Papers by Keyword: Constitutive Model

Abstract: Two types of carbon fiber-reinforced epoxy composite laminates are chosen for long-term tensile creep tests under different temperatures and load levels. Their time-dependent and non-monotonic deformations indicate clearly both temperature effect and physical aging effect. To characterize these viscoelastic behavior, two phenomenological constitutive models and one physical model are developed. The linear viscoelastic model based on the Boltzmann superposition principle is able to describe reasonably the deformations at relatively lower stress levels and temperatures. The nonlinear viscoelastic model of Schapery’s single-integral form, together with a usage of effective time theory, could describe nicely all the effects of temperature, stress, and physical aging. The physical model based on Ngai’s coupling mechanism concept is further combined with the framework of Schapery’s nonlinear viscoelastic theory, which may provide certain physical understanding about the effect of aging behavior on long-term creep deformation of the laminated composites. Numerical modelling by finite element method are implemented, and comparisons between the experimental and simulation results are demonstrated.

Abstract: In this paper, two types of W-Zr alloy with different proportions were prepared. The dynamic and quasi-static compression mechanical properties of Zr-25%W alloy and Zr-50%W alloy at various strain rates were obtained. The results showed that the tungsten component could improve the mechanical strength of the alloy, while the zirconium component could significantly improve the plasticity of the alloy. The JC constitutive models of two types of W-Zr alloys and the KHL constitutive model of Zr-25%W alloy were proposed. The fitting parameters of JC model and KHL model were determined by the dynamic and quad-static compression tests. Dynamic impact tests of two types of W-Zr alloys were carried out in argon atmosphere at various velocities. The power law distribution theory for brittle materials could also describe the high-speed impact of W-Zr alloy.

Abstract: Artificial Neural Networks (ANNs) have the potential to provide a different approach to constitutive modelling, with the main advantage that these do not require to postulate a mathematical formulation or identify empirical parameters. Currently, the training of an ANN for implicit constitutive modelling mostly relies on paired data, usually stress-strain however, stress cannot be directly measured in a real experiment. As such, the training should be carried out indirectly using measurable variables from the experimental setting, such as displacements and the applied force. In the current work, displacements and global force data are used to indirectly train an ANN to predict the stress state of a material. An experimental test is recreated numerically in order to obtain displacement and global force data for different load distributions, i.e. obtaining synthetic data using a virtual experiment. The strain from the current and previous time increments are obtained from the corresponding displacements and used as inputs for the ANN to predict the current state of stress. Training is carried out without stress labels to compute the loss. Instead, the local and global equilibrium conditions, corresponding to the application of the Virtual Fields Method (VFM) to the physical model, are employed to compute the loss and update the network parameters, until the predicted stress state is accurate.

Abstract: In the last decade, several phenomenological yield criteria for anisotropic material has been proposed to improve the modeling predictions about sheet metal-forming processes. In regard to this engineering application, two proprieties of models have been used. If the yield function and the plastic potential are not same (not equal), the normality rule is non associative flow rule (NAFR), otherwise, when the stresses yield has been completely coupled to the anisotropic strain rate ratio (plastic potential), is called the associated flow rule (AFR). The non-associated flow rule is largely adopted to predict a plastic behavior for metal forming, accurately about à strong mechanical anisotropy presents in sheet metal forming processes. However, various studies described the limits of the AFR concept in dealing with highly anisotropic materials. In this study, the quadratic Hill1948 yield criteria is considered to predict mechanical behavior under AFR and NAFR approach. Experiment and modeling predictions behaviour of normalized anisotropic coefficient r (θ) and σ (θ) evolved with θ in sheet plane. and the equibiaxial yield stress σ_b was assumed σ_b=1 but the r_b-values was computed from Yld96 [15].

Abstract: The high temperature tensile behavior of Mg-13Gd-4Y-2Zn-0.5Zr alloy was investigated at deformation temperature of 400-520 °C and strain rate of 0.001-0.5 s^-1, and the stress-strain curves were obtained by using INSTRON 3382. The high temperature tensile constitutive model and hot processing map of the alloy were established, and the reliability of the hot processing map was further verified by analyzing the microstructure of the deformed alloy. The results showed that the dynamic recrystallization (DRX) occurred of Mg-13Gd-4Y-2Zn-0.5Zr alloy during the tensile tests under high temperature conditions, and its peak stress decreased with the increase of deformation temperature or strain rate. The Arrhenius equation can be used to fit the rheological behavior of the alloy. The thermal deformation activation energy Q was 259.13kJ/mol, and the maximum error between the model and the experimental data was less than 9%. It can be concluded that the optimum deformation parameters of the alloy were temperature of 500-520 °C and strain rate of 0.01-0.001 s^-1 based on the dynamic material model and hot processing map.

