The Effect of Stress Biaxiality on Crack Shape Development
The development of shape and size of a crack in a
pressure vessel under uniaxial and biaxial loadings is important in
fitness-for-service evaluations such as leak-before-break. In this
work finite element modelling was used to evaluate the mean stress
and the J-integral around a front of a surface-breaking crack. A
procedure on the basis of ductile tearing resistance curves of high and
low constrained fracture mechanics geometries was developed to
estimate the amount of ductile crack extension for surface-breaking
cracks and to show the evolution of the initial crack shape. The
results showed non-uniform constraint levels and crack driving forces
around the crack front at large deformation levels. It was also shown
that initially semi-elliptical surface cracks under biaxial load
developed higher constraint levels around the crack front than in
uniaxial tension. However similar crack shapes were observed with
more extensions associated with cracks under biaxial loading.
[1] L. Hodulak, H. Kordisch, S. Kunzelmann, and E. Sommer, "Influence of
the load level on the development of part-through cracks,". International
Journal of Fracture, vol. 14, 1978.
[2] J. C. JR. Newman, and I. S. Raju. "An empirical stress-intensity factor
equation for the surface crack,". Engineering fracture mechanics, vol.
15, pp. 185-192, 1981.
[3] A. Carpinteri, "Shape change of surface cracks in round bars under
cyclic axial loading,". International Journal of Fatigue, vol. 15, pp. 21-
26, 1993.
[4] X. B. Lin, and R. A. Smith, "Shape evolution of surface cracks in
fatigued round bars with a semicircular circumferential notch,".
International Journal of Fatigue, vol. 21, pp. 965-973, 1999.
[5] X. B. Lin, and R. A Smith, "Finite element modelling of fatigue crack
growth of surface cracked plates, Part II: Crack shape change,".
Engineering Fracture Mechanics, vol. 63, pp. 523-540, 1999.
[6] B. Bricksatd, and I. Sattari-Far, "Crack shape development for LBB
applications,". Engineering Fracture Mechanics, vol. 67, pp. 625-646,
2000.
[7] Y. Chen, and S. Lambert, "Numerical modelling of ductile tearing for
semi-elliptical surface cracks in wide plates,". International Journal of
Pressure Vessels and Piping, Vol. 82, pp. 417-426, 2005.
[8] J. W. Hancock, W. G. Reuter, and D. M. Parks, "Constraint and
toughness parameterised by T,". "Constraint effect in fracture". ASTM
STP 1171. Philadelphia, pp. 21-40, 1993.
[9] N. P. O-Dowd, and C. F. Shih, "Family of crack-tip fields characterised
by a triaxiality parameter-1,". Structure of fields. Journal of Mechanics
and Physics of Solids, vol. 39, pp. 989-1015, 1991.
[10] N. P. O-Dowd, and C. F. Shih, "Family of crack-tip fields characterised
by a triaxiality parameter-2,". Fracture applications. Journal of
Mechanics and Physics of Solids, vol. 40, pp. 939-963, 1992.
[11] O. Terfas, and B. Bezensek, "The development of a surface crack in a
thick vessel under ductile tearing,". Proceedings of 2009 ASME
Pressure Vessels and Piping Division Conference, July 26-30, 2009,
Prague Hilton, Czech Republic.
[12] P. M. Scott, and T. W. Thorpe, "A critical review of crack tip stress
intensity factors for semi-elliptic cracks,". Fatigue of Engineering
Materials and Structures, vol. 4, pp. 291-309, 1981.
[13] X. Wang, "Two-parameter characterization of elastic-plastic crack front
fields: Surface cracked plates under tensile loading,". Engineering
Fracture Mechanics, vol. 76, pp. 958-982, 2009.
[14] E. Berg, B. Skallerud, and C. Thaulow, "Two-parameter fracture
mechanics and circumferential crack growth in surface cracked pipelines
using line-spring elements,". Engineering Fracture Mechanics, vol. 75,
pp. 17-30, 2008.
[1] L. Hodulak, H. Kordisch, S. Kunzelmann, and E. Sommer, "Influence of
the load level on the development of part-through cracks,". International
Journal of Fracture, vol. 14, 1978.
