Fabrizio Greco

Mixed mode delamination in plates: a refined approach

Abstract Energy release rate and its mode partition in layered plates are analysed by using an improved laminated plate model. The adhesion between layers is modelled by means of a linear interface acting in the opening and sliding failure mode directions. Stress singularities at the crack tip are recovered when the stiffness of the interface approaches infinity. Kirchhoff or Reissner–Mindlin plate models are employed to describe the layers. Analytical solutions of the relevant governing equations are obtained through a variational formulation of an augmented total potential energy, in which the stiffness of the interface introduces kinematics constraints in the form of a penalty functional. Closed form solutions for energy release rates are given evidencing the effectiveness and the simplicity of the proposed model. Comparisons with fracture mechanics results––when available––are shown discussing the validity of the proposed mechanical model to predict mode partition. Interesting features emerging with the introduction of the layer-wise Reissner–Mindlin model are also highlighted, particularly with reference to coupling terms arising from shear effects.

Continuum Damage-healing Mechanics with Application to Self-healing Composites

The general behavior of self-healing materials is modeled including both irreversible and healing processes. A constitutive model, based on a continuum thermodynamic framework, is proposed to predict the general response of self-healing materials. The self-healing materials’ response produces a reduction in size of microcracks and voids, opposite to damage. The constitutive model, developed in the mesoscale, is based on the proposed Continuum Damage-Healing Mechanics (CDHM) cast in a consistent thermodynamic framework that automatically satisfies the thermodynamic restrictions. The degradation and healing evolution variables are obtained introducing proper dissipation potentials, which are motivated by physically based assumptions. An efficient three-step operator slip algorithm, including healing variables, is discussed in order to accurately integrate the coupled elastoplastic-damage-healing constitutive equations. Material parameters are identified by means of simple and effective analytical procedures. Results are shown in order to demonstrate the numerical modeling of healing behavior for damaged polymer-matrix composites. Healed and not healed cases are discussed in order to show the model capability and to describe the main governing characteristics concerning the evolution of healed systems.

INTERLAMINAR DAMAGE MODEL FOR POLYMER MATRIX COMPOSITES

A constitutive model for fiber-reinforced composite materials with damage and unrecoverable deformation, which for the first time accounts for interlaminar damage, is presented. The formulation is based on Continuous Damage Mechanics coupled with Classical Plasticity Theory in a consistent thermodynamic framework using internal state variables. In-plane damage and novel formulation of interlaminar damage are included in order to describe the main failure modes of laminates structures. A novel implementation of the constitutive model into a finite element formulation incorporating geometric nonlinearity is presented. The model uses a small number of adjustable parameters, which are identified from available experimental data. Comparisons with experimental data for composite laminates under torsion loading are shown to validate the model for interlaminar damage. Coupled material and geometrical nonlinear analysis with simultaneous in-plane and interlaminar damage is demonstrated. The effect of warping on interlaminar damage is shown to be significant.

An asymptotic analysis of delamination buckling and growth in layered plates

Delamination buckling and growth in compressively loaded elastic-layered plates is analyzed. The delamination growth process is assumed to start from an initial interlaminar adhesion defect and propagate as induced by buckling. The relevant governing equations for buckling and initial postbuckling are developed by employing asymptotic analysis results. The energy release rate concept is then applied to analyze delamination growth. Two techniques are analyzed, namely the global energy approach and the local J-integral approach. For the two cases, the effects of the asymptotic approach accuracy on the postbuckling and delamination growth are investigated. A general model of the plate is proposed, in which a global instability of the whole plate can occur together with a local instability of the layers. In addition, simplified models are examined which may be useful in many engineering applications, although based on hypotheses about the plate geometry. Finally, the numerical results show the effectiveness of the developed models. Comparisons between the general model and the thin film approximation show the convergence of the former to the latter.

Damage evolution in bimodular laminated composites under cyclic loading

This work deals with layered composite structures under cyclic loading. In particular, bimodular material laminates are considered and the Bert model is adopted. The analysis is developed using a finite element procedure based on a theory which takes into account the shear deformability (layer-wise deformation plate theory). The adoption of this theory is important to improve the stress evaluation by obtaining a better utilisation of the polynomial failure criteria for the identification of the cracked zones. To determine the stiffness reduction due to the damage evolution, the Laws et al. formulas are adopted for two types of crack (penny-shaped and slit-aligned). The analysis of the structures under cyclic loading is carried out by adopting some reasonable hypotheses on the reduction of the mechanical parameters and on the crack detection.

Delamination in composite plates: influence of shear deformability on interfacial debonding

Abstract An elastic interface model is introduced to investigate the effects of in-plane and out-plane shear stresses on interfacial debonding in laminated composite plates by means of the energy release rate concept. This is done by utilising an improved laminated plate model in which the Reissner–Mindlin kinematics type for each layers is coupled with an adhesion mechanism modelled by means of a linear interface model, acting in the opening and sliding failure mode directions. The problem is faced through an analytical solution procedure. Increasing the stiffnesses of the interface leads to restoring displacement continuity at the interface between layers and to recovering energy release rate components through the work performed by the singular stress field at the crack tip. In view of the great importance of shear deformation in laminated composite plates the effect of shear stresses on the mechanism of delamination are investigated pointing out new features which emerge from the interaction of normal and shear stresses acting on the transverse section near the crack tip. Several examples of mixed mode delamination schemes used in experimental applications are examined, showing the influence of transverse shear stresses in coupling with normal stresses on energy release rates determination.

