# The analyses of the three-dimensional stress structure near the crack tip of mode I CT specimens in elastic-plastic state (II)—The analyses of the stress structure

- 40 Downloads

## Abstract

Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper. The characteristics of the stress structure in the smooth region have been found that the variable z can separated out; the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.

A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.

### Key words

stress structure singularity*Z*

_{1}region stress triaxiality

*R*σ CTOD shear lip interpolative method degree parameter of the plane strain state

## Preview

Unable to display preview. Download preview PDF.

### References

- [1]Yue, Z. F. and C. Q. Zheng, The analysis of the three-dimensional stress structure near the crack tip of Mode I CT specimens in elastic-plastic state (I)—The analyses of constraint parameters and fracture parameters,
*Applied Mathematics and Mechanics*,**14**, 7 (1993), 659–668.Google Scholar - [2]Hutchinson, J. W., Singular behaviour at the end of a tensile crack in a hardening material,
*J. Mech. Phys. Solids*,**16**(1968), 13–31.MATHCrossRefGoogle Scholar - [3]Rice, J. R. and G. F. Rosengren, Plane strain deformation near a crack tip in a power-law hardening material,
*J. Mech. Phys. Solids*,**16**(1968), 1–12.MATHCrossRefGoogle Scholar - [4]Yue, Z. F., The Computer Simulation of Ductile Fracture of Alloys, Master Thesis, Northwestern Polytechnical University, 1991. (in Chinese)Google Scholar
- [5]Su, J. and M. J. Tu, Plane stress elastic-plastic fracture criteria and constaint intensity in crack tip regions,
*Eng. Frac. Mech.*,**37**(1990), 675–680.CrossRefGoogle Scholar - [6]Shih, C. F. and M. D. German, Requirements for a one parameter characterization of crack tip fields by the HRR singularity,
*Int. J. Frac.*,**27**(1981), 27–43.MATHGoogle Scholar - [7]Su, J., Z. J. Deng, Z. H. Li and M. J. Tu, Stress triaxiality in crack tip region of bend specimens with different crack-depth and fracture criterion at initiation.
*Eng. Frac. Mech.*,**36**(1990), 321–326.CrossRefGoogle Scholar - [8]Zhuang, T., Dual-parameter elastic-plastic fracture criteria of metals and alloys in the plane strain condition,
*Acta Mechanica Sinica*, Suppl. (1987), 154–161. (in Chinese)Google Scholar - [9]Matsoukas, G., B. Cotterell and Y.-W. Mar, The effect of shallow cracks on crack tip opening displacement,
*Eng. Frac. Mech.*,**24**(1986), 837–842.CrossRefGoogle Scholar - [10]Bapu Rao, M. N., Three-dimensional analysis of a finite thick plate with a through crack,
*Int. J. Frac.*,**17**(1981), 43–45.CrossRefGoogle Scholar - [11]Bapu Rao, M. N., Three-dimensional stress problem of a finite thick plate with a through crack under tension,
*Proc. ICF6*,**2**(1986), 963–969.Google Scholar - [12]Jin, Z. H., An analysis on three-dimensional effects near the tip of a crack in an elastic plate,
*Acta Mechanics Solida Sinica*,**11**(1990), 106–116 (in Chinese)Google Scholar - [13]Chen, X. M., N. S. Yang, and Z. X. Gou, The analysis of the singularities of stress and strain near the Mode I crack in the elastic-plastic condition,
*Applied Mathematics and Mechanics*,**9**(1988), 611–616. (in Chinese)Google Scholar - [14]Chen, X. M., Z. X. Gou, and J. L. Zhuang, The FEM analysis of the stress structure near the Mode I crack in three dimensional condition,
*Appllied Mathematics and mechanics*,**8**(1987), 559–565. (in Chinese)Google Scholar - [15]Chen, X. M., Doctoral Thesis, Northwestern Polytechnical University, 1988. (in Chinese)Google Scholar
- [16]Chan, C.,
*Collective Papers of Metal Fracture Research*, Metallurgical Press, 1982. (in Chinese)Google Scholar - [17]Machida, K., M. Kikuchi, H. Miyamoto and T. Hamada, The thickness effects of the CCT specimen,
*Transaction of Japan Society of Mechanical Engineers*, 480 (1987), AGoogle Scholar - [18]Machida, K., M. Kikuchi and H. Miyamoto, The thickness effects of the side-grooved CCT specimen,
*Transaction of Japan Society of Mechanical Engineers*, 491 (1987), AGoogle Scholar - [19]Chen, X. M., N. X. Yang and Z. X. Gou, The analysis of three-dimensional stress and strain structure near Mode I crack in the elastic-plastic state,
*Acta Mechanica Solida Sinica*,**11**(1990), 191–200 (in Chinese)Google Scholar