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Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

Dynamic Crack-Tip Stress and Displacement Fields Under Thermomechanical Loading in Functionally Graded Materials

[+] Author and Article Information
Kwang Ho Lee

Department of Automotive Engineering,  Kyungpook National University, Sangju City, Kyeongbuk 742-711, Republic of Korea

Vijaya Bhaskar Chalivendra

Department of Mechanical Engineering,  University of Massachusetts Dartmouth, North Dartmouth, MA 02747

Arun Shukla1

Dynamic Photomechanics Laboratory, Department of Mechanical Engineering and Applied Mechanics,  University of Rhode Island, Kingston, RI 02881shuklaa@egr.uri.edu

1

Corresponding author.

J. Appl. Mech 75(5), 051101 (Jul 10, 2008) (7 pages) doi:10.1115/1.2932093 History: Received May 11, 2007; Revised February 08, 2008; Published July 10, 2008

Thermomechanical stress and displacement fields for a propagating crack in functionally graded materials (FGMs) are developed using displacement potentials and asymptotic analysis. The shear modulus, mass density, and coefficient of thermal expansion of the FGMs are assumed to vary exponentially along the gradation direction. Temperature and heat flux distribution fields are also derived for an exponential variation of thermal conductivity. The mode mixity due to mixed-mode loading conditions around the crack tip is accommodated in the analysis through the superposition of opening and shear modes. Using the asymptotic stress fields, the contours of isochromatics (contours of constant maximum shear stress) are developed and the results are discussed for various crack-tip thermomechanical loading conditions.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Propagating crack-tip orientation with respect to reference coordinate configuration

Grahic Jump Location
Figure 2

The isochromatics associated with a stationary crack tip in FGM under heating for k3(4)o=0.1m, K1o(KI)=1.0MPam, K2o=0, K3o=5×10−4KI∕k3o, K4o=0.2K3o, M(c∕cs)=0.02, R4o=−1×104(°C), α0=0.00008∕°C, and β=0

Grahic Jump Location
Figure 3

The isochromatics associated with a propagating crack tip in FGM under heating for k3(4)o=105m, K1o(KI)=1.0MPam, K2o=0, K3o=KI∕k3o, M(c∕cs)=0.5, K4o=0.5K3o, R4o=−1×104(°C), and α0=0.00008∕°C, and β=0

Grahic Jump Location
Figure 4

The isochromatics associated with a mixed-mode propagating crack tip in FGM under heating for K1o(KI)=1.0MPam, K1*(KII)=K1o, K2o=K2*=0, K3o=KI∕k3o, K3*=0.1K3o, k3(4)o(*)=105m, M(c∕cs)=0.5, K4o=0.5K3o, R3*=R4o=−1×104(°C), α0=0.00008∕°C, and β=0

Grahic Jump Location
Figure 5

The isochromatics associated with a mixed-mode propagating crack tip in FGM under heating for K1o(KI)=K1*(KII)=1.0MPam, K2o=K2*=0, K3o=KI∕k3o, K3*=0.1K3o, k3(4)o(*)=105m, M(c∕cs)=0.5, K4*=0.1K3o, R3*=R4o=−1×104(°C), and α0=0.00008∕°C

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