Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part II – Formability

Formability of automotive friction stir welded TWB (tailor-welded blank) sheets was experimentally and numerically investigated in this work for four automotive sheets, aluminum alloy 6111-T4, 5083-H18, 5083-O and DP590 steel sheets, each having one or two different thicknesses. In particular, formability in three applications including the simple tension test with various weld line directions, hemisphere dome stretching and cylindrical cup drawing tests was evaluated. For numerical simulations, mechanical properties previously characterized in a joint paper (Chung et al., 2010) were utilized. To represent the mechanical properties, the non-quadratic orthogonal anisotropic yield function, Yld2000-2d, was utilized along with the (full) isotropic hardening law, while the anisotropy of the weld zone was ignored for simplicity.     

Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part I – Material properties

In order to evaluate the macroscopic performance of friction stir welded automotive tailor-welded blank (TWB) sheets, the hardening behavior, anisotropic yielding properties and forming limit diagram were characterized both for base (material) and weld zones. In order to describe the Bauschinger and transient hardening behaviors as well as permanent softening during reverse loading, the modified Chaboche type combined isotropic–kinematic hardening law was applied. As for anisotropic yielding, the non-quadratic anisotropic yield function, Yld2000-2d, was utilized for base material zones, while isotropy was assumed for weld zones for simplicity. As for weld zones, hardening properties were obtained using the rule of mixture and selectively by direct measurement using sub-sized specimens. Forming limit diagrams were measured for base materials but calculated for weld zones based on Hill’s bifurcation and M–K theories. In this work, four automotive sheets were considered: aluminum alloy 6111-T4, 5083-H18, 5083-O and dual-phase steel DP590 sheets, each having one or two thicknesses. Base sheets with the same and different thicknesses were friction-stir welded for tailor-welded blank (TWB) samples.     

Forming of aluminum alloys at elevated temperatures – Part 2: Numerical modeling and experimental verification

The temperature-dependent Barlat YLD96 anisotropic yield function developed previously [Forming of aluminum alloys at elevated temperatures – Part 1: Material characterization. Int. J. Plasticity, 2005a] was applied to the forming simulation of AA3003-H111 aluminum alloy sheets. The cutting-plane algorithm for the integration of a general class of elasto-plastic constitutive models was used to implement this yield function into the commercial FEM code LS-Dyna as a user material subroutine (UMAT). The temperature-dependent material model was used to simulate the coupled thermo-mechanical finite element analysis of the stamping of an aluminum sheet using a hemispherical punch under the pure stretch boundary condition. In order to evaluate the accuracy of the UMAT’s ability to predict both forming behavior and failure locations, simulation results were compared with experimental data performed at several elevated temperatures. Forming limit diagrams (FLDs) were developed for the AA3003-H111 at several elevated temperatures using the M-K model in order to predict the location of the failure in the numerical simulations. The favorable comparison found between the numerical and experimental data shows that a promising future exists for the development of more accurate temperature-dependent yield functions to apply to thermo-hydroforming process.     

Characterization of mechanical properties by indentation tests and FE analysis – validation by application to a weld zone of DP590 steel

In this work, the mechanical properties of the metal active gas (MAG) weld zone and heat affected zone (HAZ) were characterized utilizing the continuous indentation method together with its finite element (FEM) analysis. To verify the measured properties, uni-axial tension and three point bending tests were performed for DP590 welded specimens. For numerical simulations, the isotropic hardening law was assumed along with the non-quadratic anisotropic yield function, Yld2000-2d. As for the failure criterion of the base material and weld zones particularly for the failure evaluation in the uni-axial tension test, Hill’s bifurcation theory and the M–K theory were applied to calculate the forming limit diagrams considering all measured properties including strain-rate sensitivity.     

Numerical simulation of friction stir butt welding process for AA5083-H18 sheets

Thermo-mechanical simulation of the friction stir butt welding (FSBW) process was performed for AA5083-H18 sheets, utilizing a commercial finite volume method (FVM) code, STAR-CCM+, which is based on the Eulerian formulation. Distributions of temperature and strain rate histories were calculated under the steady state condition and simulated temperature distributions (profiles and peak values) were compared with experiments. It was found that including proper thermal boundary condition for the backing plate (anvil) is critical for accurate simulation results. Based on the simulation, thermal and deformation histories of material elements were also calculated, useful to predict material characteristics of the weld such as hardness or grain size, and possibly for the susceptibility of weld to abnormal grain growth (AGG) after post-weld heat treatment.     

