非線性彈性固體微孔變形特性

蔡瑞騏(Jui-chi Tsai)

指導教授 ： 李顯智

國立中央大學/工學院/土木工程學系/碩士(2014年)

摘要

宏觀的角度下，材料可使用連體力學來進行分析。然而，對於宏觀的材料弱化行為，分析時宜加入微觀的損傷行為計算以加深了解。
本研究延續連體力學之基礎概念，並且以有限元素軟體(ABAQUS)來進行分析材料微孔之變形特性。相較於文獻中所得到的解析解以及Hou和Abeyaratne對於圓形孔洞三軸變形之近似解(HAF)，此篇用數值模型對橡膠微孔的幾何形狀、外部應力邊界條件做更廣泛的探討。藉以了解肉眼看不到的微孔的形狀與材料在受力後微孔擴張到目測能辨別時之形狀之關聯。此外，本篇所使用的橡膠材料包含neo-Hooken材料模型及Ogden材料模型。由數值分析之結果顯示，可藉由目測觀察到之孔洞幾何形狀，推測出未受力前之微孔幾何及其受力方式。

關鍵字

有限元素 ； 橡膠材料 ； HAF

並列摘要

In macroscopic scale,we usually use the concept of the continuum mechanics to analysis the behavior of the material.However,in order to analyze the weakening of materials,damages in micro scale must be taken into account.
In this thesis,we will analysis the behavior of a micro void in a rubber block by using continuum mechanics and the finite element software(ABAQUS). For the deformations of a spherical micro-void,exact solutions and analytical approximate solution(the Hau-Abeyarantne field)had beed obtained.And we focus on the behavior of non-spherical micro-void in this thesis.we try to build up the relations between the visible shapes of an expanded micro-void and the invisible shape of the undeformed micro-void.Using these results we can infer about the shape of a undeformed micro-void from the observations of the expanded micro-void.The neo-Hookean model and the Ogden model are adopted in our study.

並列關鍵字

finite element ； rubber ； Hau-Abeyarantne field

參考文獻

[1] F. A. Mcclintock , A Criterion For Ductile Fracture By The Growth Of Holes. J. Appl. Mech. 35(1968), 363-371.

[2] A. Needleman, Void Growth In An Elastic-Plastic Medium. J. Appl. Mech. 39(1972) 964-970.

[3] A. L. Gurson, Continuum Theory Of Ductile Rupture By Void Nucleation And Growth: Part I—Yield Criteria And Flow Rules For Porous Ductile Media. J. Energ. Matl. Tech. , Trans.Asme,(1977) 2-15.

[4] U. Stigh, Effects Of Interacting Cavities On Damage Parameter. J. Appl. Mech. 53(1986), 485-490.

[5] A. N. Gent ,Cavitation In Rubber: A Cautionary Tale. Rubber Chem. Tech., 63(1990) 49-53.