An anisotropic large displacement cohesive zone model for fibrillar and crazing interfaces

AbstractA new cohesive zone model to describe fracture of interfaces with a microstructurs made of fibrils with statistically distributed in-plane and out-of-plane orientations is proposed. The elementary force–displacement relation of each fibril is considered to obey the peeling theory of a tape, although other refined constitutive relations could be invoked for the adhesive constitutive response without any lack of generality. The proposed consistent 2D and 3D interface finite element formulations for large displacements account for both the mechanical and the geometrical tangent stiffness matrices, required for implicit solution schemes. After a preliminary discussion on model parameters identification, it is shown that by tailoring the spatial density of fibrils at different orientations can be a way to realize innovative interfaces enhancing adhesion or decohesion, depending on the need. For instance, it can be possible to realize microstructured adhesives to facilitate debonding of the glass cover in photovoltaic modules to simplify recycling purposes. Moreover, the use of probability distribution functions describing the density of fibrils at different orientations is a very effective approach for modeling the anisotropy in the mechanical bonding between paper tissues and for simulating the complex process of crazing in amorphous polymers

Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In the current investigation, this problem is revisited in view of the recent progresses on the phase field approach of brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and of the characteristic fracture-length scales of the dissipative models is analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk. The obtained computational trends are in very good agreement with previous experimental observations and the theoretical considerations on the competition and interplay between both fracture mechanics models open new research perspectives for the simulation and understanding of complex fracture patterns.Unión Europea FP/2007-2013/ERC 306622Ministerio de Economía y Competitividad DPI2012-37187, MAT2015-71036-P y MAT2015-71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP- 105

A 3D finite strain model for intralayer and interlayer crack simulation coupling the phase field approach and cohesive zone model

Abstract In this study, a new 3D finite element formulation which enables simulating the interaction between brittle crack propagation and interface delamination in heterogeneous materials is presented. The Phase Field (PF) model for brittle fracture has been coupled with the Cohesive Zone Model (CZM) within the framework of the large deformation analysis. These numerical techniques have been implemented within a 8-node locking-free solid shell element, relying on the enhanced assumed strain concept, and a 8-node interface finite element, respectively. The predictive capabilities of the proposed formulation have been assessed through the simulation of cracking in flat and curved geometries under in-plane and out-of-plane loading conditions. The results show the ability of the model to predict complex crack paths where intralayer crack propagation and delamination occur simultaneously and interact. The proposed formulation provides a powerful modeling tool for the simulation of fracture phenomena in heterogeneous materials and laminate structures, which are characterized by the existence of numerous interfaces, such as in photovoltaic laminates

Fracture of solar-grade anisotropic polycrystalline Silicon: A combined phase field–cohesive zone model approach

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.This work presents a novel computational framework to simulate fracture events in brittle anisotropic polycrystalline materials at the microscopical level, with application to solar-grade polycrystalline Silicon. Quasi-static failure is modeled by combining the phase field approach of brittle fracture (for transgranular fracture) with the cohesive zone model for the grain boundaries (for intergranular fracture) through the generalization of the recent FE-based technique published in [M. Paggi, J. Reinoso, Comput. Methods Appl. Mech. Engrg., 31 (2017) 145–172] to deal with anisotropic polycrystalline microstructures. The proposed model, which accounts for any anisotropic constitutive tensor for the grains depending on their preferential orientation, as well as an orientation-dependent fracture toughness, allows to simulate intergranular and transgranular crack growths in an efficient manner, with or without initial defects. One of the advantages of the current variational method is the fact that complex crack patterns in such materials are triggered without any user-intervention, being possible to account for the competition between both dissipative phenomena. In addition, further aspects with regard to the model parameters identification are discussed in reference to solar cells images obtained from transmitted light source. A series of representative numerical simulations is carried out to highlight the interplay between the different types of fracture occurring in solar-grade polycrystalline Silicon, and to assess the role of anisotropy on the crack path and on the apparent tensile strength of the material.Unión Europea FP/2007–2013/ERC 306622Ministerio de Economía y Competitividad MAT2015–71036-P y MAT2015–71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP- 105

Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model

Artículo Open Access en el sitio web el editor. Pago por publicar en abierto.The competition between crack penetration in the layers and cohesive delamination along interfaces is herein investigated in reference to laminate ceramics, with special attention to the occurrence of crack deflection and crack branching. These phenomena are simulated according to a recent variational approach coupling the phase field model for brittle fracture in the laminae and the cohesive zone model for quasi-brittle interfaces. It is shown that the proposed variational approach is particularly suitable for the prediction of complex crack paths involving crack branching, crack deflection and cohesive delamination. The effect of different interface properties on the predicted crack path tortuosity is investigated and the ability of the method to simulate fracture in layered ceramics is proven in relation to experimental data taken from the literature.Consejo de Investigación Europeo 737447Ministerio de Economía y Competitividad FEDERMAT2015-71036-PGobierno de Andalucía P12-TEP-105

Concurrently coupled solid shell-based adaptive multiscale method for fracture

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.A solid shell-based adaptive atomistic–continuum numerical method is herein proposed to simulate complex crack growth patterns in thin-walled structures. A hybrid solid shell formulation relying on the combined use of the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods has been considered to efficiently model the material in thin structures at the continuum level. The phantom node method (PNM) is employed to model the discontinuities in the bulk. The discontinuous solid shell element is then concurrently coupled with a molecular statics model placed around the crack tip. The coupling between the coarse scale and the fine scale is realized through the use of ghost atoms, whose positions are interpolated from the coarse scale solution and enforced as boundary conditions to the fine scale model. In the proposed numerical scheme, the fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened in order to reduce the computation costs. An energy criterion is used to detect the crack tip location. All the atomistic simulations are carried out using the LAMMPS software. A computational framework has been developed in MATLAB to trigger LAMMPS through system command. This allows a two way interaction between the coarse and fine scales in MATLAB platform, where the boundary conditions to the fine region are extracted from the coarse scale, and the crack tip location from the atomistic model is transferred back to the continuum scale. The developed framework has been applied to study crack growth in the energy minimization problems. Inspired by the influence of fracture on current–voltage characteristics of thin Silicon photovoltaic cells, the cubic diamond lattice structure of Silicon is used to model the material in the fine scale region, whilst the Tersoff potential function is employed to model the atom–atom interactions. The versatility and robustness of the proposed methodology is demonstrated by means of several fracture applications.Unión Europea ERC 306622Ministerio de Economía y Competitividad DPI2012-37187, MAT2015-71036-P y MAT2015-71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP -105

Typology of discharge areas on sandy solls in Doñana biologlcal reserve

A typology of discharge areas on sandy soils in Doñana has been carried out based on the vegetation, groundwater hydrochemistry and water tablc regime. Water table (annual and interannual) fluctuations have been related to the connection with different groundwater flow systerns (local, intermediate and regional). Five types of ponds are proposed largely corresponding to previous classifications: permanent ponds, temporary ponds, ephemcral ponds, "fern" ponds and wet slacks. A hypothesis of the desiccation of cphemeral ponds connccted to intermediate flows is consideredA typology of discharge areas on sandy soils in Doñana has been carried out based on the vegetation, groundwater hydrochemistry and water tablc regime. Water table (annual and interannual) fluctuations have been related to the connection with different groundwater flow systerns (local, intermediate and regional). Five types of ponds are proposed largely corresponding to previous classifications: permanent ponds, temporary ponds, ephemcral ponds, "fern" ponds and wet slacks. A hypothesis of the desiccation of cphemeral ponds connccted to intermediate flows is considere

Influence of phreatic water table on the vegetation of areas of discharge on sand in The doñana biological reserve

The relationship between the vegetation of discharge areas on the sands of Doñana Biological Reserve and both groundwater chemistry and depth of phreatic water table has been studied. Four types of waters have been detected each maintaining a defined plant community: Very mineralized waters (electrical conductivity > 1500 pS/cm) related to Tamarix canarierzsis and Juncus acutus; mineralized waters (500 pSlcm) related to Scirpus holoschoenus and Jurzcus maritimus; little mineralized waters rich in chloride (400 pS/cm) related to J.efisus, J. acutifZorus and Pteridium aquilirzum; light mineralized waters (<300 pS/cm) related to vegetation which species composition depends on water table depth (deeper water table with Halimium halimifolicim, Stauracarzthus grrzistoides and U1e.x australis, and shallow water table with Erica scoparia, Calluna vulgaris and Llaphlze gnidiinm