Mixed-mode Damage Model Research Articles

Modelling fracture due to corrosion and mechanical loading in reinforced concrete

Corrosion in reinforced concrete is an important feature which can lead to increased deformation and cracking, as well as to premature failure. In the present work, macro-mechanical modelling of corrosion is performed, namely the degradation of bond–slip between concrete and steel. A mixed-mode damage model is adopted, in which the interaction between the bond–slip law and the stress acting in the neighbourhood of the concrete–steel bar interface is taken into account. Bond–slip degradation is modelled using an evolutionary bond–slip relationship, which depends on the level of corrosion. Different relevant loading cases are studied. Special attention is given to the evolution of corrosion in time, under constant load. This is done by adopting a Total Iterative Approach, in which the structure is reevaluated each time step, upon damage increase due to corrosion. Pullout tests are presented to illustrate the performance of the model. Bending tests are also performed to evaluate the influence of corrosion at structural level.

Numerical and Experimental Investigation of Static Four-point Bending Response of Honeycomb Sandwich Structure: Failure Modes and the Effect of Structural Parameters

The aim of this study is to characterize and assess failure modes and the effect of structural parameters of honeycomb sandwich structure. The semi-finite element model of honeycomb sandwich structure under four-point bending load is established by a parametric method. Laminate delamination is exhibited by a contact algorithm with the mixed-mode damage model. Experiments are conducted to obtain load-displacement curves of honeycomb sandwich structure and thereby verify the applicability of finite element model. The failure modes of honeycomb sandwich structure have also been identified by comparing the experimental results with the numerical results. The effects of structural parameters on the mechanical properties of honeycomb sandwich structure are discussed. Results demonstrate that the overall stiffness of honeycomb structure is closely related to the honeycomb cell size such as length, height and foil thickness. In addition, the strength of honeycomb sandwich structure is sensitive to stacking sequence of composite laminate with different fiber orientation. The main failure modes of honeycomb sandwich structure are laminate fracture, delamination, core buckling and wrinkling. The achievements in this study have guiding significance to design high-performance sandwich structure.

Cohesive Zone Parameters Selection for Mode-I Prediction of Interfacial Delamination

In order to determine the normal cohesive strength of composite laminates, a new test methodology was proposed. The values of cohesive zone parameters (the cohesive strength and the separation energy) for mode I interlamiar fracture of E-glass/epoxy woven fabrication were computed from a series of experimental tests. Cohesive zone model simulation based on interface finite elements was conducted. A modified form of the Park-Paulino-Roesler (PPR) traction-separation law together with a bilinear mixed-mode damage model was used to simulate the damage processes, using Abaqus cohesive elements. The numerical results were compared with experimental tests and confirmed the adequacy of normal cohesive strength. To ensure the sufficient dissipation of energy that successfully predicts delamination onset and propagation, cohesive zone length and minimum number of cohesive elements at cohesive zone length were determined. Interfacial penalty stiffness and the resistance curve of the composite specimen were also computed. The results show that the modified PPR model accurately simulates the fracture process zone ahead of the crack tip as compared to the bilinear model.

Influence of multi-impacts on GFRP composites laminates

The behaviour of Glass Fibre Reinforced Composites (GFRPs) under single and multi-impact events of the same total energy was analysed. Experimental tests were performed considering circular simple supported plates impacted on its centre. The analyses of the results issuing from load–time, load–displacement and energy–time curves have shown that the sole impact of 3J is more detrimental for the plate, relative to the other cases of cumulative damage (1J+2J and 1J+1J+1J). A fine-tune analysis of damage evolution between subsequent impacts using a numerical procedure including a cohesive mixed-mode damage model was also performed. This analysis permits to verify the evolution of the projected delaminated area as well as the fracture process zone in the vicinity of delaminations. It was verified that a negligible evolution of damage occurs in the case of three consecutive impacts of the same energy. Additionally, it was concluded that the cumulative damage in the case of (1J+2J) is inferior to the one propitiated by the sole impact of maximum energy (3J).

Influence of open holes on composites delamination induced by low velocity impact loads

The aim of this study is to evaluate the influence of holes on delamination induced by low velocity impact on glass/epoxy composite laminates. Plates containing one and two holes were tested and the resulting damage was compared with the one of plate without hole. A finite element analysis including a cohesive mixed-mode damage model was performed in order to better understand the interaction between the resulting delamination and the presence of holes. It was verified that presence of holes increases the energy absorbed by damage as well as the delaminated areas. Delamination profile is also affected owing to alteration of interlaminar shear stress profiles which are the main responsible for delamination between different oriented layers.

Influence of the specimen thickness on low velocity impact behavior of composites

Abstract In this work, the influence of specimen thickness on low velocity impact behavior of carbon-epoxy composite laminates is studied. Plates with different thicknesses were tested under low velocity impact using a hemispherical impactor. The internal damage was mainly constituted by delaminations which were evaluated through the inspection of the impacted plates by the ultrasonic C-scan technique. It was observed that delaminations increase with plate thickness. In order to better understand the physical phenomenon explaining this result, a progressive damage model was used to simulate composites behavior under low velocity impact. In this context, a three-dimensional numerical analysis considering interface finite elements, including a cohesive mixed-mode damage model, which allows simulating delaminations onset and growth between layers, was performed. Good agreement was obtained between experimental and numerical analysis, which validated the proposed procedure. In addition, the proposed numerical methodology allowed identification of physical phenomena related to the influence of plate thickness on delamination size.

