TY - JOUR
T1 - T-stress in orthotropic functionally graded materials
T2 - Lekhnitskii and Stroh formalisms
AU - Kim, Jeong Ho
AU - Paulino, Glaucio H.
N1 - Funding Information:
We gratefully acknowledge the support from NASA-Ames, Engineering for Complex Systems Program, and the NASA-Ames Chief Engineer (Dr. Tina Panontin) through grant NAG 2-1424. We also acknowledge additional support from the National Science Foundation (NSF) under grant CMS-0115954 (Mechanics & Materials Program). In addition, we would like to thank three anonymous reviewers for their valuable comments and suggestions. Any opinions expressed herein are those of the writers and do not necessarily reflect the views of the sponsors.
PY - 2004/4
Y1 - 2004/4
N2 - A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a "generalized isoparametric formulation" and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.
AB - A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a "generalized isoparametric formulation" and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.
KW - Finite element method (FEM)
KW - Fracture mechanics
KW - Functionally graded material (FGM)
KW - Generalized isoparametric formulation (GIF).
KW - Interaction integral
KW - Orthotropic materials
KW - T-stress
KW - Two-state integral
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U2 - 10.1023/B:FRAC.0000031092.47424.f0
DO - 10.1023/B:FRAC.0000031092.47424.f0
M3 - Article
AN - SCOPUS:2942653175
SN - 0376-9429
VL - 126
SP - 345
EP - 384
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 4
ER -