Abstract: In this paper, the compression-torsion composite deformation of homogenized Mg-13Gd-4Y-2Zn-0.5Zr alloy with strain rate of 0.001 s^-1-0.5 s^-1 during the temperature interval of 350 °C-480 °C was studied by the torsional test using the equipment of Gleeble3500 unique to North University of Chain. The effects of temperature and strain rate on the flow behavior of the alloy during compression-torsion deformation were investigated. And the compression-torsion constitutive equation of the high temperature flow stress of the alloy was constructed by introducing the temperature compensation factor Z, providing a theoretical basis for subsequent finite element analysis. The results showed that the flow stress increased with the increase of strain when the flow curves of the alloy were 350 °C and 400 °C. When the deformation temperatures were 450 °C and 480 °C, the flow stress was a typical recrystallization type. The influence of temperature and strain rate on dynamic recrystallization behavior was investigated by OM observation. The results showed that the number and size of recrystallized grains increased with the increase of temperature at the same strain rate, and the number and size of recrystallized grains increased with the decrease of strain rate at the same temperature.

Abstract: Constitutive models for soils are usually adopted in numerical method to analyze the behavior of geotechnical structures. This study performs a series of consolidated-undrained triaxial tests to establish the stress-strain curve of clay. A constitutive model that considers continuous strain hardening-softening is proposed based on the results of triaxial tests. Triaxial test results reveal that undrained shear strength linearly increases with an increase in consolidated pressure , the normalized undrained shear strength is about 0.52 not only for this study but also for the other two cases around Taipei Basin. Due to undrained condition, an associated flow rule between plastic strain increment and stress tensor is adopted. As accumulative plastic strain or/and consolidated pressure change, the mobilized undrained shear strength also changes. All parameters needed for the proposed model can be expressed as a function of undrained shear strength S_u, The mobilized undrained shear strength for the proposed model during strain hardening-softening can be in term of accumulative plastic strain. This model can calculate the stress-strain curves of clayed soils accurately.

Abstract: The comprehension of the anisotropy impacts on mechanical properties of the rolled steel sheets was investigated using a non-quadratic anisotropic yield function. In this study, experimental and modelling determination of behavior of an industrial rolled sheets for a DIN 1623 St14 steel were carried out. The yield stresses and Lankford r-values in uniaxial were experimentally determined but the balanced biaxial tension stress states and rb were assumed. The parameters of the associated yield equation, derived from the three orthotropic yield functions proposed by Hill48 and Yld2000-2d, were determined. Predictions and the evolution of normalized yield stress and normalized Lankford parameters (plastic strain ratio) obtained by the presented investigative are considered. In order to describe the path of equivalent plastic behavior, the isotropic hardening function is described using the following various empirical standard formulae based on: Hollomon, Ludwick, Swift and Voce model.

Abstract: Aluminum 7000 series have been widely used in the aircraft and aerospace applications owing to its advantages of lightweight, high strength, and excellent corrosion resistance. Recently, the sheets have been applied in the automotive engineering in order to reduce the weight of commercial cars. For this demand, press forming is a common forming method used to produce a designed automotive part. However, springback is one of the main reasons to limit applications of the aluminum 7000 series. This study develops several material models that consider important material behavior including Young's modulus, Bauchinger's effect, and material anisotropy on springback prediction for the tested material. These models have been implemented in ABAQUS software to analysis a bending process and estimate springback amount. As a result, the effects of each material behavior on springback were clarified. Based on simulation results, it is found that correctly capturing the Bauchinger's effect is the major key to the success of springback prediction for such kind of material.

Abstract: Size effects extremely exist in the metal micro-forming process. When a deformation process scales down to micro scale, the appearances of geometry size and single grain size start to play a major role in deformation. Generally, the size effects are unavoidable in the experimental work and cannot be neglect in the optimization of micro-forming processes. In this paper, size effect on flow stress is investigated in the form of the coupled effect of workpiece geometry (sample thickness) and grain size, (T/D) by the micro tensile test of pure copper foil. Following the previous approaches, a new hybrid material model is projected to describe the hardening behavior of grains in polycrystalline material. Tensile tests performed on the copper foil with constant thickness and width, while to get dissimilar grain sizes, the foil annealed for different times. The ratio of thickness to grain size (T/D) is limited to larger than 1 (T/D˃1). A hybrid material model is proposed and established based on grain heterogeneity and sample thickness. The hybrid material model builds a relationship between the surface layer and sheet interior. The hybrid material model developed by the strain gradient theory in which the dislocation cell structure, cell densities (interior and wall) engaged to define the polycrystalline aggregate and calculated the dislocations in a grain (grain interior and grain wall). The results show that flow stress varies with the different values of T/D, but with an increase of the share of the grains flow stress start to decreases. After applying the hybrid material model of flow stress, the micro-tensile test of copper foil is simulated by finite element method. The simulation outcomes well matched with experimental results.