Interfacial analysis of a penny-shaped one-dimensional hexagonal functionally graded piezoelectric quasicrystal film on a temperature-dependent substrate

doi:10.1007/s10483-025-3326-9

Abstract

Abstract:

In this paper, we investigate the interfacial behavior of a thin, penny-shaped, one-dimensional (1D) hexagonal functionally graded (FG) piezoelectric quasicrystal (PQC) film bonded on a temperature-dependent elastic substrate under thermal and electrical loads. The problem is modeled as axisymmetric based on the membrane theory, with the peeling stress and bending moment being disregarded. A potential theory method, combined with the Hankel transform technique, is utilized to derive the displacement field on the substrate surface. With perfect interfacial bonding assumption, an integral equation governing the phonon interfacial shear stress is formulated and numerically solved by the Chebyshev polynomials. Explicit expressions are derived for the interfacial shear stress, the internal stresses within the PQC film and the substrate, the axial strain, and the stress intensity factors (SIFs). Numerical simulations are conducted to investigate the effects of the film’s aspect ratio, material inhomogeneity, material mismatch, and temperature-dependent material properties on its mechanical response. The results provide insights for the functional design and reliability assessment of FG PQC film/substrate systems.

Key words: one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) film, functionally graded (FG) material, three-dimensional (3D) interfacial behavior, stress intensity factor (SIF), temperature-dependent material property

2010 MSC Number:

O343.1

Kai LUO, Cuiying FAN, Minghao ZHAO, C. S. LU, Huayang DANG. Interfacial analysis of a penny-shaped one-dimensional hexagonal functionally graded piezoelectric quasicrystal film on a temperature-dependent substrate. Applied Mathematics and Mechanics (English Edition), 2025, 46(12): 2297-2316.

TrendMD

Figures/Tables 17

Fig. 1

Fig. 2

Table 1

The material properties of PQC films"

Material constant	QC1	QC2
$c 11$ /GPa	150	234.33
$c 12$ /GPa	55	57.41
$c 13$ /GPa	45	66.63
$c 33$ /GPa	90	232.22
$c 44$ /GPa	50	70.19
$e 15$ / $(C ⋅ m − 2)$	$− 0.138$	11.60
$e 31$ / $(C ⋅ m − 2)$	$− 0.160$	$− 4.40$
$e 33$ / $(C ⋅ m − 2)$	$− 0.347$	18.60
$e ′ 15$ / $(C ⋅ m − 2)$	$− 0.160$	1.16
$e ′ 33$ / $(C ⋅ m − 2)$	$− 0.350$	1.86
$K 1$ /GPa	0.084	122
$K 2$ /GPa	0.036	24
$R 1$ /GPa	$− 1.68$	0.884 6
$R 2$ /GPa	1.20	0.884 6
$R 3$ /GPa	1.20	0.884 6
$β 1$ / $(GPa ⋅ K − 1)$	$1.798 × 10 − 3$	$2.527 1 × 10 − 3$
$β 2$ / $(GPa ⋅ K − 1)$	$1.383 × 10 − 3$	$4.958 0 × 10 − 3$

Table 1

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Fig. 14

Fig. 15

Fig. 16

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