[2] J. C. JR. Newman, and I. S. Raju. "An empirical stress-intensity factor
equation for the surface crack,". Engineering fracture mechanics, vol.
15, pp. 185-192, 1981.
[3] A. Carpinteri, "Shape change of surface cracks in round bars under
cyclic axial loading,". International Journal of Fatigue, vol. 15, pp. 21-
26, 1993.
[4] X. B. Lin, and R. A. Smith, "Shape evolution of surface cracks in
fatigued round bars with a semicircular circumferential notch,".
International Journal of Fatigue, vol. 21, pp. 965-973, 1999.
[5] X. B. Lin, and R. A Smith, "Finite element modelling of fatigue crack
growth of surface cracked plates, Part II: Crack shape change,".
Engineering Fracture Mechanics, vol. 63, pp. 523-540, 1999.
[6] B. Bricksatd, and I. Sattari-Far, "Crack shape development for LBB
applications,". Engineering Fracture Mechanics, vol. 67, pp. 625-646,
2000.
[7] Y. Chen, and S. Lambert, "Numerical modelling of ductile tearing for
semi-elliptical surface cracks in wide plates,". International Journal of
Pressure Vessels and Piping, Vol. 82, pp. 417-426, 2005.
[8] J. W. Hancock, W. G. Reuter, and D. M. Parks, "Constraint and
toughness parameterised by T,". "Constraint effect in fracture". ASTM
STP 1171. Philadelphia, pp. 21-40, 1993.
[9] N. P. O-Dowd, and C. F. Shih, "Family of crack-tip fields characterised
by a triaxiality parameter-1,". Structure of fields. Journal of Mechanics
and Physics of Solids, vol. 39, pp. 989-1015, 1991.
[10] N. P. O-Dowd, and C. F. Shih, "Family of crack-tip fields characterised
by a triaxiality parameter-2,". Fracture applications. Journal of
Mechanics and Physics of Solids, vol. 40, pp. 939-963, 1992.
[11] O. Terfas, and B. Bezensek, "The development of a surface crack in a
thick vessel under ductile tearing,". Proceedings of 2009 ASME
Pressure Vessels and Piping Division Conference, July 26-30, 2009,
Prague Hilton, Czech Republic.
[12] P. M. Scott, and T. W. Thorpe, "A critical review of crack tip stress
intensity factors for semi-elliptic cracks,". Fatigue of Engineering
Materials and Structures, vol. 4, pp. 291-309, 1981.
[13] X. Wang, "Two-parameter characterization of elastic-plastic crack front
fields: Surface cracked plates under tensile loading,". Engineering
Fracture Mechanics, vol. 76, pp. 958-982, 2009.
[14] E. Berg, B. Skallerud, and C. Thaulow, "Two-parameter fracture
mechanics and circumferential crack growth in surface cracked pipelines
using line-spring elements,". Engineering Fracture Mechanics, vol. 75,
pp. 17-30, 2008.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51125", author = "Osama A. Terfas", title = "The Effect of Stress Biaxiality on Crack Shape Development", abstract = "The development of shape and size of a crack in a
pressure vessel under uniaxial and biaxial loadings is important in
fitness-for-service evaluations such as leak-before-break. In this
work finite element modelling was used to evaluate the mean stress
and the J-integral around a front of a surface-breaking crack. A
procedure on the basis of ductile tearing resistance curves of high and
low constrained fracture mechanics geometries was developed to
estimate the amount of ductile crack extension for surface-breaking
cracks and to show the evolution of the initial crack shape. The
results showed non-uniform constraint levels and crack driving forces
around the crack front at large deformation levels. It was also shown
that initially semi-elliptical surface cracks under biaxial load
developed higher constraint levels around the crack front than in
uniaxial tension. However similar crack shapes were observed with
more extensions associated with cracks under biaxial loading.", keywords = "biaxial load, crack shape, fracture toughness, surface
crack, uniaxial load.", volume = "6", number = "9", pages = "1862-6", }