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

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

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 Cohesive-frictional interface model subjected to mixed complex loading paths

The paper presents a cohesive-frictional interface model based on surface damage mechanics. The proposed model is developed under the assumption that the fracture energies in mode I and in mode II are different values, as shown by several experimental evidences. At difference with the most spread available interface models, only one isotropic interface internalvariable is adopted for the constitutive model. The interface constitutive model is developed in a Thermodynamic consistent framework with an Helmholtz free energy potential and the fulfillment of the thermodynamic principles is obtained enforcing the Clausius-Duhem inequality. The damage/friction activation functions and dissipative flow potentials are defined together with nonassociative flow rules and loading/unloading conditions. The latter loading/unloading conditions emerge directly from the nature of the proposed approach, which is framed in the mechanics dissipative process with internal variables, and then does not require any special ad-hoc unloading rule. Finally, some numerical examples of interface subjected to complex mixed loading/unloading/reloading paths are analyzed

Erratum to: Letter to the Editor [Engineering Fracture Mechanics 2003 (70) 1219-21]

Erratum and Correction