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Numerical simulation is an important tool which can be used for designing parts and production processes. Springback prediction, with the use of numerical simulation, is essential for the reduction of tool try-outs through the design of the forming tools with die compensation, therefore, increasing the dimensional accuracy of stamped parts and reducing manufacturing costs. In this work, numerical simulation was used for performing the springback analysis of car body stamping made of aluminium alloy AA6451-T4. The finite element analysis (FEM) based software PAM-STAMP 2G was used for performing the forming and springback simulations. These predictions were conducted with various combinations of material models to achieve accurate springback prediction results. Six types of yield functions (Barlat89, Barlat2000, Vegter-Lite, Hill90, Hill48 isotropic, and Hill48 orthotropic) were used in combination with the Voce hardening model. Springback analysis was conducted in three sections of the formed part; the numerical results were compared with the experimental values. It was found that the combinations of Barlat’s yield functions and the Voce hardening law were most accurate in terms of springback prediction. Additionally, it was found that the phenomena that were investigated, which are required for the determination of the kinematic hardening model, such as the change of Young’s modulus E, the transient behaviour, work-hardening stagnation, and permanent softening, were not observed in the aluminium alloy studied.

If a plastic constitutive relation is used to simulate a metal forming process, the main concern should be its ability to predict the plastic strain parameters. At present, constitutive modelling basically relies on the properties of stress parameters, and emphasizes on how to improve the prediction accuracy of initial yield and subsequent hardening stresses. Although, corresponding to the anisotropic materials, the experimental data of plastic strain ratios are also used, the experimental plastic strains data obtained from all related experiments, in addition to the one as the equivalent plastic strain, are not employed at all. The lack of the most important experimental data in the constitutive model will inevitably weaken its ability to predict the plastic strain parameters which will determine the final shape of formed parts. To make a constructed constitutive relation that can fully reflect the experimental characteristics of materials, a new theoretical framework of constitutive model is proposed, and the application of experimental plastic strain data can be achieved with the introduction of a plastic strain-increment function. To illustrate the importance of the application of plastic strain-increment function to improve the predictive accuracy of plastic strain-increments, a new constitutive model is constructed and combined with a large amount of experimental data to verify it. Experimental verifications were carried out by some sheet metals with different anisotropic properties under uniaxial and equi-biaxial tension stress states, and also deal with multiple sets of experimental data obtained under complex tension-tension and tension-compression stress states. Discussions also include the results predicted by the models constructed based on the classical theory. Calculation examples show, the stronger the anisotropic properties of material, the greater the prediction deviation of plastic strains generated by the classical-theory-based models. Moreover, such prediction deviations will gradually increase with the accumulation of predicted plastic strain-increments. Predictive ability of the new constitutive relation is completely unimpacted by the increased degree of anisotropic features of materials. Predicted results are in good agreement with all experimental data. [ABSTRACT FROM AUTHOR]

This paper investigated the main mechanical properties of TC1 titanium alloy sheets with different thicknesses, and a useful function that can describe the mechanical properties reasonably was used. Moreover, planar anisotropies of above TC1 titanium alloy sheets were studied by Barlat′89 and Yld2000-2d yield functions. The influence of M value was analyzed on describing ability for distribution characteristics of material yield stress and anisotropic coefficient, and their performances were compared on the titanium alloy sheets. [ABSTRACT FROM AUTHOR]

A non-associated flow rule (non-AFR) model is developed by adopting the Barlat89 yield function as the yield stress function and a modified Barlat89 yield function as the plastic potential function under plane stress conditions. Determination of parameters to calibrate the yield stress function requires four stresses, e.g. uniaxial yield stresses along 0°, 45°, 90° to the sheet metal rolling direction, RD, and the equi-biaxial yield stress. Four corresponding r -values (Lankford coefficients) under the same directions are used as calibration parameters for the plastic potential function. These functions capably describe anisotropic hardening behavior as well as variation of r -values during deformation. Uniaxial tensile tests, hydraulic bulge tests, and biaxial tensile tests were performed on a 980 MPa steel in order to validate the non-AFR model, which are compared with other yield functions under both associated flow rule, AFR, and non-AFR conditions. [ABSTRACT FROM AUTHOR]

