Thermal Fracture Analysis of Fibrous Composites with Variable Fiber Spacing Using Jk-Integral
In this study, fracture analysis of a fibrous composite
laminate with variable fiber spacing is carried out using Jk-integral
method. The laminate is assumed to be under thermal loading.
Jk-integral is formulated by using the constitutive relations of plane
orthotropic thermoelasticity. Developed domain independent form
of the Jk-integral is then integrated into the general purpose finite
element analysis software ANSYS. Numerical results are generated
so as to assess the influence of variable fiber spacing on mode I
and II stress intensity factors, energy release rate, and T-stress. For
verification, some of the results are compared to those obtained
using displacement correlation technique (DCT).
[1] R. F. Gibson, Principles of Composite Material Mechanics.
McGraw-Hill, Singapore, 1994.
[2] J. Hutchinson, “Singular behaviour at the end of a tensile crack in a
hardening material,” Journal of the Mechanics and Physics of Solids,
vol. 16, no. 1, pp. 13 – 31, 1968.
[3] J. R. Rice, “A path independent integral and the approximate analysis
of strain concentration by notches and cracks,” Journal of Applied
Mechanics, vol. 35, no. 2, pp. 379–386, 1968.
[4] J. Knowles and E. Sternberg, “On a class of conservation laws in
linearized and finite elastostatics,” Archive for Rational Mechanics and
Analysis, vol. 44, no. 3, pp. 187–211, 1972.
[5] T. Hellen and W. Blackburn, “The calculation of stress intensity factors
for combined tensile and shear loading,” International Journal of
Fracture, vol. 11, no. 4, pp. 605–617, 1975.
[6] B. Budiansky and J. R. Rice, “Conservation laws and energy-release
rates,” Journal of Applied Mechanics, vol. 40, no. 1, pp. 201–203, 1973.
[7] W.-H. Chen and K. Ting, “Finite element analysis of mixed-mode
thermoelastic fracture problems,” Nuclear Engineering and Design,
vol. 90, no. 1, pp. 55 – 65, 1985.
[8] W. Chen and K. T. Chen, “On the study of mixed- mode thermal fracture
using modified jk -integrals,” International Journal of Fracture, vol. 17,
p. R99R103, 1981.
[9] J. Chang and D. Wu, “Computation of mixed-mode stress intensity
factors for curved cracks in anisotropic elastic solids,” Engineering
Fracture Mechanics, vol. 74, no. 8, pp. 1360 – 1372, 2007.
[10] S. Chu and C. Hong, “Application of the jk integral to mixed mode crack
problems for anisotropic composite laminates,” Engineering Fracture
Mechanics, vol. 35, no. 6, pp. 1093 – 1103, 1990.
[11] E. Pan and B. Amadei, “Fracture mechanics analysis of cracked 2-d
anisotropic media with a new formulation of the boundary element
method,” International Journal of Fracture, vol. 77, no. 2, pp. 161–174,
1996.
[12] P. Sollero and M. Aliabadi, “Fracture mechanics analysis of anisotropic
plates by the boundary element method,” International Journal of
Fracture, vol. 64, no. 4, pp. 269–284, 1993.
[13] R. Khandelwal and J. C. Kishen, “Complex variable method of
computing jk for bi-material interface cracks,” Engineering Fracture
Mechanics, vol. 73, no. 11, pp. 1568 – 1580, 2006.
[14] R. Khandelwal and J. M. C. Kishen, “Computation of thermal
stress intensity factors for bimaterial interface cracks using domain
integral method,” Journal of Applied Mechanics, vol. 76, no. 4, pp.
041 010–041 010, 2009.
[15] ANSYS, ANSYS Basic Analysis Procedures Guide, Release 5.4,
Canonsburg, PA, USA. Ansys Inc., USA, 1997.
[16] J. Eischen, “An improved method for computing the {J2} integral,”
Engineering Fracture Mechanics, vol. 26, no. 5, pp. 691 – 700, 1987.
[17] S. Dag, E. E. Arman, and B. Yildirim, “Computation of thermal
fracture parameters for orthotropic functionally graded materials using
jk-integral,” International Journal of Solids and Structures, vol. 47, no.
2526, pp. 3480 – 3488, 2010.
[18] J.-H. Kim and G. H. Paulino, “Mixed-mode j-integral formulation
and implementation using graded elements for fracture analysis
of nonhomogeneous orthotropic materials,” Mechanics of Materials,
vol. 35, no. 12, pp. 107 – 128, 2003.
[19] S. Dag, “Mixed-mode fracture analysis of functionally graded materials
under thermal stresses: A new approach using j k -integral,” Journal of
Thermal Stresses, vol. 30, no. 3, pp. 269–296, 2007. [20] S. Dag, B. Yildirim, O. Arslan, and E. E. Arman, “Hygrothermal fracture
analysis of orthotropic materials using j k -integral,” Journal of Thermal
Stresses, vol. 35, no. 7, pp. 596–613, 2012.
[21] J.-H. Kim and G. H. Paulino, “Finite element evaluation of mixed mode
stress intensity factors in functionally graded materials,” International
Journal for Numerical Methods in Engineering, vol. 53, no. 8, pp.
1903–1935, 2002.
[1] R. F. Gibson, Principles of Composite Material Mechanics.
McGraw-Hill, Singapore, 1994.
