A parametric study of the peel test

The force required to peel a film from a substrate is generally a complex function of geometry, the constitutive properties of the film and substrate, and the interfacial cohesive properties. In most analyses, the effects of the transverse shear force that is an integral aspect of almost any peel test are neglected, although they can be incorporated in an indirect fashion through models that invoke a root-rotation angle. In this study, a complete elastic solution that incorporates all the components contributing to crack-tip deformation, including bending moment, transverse shear force and axial force, is derived in a self-consistent way. In particular, it is shown that, for a strong interface that requires a reasonably large peel strain, the transverse shear results in a significant deviation of the phase angle from earlier analyses that neglected the shear term. The present analysis also links the transverse shear component to the root-rotation angle. A cohesive-zone analysis is presented for the peeling of an elastic–plastic film. In this analysis, the interface is modeled using cohesive elements, and the film is modeled by a full, two-dimensional, finite-element analysis. This analysis allows the full effects of bending, axial loading, and transverse shear to evolve, with no a-priori assumptions being made about their relative magnitudes. The numerical results show how the peel force depends on the film thickness. When the film is relatively thin, the peel force increases with an increase in thickness as the extent of plasticity increases. This increase in plasticity is associated with (i) an increase in the contribution of bending to the deformation at the crack tip, relative to the contribution of transverse shear, and (ii) an increase in the physical limits imposed by the dimensions of the film on the volume of any crack-tip plastic zone. When the film is relatively thick, elasticity dominates the deformation of the film, and small-scale yielding effects become important. The peel force is dictated by the toughness of the interface and by crack-tip plasticity (if any) induced by the cohesive stresses. Therefore, peel forces tend to minimum values for both thick and thin films. A maximum peel force is exhibited for films with an intermediate thickness

Effects of near-tip rotation on pre-buckle crack growth of compressed beams bonded to a rigid substrate

The macroscopic pre-cracked line scratch test (MPLST), in which a debonded edge of a film is loaded in in-plane compression, has been modeled as a generic, coupled fracture–buckle problem using simple beam theory. Near crack-tip beam rotation (also called root rotation in literature), which always exists due to the eccentric loading in this type of test, has been incorporated into the governing equations. An analytical solution to the augmented problem has been derived. It is found that the near-tip rotation can introduce pre-buckle bending in the film. One important consequence of this pre-buckle bending is that it leads to the reduction of the critical buckling condition. This agrees well with the results of [Int. J. Fract. 113 (2002) 39] obtained by solving the full elastic field near the crack-tip. Furthermore, the pre-buckle bending moment at crack-tip remains negative (leading to crack closure) as long as the pre-buckle crack length is small, but it becomes positive (leading to crack opening) at larger pre-buckle crack length. The negative bending moment causes the crack-tip energy release rate to decrease as the crack propagates, which results in a stable pre-buckle crack growth. Once it becomes positive, however, the bending moment causes crack-tip energy release rate to increase rapidly as crack length increases and hence leads to an unstable (pre-buckle) crack growth. Further, the nominal phase angle is initially larger than the classic prediction of 52.1° owing to the existence of the negative crack-tip bending moment, but it drops quickly upon approaching the buckle point. All these results are confirmed by a rigorous 2D FEM calculation using cohesive zone modeling (CZM) approach. Finally the derived analytical solution has been used to analyze a set of PLST data reported in the literature. It has been demonstrated that plasticity in the adhesive layer and in the bonded film is responsible for the strong R-curve toughening characteristics in the deduced interface toughness data. It has also been shown that, once the deduced interface toughness is incorporated into a CZM simulation, both the axial loading and buckling point can be accurately predicted

Predicting failure in textile composites using the Binary Model with gauge-averaging

First introduced over a decade ago, the Binary Model has evolved into a computationally efficient tool for predicting the properties of textile composites. Key to the formulation is the question of what details of the textile composite and the distributions of stress, strain, temperature, etc., are necessary and sufficient to represent the physics of the problem adequately and to ensure useful engineering predictions. This paper is concerned specifically with the prediction of the ultimate strength in cases where failure follows a single substantial local damage event, such as the rupture or kinking of a tow or the creation of a shear band mediated by matrix damage, without further increase in the external load. The accuracy of predictions is assessed for some triaxially braided carbon/epoxy composites. A gauge length is introduced that is suggested by the micromechanics of the failure mechanisms. Predictions are made by reference to strains that are averaged over a volume whose sides are commensurate with this gauge, but nevertheless retain spatial variations associated with the textile architecture. Failure criteria for tow rupture and matrix shear failure are taken from a single un-notched tensile test; the calibrated model then successfully predicts the failure mechanism (matrix shear or fiber rupture) and ultimate strength in un-notched and open-hole tension tests for any orientation of the textile fabric relative to the load axis, as well as bending and simple shear tests. The successful predictions are made using strains calculated for an entirely elastic representation of the material, which is possible because of the brittle character of the stress–strain curves. Predictions are also attempted using strains computed under the assumption that the textile material is homogeneous. These predictions are significantly inferior

