A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

Abstract

Abstract: In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

Key words: fracture mechanics, stress intensity factor, weighted residual method, crack tip field

Zhang Ning-sheng;Zhao Xue-ren;Hsueh Dah-wei. A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS. Applied Mathematics and Mechanics (English Edition), 1991, 12(12): 1123-1134.

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References

[1] Hutchinson,J.W.,Singular behaviour at the end of a tensile crack in a hardening material,J.Mech.Phys.Solids,16,1(1968),13-31.
[2] Hutchinson J.W.,Plastic stress and strain fields at a crack tip,J.Mech.Phys,Solids,16,5(1968),337-347.
[3] Rice,J.R.and G.F.Rosengren,Plane strain deformation near a crack tip in a power-lawhardening material,J.Mech.Phys.Solids,16,1(1968),1-12.
[4] Hsueh Dah-wei,An elastic-plastic analytical analysis near a crack tip,Yeh K.Y.Ed.,Progressin Applied Mechanics,Printed in Netherlands,Martinus Nijhoff Publishers(1987),339-349.
[5] Zhao Xue-ren and Zhang Ning-sheng,A probe into the method of elastic-plastic analysis neara crack tip,J.Beijing Institute of Technology,10,2(1990),18-23. (in Chinese).
[6] Huang Ke-zhi and Gao Yu-chen,Crack-tip singularly field in fracture mechanics.Advance inMechanics,14,4(1984),405-415. (in Chinese).
[7] Fan Tian-you,Advance in fracture dynamics.Advance in Mechanics,161(1986),1-13. (in Chinese).
[8] Gao Yu-chen,On the approach solutions of the crack tip field in strain demage materials,A Collections of Chinese Scholars Papers in the 16th ICTAM,Publishing House of Dalian Institute of Technology(1987),320-332. (in Chinese).
[9] Huang Ke-zhi and Yu Shou-wen,The elastic-plastic fracture mechanics,Qinghua University Publishing House(1985).(in Chinese).
[10] Zhao Xue-ren,An approach to the elastic-plastic analysis of the plane strain mode I crack,Appl.Math,and Mech.,11,4(1990),363-366.
[11] Chien Wei-zang,Superposing the finite element method on the singular solutions to calculate the stress intensity factor,A Paper Collections on Applied Mathematics and Mechanics,Jiangsu Science and Technology Publishing House(1979),184-192. (in Chinese).
[12] Zhang Ning-sheng and Zhao Xue-ren,Superposing the finite element method on the singular solutions to calculate the stress intensity factor under dynamical loads,J.Beijing Institute of Technology,10,4(1990) 34-39. (in Chinese).
[13] Zhao Xue-ren,A probe into the calculation of stress intensity factor,J.of Ordnance,1(1987),45-49. (in Chinese).
[14] Chen Chi,A modification of the plastic zone of hardening material,Mechanics,2(1975),78-81. (in Chinese)

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