Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

Abstract

It is well known that a specimen for impact testing must be optimized in terms of its dimensions. The main reason is to reduce strain gradients due to the effects of elastic plastic wave propagation. On the other hand, when a split Hopkinson bar in tension is applied, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach a maximum strain of 0.5 the specimen length must be reduced in dimensions from 4.0 to 6.0 mm. Consequently, small diameters or lateral dimensions and lengths must be applied to assure one dimensional deformation. Such small lengths substantially perturb the determination of real material behavior. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in the behavior of short and long specimens loaded in impact tension. The finite element code ABAQUS/Explicit has been used to simulate several spec imen lengths from 10 to 40 mm submitted to impact velocities ranging from 10 to 100 m/s.Keywords: Constitutive relation; Dynamic tension; Normalization; Plastic instability; Numerical simulations Thermoviscoplastic modelingTo study the dynamic processes of plastic deformation in sheet metals, a well defined constitutive relation has earlier been proposed. Several processes of fast deformation have been previously studied by applying that relation: perforation [1], double shear by direct impact [2], the Taylor test and fast tension test [3]. With the constitutive relation, Eq. (1), the effect of temperature and strain rate on the flow stress can be studied and analyzed. It is clear that the adiabatic increase of temperature has a substantial effect on the flow stress and it induces a decrease in the ultimate tensile stress. In order to describe precisely the behavior of materials at high strain rates and temperatures, the equivalent stress r needs to be taken as the sum of two components r l and r * which are, respectively, the internal and the effective stress. The first component is directly related to the strain hardening of the material and the second defines the contribution due to the thermal activation (a combination of temperature and strain rate). The constitutive relation can be written in terms of equivalent scalar quantities:where e p is the equivalent plastic strain, T is the absolute temperature, E 0 is the YoungÕs modulus at T 0 K and E(T) is the evolution of the modulus as a function of temperature. Eq. (1) is based to some extent on physical considerations [2]. The explicit expressions for both stress components are given below:where Bð _ e p ; T Þ and nð _ e p ; T Þ are the modulus of plasticity and the strain hardening exponent, respectively. These quantities, defined by Eqs. (3) and (5), respectively, take into account the experimental observations that the strain hardening itself depends on temperature and strain rate.

Dynamic Necking of Notched Tensile Bars: An Experimental Study

“…3 show that when the incident velocity remains equal or smaller than 15 m/s, the neck forms on the impacted side, whereas at higher velocities, it now forms on the opposite side. This trend has been found and thoroughly discussed by the authors in previous works [19,20]. The location of the neck is dictated by the loading velocity, which in turn controls the processes of propagation and interaction of stress waves.…”

“…For this specimen (# 14), fracture indeed occurred in the notch but a second diffuse neck was clearly observed on the opposite side, as would be expected for a smooth specimen tested at a similar velocity (within the higher velocities tested). Such observations are quite rare, from an experimental point of view, although they can be predicted by numerical simulations [20,23]. One can therefore postulate that the "expected" location of the diffuse neck in specimen 14, together with the apparent lack of consistent pattern for specimens 11-14, all suggest some variability in the notch depth as reported in Table 2.…”

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

“…6 c, a difference between experiments and simulation takes place. This discrep ancy may be related to perturbations on the testing velocity at the beginning of the experiment related to inertia effects fre quently observed in high rate tensile testing (Rusinek et al, 2005). Such perturbation of the applied velocity, which is not considered in the simulation, may induce strain rate history effects (structure evolution) on the material behavior (Klepaczko and Rezaig, 1996) that affect the final elongation of the sample.…”

Experimental issues and interpretation of the necking phenomena in the dynamic characterization via Hopkinson bar

“…Sato et al [3] also evidenced the necking-induced progressive departure of the local true strain from the engineering strain, as it was also shown in Mirone [4] in terms of strain rate. When the strain measurements in SHTB experiments are only based on strain gauge readings, without speed camera image analysis, also the length of the specimen may greatly affect the calculation of a Corresponding author: gmirone@dii.unict.it the engineering strain, as also Rusinek et al [5], Osovski et al [6] and Rodriguez-Martinez et al [7] pointed out.…”