Elastoviscohysteresis constitutive law in convected coordinate frames: application to finite deformation shear tests

Abstract

The aim of this contribution is to present a theoretical and numerical model applied to the ®nite deformations of elastoviscoplastic metallic materials at room temperature. The constitutive equations are integrated numerically in the context of a ®nite element formulation and numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms. The model is then compared to experimental results obtained from shear tests of a mild steel for various strain rates. Model predictions show a general agreement with experimental data for monotonic and cyclic conditions on this particular material and reproduce correctly the fast plastic loadings and unloadings in the large deformation ®eld. IntroductionThe prediction of the strength of structures subjected to fast mechanical loadings requires an accurate modelling of the real behavior of the material. Moreover when the loadings include cyclic or large deformations, it is necessary to take into account, not only the monotonic and cyclic hardening effects but also the strain rate dependence, even at room temperature.In the case of mild steels, while a great number of experiments have been performed on the cyclic dynamical behavior in tension or in compression (Favier et al., 1989b), it appears that the behavior concerning other simple mechanical tests in the large deformation ®eld is not as well-known. In this case, shear tests appear to have several advantages. Firstly, both shear and tensile samples can be machined from the same plate material form. Secondly, shear tests enable cyclic or reversed deformations to be carried out. Finally, the deformation can be considered as homogeneous throughout the shear gauge section; actually near the free ends of the sample, boundary effects disturb the strain homogeneity, but it has been shown that these effects may be neglected by using a long and thin shear zone (Rauch and G'Sell, 1989).In general, the theory of viscoplasticity takes into consideration the rate-dependent material behavior with equilibrium hysteresis and incorporates all macroscopically observable phenomena. At this time, several models have been developed and applied for viscoplastic materials, which can be divided in three main approaches. The ®rst approach is based on the classical decomposition of the inelastic strain into a plastic strain and a viscoplastic strain (Perzyna, 1966). The second approach, which corresponds to a uni®ed theory, uses only one inelastic strain (Bodner and Partom, 1975;Chaboche, 1989), is built on the framework of thermodynamics with internal variables (Sidoroff, 1975). This approach is based on the superposition of elementary hardening rules (Nouailhas, 1989) and the superposition of isotropic and nonlinear kinematic rules constitutes its basic formulation (Lush et al., 1989). Additional effects such as plastic strain range memory or recovery, justi®ed on the basis of experimental results and microstructural considerations, are introduced by using new variables or modifying the basic ones. Finally, ...

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“…A shear device developed for metallic sheets is used [31,33]. Samples are rectangular and the dimensions of the gauge area are 4:5 Â 50 Â 1 mm (Fig.…”

Mechanical Properties Involved in the Micro-forming of Ultra-thin Stainless Steel Sheets

“…The simple shear tests were carried out with a dedicated device developed in the laboratory, [44] which was installed on a Instron 8803 testing machine, with the DIC system to measure the strain field. Rectangular specimens of dimensions 28 9 18 mm 2 were cut directly in the band length.…”

Anti-Buckling Device for Ultra-Thin Metallic Sheets Under Large and Reversed Shear Strain Paths

“…The tightening force is controlled by a torque wrench and set by the trial-and-error method to the value 1.25 Nm. The positioning of the support in the shearing device [26,28] is presented in Fig.2 and corresponds exactly to the distance between both grips of the machine.…”

“…The device, presented in detail in [26,28] is directly connected to a tensile test machine. Samples are rectangular with a length of L = 30 mm and a width of l = 15 mm.…”

“…Planar simple shear tests become a common practice in the characterization of metallic material in sheet form [26][27][28]. Unfortunately, the large gauge-width to thickness ratio of classical devices, the width of which is necessary to reach a sufficient accuracy in the strain measurement, and the non-homogeneity of shear deformation in ultra-thin sheet leads to unwanted side-effects such as the development of out-of-plane buckling of the sheet [29].…”