Mixed-dimensional modeling of delamination in rare earth-barium-copper-oxide coated conductors composed of laminated high-aspect-ratio thin films

Abstract

Rare earth-barium-copper-oxide (REBCO) coated conductors are promising conductors for high energy, high field and high temperature superconducting applications. In the case of epoxy-impregnated REBCO superconducting coils, however, excessive transverse stresses generated from winding, cooling, and Lorentz forces on the REBCO conductors can cause delamination, resulting in reduction in the load-carrying capacity as well as significant degradation in the coil's critical current. In this study, the stresses and strains, and delamination in a REBCO conductor are analyzed via a mixed-dimensional finite element method (FEM) based on the cohesive zone model (CZM). The mixed-dimensional method models any number of laminated high-aspect-ratio thin layers in a composite as stacked two-dimensional (2D) surfaces, thus, resolving the thickness-dependent meshing and computational problems in modeling such composites with full three-dimensional (3D) FEM approaches. In the studied coated conductor, the major thin constituent layers, namely, the silver, REBCO and buffer layers, are modeled as 2D surfaces while the relatively thick stabilizer and substrate are in 3D layers. All the adjacent layers are coupled via spring equations under the CZM framework. The mixed-dimensional delamination model is validated by a full-3D FEM counterpart model. Simulation results show that the mixeddimensional model performs simulations with much higher computational efficiency than the full-3D counterpart while maintaining sufficient accuracy. Effects of the anvil size and initial crack size on delamination behavior are discussed and compared to experimental phenomena. Furthermore, the stress distributions of the constituent layers of the conductor under different delamination initiation sites are predicted.

Measurement of Transverse Tensile Interfacial Strength of REBCO-Coated Conductors

“…The model used in this study to simulate the delamination behaviour is based on the cohesive zone model (CZM) [33], which has been widely used to simulate the delamination behaviour in both REBCO CC tapes [32,34,35] and epoxy-impregnated pancake coils [36][37][38].…”

“…Here, u max i is the current maximum separation displacement, whose details are available in [32]. Although this study focuses on transverse tensile delamination, namely, mode I delamination, debonding in an REBCO CC tape induced by a transverse anvil pull inevitably involves a mixed mode.…”

“…In this calculation, the equivalent uniform Young's modulus and Poisson's ratio of the CC tape were set to 150 GPa and 0.3, respectively; the Young's modulus and Poisson's ratio of the epoxy resin were, respectively, set to 6.725 GPa and 0.3 according to our measurement. The initial interfacial stiffness, delamination strength, and critical energy release rates of the CZM interface were set to the values presented in [32].…”

“…This is similar to the contribution of the additional boundary constraint to the tested delamination strength in the anvil transverse tension tests. In particular, for small-scale anvil transverse tension tests, such as pin-pull, when delamination occurs, not only does the cohesive binding under the anvil section resist debonding but also the elastic-plastic deformation at the crack (delamination) front contributes to the tested delamination strength [24,32], which results in a tested delamination strength that is greater than the real one. The effect of the initial defect and excess epoxy wrapping on the test results discovered through numerical simulations indicated the importance of avoiding initial failure and excess epoxy wrapping during specimen preparation.…”

“…To describe these scattered experimental data of the delamination strength, a three-parameter Weibull distribution function was suggested and a new criterion for determining the delamination strength was proposed based on the Weibull distribution function [27]. In our previous study [32], we presented a three-dimensional (3D)/two-dimensional (2D) mixed-dimensional multi-scale finite element (FE) model to overcome the meshing difficulties typically encountered in modelling laminated thin-film multilayers in full-3D FE models. Based on the model, the calculated results indicated that the effect of the scattering of experimental data on the delamination strength was associated with intrinsic defects in CC tapes and the non-interfacial elastic-plastic deformation induced by anvil tension.…”