Growth of penny-shaped crack perpendicular to graded interface of bimaterials under inclined tension and compression

Abstract

The growth of a penny-shaped crack in a functionally graded material is analyzed. The crack is perpendicular to the functionally graded interfacial zone between two fully bonded solids, and subject to inclined tension or compression loads. The functionally graded interfacial zone is treated as a nonhomogeneous solid layer with its elastic modulus varying in the thickness direction. With the superposition principle of linear elastic fracture mechanics the available stress intensity factors of the penny-shaped crack under uniformly normal and shear stresses are incorporated into the strain energy density factor criterion for prediction of crack growth. The results of the critical external loads that will cause the crack to grow at the most possible location and along the most possible direction are presented. The effects of external load direction and material parameters on the critical loads are also examined.

分析了功能梯度材料中幣型裂紋擴展問題。該裂紋體受有與裂紋面成任意角度的張應力或壓應力,裂紋垂直于無限域中功能梯度材料夾層。假定非均勻介質的功能梯度材料夾層與兩個半無限域完全結合,其彈性模量沿厚度方向變化。利用已發表的裂紋應力強度因子數據和線彈性斷裂力學的疊加原理,將應力強度因子耦合于最小應變能密度因子斷裂判據,討論了裂紋擴展的臨界荷載;并討論了荷載方向和材料性質對臨界荷載的影響。