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EM 388F Term Paper: The ERR and the effect of free surface on stress intensity factor in 3D crack problem


  In general fracture theory, stress intensity factor or energy release rate have been obtained through the assumption of 2D problem. In other words, the energy release rate is constant along the crack line(front) in the z direction. However, when we consider 3D crack problem, the energy release rates(G) value show a significant drop close to the free surface when compared to the 2D solution. This is considered due to the “free surface effect” when a crack meets a free surface. Precisely, stress intensity factor is zero on free surface and the singularity does not have the classical square-root any more.

  In this term project, I will show the tendency of energy release rates along the crack front by dint of this free surface effect. So the distribution of energy release rate, G across the specimen width will be evaluated numerically by ABAQUS/standard and then, the results will be compared to the 2D solution. A double cantilever beam(DCB) specimen is introduced for a numerical solution. The specimen is idealized 3D structure with isotropic material. Finally, I will also explain the process of obtaining the analytic solution for stress intensity factor of the free surface in a half space by introducing the Boussinesq-Papkovich-Neuber functions.

 [1] B.D. Davison, R.A. Schapery, “effect of finite width on deflection and energy release rate of an orthotropic double cantilever specimen”, J of Composite Material, Vol.22-July 1988

 [2]J.P. Benthem, “ State of stress at the vertex of a quarter-infinite crack in a half-space”, Int. J. Solids structures, 1977, Vol.13. pp 479-492

Office presentation icon EM388F Tempaper.ppt482.5 KB
PDF icon EM388F-Termpaper(Final).pdf646.73 KB


Rui Huang's picture


Please add "EM 388F Term Paper:" at the beginning of your title. 


Good example. Thank you for sharing.


Ariatedja, Julendra B

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