Plane stress yield function for aluminum alloy sheets—part 1: theory

A new plane stress yield function that well describes the anisotropic behavior of sheet metals, in particular, aluminum alloy sheets, was proposed. The anisotropy of the function was introduced in the formulation using two linear transformations on the Cauchy stress tensor. It was shown that the accuracy of this new function was similar to that of other recently proposed non-quadratic yield functions. Moreover, it was proved that the function is convex in stress space. A new experiment was proposed to obtain one of the anisotropy coefficients. This new formulation is expected to be particularly suitable for finite element (FE) modeling simulations of sheet forming processes for aluminum alloy sheets.     

On the Occurrence of Portevin–Le Châtelier Instabilities in Ultrafine-Grained 5083 Aluminum Alloys

The Portevin–Le Châtelier (PLC) instability is commonly observed in Al–Mg alloys and is manifested in serrated flow within the stress–strain response. We investigate the persistence of this instability with reduction in grain size by studying an ultrafine-grained (ufg) aluminum alloy (Al5083) and a conventional grain size Al5083. Micro-scale tensile tests combined with digital image correlation (DIC) reveal strength anisotropy and heterogeneity of the deformation in the three material directions (extrusion, rolled, and transverse). For the same applied displacement rate, the PLC effect in ufg-Al5083 is observed only over a small strain range immediately following the yield, while the coarse-grained Al5083 exhibits serrated flow over nearly the entire plastic strain range. These observations are explained using the stability analysis of Hähner (Acta Mater 45:3695–3707, 1997), and implications for nanocrystalline (nc) alloys are discussed.     

Forming of aluminum alloys at elevated temperatures – Part 1: Material characterization

A temperature-dependent anisotropic material model for use in a coupled thermo-mechanical finite element analysis of the forming of aluminum sheets was developed. The anisotropic properties of the aluminum alloy sheet AA3003-H111 were characterized for a range of temperatures 25–260 °C (77–500 °F) and for different strain rates. Material hardening parameters (flow rule) and plastic anisotropy parameters (R₀, R₄₅ and R₉₀) were calculated using standard ASTM uniaxial tensile tests. From this experimental data, the anisotropy coefficients for the Barlat YLD96 yield function [Barlat, F., Maeda, Y., Chung, K., Yanagawa, M., Brem, J.C., Hayashida, Y., Lege, D.J., Matsui, K., Murtha, S.J., Hattori, S., Becker, R.C., Makosey, S., 1997a. Yield function development for aluminum alloy sheets. J. Mech. Phys. Solids 45 (11/12), 1727–1763] in the plane stress condition were calculated for several elevated temperatures. Curve fitting was used to calculate the anisotropy coefficients of Barlat’s YLD96 model and the hardening parameters as a function of temperature. An analytical study of the accuracy and usability of this curve fitting technique is presented through the calculation of plastic anisotropy R-parameters and yield function plots at different temperatures.     

Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy

The experimental and numerical work presented in this paper reveals that stress state has strong effects on both the plastic response and the ductile fracture behavior of an aluminum 5083 alloy. As a result, the hydrostatic stress and the third invariant of the stress deviator (which is related to the Lode angle) need to be incorporated in the material modeling. These findings challenge the classical J₂ plasticity theory and provide a blueprint for the establishment of the stress state dependent plasticity and ductile fracture models for aluminum structural reliability assessments. Further investigations are planned to advance, calibrate and validate the new plasticity and ductile fracture models.     

