Large aerospace parts are typically certified by testing narrow specimens, such as curved laminates, which have exposed free edges. These edges (not present in the production part) have been found to reduce the 3D strength of curved laminates by over 20%, showing this certification method is unreasonably conservative. The free edges also create a singularity, such that Finite Element (FE) modelling is challenging, which is typically approximated using non-linear analysis of cohesive interlaminar zones. A new treatment process is developed whereby a layer of resin is applied to the free edges of curved laminates. This significantly reduces the edge effect and delays failure. The resin edge treatment increases the strength of the curved laminate test specimens by 16%. The treatment also simplifies FE modelling by allowing for non-zero stresses normal to the laminate edge, removing the singularity. This enables use of linear FE models, which converge at the laminate edge. A linear FE method developed in this paper is conservative and predicts the strength of treated curved laminates to within 5% of the average test value. Hence it is shown that the resin edge treatment can be used to improve reliability of both certification tests and FE models.
Finite element (FE) analysis has the potential to offset much of the expensive experimental testing currently required to certify aerospace laminates. However, large numbers of degrees of freedom are necessary to model entire aircraft components whilst accurately resolving micro-scale defects. The new module dune-composites, implemented within DUNE by the authors, provides a tool to efficiently solve large-scale problems using novel iterative solvers. The key innovation is a preconditioner that guarantees a constant number of iterations regardless of the problem size. Its robustness has been shown rigorously in Spillane et al. (Numer. Math. 126, 2014) for isotropic problems. For anisotropic problems in composites it is verified numerically for the first time in this paper. The parallel implementation in DUNE scales almost optimally over thousands of cores. To demonstrate this, we present an original numerical study, varying the shape of a localised wrinkle and the effect this has on the strength of a curved laminate. This requires a high-fidelity mesh containing at least four layers of quadratic elements across each ply and interface layer, underlining the need for dunecomposites, which can achieve run times of just over 2 minutes on 2048 cores for realistic composites problems with 173 million degrees of freedom.
The Caledonian mafic and ultramfic intrusions of the Grampian region of northeast Scotland are synorogenic tholeiitic plutons of middle Ordovician age. They include layered cumulates and xenolithic, contaminated and granular gabbroic varieties. The structurally complex Huntly–Knock intrusions contain locally significant quantities of Fe–Ni–Cu sulphide, while the associated country rock metasediments are sporadically enriched in Fe-sulphide. Sulphur isotope analyses on sulphide from within and around the intrusions give the following ranges of δ 34 S; – 0.1 to —1.7‰ for disseminated to massive sulphides in the complex and deformed Littlemill-Auchencrieve contact zone; +0.7 to +4.3‰ for disseminated interstitial sulphides within cumulate and granular rocks; + 1.7 to +6.0‰ for graphitic and sulphidic pyroxenitic pegmatites; –6.0 to +16.5‰ for disseminated sulphide from country rock metasediments; –4.0 to +8.2‰ for sulphides in partially melted sediments. δ 34 S of sulphides in the igneous rocks (χ̄ = +0.5 ± 2.4‰ (1 σ ), n = 36) lie within the range usually indicated for primary magmatic sulphur, i.e. 0 ±3‰, so that the sulphide system was probably dominated by magmatic sulphur. There is, however, a distinct difference between the isotopically heavier cumulate and granular rocks ( =±2.4 ± 1.2‰ (1 σ ) n = 9) and the lighter sulphide of the contact zone (χ̄ = –1.1 ± 0.4‰ (l σ ), n = 21 ) . The possibility that the slightly negative δ 34 S values of the contact zone are due to a contribution of 32 S rich sulphur from sulphidic calcareous units is considered unlikely, due to the homogeneity of the contact zone δ 34 S values, and so the variation between the two groups is attributed to processes operative within the magma. Locally, an input from country rock sulphur has occurred as suggested by the δ 34 S values for xenolithic gabbro (+6.5‰), some of the graphitic and sulphidic pyroxenitic pegmatites (+5.9, +6.0‰) and possibly a basal olivine cumulate (+4.3‰). Although the data from the Littlemill-Auchencrieve contact zone are isotopically distinct from those Ni-Cu deposits dominated by crustal sulphur, petrographic evidence suggests that crustal involvement may have been important in the siting of the ore.
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