鋁合金在軸扭內壓空間降伏面演化之實驗與分析

本文旨在探討鋁合金6061在軸扭環(σ zz , σ zθ , σ θθ )三維應力空間中降伏面演化之現象。利用同一預加載路徑下, 不同截面之降伏應力資料點, 建立三維應力空間中的降伏面。在探尋降伏點的過程中, 經由設計實驗定性分析發現, 鋁合金6061中空試桿的彈性行為並非等向性, 而是立方性。因此本文根據立方線彈性組成律設計降伏點判定準則, 使探尋路徑由定環應力截面推展至定扭應力截面。由五種不同方向、不同大小之預加載路徑探尋降伏面之實驗結果可以整理出降伏面在三維應力空間之演化情形, 其共通的特性為接續降伏面均會朝預加載方向移動, 並在預加載方向逐漸變尖, 而旋轉現象則各有不同。軸向預應變及自由端扭向預應變之接續降伏面會繞著σ zz − σ zθ 平面上之斜線旋轉; 而軸環比例路徑預應力與環向預應力之接續降伏面分別以預加載方向與σ zθ 方向為軸旋轉 ; 固定環向應力20MPa 時之自由端扭向預應變之接續降伏面, 其旋轉軸則不在座標面上。本文也搭配三元三次多項式擬合出三維空間之接續降伏面, 以輔助觀察在(σ zz , σ zθ , σ θθ )空間中接續降伏面演化現象。

關鍵字

降伏面；降伏面演化；降伏面旋轉；軸扭環實驗；鋁合金6061 ；立方材料；三元三次多項式

並列摘要

The evolution of yield surface in three dimentional axial-torsional-hoop stress space for aluminum alloy Al 6061 was studied in this thesis. Yield surface of three dimensional stress space was conducted by the yield points of several planer detections under a pre-loading path. By virtue of speciﬁed experiments and qualitative analysis, we found the elastic behavior of Al 6061 is not isotropic but cubic. Therefore, we designed a criterion of yield stress determination based on the incremental relationsof linear elasticity for cubic material. It enable us to conduct probing paths not only on the plane of constant hoop stress but also on the plane of constant torsional stress. After ﬁve kinds of diﬀerent pre-loading paths, we observed that the subsequent yield surfaces move toward pre-loading directions, and show a sharp front in the pre-loading directions. Diﬀerent characteristics of rotation are exhibited in our experiments. The sub- sequent yield surfaces for axial pre-strain and for free-end pre-torsion rotate each around an axis on the σ θθ = 0 plane. The yield surfaces for axial-hoop proportional pre-stress and hoop pre-stress show the rotation around the pre-loading direction and the σ zθ axis respectively. The rotation axis of free-end pre-torsion with σ θθ = 20 MPa is not on the coordinate planes. The ﬁtted results of cubic polynominals in three variables are supplemented our observation on yield surface evolution in the (σ zz , σ zθ , σ θθ ) stress space.

並列關鍵字

Al 6061 ； cubic material ； yield surface ； axial-torsional-hoop dimentional stress space ； rotation ； cubic polynominal

參考文獻

for the Royal Society of London, Vol. 230, pp. 323-362, 1932.

[1] Ivey, H. J., Plastic stress-strain relations and yield surfaces for aluminum alloys, Journal

[2] Hecker, S. S., Yield surface in prestrained aluminum and copper, Metallurgical and Ma-

terials Transactions., Vol. 2, pp. 2077-2086, 1971.

[3] Hill, R., Hecker, S. S., and Stout, M. G., An investigation of plastic ﬂow and diﬀerential

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鋁合金在軸扭內壓空間降伏面演化之實驗與分析

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