3D geometrically nonlinear augmented finite element method for arbitrary cracking in composite laminates

•Large-deformation formulation of 3D A-FEM for multiple crack evolution in composites.•Nonlinear element augmentation procedure for element stiffness and residual.•Seamless coupling of intra- and inter-laminar cracks with geometric nonlinearity.•Demonstrated analysis capability for coupled damage evolution in composite. This paper, for the first time in literature, formulated and validated a three-dimensional, nonlinear augmented finite element method (3D A-FEM) that can account for multiple crack evolution in laminated composites under large deformation. The 3D A-FEM accounts for all major cracking events (intra-ply matrix cracking, fiber rupture/kinking, and inter-ply delamination) with explicit cohesive cracks. The computational scheme is achieved by coupling the 3D A-FEs for intra-ply cracks with 3D cohesive interface elements for inter-ply delamination. The strong discontinuities of both intra- and inter-ply cracks are explicitly represented by the geometrically nonlinear cohesive zone models (CZMs). The numerical capability is demonstrated by several benchmark tests with both in-plane and out-of-plane loadings. Results show that the A-FEM predicted progressive damage processes, including the arbitrary initiation of multiple cracks and their nonlinearly coupled progression with delamination all the way up to the final catastrophic failure, are all in good agreement with experimental results

Interlaminar toughening mechanisms: in situ growth and modelling

Modelling composite toughness and what mechanisms are responsible for added toughness has been less tackled within the composites community. With the advances of computational resources and the development of arbitrary cracking models, such as the Augmented Finite Element Method (AFEM), more complex microstructures can now be tackled with multiple interacting cracks. It has been established that Mode I crack propagation in particle-toughened interlayers within a CFRP laminate involve a process zone rather than a distinct crack tip. This involves multiple cracks forming ahead of the main crack that then coalesce and leave behind bridging ligaments that provide traction across the crack flanks. Preliminary idealised 2D AFEM models are presented in this work, that highlight the effects of the relative role of neat resin to ply interface cohesive properties, and the fraction of ‘idealised de-bonds’/discontinuities, in keeping the crack path within the interlayer. 4- dimensional time-resolved Computed Tomography (CT) experiments complement the abstract models, with the chronology of damage events and resultant crack paths being directly identified in different toughened microstructures. Additionally, quantification of the bridging behaviour elucidated micromechanical differences between the systems, with the number of bridging ligaments and the total bridged area being quantified and compared to macro-scale toughness. This work is intended to improve understanding around interlaminar toughness, and lead to the development and validation of physically representative micro-mechanical model

Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation

An embedded-process-zone (EPZ) model was used to study the coupling between fracture of the interface and plastic deformation of the adherends in an adhesively-bonded joint. In this model, it was assumed that the primary role of the adhesive layer is to provide a traction-separation law for the interface. A series of experiments were performed in which thin, adhesively-bonded, symmetrical, double-cantilever beams made of an aluminum alloy were split by inserting different sizes of wedges along the interface. The parameters for the interfacial traction-separation law were determined by comparing the results of these experiments with numerical simulations using the EPZ model. It was found that once these parameters had been established for one thickness of specimen, the EPZ model could be used without further modification to predict the effect of the wedges on specimens made with different thicknesses of aluminum. These predictions showed excellent agreement with experimental observations. A subsequent series of tests involved monitoring the load, displacement and deformed shapes of a series of T-peel specimens made with the same combination of adhesives and adherends. Without changing any of the parameters determined from the wedge tests, the EPZ model gave excellent quantitative predictions for the results of these T-peel tests

Elastic–plastic mode-II fracture of adhesive joints

A numerical study of the elastic–plastic mode-II fracture of adhesive joints is presented in this paper. A traction–separation law was used to simulate the mode-II interfacial fracture of adhesively bonded end-notched flexure (ENF) specimens loaded in three-point bending, with extensive plastic deformation accompanying failure. The fracture parameters for the traction–separation law were determined by comparing the numerical and experimental results for one particular geometry. These parameters were then used without further modification to simulate the fracture of other ENF specimens with different geometries. It was found that the numerical predictions for the loads and deformation were in excellent agreement with the corresponding experimental results