Plastic Behavior Of Sheet Metals Research Articles

Development of a Novel Plastic Hardening Model Based on Random Tree Growth Method

The flow functions for plastic deformation have been developed to describe the plastic behavior of sheet metals. In order to explain the plastic behavior of material in metal forming processes via finite element analyses, two basic input functions should be applied. One is the yield function that determines the yielding behavior. The other is flow function to describe the hardening property of sheet metal. To describe the hardening properties of sheet materials under quasi-static tension condition in a wide range of plastic straining, various different equations are known such as classical Swift, Voce, Holloman, combined Swift-Voce, and recently proposed Kim-Tuan equations, etc. Those hardening equations are based on metallurgical or phenomenological investigations, and however the application of each equation has some limitation. In this study, the random growth of the binary tree method is introduced to develop the reliable hardening equations of various sheet metals (i.e. DP980, Pure Ti, AA5052-O, STS304, Ti-Gr2, and Mg-AZ31B) with no knowledge of existing hardening equation types. To evaluate the proposed method, the proposed equations developed by new approach are compared with the Voce, Swift, and Kim-Tuan hardening equations for stress-strain curve and the plastic instability point. Consequently, the proposed approach was proven to be very efficient to find the reliable and accurate hardening equation for any kind of materials.

Application of the virtual fields method to large strain anisotropic plasticity

The identification of the plastic behaviour of sheet metals at severe deformation is extremely important for many industrial application such as metal forming, crashworthiness, automotive, aerospace, piping, etc. In this paper, the virtual fields method (VFM) was employed to identify the constitutive parameters of anisotropic plasticity models. The method was applied using the finite deformation theory in order to account for large strains. First the theoretical principles to implement the method are described in details, especially how to derive the stress field from the strain field. Afterwards a numerical validation was performed using the Hill48 model. Several aspects were studied with the numerical model: the effect of the used virtual fields, the minimum number of specimens required to identify the parameters, the stress distribution obtained from the specimen and its influence in the identification performance. A brief analysis on the influence of noise is also conducted. Finally a series of experiments was conducted on notched specimens of stainless steel, cut along different anisotropic directions. The displacement and strain fields were obtained by digital image correlation. Afterwards, the VFM was used to identify the parameters of the Hill48 model and the Yld2000-2D model. In this case, the Hill48 model was not able to correctly describe the material behaviour, while a rather good agreement was found with the Yld2000-2D model. The potential and the limitation of the proposed method are finally discussed.

Failure Orientation in Stretch Forming and Its Correlation with a Polycrystal Plasticity-Based Material Model for a Collection of Highly Formable Sheet Steels

Robust design optimization techniques have been developed in recent years within the automotive industry with the aim of reducing scrap rates and improving process stability in sheet metal forming. These new techniques are able to take process variations and other sources of material scatter into account. Among the many material variables and inputs used, the yield criterion is an important aspect and this is used to describe the plastic behavior of sheet metals. To achieve a reliable output in an optimization study, the yield criterion selected must be representative of material response and scatter. However, simple material models that deviate from real material behavior are often used due to a lack of material data, which is usually a requirement when using more complex models. In the present research, a polycrystal plasticity-based CTFP model has been evaluated in stretch forming for a collection of highly formable sheet steel materials. The results demonstrate that the CTFP model can capture the yielding character and also detect the minor deviations presented by different coils. The stretching factor derived from the CTFP model, as opposed to the work hardening and ductility, has a dominant effect on failure for a collection of materials with similar mechanical properties. Results also indicate that plastic deformation causes texture evolution and, consequently, an evolving yield locus. Such changes in the yield locus during deformation have an effect on stretching and friction calibration in FE simulations.

Identification of the Mechanical Properties of High-Strength Steel Using Digital Image Correlation

Identification of the mechanical properties of high-strength steel using digital image correlation. In this paper an experimental procedure to identify the plastic behaviour of sheet metals up to large strains using full field measurement is presented. The tests were conducted on notched specimens. This geometry generates a heterogeneous strain field which was measured during the test using a digital image correlation system. The advantage of using a heterogeneous strain field in the identification procedure is that a complex state of stress-strain can be analyzed at the same time and much more information can be obtained in a single test. On the other hand, the stress field cannot be directly computed from the test and a suitable identification procedure must be developed. Here, the virtual fields method (VFM) adapted for large strains and plasticity was used to identify the hardening behaviour and the anisotropy of the material. The values obtained with the VFM were compared with the results from a standard identification made using uniaxial tensile tests.

An extended homogenous yield function based anisotropic hardening model for description of anisotropic hardening behavior of materials

Except for the Bauschinger effect and permanent softening, work hardening stagnation and cross-effect are often observed deformation behaviors for sheet metals subjected to strain path changes. These complex deformation behaviors are assumed to have great effect on the sheet forming process and the following spring back. To constitutively, and more precisely model these plastic behaviors, extensive models have been successfully developed. Particularly, the combined isotropic-kinematic hardening model is powerful to capture the plastic behavior of sheet metals during forward and reverse loading. However, there is strong coupling between anisotropic yielding and anisotropic hardening with the kinematic hardening. Recently, Barlat et al. (2011) [61] proposed a homogenous yield function based anisotropic hardening model to describe the Bauschinger effect, which is not formulated with the kinematic hardening rule. In the present work, the original anisotropic hardening model is extended to capture the often observed cross-effect during multi-stage loading and work hardening stagnation during reverse loading. Although only four coefficients are newly introduced in the extended model, it can capture well the main trends of work hardening stagnation and cross-effect. The capability of this extended model is demonstrated with applications to two materials, namely, high strength steel and mild steel DC06.

