Effect of plastic anisotropy and Portevin-Le Chatelier bands on hole-expansion in AA7075 sheets in -T6 and -W tempers
Graphical abstract
Introduction
As automobile industries strive to increase fuel efficiency due to environmental regulations, aluminum alloys have received high attention as an alternative to steel, for structural components of reduced weight. In particular, 7000 series aluminum alloys are of great interest due to superior mechanical properties such as high strength, corrosion resistance, and high fracture toughness. However, its inferior formability at room temperature (RT) arouses an attention of technical aids to form parts successfully, such as forming at an elevated temperature. For example, Wang et al. (2012) investigated the effect of warm temperatures (e.g., 140−220 °C) on the mechanical properties of AA7075 after forming. Zheng et al. (2019) studied microstructural evolution at elevated temperatures. Merklein et al. (2012) suggested multi-stage forming processes, including an intermediate heat treatment locally subjected in a blank to induce heterogeneous mechanical properties, for AA6016-T4 and observed significant effect of heating temperature and applying location on the cup-drawing formability. Merklein and Geiger (2002) and Kinsey et al. (2000) reported partial heating can be effective to enhance the formability of tailor-welded blank. These temperature-aided forming processes are successfully implemented to improve the formability of high-strength aluminum alloys, but three major issues remain: a) post-forming mechanical properties, b) adhesion of aluminum to the tool surfaces, and c) friction and lubrication at elevated temperatures.
As an alternative, Polmear (1997) referred the forming in -W temper, i.e., super saturated condition by solution heat treatment (SHT) followed by water quenching. de Argandona et al. (2015) commented on the -W forming (The detailed procedure for -W forming is illustrated in Fig. 1, in orders of the SHT, water-quenching, cold forming, natural and artificial aging.) as a promising process which enhances the formability at RT.
Microstructurally, in -W temper, SHT dissolves most of the alloying elements, including pre-existing precipitates, in a solid solution, and water quenching keeps the microstructure temporarily from generating precipitations. This results in the reduced strength and the enhanced ductility compared to the as-received condition, i.e., -T6 temper, as reported by Kumar and Ross (2016) and Senkov et al. (2008). This microstructural characteristics of the material in –W temper promotes the formability of the high strength aluminum such as 6000 and 7000 series even at RT. This is a definite advantage compared to any forming processes requiring heat, and alleviates concerns of poor formability or insufficient tonnage of the press typically associated with RT forming.
Feasibility of -W forming process to industrial applications has been demonstrated for several high strength aluminum alloys. Mendiguren et al. (2016) investigated formability of AA7075-T6 to form a channel shape of automotive part using -W forming and hot stamping processes. The -W forming showed a comparable result to the hot forming process, and the part can be formed without cracks. Lee et al. (2019a, 2019b) evaluated formability of AA7075 in -W temper by Nakajima test and formed a center floor tunnel, an automotive component, successfully. Schuster et al. (2019) analyzed springback and hardness of a U-channel drawn part using -W forming and hot stamping of 7000 series aluminum alloy. Kumar et al. (2017) reported -W forming showed the greatest formability improvement for 7000 series aluminum alloy compared to other heat assisted forming processes. Choi et al. (2020) examined the springback and the Forming Limit Diagram (FLD) of AA7075 in -W and -T6 tempers.
Despite the great advantage of -W temper forming, the process requires sensitive forming time scheduling due to the mechanical properties change with time due to natural aging. Leacock et al. (2013) investigated the change of mechanical properties within 120 min after water quenching and found that the yield stresses linearly increase with respect to time for the natural aging while r-values are relatively consistent. Staley (1974) and Cuniberti et al. (2010) observed that sufficient time of natural aging in the uniaxial tension leads to the strength recovering by almost 80 % of -T6 temper without any additional mechanical, thermal or chemical process, while Shabadi et al. (2012) showed that the property at biaxial stretch is not significantly affected during the natural aging. Clark et al. (2005) also researched the influence of SHT temperatures and quenching media on mechanical properties of AA7075-T6 and found that excellent linear correlation between the hardness and tensile strength. Tanner and Robinson (2004) and Moon et al. (2021) investigated an effect of quenching-rate on the precipitation hardening. Choi et al. (2019) observed the pre-strain limit can exist which could negatively affect on the final strength after artificial aging even at a small pre-strain beyond the uniform elongation.
Certain aluminum alloys in -W temper exhibit serrated, jerky flow, even though the flow in the as-received condition is homogeneous, e.g., AA7075-W vs. -T6. This serrated flow appears as band translation on the specimen surface, which is named as the Portevin-Le Chatelier (PLC) effect. Cottrell (1953) explained this serrated effect is attributed to dynamic interactions between solute and dislocation, so called dynamic strain-aging (DSA). McCormigk (1972) suggested a model for PLC effect in substitutional alloy. This results in an inhomogeneous strain field in the test-section, showing bands of higher strain than their surroundings that translate during deformation.
Many researches have investigated multiple factors related to the appearance of PLC bands such as the strain-rate (Picu et al. (2005) and Pandya et al. (2020)), stress state (Mansouri et al. (2019)), and temperature (Majidi et al. (2016) and Smerd et al. (2005)). In addition, Kang et al. (2006) observed that inhomogeneous deformation can trigger early failure during tensile deformation, and Morgeneyer et al. (2016) investigated tearing based on the 3D in situ measurement of aluminum 2000 series. Choi et al. (2020) studied the influence of early fracture on aluminum 7000 series on other formability aspect.
