In this paper, an elastic-constant stress cohesive zone model is developed to analyze the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film bonded to a couple-stress half-plane substrate, with surface effects taken into account. By imposing perfect bonding conditions and adopting a membrane assumption, the governing integral equation is constructed and numerically solved using the Chebyshev polynomial expansions. An iterative method is proposed to determine the cohesive zone size, and analytical expressions for the stress and strain distributions are derived. Systematic parametric studies are performed to elucidate the effects of characteristic length scales, substrate couple-stress length, film’s aspect ratio, and substrate-to-film stiffness ratio on the stress–strain fields and the evolution of the cohesive zone. The results provide foundational insights into interfacial mechanics and offer design guidelines for developing reliable, high-performance piezoelectric quasicrystal film devices.
BalbyshevVNKingDJKhramovAN, et al. Investigation of quaternary Al-based quasicrystal thin films for corrosion protection. Thin Solid Films2004; 447: 558–563.
2.
WangZXZhangSAXingQ, et al. Microstructure and properties of Al-Cu-Fe quasicrystal coating prepared by explosive spraying. Surf Tech2023; 52: 197–206.
3.
ZhangSXingQLiZ, et al. Study on tribological properties of explosion sprayed AlCuFeSc quasicrystal coating. Mater Sci Tech2024; 32: 25–33.
4.
JafariRCizekJLukacF, et al. A comparative study on wear resistance of cold-sprayed aluminum/quasicrystal composite coatings. J Therm Spray Tech2024; 33: 705–718.
5.
MishraSSKumbhakarPNellaiappanS, et al. Two-dimensional multicomponent quasicrystal as bifunctional electrocatalysts for alkaline oxygen and hydrogen evolution reactions. Energy Tech2023; 11: 2370021.
6.
BenderskyLABurtonB. A warm welcome to quasicrystals. J Phase Equilib Diff2012; 33: 83–84.
7.
ZhouYBHuangSN. The interaction between a piezoelectric screw dislocation and collinear rigid lines in one-dimensional hexagonal quasicrystals. Math Mech Solids2024; 30: 2446–2465.
8.
GuoXPChenJFYuHL, et al. A study on the microstructure and tribological behavior of cold-sprayed metal matrix composites reinforced by particulate quasicrystal. Surf Coat Tech2015; 268: 94–98.
9.
LiCLLiuYY. The physical property tensors of one-dimensional quasicrystals. Chinese Phys B2004; 13: 924.
10.
HuangRKDingSHZhangX, et al. Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer. Arch Appl Mech2021; 91: 1–24.
11.
HuangYZChenJZhaoM, et al. Electromechanical coupling characteristics of double-layer piezoelectric quasicrystal actuators. Int J Mech Sci2021; 196: 106293.
12.
ZhangLYZhangHLLiY, et al. Static electro-mechanical response of axisymmetric one-dimensional piezoelectric quasicrystal circular actuator. Materials2022; 15(9): 3157.
13.
DingDHQinYLWangRH, et al. Generalization of Eshelby method to the anisotropic elasticity theory of dislocations in quasi-crystals. Chinese Phys B1995; 4(11): 816–824.
14.
AltayGDökmeciMC. On the fundamental equations of piezoelasticity of quasicrystal media. Int J Solids Struct2012; 49: 3255–3262.
15.
MaYYZhaoXFLuSN, et al. Dynamic behavior of interface cracks in 1D hexagonal piezoelectric quasicrystal coating-substrate structures subjected to plane waves. J Eng Mech2024; 150: 04024090.
16.
DangHYQiDPZhaoMH, et al. Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film. Appl Math Mech-Engl2023; 44: 841–856.
17.
DangHYQiDPZhaoMH, et al. The thermally induced interfacial behavior of a thin two-dimensional decagonal quasicrystal film. Int J Fract2024; 246: 103–116.
18.
OlssonSBroitmanEGarbrechtM, et al. Mechanical and tribological properties of AlCuFe quasicrystal and Al(Si)CuFe approximant thin films. J Mater Res2016; 31: 232–240.
