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.

The generation of residual stresses in orthogonal machining is analysed by using an Arbitrary Lagrangian Eulerian (ALE) finite element approach. It is shown that a substantial level of tensile residual stresses can be obtained in the vicinity of the machined surface without any contribution of thermal effects. This motivates the development of a parametric study to analyse the effects of the thermomechanical coupling parameters on residual stresses. The roles of thermal expansion, of thermal softening and of the Taylor-Quinney coefficient (controlling the heat generated by plastic flow) are considered separately. The influence of friction is also analysed by assuming dry cutting conditions and a Coulomb friction law. The friction coefficient has a complex effect by controlling heat generation (frictional heating) along the tool rake and clearance faces and the propensity for the chip to stick to the tool. Geometrical effects such as the tool rake angle and the tool edge radius are also discussed.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. The response of the tool-chip interface is characterized in the orthogonal cutting process by numerical and analytical means and compared to experimental results. We study the link between local parameters (chip temperature, sliding friction coefficient, tool geometry) and overall friction characteristics depicting the global response of the tool-chip interface. Sticking and sliding contact regimes are described. The overall friction characteristics of the tool are represented by two quantities: (i) the mean friction coefficient qualifies the global response of the tool rake face (tool edge excluded) and (ii) the apparent friction coefficient reflects the overall response of the entire tool face, the effect of the edge radius being included. When sticking contact is dominant the mean friction coefficient is shown to be essentially the ratio of the average shear flow stress along the sticking zone by the average normal stress along the contact zone. The dependence of overall friction characteristics is analyzed with respect to tool geometry and cutting conditions. The differences between mean friction and apparent friction are quantified. It is demonstrated that the evolutions of the apparent and of the mean friction coefficients are essentially controlled by thermal effects. Constitutive relationships are proposed which depict the overall friction characteristics as functions of the maximum chip temperature along the rake face. This approach offers a simple way for describing the effect of cutting conditions on the tool-chip interface response. Finally, the contact length and contact forces are analyzed. Throughout the paper, the consistency between numerical, analytical and experimental results is systematically checked.