The method of continuously distributed dislocations is used to study the distribution of screw dislocations in a linear array piled up near the interface of a two-phase isotropic elastic thin film with equal thickness in each phase. The resulting singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of dislocations in the pileup.
EshelbyJDFrankFCNabarroFRN. The equilibrium of linear arrays of dislocations. Phil Mag1951; 42: 351–364.
2.
ChouYT.Linear dislocation arrays in heterogeneous materials. Acta Metall1965; 13: 779–783.
3.
ChouYTChouTWLiJCM. Screw dislocation pileups and shear cracks in a lamellar composite. J Appl Phys1970; 41(11): 4448–4450.
4.
BarnettDM.The effect of shear modulus on the stress distribution produced by a planar array of screw dislocations near a bi-metallic interface. Acta Metall1967; 15: 589–594.
5.
BarnettDMTetelmanAS.The stress distribution produced by screw dislocation pile-ups at rigid circular cylindrical inclusions. J Mech Phys Solids1966; 14: 329–348.
6.
BarnettDMTetelmanAS.The stresses produced by a screw dislocation pileup at a circular inclusion of finite rigidity. Can J Phys1967; 45: 841–863.
7.
KuangJGMuraT.Dislocation pile-up in two-phase materials. J Appl Phys1968; 39: 109–120.
8.
KuangJGMuraT.Dislocation pile-up in half-space. J Appl Phys1969; 40: 5017–5021.
9.
KuanHHirthJP.Dislocation pileups near the interface of a bimaterial couple. Mater Sci Engng1976; 22: 113–131.
10.
WagonerRH.Calculating dislocation spacings in pile-ups at grain boundaries. Metall Trans A1981; 12A: 2015–2023.
11.
VoskoboinikovREChapmanSJMcLeodJB, et al. Asymptotics of edge dislocation pile-up against a bimetallic interface. Math Mech Solids2009; 14: 284–295.
12.
LubardaVA.An analysis of edge dislocation pileups against a circular inhomogeneity or a bimetallic interface. Int J Solids Struct2017; 129: 146–155.
13.
YoonJRuCQMioduchowskiA.Surface instability of a bilayer elastic film due to surface van der Waals forces. J Appl Phys2005; 98: 113503.
14.
ChuSNG.Screw dislocation in a two-phase isotropic thin film. J Appl Phys1982; 53(4): 3019–3023.
15.
ErdoganFGuptaGD.On the numerical solution of singular integral equations. Quarterly Appl Math1972; 29: 525–534.
