Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials

Year 2024, Volume: 30 Issue: 1, 1 - 9, 29.02.2024

Toros Arda Akşen Murat Özsoy Mehmet Fırat

Abstract

In the cup drawing process, the tensile stress in the radial direction is dominant during the drawing. However, the sheet bends around the punch and die radiuses, and the fibers touching the punch and die are exposed to compression, while the outer surfaces are exposed to tension. Therefore, the stress state at the radius regions of punch and die becomes complicated to overcome due to the bending and may influence the final earing form. The present study investigates the influence of a plasticity model involving an advanced yield criterion coupled with a combined hardening model on the earing prediction in the cup drawing process of AA6016-T4 aluminum alloy. Therefore, isotropic hardening and combined hardening models are implemented, respectively so as to show the kinematic hardening effect on the earing prediction performance. The combined hardening model comprises Armstrong-Frederic kinematic hardening and isotropic hardening rules together to characterize the hardening behavior of the sheet, and the parameters of the hardening model were obtained by considering a reversal shear test. A sixth-order polynomial-based yield criterion was implemented to represent the anisotropic response of the sheet successfully. The Hill48 yield criterion was also considered in the present study for comparison purposes. The analyses were conducted based on the additive plasticity approach and using the implicit stress update scheme in Marc commercial software. The punch force-displacement responses and earing profile predictions were obtained numerically and compared with the experimental outcomes. It was seen that introducing the combined hardening model enhances the earing prediction capability for both yield criteria. With the incorporation of the combined hardening rule, the improvement in the prediction of the earing profile was more apparent in HomPol6 results compared to Hill48. The HomPol6 yield criterion coupled with the combined hardening rule led to a better agreement in the prediction of ear formation.

Keywords

Cup drawing, Earing, Kinematic hardening, Plasticity

Homojen polinom tabanlı akma fonksiyonunun birleşik pekleşme modeli ile kullanımının anizotropik metalik malzemeler üzerindeki kulaklanma tahmin performansı

Abstract

Kap çekme işlemi esnasında, radyal yön boyunca çekme gerilmesi mevcuttur. Bununla birlikte şekillendirilecek sac, zımba ve kalıp köşelerinin etrafında bükülmektedir ve köşelere temas eden iç yüzeyler basma gerilmesi etkisi altındayken, dış yüzeyler ise çekme etkisi altındır. Bu durum sacın zımba ve kalıp köşelerinde bükülen bölümlerindeki gerilme durumunu karmaşık bir hale getirmektedir ve nihai kulak formunu etkileyebilmektedir. Bu çalışma, gelişmiş bir akma fonksiyonu ve bir birleşik pekleşme modeli içeren bir plastisite modelinin kulaklanma tahmin performansını incelemektedir. Bu kapsamda AA6016-T4 alüminyum alaşımının derin çekme işlemi incelenmiştir. Birleşik pekleşme modelinin kulaklanma tahmin performansına etkisini daha net ortaya koymak amacıyla, izotropik ve birleşik pekleşme kuralları ayrı ayrı analizlere entegre edilmiştir. Malzemenin pekleşme davranışını tanımlamak amacıyla kullanılan birleşik pekleşme modeli, Armstrong-Frederic kinematik pekleşme ve izotropik pekleşme modellerinin birleşimidir ve birleşik pekleşme modelinin parametreleri bir tersinir kayma testinin verileri kullanılarak elde edilmiştir. Sacın anizotropik davranışını isabetli bir şekilde tanımlamak amacıyla altıncı dereceden homojen polinom tabanlı bir akma fonksiyonu kullanılmıştır. HomPol6 kriterinin tahmin performansını göstermek için simülasyonlar Hill48 akma kriteri kullanılarak da yürütülmüştür. Simülasyonlar Marc ticari yazılımında eklemeli plastisite yaklaşımı ve kapalı zaman adımlı gerilme güncelleme şeması kullanılarak yürütülmüştür. Zımba kuvvet-deplasman davranışları ve kulak profil tahminleri sayısal olarak elde edilmiş ve deneysel sonuçlarla kıyaslanmıştır. Birleşik pekleşme modelinin kulaklanma tahmin yeteneğini iki akma kriteri için de iyileştirdiği görülmüştür. Bu iyileşmenin HomPol6 sonuçları için daha belirgin olduğu da kaydedilmiştir. En iyi kulak oluşum tahmininin, HomPol6 akma kriteri ile birleşik pekleşme kuralı kullanıldığında gerçekleştiği görülmüştür.

Keywords

Kap çekme, Kulaklanma, Kinematik pekleşme, Plastisite

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