An incompatible singular elastic element for two- and three-dimensional crack problems

A new 3 node singular finite element has been derived. This element is incompatible and has to be used in conjunction with incompatible 4 node quadrilateral elements. An extension to three dimensional problems is also presented. This element is used to compute the stress intensity factor along the crack border in a wire with a semi elliptical surface crack subject to tension and for a large variety of elliptical shapes.RésuméOn a établi un nouvel élément fini á trois nodes, de caractère incompatible, et devent être utilisé de concert avec un élément quadrilatéral à quatre nodes. On présente également une extrapolation à des problèmes tridimensionnels.Cet élément est utilisé pour calculer le facteur d'intensité de contraintes le long du bord d'une fissure dans un fil, en considérant une fissure de surface semi-elliptique soumise à traction, et dans le casa d'une grande variété de formes elliptiques.

[1]  W. S. Blackburn.  Calculation of stress intensity factors for straight cracks in grooved and ungrooved shafts , 1976 .

[2]  A. Din,et al.  Stress intensity factors for fatigue cracking of round bars , 1981 .

[3]  J. Z. Zhu,et al.  The finite element method , 1977 .

[4]  A. Athanassiadis,et al.  Linear elastic fracture mechanics computations of cracked cylindrical tensioned bodies , 1981 .

[5]  A. R. Luxmoore,et al.  An assessment of crack tip singularity models for use with isoparametric elements , 1979 .

[6]  J. Jalouneix,et al.  On the front surface correction factor for semi-elliptical surface cracks , 1982 .

[7]  G. C. Sih,et al.  Applications of the finite element method to the calculations of stress intensity factors , 1973 .

[8]  Huy Duong Bui,et al.  An integral equations method for solving the problem of a plane crack of arbitrary shape , 1977 .

[9]  D. M. Tracey.  Finite elements for three-dimensional elastic crack analysis , 1974 .

[10]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .

[11]  D. J. Cartwright,et al.  Strain-energy release rate for a single-edge-cracked circular bar in tension , 1978 .

[12]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

[13]  G. C. Sih,et al.  Methods of analysis and solutions of crack problems : recent developments in fracture mechanics : theory and methods of solving crack problems , 1973 .

[14]  D. M. Parks.  A stiffness derivative finite element technique for determination of crack tip stress intensity factors , 1974 .

[15]  Tian-You Fan,et al.  The approximate analytical solution for both surface and embedded cracks in cylinder with finite size , 1982 .

[16]  Thomas A. Cruse,et al.  THREE-DIMENSIONAL FRACTURE MECHANICS ANALYSIS , 1977 .

[17]  T. K. Hellen.  On the method of virtual crack extensions , 1975 .

[18]  W. K. Wilson.  Finite element methods for elastic bodies containing cracks , 1973 .

[19]  R. Barsoum,et al.  Discussion of paper by R. D. Henshell and K. G. Shaw , 1976 .

[20]  H. Abé,et al.  Stress intensity factors for a semi-elliptical crack in the surface of a semi-infinite solid , 1980 .

[21]  T. K. Hellen,et al.  Calculation of stress intensity factors in three dimensions by finite element methods , 1977 .

[22]  D. M. Tracey,et al.  Finite elements for determination of crack tip elastic stress intensity factors , 1971 .

[23]  Ka Peters,et al.  Stress Intensity Factors for Single-Edge-Crack Solid and Hollow Round Bars Loaded in Tension , 1981 .

[24]  R. D. Henshell,et al.  CRACK TIP FINITE ELEMENTS ARE UNNECESSARY , 1975 .