19.
ParsamehrHChangSYLaiCH. Mechanical and surface properties of Aluminum-Copper-Iron quasicrystal thin films. J Alloy Compd2018; 732: 952–957.
20.
WuYRLiLLiLH. Study on the effective elastic performance of composites containing decagonal symmetric two-dimensional quasicrystal coatings. Appl Math Mech-Engl2024; 45: 1655–1664.
21.
LiYYangLZZhangLL, et al. Nonlocal free and forced vibration of multilayered two-dimensional quasicrystal nanoplates. Mech Adv Mater Struct2021; 28: 1216–1226.
22.
LiYYangLZZhangLL, et al. Size-dependent effect on functionally graded multilayered two-dimensional quasicrystal nanoplates under patch/uniform loading. Acta Mech2018; 229(8): 3501–3515.
23.
HuZLZhangXYLiXF. Oscillatory singularity for bending of a partially clamped nanoplate with consideration of surface effect. Eng Fract Mech2023; 290: 109495.
24.
ZhouJSLuPXueYH, et al. A third-order plate model with surface effect based on the Gurtin-Murdoch surface elasticity. Thin Wall Struct2023; 185: 110606.
25.
AlrubAM. Study the surface effect on BiMnO3 multiferroic thin film by using Landau theory. Surf Sci2019; 681: 70–75.
26.
LiuYYuJGZhangB, et al. Lamb wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal couple-stress plates. In: 18th Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA), Dongguan, China, 8–11 November 2024, pp. 367–372. New York: IEEE.
27.
ZhangMGuoJHLiYS. Bending and vibration of two-dimensional decagonal quasicrystal nanoplates via modified couple-stress theory. Appl Math Mech-Engl2022; 43: 371–388.
28.
TvergaardVHutchinsonJW. The relation between crack-growth resistance and fracture process parameters in elastic plastic solids. J Mech Phys Solids1992; 40: 1377–1397.
29.
MiYCrisfieldMADaviesGAO, et al. Progressive delamination using interface elements. J Compos Mater1998; 32: 1246–1272.
30.
LongHLiuYWWeiYG. Debonding characterization of stiff film/compliant substrate systems based on the bilinear cohesive zone model. Eng Fract Mech2022; 265: 108363.
31.
FrancoARoyer-CarfagniG. Cohesive debonding of a stiffener from an elastic substrate. Compos Struct2014; 111: 401–414.
32.
FrancoARoyer-CarfagniG. Effective bond length of FRP stiffeners. Int J Nonlin Mech2014; 60: 46–57.
33.
GülerMAAliniaY. An elastic-constant stress cohesive zone model for an orthotropic piezoelectric actuator adhesively bonded to a substrate. Eng Fract Mech2024; 309: 110391.
34.
DingHJYangWGHuCZ, et al. Generalized elasticity theory of quasicrystals. Phys Rev B1993; 48: 7003–7010.
35.
FanTYXieLYFanL, et al. Interface of quasicrystal and crystal. Chinese Phys B2011; 20: 076102.
36.
FengXKeLLGaoY. Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects. Appl Math Mech-Engl2024; 45(4): 619–632.
37.
SongHXKeLLWangYS. Sliding frictional contact analysis of an elastic solid with couple stresses. Int J Mech Sci2017; 133: 804–816.
38.
RadiE. Loaded beam in full frictionless contact with a couple stress elastic half-plane: effects of non-standard contact conditions. Int J Mech Sci2021; 232: 111175.
39.
GulerMAAliniaYRadiE. Couple-stress effects in a thin film bonded to a half-space. Math Mech Solids2024; 29(4): 629–644.
40.
ShieldTWKimKS. Beam theory models for thin film segments cohesively bonded to an elastic half space. Int J Solids Struct1992; 29: 1085–1103.
41.
DangHYZhaoMHFanCY, et al. Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: Numerical Method. Eng Fract Mech2017; 180: 268–281.