铝合金与槽型界面钢板的爆炸焊接

采用尺寸为4 mm×410 mm×410 mm的5083铝合金和尺寸为15 mm×400 mm×400 mm、表面开有燕尾槽的Q345钢板作为爆炸焊接的覆板与基板,根据理论公式得到铝合金-钢爆炸焊接下限后,选取其附近的参数进行爆炸焊接,再通过力学性能检测和微观形貌观察研究5083/Q345复合板界面的结合性能。实验结果表明:铝合金与钢在冶金结合和燕尾槽的挤压啮合共同作用下实现爆炸复合;铝合金与燕尾槽上底面、倾斜面和下底面的界面均呈平直状。铝合金与燕尾槽上底面、下底面以直接结合和不连续熔化块相结合的方式复合,而铝合金与燕尾槽倾斜面以连续熔化层的方式复合;复合板的剪切强度大于172 MPa,满足Al/Fe复合板结合强度的要求。     

Spring-back evaluation of automotive sheets based on isotropic–kinematic hardening laws and non-quadratic anisotropic yield functions,part III: applications

In order to improve the prediction capability of spring-back in the computational analysis of automotive sheet forming processes, the modified Chaboche type combined isotropic–kinematic hardening law was formulated to account for the Bauschinger and transient behavior in Part I. As for the yield stress function, the non-quadratic anisotropic yield potential, Yld2000-2d, was utilized under the plane stress condition. Experimental procedures to obtain the material parameters of the combined hardening law and the yield potential were presented in Part II for three automotive sheets. For verification purposes, comparisons of simulations and experiments were performed here for the unconstrained cylindrical bending, the 2-D draw bending and the modified industrial part (the double-S rail). For all three applications, simulations showed good agreements with experiments. Simplified one-dimensional plane strain analytical and numerical methods were also developed here to better understand the spring-back in forming processes.     

Inflation and burst of aluminum tubes. Part II: An advanced yield function including deformation-induced anisotropy

In a recent study [Korkolis, Y.P., Kyriakides, S., 2008. Inflation and burst of anisotropic aluminum tubes for hydroforming applications. Int’l. J. Plasticity 24, 509–543], the formability of aluminum tubes was investigated using a combination of experimental and numerical approaches. The tubes were loaded to failure under combined internal pressure and axial load along radial paths in the engineering stress space. The experiments were then simulated using appropriate FE models and two established anisotropic yield functions. It was found that for some loading paths the computed deformations did not agree with the experimental ones, whereas rupture was generally overpredicted. In the current study the problem is tackled using a more advanced yield function [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.-H., Chu, E., 2003. Plane stress function for aluminum alloy sheets – part I: theory. Int’l. J. Plasticity 19, 1297–1319]. Three different calibration schemes of this function are employed, in two of which the experimentally observed deformation-induced anisotropy is taken into account. It is demonstrated that both deformation and failure can ultimately be predicted successfully, albeit arduously, using a hybrid procedure detailed herein.     

Tension–compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior

In-plane tension and compression experiments on copper alloy sheets (phosphor bronze) and 6000 series aluminum alloy sheets (AA6016-T4) were conducted using a specially designed testing apparatus. The apparatus is equipped with comb-type dies so that stress–strain curves of a sheet specimen subjected to tension followed by compression, and vice versa, can be measured without buckling of the specimen, as well as those for monotonic tension and compression. A difference was observed in the flow stresses between tension and compression for the as-received copper alloy, but not for the aluminum alloy. Moreover, stress reversal tests, such as tension followed by compression and compression followed by tension, were carried out in order to measure the Bauschinger effect. In the second part of the experiment, bending moment–curvature diagrams were measured for the as-received and pre-stretched specimens. The bending moment–curvature diagrams were compared with those calculated using the stress–strain curves obtained from the tension–compression tests, and were in good agreement with those calculated with the tension–compression asymmetry and the Bauschinger effect correctly reproduced.     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets

Magnesium alloy sheets have been extending their field of applications to automotive and electronic industries taking advantage of their excellent light weight property. In addition to well-known lower formability, magnesium alloys have unique mechanical properties which have not been thoroughly studied: high in-plane anisotropy/asymmetry of yield stress and hardening response. The reason of the unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of HCP metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A hardening law based on two-surface model was further extended to consider the general stress–strain response of metal sheets including Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous in-plane tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker–Prager’s pressure dependent yield surface was modified to include the anisotropy of magnesium alloy. The numerical formulations and characterization procedures were also presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.     

Convex polynomial yield functions

It is shown that some of the recently proposed orthotropic yield functions obtained through the linear transformation method are homogeneous polynomials. This simple observation has the potential to simplify considerably their implementation into finite element codes. It also leads to a general method for designing convex polynomial yield functions with powerful modeling capabilities. Convex parameterizations are given for the fourth, sixth and eighth order plane stress orthotropic homogeneous polynomials. Illustrations are shown for the modeling of biaxial and directional yielding properties of steel and aluminum alloy sheets. The parametrization method can be easily extended to general, 3D stress states.     

