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Research Papers

Elastodynamic Interaction of Two Offset Interfacial Cracks in Bonded Dissimilar Media With a Functionally Graded Interlayer Under Antiplane Shear Impact

[+] Author and Article Information
Hyung Jip Choi

School of Mechanical Systems Engineering,
Kookmin University,
Seoul 136-702, Republic of Korea
e-mail: hjchoi@kookmin.ac.kr

Manuscript received January 17, 2014; final manuscript received May 3, 2014; accepted manuscript posted May 7, 2014; published online May 20, 2014. Assoc. Editor: Glaucio H. Paulino.

J. Appl. Mech 81(8), 081008 (May 20, 2014) (10 pages) Paper No: JAM-14-1041; doi: 10.1115/1.4027608 History: Received January 17, 2014; Accepted March 07, 2014; Revised May 03, 2014

The impact response of bonded media with a functionally graded interlayer weakened by a pair of two offset interfacial cracks is investigated under the condition of antiplane deformation. The material nonhomogeneity in the graded interlayer is represented in terms of power-law variations of shear modulus and mass density between the dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the crack problem to solving a system of Cauchy-type singular integral equations in the Laplace domain. The crack-tip behavior in the physical domain is recovered through the inverse Laplace transform to evaluate the dynamic mode III stress intensity factors as a function of time. As a result, the transient interaction of the offset interfacial cracks spaced apart by the graded interlayer is illustrated. The peak values of the dynamic stress intensity factors are also presented versus offset crack distance, elaborating the effects of various material and geometric parameters of the bonded system on the overshoot characteristics of the transient behavior in the near-tip regions, owing to the impact-induced interaction of singular stress fields between the two cracks.

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Figures

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Fig. 1

(a) Schematic of the crack problem for bonded dissimilar half-planes with a functionally graded interlayer; (b) distributions of material properties

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Fig. 2

Variations of dynamic stress intensity factors: (a) KUinner(t)/Ko; (b) KLinner(t)/Ko as a function of nondimensional time cst/a for different combinations of (μ1μ3, ρ1/ρ3) and Γ = (a + b)/(e + a + b) = 0.1 where h/a=0.5, b/a = 1.0, and Ko = τoa1/2

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Fig. 3

Variations of dynamic stress intensity factors: (a) KUinner(t)/Ko; (b) KUouter(t)/Ko; (c) KLouter(t)/Ko; and (d) KLinner(t)/Ko as a function of nondimensional time cst/a for different combinations of (μ1/μ3, ρ1/ρ3) and Γ = (a + b)/(e + a + b) = 0.5 where h/a=0.5, b/a = 1.0, and Ko = τoa1/2

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Fig. 4

Variations of dynamic stress intensity factors: (a) KU(t)/Ko; (b) KL(t)/Ko as a function of nondimensional time cst/a for different combinations of (μ1/μ3, ρ1/ρ3) and Γ = (a + b)/(e + a + b) = 1.0 where h/a=0.5, b/a = 1.0, and Ko = τoa1/2

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Fig. 5

Peak values of dynamic stress intensity factors: (a) [KUinner]peak/Ko; (b) [KUouter]peak/Ko; (c) [KLouter]peak/Ko; and (d) [KLinner]peak/Ko versus Γ = (a + b)/(e + a + b) for different combinations of (μ1/μ3, ρ1/ρ3) where h/a=0.5, b/a = 1.0, and Ko = τoa1/2

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Fig. 6

Peak values of dynamic stress intensity factors: (a) [KUinner]peak/Ko; (b) [KUouter]peak/Ko; (c) [KLouter]peak/Ko; and (d) [KLinner]peak/Ko versus Γ = (a + b)/(e + a + b) for different combinations of (μ1/μ3, h/a) where ρ1/ρ3=1.0, b/a = 1.0, and Ko = τoa1/2

Grahic Jump Location
Fig. 7

Peak values of dynamic stress intensity factors: (a) [KUinner]peak/Ko; (b) [KUouter]peak/Ko; (c) [KLouter]peak/Ko; and (d) [KLinner]peak/Ko versus Γ = (a + b)/(e + a + b) for different combinations of (μ1/μ3, b/a) where ρ1/ρ3 = 1.0, h/a=0.5, and Ko = τoa1/2

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