Numerical analysis of the dual actuator load test applied to fracture characterization of bonded joints

The dual actuator load test was numerically analyzed in order to assess its adequacy for fracture characterization of bonded joints under different mixed-mode loading conditions. This test enables asymmetric loading of double cantilever beam specimens, thus providing a large range of mixed-mode combinations. A new data reduction scheme based on specimen compliance, beam theory and crack equivalent concept was proposed to overcome several difficulties inherent to the test. The method assumes that the dual actuator test can be viewed as a combination of the double cantilever beam and end loaded split tests, which are used for pure modes I and II fracture characterization, respectively. A numerical analysis including a cohesive mixed-mode damage model was performed considering different mixed-mode loading conditions to evaluate the test performance. Some conclusions were drawn about the advantages and drawbacks of the test.

Stress and Failure Analysis of Repaired Sandwich Composite Beams using a Cohesive Damage Model

The behavior of a repaired sandwich beam subjected to four-point bending is investigated numerically using the ABAQUS® software and specially developed interface elements including a cohesive mixed-mode damage model based on the indirect use of fracture mechanics. The two major repair configurations for sandwich structures, namely overlap and scarf repair, are studied. The interface elements, placed at the middle of the adhesive, parent laminate/adhesive and adhesive/patch interfaces, allow to obtain stress distributions at these locations as well as to simulate damage onset and growth. The influence of several geometrical parameters, such as overlap length and patch thickness for overlap repairs, and scarf angle for scarf repairs, is evaluated in terms of stress analysis and strength predictions. Conclusions were drawn about design guidelines of the sandwich composite repair.

Mixed-Mode Cohesive Damage Model Applied to the Simulation of the Mechanical Behaviour of Laminated Composite Adhesive Joints

A study of the mechanical behaviour of laminated composite adhesive joints is presented in this paper. The study consists of both numerical simulations and experimental tests. It concentrates on single lap-shear joints made of carbon–epoxy laminated composites and an epoxy adhesive. The main objective is to verify the adequacy of cohesive damage models for the strength prediction of bonded joints. These models are attractive in modelling fracture problems since they do not require the definition of an initial crack and they model damage propagation without any user intervention. A mixed-mode cohesive damage model is used to simulate damage onset and growth in the adhesive layer. The model is an extension of pure mode (I and II) trapezoidal cohesive damage models. The trapezoidal shape in the constitutive law is more valid when ductile adhesives are used. The mixed-mode model requires a complete characterization of the cohesive parameters in pure modes, determined with an inverse method. Tensile tests are performed for joints with different overlap lengths. It is shown that the numerical simulations represent with a reasonable accuracy the mechanical behaviour of the joints tested.

Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.

Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre–metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values.

An experimental and numerical assessment of DCB tests on glass/polyester curved beams cut out from pipes

The aim of this work is to define a suitable procedure in order to measure the interlaminar fracture toughness of circumferential specimens cut out from ready-to-use glass reinforced polymer (GRP) pipes made by centrifugal casting. Double Cantilever Beam (DCB) tests were performed to assess the critical strain energy release rate in mode I ( G Ic), which was considered equal to initiation values. In fact, the intrinsic heterogeneous composition of these GRP pipes promoted the occurrence of uncontrollable fibre bridging, which disturbed crack propagation and avoided the attainment of a smooth R-curve. The specimen's geometry leads the mode I loading into a complex stress state at the tip of the crack opening. This mixed-mode situation was numerically quantified using the virtual crack closure technique. For that purpose, a 2D FEM analysis with interface finite elements was used. A progressive failure analysis including a cohesive mixed-mode damage model was also performed. This numerical model reproduced the DCB tests and allowed the estimation of mode II influence on the measured G Ic values. Two different data reduction schemes, modified compliance calibration (MCC) and compliance-based beam method (CBBM), were used to calculate the G Ic values. Both methods are based on the classical beam theory since it was proved by comparison with curved beam theory that this gives accurate results for the present case. These methods were assessed using a numerical model.

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.

