A nonlinear finite element approach with cohesive-frictional interfaces for mode II Transverse Crak Tension test insight

In many circumstances structural failure modes are driven by the formation and propagation of fractures. For instance in composite laminate structures one of the most worrying condition is delamination, which is an interlaminar progressive fracture. Fracture toughness is the material mechanical parameters which ensure fracture safe condition and it is also an essential parameter for performing nonlinear structural analysis, no matter if based on Fracture Mechanics or by means of Interface Cohesive theories. It is then of paramount relevance to evaluate the critical fracture energy by means of simple and reliable laboratory tests. Several tests are available for the direct determination of mode I and mode II fracture energies. If for mode I, fracture energy determination is nowadays well defined and the Double Cantilever Beam (DCB) test is normed and universally adopted, it is not the same for mode II fracture energy. The tests based on bending beams theory such as End Notched Flexure (ENF), End Loaded Split (ELS) test and Four Point End Notched Flexure (4ENF) are all widely used tests, which however for different reasons have not been fully accepted

Multiple surface cracking and debonding failure for thin thermal coatings

A mechanical analysis of thin films of quasi-brittle materials used as thermal coatings for superalloy substrate is proposed. The study considers a bi-material element subjected to uniform tension formed by a thin layer of quasi-brittle material (typically a ceramic) bonded on an elastic substrate. The bounding between the coating film and the substrate is realized by a very thin primer which mechanically modeled as a zero thickness cohesive frictional interface. The analysis is developed by a non-linear finite element simulation in which, in order to consider damage size effects, a non-local isotropic damage model is adopted for the quasi-brittle coating. The results of the analysis shows the formation of multiple cracks on the coating surface which propagate up to the interface. At the same time, due to the mismatch between the elastic moduli between the coating and the substrate and the development of the transverse cracks, a competing debonding mechanism along the interface develops. The numerical results show also, for thick coating layers, the development of skew crack bands, which forecast coating spalling

Hybrid equilibrium element with high-order stress fields for accurate elastic dynamic analysis

In the present article the two-dimensional hybrid equilibrium element formulation is initially developed, with quadratic, cubic, and quartic stress fields, for static analysis of compressible and quasi-incompressible elastic solids in the variational framework of the minimum complementary energy principle. Thereafter, the high-order hybrid equilibrium formulation is developed for dynamic analysis of elastic solids in the variational framework of the Toupin principle, which is the complementary form of the Hamilton principle. The Newmark time integration scheme is introduced for discretization of the stress fields in the time domain and dynamic analysis of both the compressible solid and quasi-incompressible ones. The hybrid equilibrium element formulation provides very accurate solutions with a high-order stress field and the results of the static and dynamic analyses are compared with the solution of the classic displacement-based quadratic formulation, showing the convergence of the two formulations to the exact solution and the very satisfying performance of the proposed formulation, especially for analysis of quasi-incompressible elastic solids

A frictional interface model for the propagation of cohesive fracture under cyclic loading

The paper presents an extension of a recent presented mechanical interface model, [1-2], for the description of the smooth cohesive/frictional transition along potentially active cohesive fracture surfaces. The model presented includes the description of internal frictional dissipative mechanisms which are active under combined compressive/sliding loading in either the cohesive process zone, or in the fully fractured interface portion. Moreover, always under compressive/sliding loading conditions, frictional dissipation mechanisms can also develop in the undamaged (or sound) portion of the interface, justified by the circumstance that also at the virgin state in the bonding surface are present initial defects (stable micro-fracures or microvoids) which might generate friction. The main features of the proposed model may be better understood considering deformation mechanisms involved in the interface layer of finite thikness analyzed at the microscale level, i.e. by investigating the microstrural response of an heterogeneous damageable thin layer. Mechanical information passages from the microscale response to the macro interface constitutive relations are investigated in a multiscale point of view. The interface, zero thickness, constitutive model has been implemented in a FE environment and specific nonlinear numerical response are reported for cyclic loading, as well as for monotonic increasing loading. Finally, it will be shown as the model is able to reproduce the cyclic response and the progressive fracture propagation, also in the case of high number of low constant amplitude cyclic loading. The high number cyclic failure is shown to be promoted by the internal friction mechanisms which induces a further low-intensity damage development in the cohesive zone and then fatigue-type failure. The numerical response obtained with the proposed model is also compared with corresponding experimental data. Acknowledgements: A grant from MIUR for PRIN09, 2009XWLFKW project Multi-scale modelling of materials and structures is acknowledged. References [1] Parrinello, F., Failla. B. and Borino, G. \u201cCohesive\u2013frictional interface constitutive model,\u201d Int. J. Solids Strct., 46, 2680-2692 (2009). [2] Marannano G., Pasta, A., Borino, G., Parrinello F. and Terranova, M. \u201cEffetto dell\u2019attrito nell\u2019avanzamento della delaminazione per modo II di frattura, \u201d in: Proc. 40\ub0 Conv. AIAS, Palermo, September 7-10, 2011

