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The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward.Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σ max , approach. In the present paper, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σ max and deciding which is the better approach for defining fracture, when suitable definitive experiments are undertaken.Keywords: cohesive zone models; fracture mechanics; laminates; peel tests; plastic deformation. 2 INTRODUCTIONThe peel test is a popular test method for measuring the peeling energy between flexible laminates [e.g. [1][2][3]. The simple single-arm form is shown in Figure 1a and the 'T-peel' variant is illustrated in Figure 1b. For the former test method, the total energy input, G, is related to the applied steady-state peel load, P, the width, b, of the specimen and the peel angle, θ, by:(1 cos )and for the 'T-peel' we essentially have two such specimens 'back-to-back', each with 2 π θ = , such that:This value of G includes the adhesive fracture energy, G c , and any plastic work done in bending the peeling arm(s). The value of the adhesive fracture energy, G c , is assumed to be a 'characteristic' property of the adhesive, or interface, and ideally independent of geometrical details of the peel test such as the thickness, h, of the peel arm and the peel angle, θ.However, the value of G c would, of course, be expected to typically be dependent upon the test rate and temperature, since we are dealing with viscoelastic materials.When only elastic deformation occurs in the peeling arm there is no energy dissipation, so that c G G = . However, in many cases, there is a rather complex bending and unbending process, as shown, for 2 π θ = in Figure 2a where the peeling arm is initially bent and then gradually straightened as the peeling proceeds. A schematic diagram of the bending moment, M/b, per unit width in the peel arm and the inverse of the local radius, 1/R, of curvature at the peel front is shown in Figure 2b and the area under the curve is the plasticenergy dissipated in bending. When a non-work hardening material is used for the peel arm, the moments tend to the plastic limit:3 where M p is the fully plastic moment, y σ is the yield stress and h is the thickness of the peel arm, and for large values of the plastic-energy dissipation:A crucial factor in the analysis is the root rotation, o θ , illustrated in Figure 3. This arises from stretching of the substrate peeling arm before it debonds and reduces the plastic work done such that the proportion of G going into plastic work,Considering now only the 90° peel test, and assuming o θ to be small, then...

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The current article presents a new implicit cell-centred Finite Volume solution methodology for linear elasticity and unstructured meshes. Details are given of the implicit discretisation, including use of a Finite Area method for face tangential gradients and implicit non-orthogonal correction. A number of 2-D and 3-D linear-elastic benchmark test cases are examined using hexahedral, tetrahedral and general polyhedral meshes; solution accuracy and efficiency are compared with that of a segregated procedure and a commercial Finite Element software, where the new method is shown to be faster in all cases.

This paper describes a self-contained parallel fluid-structure interaction solver based on a finite volume discretisation, where a strongly coupled partitioned solution procedure is employed.The incompressible fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form, and the solid deformation is described by the Saint Venant-Kirchhoff hyperelastic model in the total Lagrangian form. Both the fluid and the solid are discretised in space using the second-order accurate cell-centred finite volume method, and temporal discretisation is performed using the second-order accurate implicit scheme. The method, implemented in open-source software OpenFOAM, is parallelised using the domain decomposition approach and the exchange of information at the fluid-solid interface is handled using global face zones. The performance of the solver is evaluated in standard two-and threedimensional cases and excellent agreement with the available numerical results is obtained.

In the current work, the microstructure and fracture performance of carbon fibre-reinforced polymer (CFRP) composites based upon matrices of an anhydride-cured epoxy resin (formulated with a reactive diluent), and containing silica nanoparticles and/or polysiloxane core-shell rubber (CSR) nanoparticles, were investigated. Double cantilever beam tests were performed in order to determine the interlaminar fracture energy of the CFRP composites, while the single-edge-notched bend specimen was employed to evaluate the fracture energy of the bulk polymers. The fracture energy of the bulk epoxy polymers increased from 173 J/m 2 for the unmodified polymer to a maximum of 1237 J/ m 2 with the addition of 16 wt% of CSR nanoparticles. The toughening mechanisms were identified as (a) localised plastic shear yielding and (b) cavitation of the CSR particles followed by plastic void growth of the matrix. The steady-state propagation value of the interlaminar fracture energy of the CFRP composites increased with increasing nanoparticle concentration, from 1246 J/m 2 for the unmodified epoxy matrix to a maximum of 1851 J/m 2 with 4 wt% of silica nanoparticles and 8 wt% of CSR nanoparticles. Crack growth in the CFRP composites was dominated by fibre-bridging toughening mechanisms. The efficiency of the transfer of toughness from the bulk polymers to the carbon fibre composites was considered. The measured fracture energy of both bulk and composite materials decreased at a test temperature of -80°C, compared with room temperature, i.e. 20°C. Nevertheless, the toughening effects of both the silica and CSR nanoparticles on the bulk epoxy polymers and the CFRP composites, compared with the unmodified epoxy polymers, were still evident even at the lower temperature. Indeed, the toughening effect of the silica nanoparticles was greater at -80°C than at room temperature.