[2] J. Hutchinson, “Singular behaviour at the end of a tensile crack in a
hardening material,” Journal of the Mechanics and Physics of Solids,
vol. 16, no. 1, pp. 13 – 31, 1968.
[3] J. R. Rice, “A path independent integral and the approximate analysis
of strain concentration by notches and cracks,” Journal of Applied
Mechanics, vol. 35, no. 2, pp. 379–386, 1968.
[4] J. Knowles and E. Sternberg, “On a class of conservation laws in
linearized and finite elastostatics,” Archive for Rational Mechanics and
Analysis, vol. 44, no. 3, pp. 187–211, 1972.
[5] T. Hellen and W. Blackburn, “The calculation of stress intensity factors
for combined tensile and shear loading,” International Journal of
Fracture, vol. 11, no. 4, pp. 605–617, 1975.
[6] B. Budiansky and J. R. Rice, “Conservation laws and energy-release
rates,” Journal of Applied Mechanics, vol. 40, no. 1, pp. 201–203, 1973.
[7] W.-H. Chen and K. Ting, “Finite element analysis of mixed-mode
thermoelastic fracture problems,” Nuclear Engineering and Design,
vol. 90, no. 1, pp. 55 – 65, 1985.
[8] W. Chen and K. T. Chen, “On the study of mixed- mode thermal fracture
using modified jk -integrals,” International Journal of Fracture, vol. 17,
p. R99R103, 1981.
[9] J. Chang and D. Wu, “Computation of mixed-mode stress intensity
factors for curved cracks in anisotropic elastic solids,” Engineering
Fracture Mechanics, vol. 74, no. 8, pp. 1360 – 1372, 2007.
[10] S. Chu and C. Hong, “Application of the jk integral to mixed mode crack
problems for anisotropic composite laminates,” Engineering Fracture
Mechanics, vol. 35, no. 6, pp. 1093 – 1103, 1990.
[11] E. Pan and B. Amadei, “Fracture mechanics analysis of cracked 2-d
anisotropic media with a new formulation of the boundary element
method,” International Journal of Fracture, vol. 77, no. 2, pp. 161–174,
1996.
[12] P. Sollero and M. Aliabadi, “Fracture mechanics analysis of anisotropic
plates by the boundary element method,” International Journal of
Fracture, vol. 64, no. 4, pp. 269–284, 1993.
[13] R. Khandelwal and J. C. Kishen, “Complex variable method of
computing jk for bi-material interface cracks,” Engineering Fracture
Mechanics, vol. 73, no. 11, pp. 1568 – 1580, 2006.
[14] R. Khandelwal and J. M. C. Kishen, “Computation of thermal
stress intensity factors for bimaterial interface cracks using domain
integral method,” Journal of Applied Mechanics, vol. 76, no. 4, pp.
041 010–041 010, 2009.
[15] ANSYS, ANSYS Basic Analysis Procedures Guide, Release 5.4,
Canonsburg, PA, USA. Ansys Inc., USA, 1997.
[16] J. Eischen, “An improved method for computing the {J2} integral,”
Engineering Fracture Mechanics, vol. 26, no. 5, pp. 691 – 700, 1987.
[17] S. Dag, E. E. Arman, and B. Yildirim, “Computation of thermal
fracture parameters for orthotropic functionally graded materials using
jk-integral,” International Journal of Solids and Structures, vol. 47, no.
2526, pp. 3480 – 3488, 2010.
[18] J.-H. Kim and G. H. Paulino, “Mixed-mode j-integral formulation
and implementation using graded elements for fracture analysis
of nonhomogeneous orthotropic materials,” Mechanics of Materials,
vol. 35, no. 12, pp. 107 – 128, 2003.
[19] S. Dag, “Mixed-mode fracture analysis of functionally graded materials
under thermal stresses: A new approach using j k -integral,” Journal of
Thermal Stresses, vol. 30, no. 3, pp. 269–296, 2007. [20] S. Dag, B. Yildirim, O. Arslan, and E. E. Arman, “Hygrothermal fracture
analysis of orthotropic materials using j k -integral,” Journal of Thermal
Stresses, vol. 35, no. 7, pp. 596–613, 2012.
[21] J.-H. Kim and G. H. Paulino, “Finite element evaluation of mixed mode
stress intensity factors in functionally graded materials,” International
Journal for Numerical Methods in Engineering, vol. 53, no. 8, pp.
1903–1935, 2002.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:74998", author = "Farid Saeidi and Serkan Dag", title = "Thermal Fracture Analysis of Fibrous Composites with Variable Fiber Spacing Using Jk-Integral", abstract = "In this study, fracture analysis of a fibrous composite
laminate with variable fiber spacing is carried out using Jk-integral
method. The laminate is assumed to be under thermal loading.
Jk-integral is formulated by using the constitutive relations of plane
orthotropic thermoelasticity. Developed domain independent form
of the Jk-integral is then integrated into the general purpose finite
element analysis software ANSYS. Numerical results are generated
so as to assess the influence of variable fiber spacing on mode I
and II stress intensity factors, energy release rate, and T-stress. For
verification, some of the results are compared to those obtained
using displacement correlation technique (DCT).", keywords = "Jk-integral, variable fiber spacing, thermoelasticity,
t-stress, finite element method, fibrous composite.", volume = "11", number = "3", pages = "521-8", }
