本研究採用修正型Gurson降伏準則，描述具備平面異向性之多孔金屬薄板材料行為，基材塑性行為係遵循YLD2000-2D降伏函式。同時導入受應變誘發成核(strain-induced nucleation)模型，受應力控制成核(stress-controlled nucleation)模型，孔洞成長模型，與孔洞匯合(coalescence)模型，藉以描述孔洞於材料承受塑性負載過程之發展。本研究應用有限元素分析軟體結合材料使用者副程式，檢視多孔鋁合金屬薄板於半圓球沖頭張伸(hemispherical punch stretching)成形負載條件下，薄板發生破裂之時機與位置。模擬結果與相對應實驗及相關文獻結論進行比較，獲致良好之吻合度。

A finite element analysis is carried out to assess damage evolution and crack occurrence of aluminum sheets under the hemispherical stretching procedures in the present study. A modified Gurson yield criterion is adopted to account for macroscopic behaviors of the sheet metal with porosity. Plastic responses of the matrix surrounding voids are assumed to follow the planar anisotropic yield function YLD2000-2D. Various void evolution mechanisms including nucleation, growth, and coalescence are implemented into the numerical simulations. The ultimate void volume fraction is set to characterize the failure of elements without load-carrying capacity. Calculated results show that the void growth following the Cocks and Ashby model dominates the corresponding damage accumulation. Rupture locations of the sheet based on the simulations are in fair agreement with those based on the experimental measurements reported in the literature.

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