As an evaluation method of edge-formability, hole-expansion (HE) (ISO 16630, 2009) using a conical punch has been widely used to understand the edge quality on the formability. On the other hand, beyond the formability evaluation, the HE experiment can be a great method to validate the material modeling, including plastic anisotropy. Since 1) larger deformation can be achieved than a standard uniaxial tension due to compatibility with the surrounding material and 2) the material is deformed under various stress states between uniaxial tension, plane-strain tension, and equibiaxial tension, from the hole edge and radially inland. Parmar and Mellor (1978) suggested an analytical model to calculate the stress and strain variation around the hole. Korkolis et al. (2016) and Ha et al. (2019b) validated material models, in particular, anisotropic non-quadratic yield functions. Ha et al. (2020) applied uniaxial straining prior to the HE experiment to investigate anisotropic strain hardening effect. Cohen et al. (2009) and Kuwabara et al. (2011) investigate the role of orthotropic or more general yield function.
In this paper, the formability of AA7075 sheet in -W temper, i.e., AA7075-W, is investigated using the HE experiment, and compared with -T6 temper. Beyond HE, the experiments include the plastic anisotropy characterization of each temper, to calibrate constitutive models involving a non-quadratic anisotropic yield function (Yld2000-2d) and an isotropic hardening model (combined Swift-Voce). In parallel, finite element (FE) simulations are performed and the results are compared with the experiments regarding global (force-displacement curve) and local (thickness strain variation around the hole) metrics. For -W temper, the result is analyzed with an extended discussion to the PLC effect. To the authors’ knowledge, this is the first time to investigate the PLC effect on a spatially-inhomogeneous stress field like HE experiment and analyze regarding formability aspect.
Section snippets
Material preparation
The material of this study is the Al-Zn-Mg-Cu alloy AA7075 with the chemical composition listed in Table 1. Sheets of AA7075 of 1.5 mm thickness, in two different tempers, are investigated: one is the as-received condition in a peak-aged temper, i.e., AA7075-T6, and the other one is solution heat-treated (SHT) followed by water quenching, i.e., AA7075-W. The material in the -W temper is prepared through SHT at 470 °C for 15 min (Chen et al. (2020) and Omer et al. (2018) showed that the solid
Material modeling
The material behavior in both tempers, i.e., AA7075-T6 and AA7075-W, is modeled based on the experiments presented in Section 2. Plastic flow is described by a non-quadratic anisotropic yield function, i.e., Yld2000-2d suggested by Barlat et al. (2003), incorporating a rate-independent, associated flow rule and a strain hardening model, i.e., combined Swift-Voce suggested by Eller et al. (2016) and Roth and Mohr (2014). Linear isotropic elasticity is assumed with Young’s modulus E = 70 GPa and
Numerical model
The HE simulation is conducted using the commercial FE software Abaqus/Standard version 6.12 (implicit solver) (Abaqus User Manual, 2020) with a user-defined material subroutine (UMAT) for the constitutive models, i.e., Yld2000-2d yield function and combined Swift-Voce hardening model. The FE model for HE is built as a quarter of the problem, considering two-fold symmetry, as shown in Fig. 12a.
All components of the tooling, i.e., punch, blankholder and die, are created by non-deformable,
Discussion
The fact that the experiments and the FE prediction for -T6 and -W tempers are generally in good agreement (see Fig. 13) indicates that the constitutive models implemented in the simulation work reasonably well. The overall structural response (see Fig. 13a) is captured very well, which is somewhat expected as it is typically not very sensitive to the plastic anisotropy. This was also demonstrated earlier in a variety of other problems from Korkolis and Kyriakides (2011), Giagmouris et al.
Summary, conclusions and future work
This study investigated the effect of -W tempering on the formability of an AA7075 sheet in hole-expansion. The HE experiments were conducted using a flat-headed punch with a recess in the center to eliminate contact with the hole-edge. The strain evolution on the specimen surface was measured using the 3D-DIC technique. A combined Swift-Voce hardening law and non-quadratic anisotropic yield function Yld2000-2d were implemented in the FE simulation. The major findings of this study are:
- •
The -W
Funding
This research was partially supported by the US National Science Foundation (NSF) under awards 1563216 and 1929873. Start-up funds at The Ohio State University are acknowledged for contributing to the visit of YMC. YMC appreciates partial support from National Research Foundation of Korea (NRF-2012R1A5A1048294). The material is supplied by MS-Autotech.
CRediT authorship contribution statement
Yumi Choi: Methodology, Software, Formal analysis, Investigation, Data curation, Visualization, Writing - original draft. Jinjin Ha: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Supervision. Myoung-Gyu Lee: Conceptualization, Data curation, Writing - review & editing, Supervision, Funding acquisition. Yannis P. Korkolis: Conceptualization, Data curation, Writing - review & editing, Supervision, Funding
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The assistance of Chris Dunn in the HE experiments is acknowledged with thanks. The authors sincerely acknowledge the partial support for this work provided by Inje Jang, Chanyang Kim, Hongjin Choi, and Kijung Lee. MGL and YMC appreciate partial support from KIAT (No. N0002598).
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