Papers by Keyword: Constitutive Equation

Abstract: The present paper aims at a theoretical study of the forming limits of a sheet metal subjected to double strain path changes by using as reference material the AA6016-T4 aluminum alloy sheet. The simulation of plastic instability is carried out through the Marciniak-Kuczynski analysis. The initial shape of the yield locus is given by the Yld2000-2d plane stress yield function. The strain hardening of the material is described by the Voce type saturation law. Linear and several complex strain paths involving single and double strain path changes are taken into account. The validity of the model is assessed by comparing the predicted and experimental forming limits under linear and selected one strain path change. A good accuracy of the developed software on predicting the forming limits is found. A sensitive analysis of the influence of the type and value of the double prestain in the occurrence of the plastic flow localization is performed. A remarkable effect of the double strain path change on the sheet metal forming limits is observed.

Abstract: The complex loading paths of non-conventional or rapid forging processes, especially as regards the important gradients of the plastic strain and strain rate characterizing the material deformation, require a reliable knowledge of the rheological constitutive equations. Some recent studies propose adequate phenomenological formulations taking into account the corresponding local physical mechanisms and the sensitivity of the true stress with respect to all mechanical variables. At the same time important scientific efforts have been focused in order to identify correctly all the constitutive law parameters, using adequate mechanical tests and robust numerical tools based generally on the inverse analysis principle. It is known that this new method requires building of a rigorous and adequate experimental space, using data obtained from loading conditions close to the industrial forming process. Then to explore high variations of plastic strain and strain rate, one of the most suitable tests are based on high speed hydraulically press and on the Split Hopkinson Pressure Bars test (SHPB). Consequently this paper propose to improve the experimental data accuracy obtained from the SHPB device by using finite element simulations of the entire high speed mechanical experiment together with the description of the inverse analysis strategy applied in order to analyze the thermo-mechanical constitutive behavior of metallic materials behavior and to identify the corresponding rheological parameters. The first part of this study will be dedicated to a short description of the experimental SHPB test analysis and to the analysis of the measurement data which can be used to describe the real mechanical loadings of the specimen. A new experimental calibration method of the acquisition signals, based on the finite element modeling of the elastic bars deformation during an impact without specimen, will be detailed. Using ABAQUS and CAST3M software, this method is validated from the comparison of the elastic strains variation obtained by the numerical simulations. In a second part will be detailed the inverse analysis strategy together with a real application concerning the rheological behavior of an aluminum alloy using a “dumbbell” specimen during a high speed upsetting test starting from a proposed constitutive relationship. Finally, special “cap” geometries of the material sample will be analyzed during a SHPB compression test in order to understand the feasibility of the proposed method to expand the material constitutive behavior identification to severe loadings. It is then shown the capacity to describe deformation path close to the rapid manufacturing processes and high speed machining.

Abstract: Incremental Sheet Forming (ISF) is able to produce highly customized products at a reasonable manufacturing cost and it has gain importance in the last years, becoming the focus of interest for many researchers and institutions. Some recent publications have revealed an increasing interest in forming thermoplastic materials. There is a tremendous amount of effort put in developing a model that may describe the equilibrium hysteresis and rate-dependence of thermoplastic materials in ISF. This paper will present a brief review of the most common constitutive equations that are able to model the behaviour of glassy polymers. It will be shown that by using a small number of material parameters defined in the Marlow model, it is possible to accurately predict experimental data collected on samples of PVC subjected to simple uniaxial test performed at room temperature. Additionally, some parts have been formed with ISF in order to verify whether the material is incompressible or not. It can be concluded that Marlow model might be used in future work to model the ISF manufacturing process.

Abstract: The flow behavior and microstructural evolution of an as-wrought duplex stainless steel has been investigated by Gleeble-3500 thermal-mechanical simulator within the temperature range of 950-1200°C and the strain rate range of 0.1-10s-1. The flow curves exhibited a peak stress characteristic followed by dynamic softening and the strain for appearance of steady stress is bigger at higher strain rate than at lower strain rate. The apparent activation energy (Q) and the apparent stress exponent (n) of the test steel are obtained to be about 462 kj/mol and 3.95, respectively. The relationship between peak stress (σp) and Zener-Holomon parameter (Z) is obtained, whereby the σp can be predicted at differern hot working conditons. The results of microstructural observation show that the austenite softens by the dynamic recrystallization (DRX) which can be dominantly responsib le for dynamic softening, while the ferrite phase mainly continues to exhibit dynamic recovery (DRV).

