Material characterization at high strain rate by Hopkinson bar tests and finite element optimization

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Abstract

In the present work, dynamic tests have been performed on AISI 1018 CR steel specimens by means of a split Hopkinson pressure bar (SHPB). The standard SHPB arrangement has been modified in order to allow running tensile tests avoiding spurious and misleading effects due to wave dispersion, specimen inertia and mechanical impedance mismatch in the clamping region. However, engineering stress–strain curves obtained from experimental tests are far from representing true material properties because of several phenomena that must be taken into account: the strain rate is not constant during the test, the specimen undergoes remarkable necking, so stress and strain distributions are largely non-uniform, and the temperature increases because of plastic work. Experimental data have been post-processed using a finite element-based optimization procedure where the specimen dynamic deformation is reproduced. Optimal sets of material constants for different constitutive models (Johnson–Cook, Zerilli–Armstrong and others) have been computed by fitting, in a least mean square sense, the numerical and experimental load–displacement curves.

Introduction

The interest in the mechanical behavior of materials at high strain rates has increased in recent years, and by now it is well known that mechanical properties can be strongly influenced by the speed of load application. The split Hopkinson pressure bar (SHPB) has become a widely used experimental method to determine, for several classes of materials, the dynamic stress–strain curves at strain rates that range from 102 to 104 s−1. Historically, the first who used long thin bars for measuring impact generated pressure waves, was Hopkinson [1]; later, this method was further developed by Kolsky [2]. More recently, the Hopkinson bar technique, initially focused on compression tests, has been modified and successfully applied to tensile [3], [4] and torsion tests [5]. Moreover, in addition to metallic materials that are now routinely studied, its use has been extended to many other kind of materials, such as polymers, ceramics, composites and foams. In order to study this wide variety of materials, including brittle materials [6], a lot of studies have been conducted with the aim of improving the experimental methodology and the response quality in the range of small deformations that typically is the weak spot of the SHPB technique. Anyway, also dealing with the large plastic deformations, distinctive of ductile metallic materials, a lot of work is still needed to completely understand and modeling the phenomena that are experimentally observed. In fact, as it will be shown in the next sections, the engineering stress–strain curves obtained from experimental tests are far from representing true material properties and, up to now, there is not any unified and universally accepted methodology to compute the actual material behavior from experimental data.

In this work, an experimental SHPB device has been used to perform tension tests on steel specimens. The collected data has been post-processed using an optimization procedure based on a finite element model in order to estimate the material constants for some constitutive models that are generally adopted in impact applications.

Section snippets

Theoretical background

The compression Kolsky bar, or split Hopkinson pressure bar, consists of two long metal bars. These bars sandwich a short cylindrical specimen, as schematically reproduced in Fig. 1. The free end of the first (input) bar is impacted by a projectile that usually consists in a third bar (striker bar); the compressive pulse generated by the impact propagates down the input bar into the specimen. Several reverberations take place within the specimen, causing the rise of its stress; in the

Experimental device

To perform tensile tests, the indirect tension method has been used [15]; in Fig. 2, a picture of the experimental apparatus is given together with two details of the clamping region. The threaded-ends of the impact tension specimen can be screwed directly into the Hopkinson bars or by means of two threaded collars. The first solution has been preferred because it reduces the unavoidable spurious reflections (due to mechanical impedance variation) of the first wave when it transits across the

Experimental results

With the apparatus just described, dynamic tension tests have been performed on AISI 1018 CR steel specimens; the experimental results, in terms of engineering stress–strain curves computed by formulas (2), (3), are shown in Fig. 3a, while the engineering strain rates are reported in Fig. 3b.

As outlined, different average strain rates have been achieved by using different specimen lengths, precisely 2, 4 and 8 mm with 4 mm constant diameter: accordingly to (6a), (6b), the shortest specimen

Constitutive models for the material

A variety of constitutive models exists for the representation of engineering materials behavior when the strain rate and the temperature effects cannot be neglected; their objective is to fit the experimental data such as shown in Fig. 4 with only one equation. A review of the most used models is given in [18]; in this paper some of them have been implemented.

At low and constant strain rate, and at room temperature, metals are known to work harden along a path usually described with the

Finite element optimization

Within the optimization module of the Ansys® finite element commercial code [23], the experimental tests described in previous sections have been numerically reproduced. Preliminary finite element simulations showed that the lateral extremities of the specimen remain within the elastic limit and no relevant error is committed if they are considered infinitely rigid. Accordingly to this simplifying assumption and taking advantage of the symmetrical geometry, only the “useful” part of a

Comparing results

An overview of the principal results of the FE optimization is given in the next pictures and in Table 3. In Fig. 7, the objective functions are plotted as 3D meshed surfaces with some contour lines for the two-parameter models Johnson–Cook, Klopp–Clifton and Perzyna; the local minimums at the optimal design variable values, specified in Table 3, are clearly visible. The contour lines refer to isohypses of the 3D objective function in geometrical progression starting from the minimum + 4 MPa to

Conclusions

In this work, high strain rate tension tests have been performed on AISI 1018 CR steel specimens, by means of a SHPB device; afterwards, the same tests have been numerically reproduced with a finite element commercial code simulating the large deformation process underwent by the specimens.

Analysis of the numerical results showed that the specimens are interested by widely non-uniform stress and strain distributions; moreover, different internal points of the specimen have been demonstrated to

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