Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials
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Ernian Pan Department of Civil Engineering and Department of Mathematics, University of Akron, Akron, Ohio 44325, USA (Received 1 May 2017; accepted 30 June 2017)
The interaction between interface dislocation networks and a single lattice Volterra-type dislocation is analyzed by superposition using anisotropic elastic theory in dissimilar materials. The general and nontrivial field solutions for the displacements and stresses are derived by applying the Stroh sextic formalism and Fourier transform in heterogeneous bimaterials. The present approach therefore enables the calculation of the elastic interaction forces for the glide and climb components with different elastic constants and unequal partitioning of elastic fields between adjacent crystals neighboring a semicoherent heterophase interface. Two-dimensional application examples to the pure misfit Au/Cu interface are evaluated, where the infinitely long straight lattice dislocation, parallel to the interface dislocations, is embedded in Au. The repulsive and attractive interaction forces between these two types of (intrinsic and extrinsic) defects are investigated and discussed, for which the results provide a novel basis for examining multiple large-scale dislocation interactions in anisotropic interface-dominated materials with accurate mechanical boundary conditions.
I. INTRODUCTION
The theory of misfit accommodation by dislocations at semicoherent interfaces between two adjacent materials has been pioneered by Frank and van der Merwe1 and later extended by van der Merwe2–4 for describing the elastic field and energy of intrinsic dislocation networks. Using the Peierls-Nabarro model5,6 between two dissimilar isotropic media, analytical efforts have been focused on the determination of the critical thickness in thin films during epitaxial growth at which it becomes energetically favorable to accommodate uniform lattice-mismatched strain fields by inserting stress-annihilator dislocations at interfaces.7 These calculations are mainly based on various assumptions about interfacial forces that lead to equilibrium values of the critical thickness with respect to the corresponding interface dislocation density.8–11 Besides, theoretical approaches dedicated to misfit dislocations with more accurate boundary conditions at heterophase interfaces using anisotropic elasticity theory in high-symmetry cases have been addressed to compute the elastic fields generated by single dislocations and dislocation arrays.12–20 Combining the Stroh formalism21,22 with the quantized Frank–Bilby equation,23–25 a methodology has been proposed to describe the interfacial networks Contributing Editor: Johan Brand Malherbe a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2017.287
with two sets of dislocations under the condition of vanishing far-field stresses.26–28 The present approach enables the determination of a reference state for interface misfit dislocations, within which the Burgers vectors of individual dislocations are defined. This framework
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