Abstract
Forming limit curve (FLC) is an important failure criterion for sheet metals in sheet metal forming, while the M-K model is widely used for the prediction of the FLC. In the M-K model, such prediction is greatly influenced by the initial thickness imperfection factor and material properties, from which the original M-K model’s theoretical derivation is proposed as a solution to the above mentioned issue in this paper. Then the relationship between the M-K model and Keeler’s empirical formula is then studied, from which a new method to predict FLC is proposed that combines the M-K model with Keeler’s empirical formula according to the previous analyses. It turns out that this new method can simplify the calculation procedure. Finally, the experimental results of two kinds of aluminum alloys, AA6016 and AA5182, have verified the effectiveness of the proposed method.
Highlights
Lightweight materials are currently a hot issue in the automotive and aerospace industry
In order to predict the forming limit curve (FLC) more precisely, the M-K method is combined with Keeler’s empirical formula, where FLC0 is calculated by the M-K method, and the accurate FLC is calculated according to Equation (15)
Calculating FLC0 under the M-K method, and the FLC curve according to Equation (15), the FLCs are presented in Figures 10 and 11
Summary
Lightweight materials are currently a hot issue in the automotive and aerospace industry. The performance of the original M-K model on prediction of the FLC for aluminum alloy is in need of further research. Relationship between M-K Model and Keeler’s Empirical Formula The hardening model is expressed as σ = Kεn, During each iteration, σ1AtA is a constant, while the stress component σ1B and the thickness tB are determined by the strain increment of zone B dεBi. That is to say, e is a function of dεBi. From Equations (2) and (6), the strain increment dε is a function of dεBi. we have σ1B = σ dεBi g dεBi = Kh dεBi ,. There is a slight difference between Keeler’s empirical formula and M-k method The former is dependent on the thickness of the sheet metal, which is expressed as Equations (15) and (16), while the latter introduces the thickness imperfection
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