Papers by Keyword: Non-Associated Flow Rule

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: Recently, advanced high strength steels (AHSSs) have been widely applied to the structural parts of vehicles thanks to their good combination of strength and ductility. When one makes parts with AHSSs, however, fractures in sharp corners of the parts are frequently observed below forming limit, which is normally defined by strain based FLC(Forming Limit Curve). This phenomenon is well-known as “Shear Fracture”. Recent researches point out that additional numerical techniques should be considered in order to predict it accurately. Kim et al. [1] suggested that shear fracture can be predictable with continuum-based finite elements rather than conventional shell elements, and more constitutive informations for large strain thermo-mechanical simulation are needed to improve accuracy. Luo and Wierzbicki [2] showed that shear fracutre in stretch-bending test can be fully characterized by proposed MMC(Modified Mohr-Coulomb). This paper shows that solid-shell approach based on hyper-elastoplastic material model enables one to properly predict shear fracture pheonomenon without any special failure criteria. Furthermore, the effects of non-associated flow rule on shear fracture will be also discussed with several numerical examples.

Abstract: The present paper proposed a cyclic plasticity model with a non-associativity parameter, i.e., the model includes non-associative flow rule and associative one. In the present model, the non-associative parameter controls the non-associativity. The model is derived based on the non-linear kinematical hardening rule with two hardening parameters for both the volumetric and deviatoric strains. From the simulation by the present model, we have found the strong non-associativity leads to the large decrease in the mean effective stress, i.e. almost zero mean effective stress during the cyclic deformations under undrained conditions while the model with associated flow rule is not.

Abstract: In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

Abstract: In this paper we discuss properties of dense granular °ows and elaborate on some properties of a model which generalises the classical plastic potential model using elements of the double shearing model. It is shown how the model is embedded into a Cosserat continuum model. The proposed model recti¯es the ill-posedness of both the non-associated °ow rule and the double shearing model and may be used for both granular materials and also for metals which possess a micro-structure which is capable of rotation.