The combined loading tests of 5754O aluminum alloy sheet are used to verify the yield function. Three yield functions are implemented into the commercial finite element model (FEM) code ABAQUS as a user material subroutine UMAT for the FEM simulation of the combined loading tests. The comparison of the simulating and experimental results shows that the modified Yld2000-2d yield function can describe the mechanical behavior of 5754O aluminum alloy sheet under combined loading paths reasonably while other three yield functions do not. The performance of the modified Yld2000-2d yield function on describing the mechanical behavior under combined loading paths is analyzed in detail. It is concluded that the modified Yld2000-2d yield function can be adopted to describe the deformation behavior of 5754O aluminum alloy sheet for industrial applications. [ABSTRACT FROM AUTHOR]

A new yield function for lamellar gray cast iron materials is proposed. The new model is able to describe the results of recently performed microstructure-based finite-element computations that resolve the three dimensional yield surface of three different gray cast irons. The yield function requires only the yield stress in tension and compression of the respective material as model parameters. Furthermore, the algorithmic formulation of the new model is assessed for numerical robustness and efficiency. [ABSTRACT FROM AUTHOR]

On the basis of neutron monitor data, we estimate the energy spectrum, anisotropy axis direction, and pitch-angle distribution of solar energetic particles during two major ground-level enhancements (GLE 59 on 14 July 2000 and GLE 70 on 13 December 2006). For the analysis we used a newly computed neutron monitor yield function. The method consists of several consecutive steps: definition of the asymptotic viewing cones of neutron monitor stations considered for the data analysis by computing the cosmic ray particle propagation in a model magnetosphere with the MAGNETOCOSMICS code, computing the neutron monitor model responses, and deriving the solar energetic particle characteristics on the basis of inverse problem solution. The pitch-angle distribution and rigidity spectrum of high-energy protons are obtained as a function of time in the course of ground-level enhancements. A comparison with previously reported results is performed and reasonable agreement is achieved. A discussion of the obtained results is included. [ABSTRACT FROM AUTHOR]

The Yld2004-18p yield criterion uses 18 parameters to define anisotropy for a full 3D stress state. It is demonstrated in this paper that dependencies between the parameters exist and for a given set of experimental data the parameters are not uniquely defined. Analysis of the yield function shows that two specific combinations of parameters do not contribute to the value of the yield function. Therefore, the number of parameters can be reduced to 16, without any loss of flexibility. Similarly, the number of parameters for the plane stress version of this yield criterion reduces from 14 to 12. [ABSTRACT FROM AUTHOR]

A numerical model for assessment of the effective dose and ambient dose equivalent produced by secondary cosmic ray particles of galactic and solar origin at commercial aircraft altitudes is presented. The model represents a full chain analysis based on ground-based measurements of cosmic rays, from particle spectral and angular characteristics to dose estimation. The model is based on newly numerically computed yield functions and realistic propagation of cosmic ray in the Earth magnetosphere. The yield functions are computed using a straightforward full Monte Carlo simulation of the atmospheric cascade induced by primary protons and α-particles and subsequent conversion of secondary particle fluence (neutrons, protons, gammas, electrons, positrons, muons and charged pions) to effective dose or the ambient dose equivalent. The ambient dose equivalent is compared with reference data at various conditions such as rigidity cut-off and level of solar activity. The method is applied for computation of the effective dose rate at flight altitude during the ground level enhancement of 13 December 2006. The solar proton spectra are derived using neutron monitor data. The computation of the effective dose rate during the event explicitly considers the derived anisotropy i.e. the pitch angle distribution as well as the propagation of the solar protons in the magnetosphere of the Earth.

This study aimed to evaluate the effect of constitutive equations on springback prediction accuracy in cold stamping with various deformation modes. This study investigated the ability of two yield functions to describe the yield behavior: Hill’48 and Yld2000-2d. Isotropic and kinematic hardening models based on the Yoshida-Uemori model were adopted to describe the hardening behavior. The chord modulus model was used to calculate the degradation of the elastic modulus that occurred during plastic loading. Various material tests (such as uniaxial tension, tension-compression, loading-unloading, and hydraulic bulging tests) were conducted to determine the material parameters of the models. The parameters thus obtained were implemented in a springback prediction finite element (FE) simulation, and the results were compared to experimental data. The springback prediction accuracy was evaluated using U-bending and T-shape drawing. The constitutive equations wielded significant influence over the springback prediction accuracy. This demonstrates the importance of selecting appropriate constitutive equations that accurately describe the material behaviors in FE simulations.

