of inertia force and its resultant stress has been extremely challenging, if not impossible, from an experimental standpoint. Hdowever, recent advances in the fields of high speed photography and full-field measurements have facilitated an accurate means for direct quantification of inertia effects in dynamic testing of materials [6–9]. In light of this, the present work aims to employ the recently developed ultra-high speed HPV-X camera to study the fullfield deformation response during central impact of a three-point bend copper specimen. The impact tests were carried out in a Hopkinson
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