Characterization of plastic behaviour of sheet metals by hydraulic bulge test

In the hydraulic bulge tests, dies with both circular and elliptical apertures were used. A recently proposed methodology was used to determine the equivalent stress—strain curves by bulging through elliptical dies. This methodology combines an analytical approach with the experimental data measured by an ARAMIS system. In the hydraulic bulge test using elliptical dies, as the die ellipticity ratio decreases, the equivalent stress—strain curves tend to move away from the curve obtained from bulging through circular die. The forming limit diagram in the range of positive minor strain of a DC04 sheet steel is also determined by using bulge test.

Identification of the Stress Fields from the Strain Fields in the Isotropic Materials

Abstract The identification of the material properties in sheet metals is usually achieved using uniaxial tests. The main attention of this article is focused on the identification of the plastic behaviour of sheet metals using full field measurement. The results were compared for notched specimen and specimen with a hole. These geometries create a heterogeneous strain fields which were measured during the test using high-speed cameras JAI Pulnix TM – 4000 CL which are used in digital image correlation system. DIC is non-conventional optical method for contactless measurement of spatial deformation and displacement and is more and more applied in experimental mechanics. The benefit of using a heterogeneous strain field in the identification process is that a complex state of stress-strain can be analyzed at the same time and much more information can be obtained in a single test. However, the stress field cannot be directly computed from the test and a suitable identification process has to be developed. The article contains virtual fields method (VFM) adapted for strains and plasticity which has been used to identify the hardening behaviour. The results obtained with the VFM have been compared with the results coming from a standard identification made with uniaxial tensile tests.

Role of yield criteria and hardening laws in the prediction of forming limit diagrams

Forming limit diagrams (FLDs) are calculated based on an extension of previous analyses by Jones and Gillis,[1] Choi et. al.[2] and Pishbin and Gillis.[3] They considered the plastic behavior of sheet metals in three deformation phases using a generalized flow law and using the commonly used power hardening law to describe the stress-strain behavior. In the present study, however, the yield criterion proposed by Hosford is used in conjunction with both power-law and Voce material constitutive equations to develop a model. This model is capable of predicting the forming limit strains achievable during sheet metal forming operations for sheets having planar isotropy. The predictions from Voce and power-law equations have been compared with the experimental forming limits determined by hemispherical punch stretching of gridded blanks of AA3105 and AA8011 aluminum alloys. The results indicate good prediction of limit strains for the two alloys when the Voce equation is applied.

Endochronic description of plastic anisotropy in sheet metal

It is shown in this paper that an extended form of Hills quadratic yield criterion for anisotropic sheet metal can be derived from an endochronic theory of plasticity. The extended form considers the combined isotropic–kinematic hardening and the anomalous behavior observed in the anisotropic plastic behavior of sheet metals can be accounted for by the concept of kinematic hardening. This form of anisotropic endochronic theory can accommodate the usual requirement of normality between the plastic strain rate and the yield function. In addition, the theory leads naturally to the expressions for back stresses. This work provides an additional example to show that the form of the intrinsic time is directly related to the form of the yield function. It is suggested that the coefficients of the quadratic yield function be determined from the yield stresses obtained from a set of tension tests.

Effects of yield surface shape on sheet metal forming simulations

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell nite element formulation based on the virtual work principle is derived for the three yield criteria. The eects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain drawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not aect the punch force and the strain distribution signicantly for the plane strain drawing operation. ? 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng., 41, 559{584 (1998)

Effects of yield surface shape on sheet metal forming simulations

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell finite element formulation based on the virtual work principle is derived for the three yield criteria. The effects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain rawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not affect the punch force and the strain distribution significantly for the plane strain drawing operation. © 1998 John Wiley & Sons, Ltd.

Modelling of sheet metal testing

Flow stress, work hardening rate and anisotropy characterize plastic behavior of sheet metals during pressforming operations. This paper concentrates on modelling forming limits and limiting drawing ratios by using a new flow curve description. The flow curve description is based on the dislocation theory and allows the separate analysis of yield stress and work hardening rate effects. The theoretical investigations are compared with experiments.

Forming limit diagrams calculated using Hill’s nonquadratic yield criterion

Forming limit diagrams (FLD) are calculated based on an extension of previous analyses by Jones and Gillis[4,5,6] and Choiet al. [8,9] They idealized the sheet metal deformation into three phases: (I) homogeneous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with a precipitous drop in load. They described the plastic behavior of sheet metals using a generalized quadratic flow law proposed by Jones and Gillis (JG). In the current analysis, Hill’s nonquadratic flow law for sheets having in-plane isotropy{su[101]} is used in conjunction with the three-stage deformation approximation. Calculated FLDs com- pare very favorably to experimentally determined results for aluminum-killed (AK) steel and aluminum alloys 2036-T4, 1100-H19, 5052-H32, 3003-0, and 3004-0. The comparison is fair for the titanium alloy Ti-6A1-4V. The agreement is poor for the strain rate-insensitive aluminum alloys 5052-0, 5052-H241, 5154-H111, and 6061-T4.

Relationship between the coefficients of normal anisotropy in the plastic behaviour of sheet metals

Relationship between the coefficients of normal anisotropy in the plastic behaviour of sheet metals