TY - JOUR

T1 - A crack in a viscoelastic functionally graded material layer embedded between two dissimilar homogeneous viscoelastic layers - antiplane shear analysis

AU - Paulino, Glaucio H.

AU - Jin, Z. H.

N1 - Funding Information:
We would like to acknowledge the support from the National Science Foundation (NSF) under grant No. CMS-9996378 (Mechanics & Materials Program). We also acknowledge Mr Jeong-Ho Kim for doing finite element calculations for the in-plane case analogous to that of Figure 9 for µ2/µ1 = 5.0.

PY - 2001/10

Y1 - 2001/10

N2 - A crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous viscoelastic layers is studied under antiplane shear conditions. The shear relaxation modulus of the FGM layer follows the power law of viscoelasticity, i.e., μ = μ0 exp(βy/h)[t0 exp(δy/h)/t]q, where h is a scale length, and μ0, t0, β, δ and q are meterial constants. Note that the FGM layer has position-dependent modulus and relaxation time. The shear relaxation functions of the two homogeneous viscoelastic layers are μ = μ1(t1/t)q for the bottom layer and μ = μ2(t2/t)q for the top layer, where μ1 and μ2 are material constants, and t1 and t2 are relaxation times. An elastic crack problem of the composite structure is first solved and the 'correspondence principle' is used to obtain stress intensity factors (SIFs) for the viscoelastic system. Formulae for SIFs and crack displacement profiles are derived. Several examples are given which include interface cracking between a viscoelastic functionally graded interlayer and a viscoelastic homogeneous material coating. Moreover, a parametric study is conducted considering various material and geometric parameters and loading conditions.

AB - A crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous viscoelastic layers is studied under antiplane shear conditions. The shear relaxation modulus of the FGM layer follows the power law of viscoelasticity, i.e., μ = μ0 exp(βy/h)[t0 exp(δy/h)/t]q, where h is a scale length, and μ0, t0, β, δ and q are meterial constants. Note that the FGM layer has position-dependent modulus and relaxation time. The shear relaxation functions of the two homogeneous viscoelastic layers are μ = μ1(t1/t)q for the bottom layer and μ = μ2(t2/t)q for the top layer, where μ1 and μ2 are material constants, and t1 and t2 are relaxation times. An elastic crack problem of the composite structure is first solved and the 'correspondence principle' is used to obtain stress intensity factors (SIFs) for the viscoelastic system. Formulae for SIFs and crack displacement profiles are derived. Several examples are given which include interface cracking between a viscoelastic functionally graded interlayer and a viscoelastic homogeneous material coating. Moreover, a parametric study is conducted considering various material and geometric parameters and loading conditions.

KW - Antiplane shear

KW - Correspondence principle

KW - Fracture

KW - Functionally graded material

KW - Stress intensity factor

KW - Viscoelasticity

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U2 - 10.1023/A:1012207008887

DO - 10.1023/A:1012207008887

M3 - Article

AN - SCOPUS:0035473292

VL - 111

SP - 283

EP - 303

JO - International Journal of Fracture

JF - International Journal of Fracture

SN - 0376-9429

IS - 3

ER -