The multiaxial deformation behaviors of amorphous epoxy polymers were characterized using planar biaxial compression tests and finite element (FE) analyses of cruciform specimens. The multiaxial limit of elastic deformation was investigated considering buckling instability of the planar biaxial compression tests. An offset-based yield criterion was proposed to determine the initial yield surface considering the nonlinear elastic deformation characteristics observed in the deformation tests. An FE analysis confirmed using the results of the tests revealed that the proposed method captured the initial multiaxial yielding in the central gauge of the specimen, demonstrating that existing pressure-dependent classical yield functions, such as the paraboloidal and conical yield functions, cannot appropriately describe the initial yield surface of the epoxy polymer. The yield function previously customized from molecular dynamics (MD) data exhibited a relatively good agreement with the initial yield surface. The determined shape of the initial yield surface and its agreement with the MD data–driven yield function were not consistently maintained during subsequent yielding. The results indicate that a new customized yield function properly describing the broader initial yield surface than those of the classical yield functions and its shape transition to plastic behavior is necessary to accurately reflect the entire multiaxial deformation behavior. [ABSTRACT FROM AUTHOR]

A linear stress path (LSP) experiment was performed using uniaxial and biaxial tensile tests with a cold-rolled mild steel sheet (SPCD; nominal thickness: 0.8 mm) as the test material. In the LSP experiment, the contours of plastic work and the directions of the plastic strain rates, β , for a plastic strain range of 0.002 ≤ ε 0 p ≤ 0.234 were measured. Then, the Yld2000-2d yield function was used to identify a material model that accurately reproduces the experimental data. Stepped nonlinear stress path (NLSP) experiments were also performed; the NLSPs consisted of several linear stress paths without intermediate elastic unloading. The measured work hardening behavior and β values were compared with those calculated using the yield functions identified from the LSP experiment, namely the von Mises, Hill's quadratic, and Yld2000-2d yield functions. For the Yld200-2d yield function, both isotropic and differential hardening models were investigated. It was found that the data measured in the NLSP experiment are consistent with calculation results obtained using the Yld2000-2d yield function identified from the LSP experiment. Thus, it can be concluded that within the range of stress paths adopted in the NLSP experiment, the deformation behavior of a test sample can be accurately predicted using the material model identified from an LSP experiment. [ABSTRACT FROM AUTHOR]

The strength and failure behaviors of geomaterials, such as soils and rocks, are commonly anisotropic because of lamination and sedimentation. The main purpose of this study is to investigate the effect of anisotropy on the localization pattern and bearing capacity of geostructures by finite-element simulation. To this aim, an extended Drucker-Prager yield criterion is developed for transversely isotropic geomaterials based on the Cosserat continuum. In this criterion, the internal frictional angle is related to the material principal direction and the mixed invariant of the stress tensor and the microstructure tensor. The corresponding stress update and consistent elastoplastic tangent modulus matrix are presented. Numerical results show that the localization pattern and the bearing capacity of the geostructures are very sensitive to the material principal direction as well as the anisotropic degree. [ABSTRACT FROM AUTHOR]

In this paper, the initial multiaxial yield behavior of three different gray cast iron materials with lamellar shaped graphite inclusions is numerically investigated by means of the finite-element method. Therefore, volume elements including the real microstructure of the materials are loaded bi- and triaxially beyond macroscopic yield. The shape of the obtained yield surfaces are compared to the surfaces of four continuum models which, amongst others, are proposed in literature to describe the inelastic behavior of gray cast iron with lamellar shaped graphite inclusions. It is found that the presented continuum models and the macroscopic yield surfaces obtained with microstructure-based finite-element models deviate. Furthermore, the initial inelastic flow direction is computed at the onset of macroscopic yielding. The analysis show that the inelastic flow is normal to the yield surface. [ABSTRACT FROM AUTHOR]