Fig. 1

Illustrations of (a) the frictionless elastic contact between an FG coating-homogeneous substrate structure and a rigid cylinder, (b) the theoretical modeling based on the plane-strain assumption, (c) the treatment of the void regions flanking the actual coating as two zero-modulus segments to extend the finite-width coating to a fictitious infinite-width coating, and (d) the replacement of the fictitious infinite-width coating with a finite-width inclusion (color online)"

Fig. 2

Flowchart for solving the contact problem of interest (color online)"

Table 1

Computational parameters"

Fig. 3

Comparisons of the normal traction between the present model and FE simulations under various widths and moduli of an elastically graded coating: (a) β=1 and L1/L=0.5; (b) β=1 and L/a0−L1/a0=6; (c) β=0.5; (d) β=1; (e) β=2 (color online)"

Fig. 4

Variations of the normal traction with the gradient factor β for L/L1=2 under different dimensionless coating half-widths: (a) L1/a0=1.2; (b) L1/a0=1.8; (c) L1/a0=6 (color online)"

Fig. 5

Variations of the von Mises equivalent stress distributions with the gradient factor β for L/L1=2 under different dimensionless coating half-widths: (a)–(c) L1/a0=1.2; (d)–(f) L1/a0=1.8; (g)–(i) L1/a0=6. Left column β=0.5; middle column: β=1; right column: β=2. These bold black lines in stress contours indicate the free edges of the coated structure. Here, the equivalent stress is nondimensionalized using the Hertzian solution of the maximum normal traction p0 (color online)"

Fig. 6

Variations of the maximum normal traction, left contact half-width, and right contact half-width for L/L1=2 under different levels of β: (a) β=0.5; (b) β=1; (c) β=2 (color online)"

Fig. 7

Variations of the subsurface equivalent stress distributions for L/L1=0.2 under different levels of β: (a)–(d) β=0.5; (e)–(h) β=1; (i)–(l) β=2. The dimensionless coating half-widths in the first, second, third, and fourth columns are set to 2.5, 3, 4, and 5, respectively. These bold black lines in stress contours indicate the free edges of the coated structure. Here, the equivalent stress is nondimensionalized using the Hertzian solution of maximum normal traction p0 (color online)"

Fig. 8

Variations of the surface contact stresses for L/a0−L1/a0=5 and β=1: (a) the normal traction (i.e., −σ33 (x3/a0=0)); (b) the in-plane stress (x3/a0=0) (color online)"

Fig. 9

Variations of the maximum normal traction, left contact half-width, and right contact half-width for L/a0−L1/a0=5 and β=1 (color online)"

Fig. 10

Variations of the subsurface equivalent stress distributions for β=1 and L/a0−L1/a0=5: (a) L1/a0=0.8; (b) L1/a0=1.2; (c) L1/a0=1.6; (d) L1/a0=2. These bold black lines in stress contours indicate the free edges of the coated structure. Here, the equivalent stress is nondimensionalized using the Hertzian solution of maximum normal traction p0 (color online)"

Fig. 11

Variations of the normal traction under different coating widths and gradient factors: (a) L/L1=2, L1/a0=1.2, and β=0.5; (b) L/L1=2, L1/a0=1.2, and β=1; (c) L/L1=2, L1/a0=1.2, and β=2; (d) L/a0−L1/a0=5, L1/a0=1.2, and β=1 (color online)"