一种考虑孔洞形状变化的损伤细观模型及其在孔洞闭合过程中的应用
A Microscopic Damage Model Considering the Change of Void Shape and Application in the Void Closing
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摘要: 本文在一种特殊的坐标系下,建立了非线性的基体材料,有限大的椭球体中含椭球形孔洞的损伤细观模型,考虑了孔洞形状的影响.得出的粘性约束方程(或称屈服面方程)除应力∑ij,孔隙度f,幂硬化指数m外,还与孔洞的形状有关.通过曲线拟合的方法,对Gurson方程进行了修正,使之适合于非线性的基体材料、变形状孔洞的情形.最后将此模型用于分析非线性材料内部孔洞的闭合过程.Abstract: A microscopic damage model of ellipsoidal body containing ellipsoidal void for nonlinear matrix materials is developed under a particular coordinate. The change of void shape is considered in this model. The viscous restrained equation obtained from the model is affected by stress ∑ij, void volume fraction f, material strain rate exponent m as well as the void shape. Gurson's equation is modified from the numerical solution. The modified equation is suitable for the case of nonlinear matrix materials and changeable voids. Lastly, the model is used to analyze the closing process of voids.
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Key words:
- nonlinear material /
- ellipsoidal void /
- void shape /
- void closing
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[1] Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth, Part Ⅰ, Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Tech., 98(1977), 2. [2] Yamamoto, H., Conditions for shear localization in the ductile fracture of void-containing materials, Int. J. Fracture, 347(1978), 14. [3] Aravas, N., The analysis of void growth that leads to central burst during extrusion, J. Mech. Phys. Solids, 34(1986), 55. [4] Tvergaard, V., Influence of void on shear band instabilities under plane strain conditions, Int. J. Fracture, 17(1981), 389. [5] 王自强、秦嘉亮,含空洞非线性材料的本构势和空洞扩展率,固体力学学报,(2)(1989), 127 [6] Zhu Ming and Jin Quan-lin, A constitutive relation for materials containing voids and application in closing of voids, Advances in Constitutive Laws for Engineering Materials, Ed. by Fan Jing-hong and Sumio Murakami, Pergamon Press, Oxford(1989), 542. -
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