Influence of micro-cracking and contact on the effective properties of composite materials

Abstract In the present work a novel micro-mechanical approach to analyze the influence of micro-crack evolution and contact on the effective properties of elastic composite materials is proposed, based on homogenization techniques, interface models and fracture mechanics concepts. By means of the finite element method, enhanced non-linear macroscopic constitutive laws are developed by taking into account changes in micro-structural configuration associated with the growth of micro-cracks and with contact between crack faces. Numerical simulations are carried out for the cases of a porous composite with edge cracks and of a debonded fibre reinforced composite, loaded along extension/compression uniaxial macro-strain paths. Micro-crack propagation is modelled by using an original methodology based on the J-integral technique in conjunction with an interface model taking into account the unilateral contact of crack faces. In the context of a micro-to-macro transition obtained by controlling the macro-deformation of the micro-structure, the effects of adopting three types of boundary conditions on the macroscopic constitutive law, namely linear deformation, uniform tractions and periodic deformations and anti-periodic tractions, are studied. As a consequence, the proposed method can be applied to a large class of problems including periodic, locally periodic and irregular composite materials. Micro-crack and contact evolution result in a progressive loss of stiffness and can lead to failure for homogeneous macro-deformations associated with unstable crack propagation.

An analytical delamination model for laminated plates including bridging effects

A penalised interface model, whose strain energy is the penalty functional related to interface adhesion constraint, is introduced in conjunction with a damageable interface whose local constitutive law, in turn, represents bridging stress effects, in order to analyse delamination and bridging phenomena in laminated plates. The laminate is modelled by means of first-order shear deformable layer-wise kinematics and the governing equations are formulated in the form of a non-linear differential system with moving intermediate boundary conditions related to opportune delamination and bridging growth conditions. The problem is solved through an analytical approach. The model leads to an accurate and self-consistent evaluation of the energy release rate and its mode components due to the inclusion of significant contributions arising from coupling between in-plane and transverse shear stresses, and to an asymptotic estimate of interlaminar stresses. The salient features of the proposed model are investigated in the context of an energy balance approach and of a J-integral formulation, thus providing simple results useful to model delamination growth and bridging behaviour when mixed mode loading is involved. The accuracy of the proposed model is substantiated through comparisons with results from continuum analysis obtained by a finite element (FE) procedure. The effectiveness of the proposed model is highlighted by showing the solution of a two-layered plate scheme subjected to pure and mixed mode loading conditions and to fibre bridging stresses. The results point out that the present model, despite its low computational cost in comparison with more complex FE analyses, is an efficient tool to predict delamination and bridging evolution.

Computation of Energy Release Rate and Mode Separation in Delaminated Composite Plates by Using Plate and Interface Variables

Abstract A model for analyzing mixed-mode delamination problems in laminated composite plates under general loading conditions is studied. The first-order shear deformable laminated plate theory and the interface methodology, which in turn is based on fracture mechanics, are adopted. The laminate is modeled as an assembly of laminated plate and interface layers in the thickness direction. When the limit case of interface stiffness coefficients approaching infinity is considered, a perfect adhesion between plate models is simulated. On the other hand, delamination between sublaminates is taken into account by assuming zero values for interface stiffnesses. Lagrange and penalty methods are adopted to simulate connections between plate elements. By using a variational approach and the virtual crack closure concept, expressions for total energy release rate and its mode components along the delamination front are obtained, in terms of both interface variables and plate stress resultant discontinuities. These formulas shed light on the effect of transverse shear in interface fracture analysis and establish the improvement and the accuracy of the proposed formulation compared to other plate-based delamination models existing in the literature. The method is implemented in a two-dimensional finite element analysis, which makes use of shear deformable plate elements and interface elements. To illustrate the present method, some typical delamination problems involving mode I, mode II, and mode III are examined and the numerical energy release rate distributions are compared to highly accurate three-dimensional (3D) finite element solutions. These results show that the procedure is accurate when a reasonable number of plate models are included in the analysis and more computationally efficient than 3D finite element models, for which determining fracture energies may lead to a remarkable increase in model complexity.

Dynamic Mode I and Mode II Crack Propagation in Fiber Reinforced Composites.

Dynamic crack phenomena in unidirectional composite laminates are investigated. The proposed formulation is based on the combination of beam and interface methodologies, which are utilized to predict crack behavior in the context of the steady state fracture mechanics. The relevant quantities related to delamination phenomena are discussed with reference to Lagrange and penalty methods utilized to simulate the connection between the sublaminates adjoining the delamination plane. Analytical solutions of the governing equations are proposed and closed form expressions for simple cases, involving pure mode I and mode II components, are provided. The accuracy of the proposed approach is validated through comparisons with results arising from continuum analysis obtained by finite element procedures. Some applications are developed to point out the influence of the crack front speed, the shear deformability and the inertial contributions on the energy release rate. The main features of the proposed model are investigated in the context of an energy balance approach based on the J-integral formulation and thus providing results useful to model delamination growth for simple cases involving pure mode I and mode II loading conditions. Special attention is devoted to analyzing the allowable speeds of the moving crack. In particular, a parametric study in terms of the main characteristic geometric parameters of the laminate is proposed to show the main features of the crack tip behavior.