A Cohesive interface formulation in large displacements

Mechanical interfaces are theoretical and computational tools able to properly reproduce the progressive decohesion along predefined surfaces. Scientific literature is rich of interface models, developed under very different conctitutive framework, but mostly developed in small displacements, whereas a few of them assess the problem in a geometrically nonlinear setting. In the present contribution interface formulation is rigorously developed in the large displacements regime. The relevant cohesive interface constitutive relations are defined in the local reference with normal and tangential axes to the middle surface in the current configuration. The interface is defined as a zero thickness layer with the traction vector acting between the two connected surfaces. Membrane forces are assumed negligible and separation displacement is assumed to remain small, at least up to full debonding

Finite Displacements and Corrotational Interfaces: Consistent formulation and Symmetry of the Stiffness Matrix

Mechanical interfaces are theoretical and computational tools able to properly reproduce then progressive delamination of composite structures. Scientific literature is rich of interface models, mostly developed in small displacements, whereas a few of them assess the problem in a geometrically nonlinear setting. In the present paper interface formulation is rigorously developed in a geometrically nonlinear setting, and the relevant interface constitutive relations are defined in the local reference with normal and tangential axes to the middle surface in the current configuration. The interface is defined as a zero thickness layer with tractions acting between the two connected surfaces. Membrane forces are assumed negligible and separation displacement is assumed to remain small, at least up to full debonding. Under this “constitutive” hypothesis rotational equilibrium is implicitly verified

An extrinsic interface developed in an equilibrium based finite element formulation

The phenomenon of delamination in composite material is studied in the framework of hybrid equilibrium based formulation with extrinsic cohesive zone model. The hybrid equilibrium formulation is a stress based approaches defined in the class of statically admissible solutions. The formulation is based on the nine-node triangular element with quadratic stress field which implicitly satisfy the homogeneous equilibrium equations. The inter-element equilibrium condition and the boundary equilibrium condition are imposed by considering independent side displacement fields as interfacial Lagrangian variable, in a classical hybrid formulation. The hybrid equilibrium element formulation is coupled with an extrinsic interface, for which the interfacial separation is zero for a sound interface. The extrinsic interface is defined as a rigid-damage cohesive zone model (CZM) in the rigorous thermodynamic framework of damage mechanics and is defined as embedded interface at the hybrid equilibrium element sides

Non associative damage interface model for mixed mode delamination and frictional contact

The present paper proposes a new interface constitutive model based on the non-associative damage mechanics and frictional plasticity. The model is developed in a thermodynamically consistent framework, with three independent damage variables. The non associative flow rules drive the concurrent evolution of the three damage variables. The interface model provides two independent values for the mode I fracture energy and the mode II fracture energy and it is able to accurately reproduce arbitrary mixed mode fracture conditions. The model can also take into account the presence of frictional effects both at the fully debonded zones and at the partially debonded ones. The experimental tests developed by Benzeggagh and Kenane with seven different mixed mode ratios have been numerically simulated with a unique set of constitutive parameters. The split shear torsion, for the evaluation of the mode III delamination toughness, has been analysed by a three-dimensional numerical simulation

Consistent shakedown theorems for materials with temperature dependent yield functions

The (elastic) shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic-plastic rate-independent associative material models with temperature-dependent yield functions. Assuming the yield functions convex in the stress/temperature space, a thermodynamically consistent small-deformation thermo-plasticity theory is provided, in which the set of state and evolutive variables includes the temperature and the plastic entropy rate. Within the latter theory the known static (Prager's) and kinematic (König's) shakedown theorems - which hold for yield functions convex in the stress space - are restated in an appropriate consistent format. In contrast with the above known theorems, the restated theorems provide dual lower and upper bound statements for the shakedown limit loads; additionally, the latter theorems can be expressed in terms of only dominant thermo-mechanical loads (generally the vertices of a polyhedral load domain in which the loadings are allowed to range). The shakedown limit load evaluation problem is discussed together with the related shakedown limit state of the structure. A few numerical applications are presented. © 2000 Elsevier Science Ltd. All rights reserved

A microplane model for plane-stress masonry structures

A microplane model is presented for the nonlinear finite element analysis of masonry structures. The model is developed for plane-stress problems. For each microplane a damage constitutive law is defined which correlates normal and tangential components of the strain vector acting on the specific microplane with the corresponding stress vector components. Some numerical analyses are performed on masonry panels and the results compared with experimental data