Modelling of plastic flow localisation and damage development in friction stir welded 6005A aluminium alloy using physics based strain hardening law

Plastic flow localisation and ductile failure during tensile testing of friction stir welded aluminium specimens are investigated with a specific focus on modelling the local, finite strain, hardening response. In the experimental part, friction stir welds in a 6005A-T6 aluminium alloy were prepared and analysed using digital image correlation (DIC) during tensile testing as well as scanning electron microscopy (SEM) on polished samples and on fracture surfaces. The locations of the various regions of the weld were determined based on hardness measurements, while the flow behaviour of these zones was extracted from micro-tensile specimens cut parallel to the welding direction. The measured material properties and weld topology were introduced into a 3D finite element model, fully coupled with the damage model. A Voce law hardening model involving a constant stage IV is used within an enhanced Gurson type micro-mechanical damage model, accounting for void nucleation, growth and coalescence, as well as void shape evolution. The stage IV hardening, observed in Simar et al. (2010), was found to increase the stiffness during plastic flow localisation as well as to postpone the onset of fracture as determined by the void coalescence criterion. Furthermore, the presence of a second population of voids was concluded to strongly affect the fracture strain of the high strength regions of the welds. This modelling effort links the microstructure and process parameters to macroscopic parameters relevant to the optimisation of the welds.     

A yield function for anisotropic materials Application to aluminum alloys

A phenomenological yield function is proposed to represent the plastic anisotropy of aluminum sheets. It is an extension of the functions given by Barlat et al. [Int. J. Plasticity 7 (1991) 693] and Karafillis and Boyce [J. Mech. Phys. Solids 41 (1993) 1859]. The anisotropy is represented by 12 parameters in the form of two fourth order symmetric tensors. Four other parameters influence the shape of the yield surface uniformly. The role of each parameter is described in detail. The convexity of the yield surface is proved. The implementation of the proposed yield function is done in the 3D general case in an object-oriented finite element code. It is used to represent the anisotropy of a 2024 aluminum thin sheet and the adjustment is excellent. Other anisotropic materials from the literature are also well described by the proposed yield function.     

Effect of yield surface evolution on bending induced cross sectional deformation of thin-walled sections

Bend–stretch forming is commonly used to shape extruded tubular aluminum parts for automotive and other applications. The tubes are pre-stretched, pressurized and bent over rigid curved dies. Tension prevents buckling of the compressed side and helps reduce springback. An unwanted byproduct of the process is distortion of the cross section. Small amounts of pressure applied during forming can reduce this distortion. The problem was studied through a combination of experiment and analysis. In numerical models of the process the inelastic behavior of the aluminum alloy was modeled through isotropically hardening plasticity. With the limitations imposed by this model, use of a J₂-type yield surface resulted in uniform underprediction of cross sectional deformation. The predictions matched the measurements when a non-quadratic yield function appropriately “calibrated,” was used instead. The change in yield function shape alters the instantaneous normals to the yield surface which, in turn, affect the calculated strain increments. This paper demonstrates how suitably calibrated nonlinear kinematic hardening models can have the same corrective effect. The calibration involves selection of a suitable kinematic hardening rule. Changes in the hardening direction alter the instantaneous normals and therefore alter the plastic strain increments resulting in approximately the same net effect as the switch from the von Mises to the non-quadratic yield function.     

锌基合金焊接区摩擦磨损性能研究

在ＭＭ－２００型摩擦磨损试验机上分别考察了锌基合金熔化焊（ＴＩＧ焊、气焊）焊接区熔敷金属及ＨＡＺ组织模拟试样的摩擦学性能,并用扫描电子微镜对其磨损表面形貌进行了观察和分析。结果表明：与母材相比,锌基合金熔化焊（ＴＩＧ焊、气焊）焊接区的耐磨性均有所提高,随负荷增大,磨损呈上升趋势。在２种不同熔化焊方法中,ＴＩＧ焊焊接区熔敷金属及ＨＡＺ组织模拟试样的耐磨性比气焊对应区域的耐磨性高。