Computational Modelling of the Residual Strength of Repaired Composite Laminates Using a Cohesive Damage Model

This work reports on a three-dimensional numerical analysis to assess the residual strength of single and double-strap repaired CFRP composite laminates, under tensile, compressive and bending loads. Interface finite elements including a triangular cohesive mixed-mode damage model are used in order to simulate damage onset and growth. The influences of several geometric changes on damage onset as well as growth and on the repair residual strength are addressed. The geometric changes include chamfering the outer and inner patch faces, filling the drilled hole with adhesive (plug filling), use of fillets of different shapes and dimensions at the outer edge of the overlap, chamfering the outer and inner parent laminate faces and combinations thereof. This work showed that with the correct repair geometry, a significant strength improvement could be achieved for all the loads considered and for both single and double-strap geometries. © Koninklijke Brill NV, Leiden, 2008

Using a cohesive damage model to predict the tensile behaviour of CFRP single-strap repairs

This work addresses both experimental and numerical analyses regarding the tensile behaviour of CFRP single-strap repairs. Two fundamental geometrical parameters were studied: overlap length and patch thickness. The numerical model used ABAQUS ® software and a developed cohesive mixed-mode damage model adequate for ductile adhesives, and implemented within interface finite elements. Stress analyses and strength predictions were carried out. Experimental and numerical comparisons were performed on failure modes, failure load and equivalent stiffness of the repair. Good correlation was found between experimental and numerical results, showing that the proposed model can be successfully applied to bonded joints or repairs.

The Effect of the Impactor Diameter and Boundary Conditions on Low Velocity Impact Composites Behaviour

The aim of present work is to study the influence of the impactor diameter and boundary conditions on low velocity impact on carbon-fibre-reinforced epoxy laminates. Experimental tests were performed on [04,904]s laminates, using a drop weight-testing machine. Circular plates were tested under low velocity impacts for two diameters of the hemispherical impactor, 12.7 mm and 20 mm, and considering similar impact energies, 2.6 J for the first impactor and 3 J for the second one. Rectangular and square plates were analysed under low velocity impacts with different boundary conditions. The impacted plates were inspected by X-radiography. Numerical simulations were also performed considering interface finite elements compatible with three-dimensional solid elements including a cohesive mixed-mode damage model, which allows to model delamination between layers. The impact tests showed that both the impactor’s diameter and boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of damage was obtained.

A mixed-mode damage model for delamination growth applied to a new woven composite

In this paper, delamination initiation and propagation of reinforced fibrous composite laminate, in single and mixed mode, are numerically predicted by taking into account the existence of imperfect interfaces between the plies. The bonding conditions between layers are characterised by jumps in displacements which are proportional to the traction stresses. In order to describe the interface damage an approach based on the indirect use of fracture mechanics considering a softening stress-relative displacements law is presented. The accuracy of the predictions is evaluated in single-mode delamination tests, in the mixed-mode bending test, and in a structural configuration consisting of the debonding of a new woven laminated composite reinforced by particles of date cores for orthopedic use. The interface is regarded as being a whole of several interfacial bonds. Each bond is supposed to be made up of three stiffnesses acting in the three directions.

Stress and failure analyses of scarf repaired CFRP laminates using a cohesive damage model

This study describes stress and failure analyses of tensile loaded repaired Carbon Fibre Reinforced Composite (CFRP) laminates, using scarf configuration. A numerical model including interface finite elements was used to obtain peel and shear-stress distributions in the directions tangent and normal to the scarf. These stresses were evaluated at several locations in the repair, namely in the middle of the adhesive, at interfaces between adhesive and patch, and between adhesive and parent material. Several scarf angle values were considered in the analysis. A cohesive mixed-mode damage model was also used to carry out the failure analysis, in order to assess the efficiency of the repairs, for different stacking sequences. A study was performed to evaluate the influence of the mechanical properties of the adhesive and parent laminate/adhesive and adhesive/patch interfaces on the strength and failure modes of the joint. It was concluded that the strengths of the adhesive and interfaces are more important than the fracture properties in the failure process of the repair. It was also verified that the strength of the repair increased exponentially with the scarf angle reduction.

Simulation of mechanical behaviour of composite bonded joints containing strip defects

The objective of this work is to evaluate the influence of strip defects on the mechanical behaviour of composite bonded joints. Experimental tests were performed using carbon-epoxy single-lap bonded joints. Numerical simulations included interface finite elements and a mixed-mode damage model based on the indirect use of fracture mechanics. The interface finite elements allow the calculation of stresses at the adherend–adhesive interfaces and the damage model allows the simulation of damage initiation and growth. The application of the model to a single-lap joint is presented. The influence of a defect on the stress fields, joint strength and type of failure was evaluated. It was verified that specific strength of the joints was not affected by the size of the defect. The numerical results showed good agreement with the experimental ones.

Modelling single and double-lap repairs on composite materials

The present work is dedicated to the study of single and double-lap repairs on composite materials, using the ABAQUS ® software and special developed interface finite elements including a cohesive mixed-mode damage model based on the indirect use of Fracture Mechanics. The objectives of this work are to evaluate the stress distributions and the residual strength under tensile loading of a repaired composite plate. It was verified that the main parameters concerning the good performance of the repair are the specimen geometry, stacking sequence and patch thickness. The numerical model allowed the simulation of damage initiation and growth. Different kinds of failure modes of these joints were observed. The influence of the properties of the layers and of the adherend/adhesive, as well as adhesive/patch interfaces in the damage modes was also evaluated. One of the main findings is related to the important influence that the strengths of the adhesives have on the failure mode, whilst adhesive and interface fracture toughness present a little influence on this phenomenon. Some conclusions were drawn about design guidelines of composite repairs.