Papers by Keyword: Yield Function

Abstract: This research characterized the strain hardening behavior of AZ31 under different stress states from shear to balanced biaxial tension with a newly proposed yield function. Experiments are conducted for AZ31 magnesium alloy by in-plane shear specimens, dogbone specimens, notched specimens and bulging specimens to characterize the flow behavior under different stress states. The flow behaviors are characterized by a newly proposed yield function in a form of the three stress invariants. The proposed yield function is implemented into ABAQUS/Explicit to predict the plastic response of the alloy under different stress states. It is shown that the proposed yield function can precisely predict the distinct flow behaviors and reaction forces from shear to equibiaxial tension from the initial yielding to fracture.

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: A sixth order yield function was used to analyze the anisotropic plasticity behavior of sheet metal forming. Based on a complete sixth order homogenous polynomial in plane stress, the yield function was implemented as user material subroutines in the FE code ABAQUS Explicit and Standard. The associated flow rule and isotropic hardening were assumed. Material parameter values in the yield function were decided by uniaxial yield stresses and plastic strain ratios along 7 different loading orientations and plane strain yield and equal biaxial stresses and plastic strain ratio. To show the superiority of the sixth order yield function, the hole expansion test by Kuwabara et al.[1] was considered. The results of finite element simulation using the sixth order yield function showed a better agreement with the test results than YLD2000-2D yield function with M=6.

Abstract: A plane stress yield function which is described by multi-segment spline curve is proposed. This model is able to consider an arbitrary number of multi-axial stress states and its normal directions on the yield surface. Moreover by using interpolation based on cubic spline function, planar anisotropy is also described precisely. To show the applicability of the model, some evaluation of material properties and simulation results of hole expansion test are discussed.

Abstract: A new plane stress yield function using the 3rd-degree spline curve is proposed for the anisotropic behavior of sheet metals. This yield function considers the evolution of anisotropy in terms of both r values and stresses. In order to demonstrate the applicability of the proposed yield function, hole expanding tests with mild steel and 6000 series aluminum alloy sheets were simulated.

Abstract:

Using constitutive modelling principle of thermodynamics with internal variables, the yield surfaces rotation of saturated sands subjected triaxial compression stress state are justified and explained. The explanation for the yield surfaces rotation of saturated sands prove the correctness and feasibility for the principle of thermodynamics with internal variables to construct elastoplastic constitutive relation of saturated soils.

Abstract: The paper investigates by numerical modeling the effects of crystallographic texture and grain shape on the shape of the yield surface of aluminum sheet material at small strains. Different representative volume elements (RVEs) of the material are considered. Plane stress state is assumed in the sheet. A rate-dependent model of crystal plasticity (CP) is used in combination with either the full-constraint (FC) Taylor model or the finite element method (FEM) to compute the volume averaged stress of the material. The effect of different crystallographic textures observed in aluminum alloys on the shape of the yield surface is firstly investigated. An analytical yield function is used to generate yield surfaces for the different crystallographic textures. The deviation between the stress states at yielding computed by FC-Taylor model and the analytical yield surface is used to evaluate the capability of the yield function to fit the anisotropic yield surfaces representing different strong crystallographic textures. Two different shapes of the grains are introduced in the RVEs of CP-FEM in order to study the effect of the grain morphology. Small effects of grain shape are found at small strain compared with the marked influence of crystallographic texture.

Abstract: The multiaxial plastic deformation behavior of a cold rolled interstitial-free steel sheet with a thickness of 0.65 mm was measured using a servo-controlled multiaxial tube expansion testing machine for the range of strain from initial yield to fracture. Tubular specimens were fabricated from the sheet sample by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the contours of plastic work in stress space up to an equivalent plastic strain of 0.289 along with the directions of plastic strain rates. The test material exhibited differential hardening (DWH). A material modeling method for reproducing the DWH in a finite element simulation has been developed. Hydraulic bulge forming simulation results based on the DWH model had a closer agreement with the experimental results than those calculated using the isotropic hardening models with selected yield functions.

Abstract: In-plane tension/compression tests of a dual phase steel sheet with a tensile strength of 780 MPa were carried out using in-plane stress reversal testing machine. Remarkable tension/ compression asymmetry of flow stress (TCA) has been observed. Moreover, biaxial tensile tests using cruciform specimens were performed to measure contours of plastic work. The test material exhibited differential work hardening (DWH). In order to reproduce the TCA, an asymmetric quadratic yield function proposed by Verma et al. (2011) was used. The parameters of the yield function were changed as a function of reference plastic strain to reproduce the DWH. Furthermore, to assess the springback prediction accuracy of the developed model, a 3-point bending experiment and finite element analyses (FEA) were performed. It is concluded that the use of the material model that is capable of reproducing DWH and TCA is a must for a highly accurate FEA of springback.

Abstract: In the present work the disc compression test used to determine the balanced biaxial strain-ratio $r_b$ is analyzed in terms of the influence of contact friction using non-linear finite element analysis (FEA). The FEA results reveal an unexpectedly strong sensitivity of the $r_b$-value on contact friction, which is discussed in detail. The most important outcome of the present work is that the FEA can reproduce the $r_b$-value imposed by the utilized yield function very well, but only when the prescribed Coulomb friction coefficient has a very small value; for increasing friction coefficients a gradual deviation from the imposed $r_b$-value can be observed. This finding implies that in experiments contact friction must be eliminated to a larger extent than commonly expected, otherwise the determined $r_b$-value using disc compression testing will considerably deviate from the actual one, particularly when $r_b$ is far from one.