Abstract: Aiming at Pbfree solder Sn4.0Ag0.5Cu (in short, SAC405), the uniaxial tensile tests are accomplished with constant strain-rate under different temperature and strain-rate load conditions. The elastic-viscoplastic behaviors of SAC405 solders are studied. The rate-dependent material main properties are analyzed, such ad yield limit, tensile strength, saturation stress, etc. Partitioned constitutive model is accepted to describe the constitutive behavior of SAC405 solder. The seven parameters in partitioned model are determined by experiment data. The results of numerical simulation are fitted with the experimental values.

Abstract: The flow stress of a high-Mn austenitic Fe-20Mn-3Si-3Al TRIP steel was investigated by isothermal compression tests on Gleeble 3500D thermo-mechanical simulator in the temperature ranges from 900°C to 1100°C and the strain rate ranges from 0.01s-1 to 10s-1. The results show that the flow stress is sensitively dependent on deformation temperature and strain rate, and the flow stress increases with strain rate and decreases with deformation temperature. The flow stress during isothermal compression can be described by the Zener-Hollomon (Z) parameter in the hyperbolic sine equation with the hot deformation activation energy Q of 385.2kJ/mol.

Abstract: Recent experiments on polycrystalline materials show that nanocrystalline materials have a strong dependency to the strain rate and grain size in contrast to the microcrystalline materials. In this study, mechanical properties of polycrystalline materials in micro and nanolevel were studied and a unified notation for them was presented. To completely understand the rate-dependent stress-strain behavior and size-dependency of polycrystalline materials, a dislocation density based model was presented that can predict the experimentally observed stress-strain relations for these materials. In nanocrystalline materials, crystalline and grain-boundary were considered as two separate phases. The mechanical properties of the crystalline phase were modeled using viscoplastic constitutive equations, which take dislocation density evolution and diffusion creep into account, while an elasto-viscoplastic model based on diffusion mechanism was used for the grain boundary phase. For microcrystalline materials, the surface-to-volume ratio of the grain boundaries is low enough to ignore its contribution to the plastic deformation. Therefore, the grain boundary phase was not considered in microcrystalline materials and the mechanical properties of the crystalline phase were modeled using an appropriate dislocation density based constitutive equation. Finally, the constitutive equations for polycrystalline materials were implemented into a finite-element code and the results obtained from the proposed constitutive equations were compared with the experimental data for polycrystalline copper and good agreement was observed.

Abstract: The constitutive equation in hot working for Al 7075 aluminum alloy was obtained employing experimental data of stress-strain curve, in a wide range of temperature (250-450°C) and strain rate (0.002-2 s-1). The influence of temperature and strain rate on the deformation behavior is represented by the equation proposed by Sellar and McTegart, all material parameters are considered as function of equivalent strain. The force-height data was corrected with interpolation method in the way to eliminate the error at the measurement. To verify the constitutive equation two parameter were calculated average absolute relative error (AARE=6.42) and correlation coefficient (R=0.998), for the same purpose the measuring and calculated flow curve are plotted together, the results shows that the constitutive equation obtained is good describing the behavior of the material.

Abstract: The hot deformation behavior of hypereutectic aluminium-silicon alloy was investigated by thermal simulation test at the deformation temperature of 330-480 and the strain rate of 0.1-10s^-1 using the Gleeble-1500 thermal mechanical simulator. The relationship of flow stress, temperature and strain rate was appropriately described by the deformation constitutive equation, and the deformation activation energy is 187.418 KJ/mol. In addition, the microstructures of these specimens were analyzed and the result showed that the inhomogeneous deformation enhances with increasing strain rate and decreasing deformation temperature, and the presence of primary silicon had a strong influence on the uneven deformation.

Abstract: Hot compressive deformation of Udimet720Li alloy was carried out on Gleeble-3500 thermal mechanical simulator. The flow stress behavior of Udimet720Li alloy during hot compression was studied in the temperature range of 1100-1160 and at a strain rate of 0.001-1s ^-1. The results showed that the flow stress was controlled by both strain rate and deforming temperature. The flow stress decreased with the increase of deforming temperature, while increased with the increase of strain rate. The change of flow stress with deformation thermal parameters was revealed from true stress-true strain curves, and constitutive relationship of Udimet720Li alloy was obtained on the base of Arrhenius equations and the deformation activation energy was calculated.