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

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

Análisis numérico de pandeo de paneles rigidizados de material compuesto

COMATCOMP 09 : Donostia - San Sebastian, 7, 8 y 9 de octubre de 2009Uno de los elementos estructurales que mayor interés ha despertado en las últimas décadas para su fabricación con materiales compuestos han sido los paneles rigidizados empleados en los recubrimientos de los fuselajes, estabilizadores y alas de las aeronaves. Estos componentes están formados por una lámina o piel delgada a la que se unen rigidizadores, siendo las secciones transversales más habituales las secciones tipo T, I y W, para aportarle la rigidez necesaria. La configuración de los paneles hace que sean estructuras muy sensibles a fenómenos de inestabilidad, fundamentalmente por abolladuras de la pie aunque ello no supongan el fallo del componente. Para aprovechar esta característica, los criterios de diseño permiten sobrepasar la primera carga de pandeo en un cierto margen. El objetivo de este trabajo es el análisis mediante simulaciones numéricas de las cargas y modos de pandeo de un panel rigidizado cilíndrico de material compuesto. El panel considerado tiene dispuestos dos rigidizadores en dirección circunferencial con sección transversal en W y se encuentra sometido a una presión uniforme sobre la piel. La resolución numérica de la estructura se ha realizado a través del programa de Elementos Finitos ABAQUS/Standard, usando elementos lineales tipo lámina de integración reducida para la discretización de la estructura. En esta investigación se han llevado a cabo diversas variaciones de ciertos parámetros del sistema, concretamente la secuencia de apilado de las láminas y la distancia entre rigidizadores, para proceder a realizar un análisis de la influencia de los mismos en las cargas y modos de pandeo del componente.Junta de Andalucía P06-TEP- 0204

Crack patterns in heterogenous rocks using a combined phase field-cohesive interface modeling approach: A numerical study

Rock fracture in geo-materials is a complex phenomenon due to its intrinsic characteristics and the potential external loading conditions. As a result, these materials can experience intricate fracture patterns endowing various cracking phenomena such as: Branching, coalescence, shielding, and amplification, among many others. In this article, we present a numerical investigation concerning the applicability of an original bulk-interface fracture simulation technique to trigger such phenomena within the context of the phase field approach for fracture. In particular, the prediction of failure patterns in heterogenous rock masses with brittle response is accomplished through the current methodology by combining the phase field approach for intact rock failure and the cohesive interface-like modeling approach for its application in joint fracture. Predictions from the present technique are first validated against Brazilian test results, which were developed using alternative phase field methods, and with respect to specimens subjected to different loading case and whose corresponding definitions are characterized by the presence of single and multiple flaws. Subsequently, the numerical study is extended to the analysis of heterogeneous rock masses including joints that separate different potential lithologies, leading to tortuous crack paths, which are observed in many practical situations.Ministerio de Economía y Competitividad MAT2015-71036-

Análisis de postpandeo de un panel rigidizado de material compuesto mediante técnicas de modelado multi-global-local incluyendo daño interlaminar

XI CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Móstoles los días 6, 7 y 8 de julio de 2015El uso de paneles rigidizados de material compuesto ha sido incorporado en numerosas aplicaciones. En las situaciones en las que las cargas originan estados tensionales de compresión, éstas pueden producir fenómenos de pandeo local. Una vez superada la carga crítica, a lo largo de la evolución de postpandeo, el desarrollo de dichas inestabilidades puede generar la aparición de daño en el componente, causando el colapso estructural del mismo. Este trabajo presenta el análisis numérico y experimental de un panel multi-rigidizado de material compuesto hasta el colapso. El estudio numérico es llevado a cabo a través de metodologías global-local incluyendo elementos finitos cohesivos para el modelado del daño interlaminar piel-rigidizador.Ministerio de Economía y Competitividad DPI2012-37187Junta de Andalucía TEP-709

Phase field modeling of brittle fracture in large-deformation solid shells with the efficient quasi-Newton solution and global–local approach

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).To efficiently predict the crack propagation in thin-walled structures, a global–local approach for phase field modeling using large-deformation solid shell finite elements considering the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods for the alleviation of locking effects is developed in this work. Aiming at tackling the poor convergence performance of standard Newton schemes, a quasi-Newton (QN) scheme is proposed for the solution of coupled governing equations stemming from the enhanced assumed strain shell formulation in a monolithic manner. The excellent convergence performance of this QN monolithic scheme for the multi-field shell formulation is demonstrated through several paradigmatic boundary value problems, including single edge notched tension and shear, fracture of cylindrical structure under mixed loading and fatigue induced crack growth. Compared with the popular alternating minimization (AM) or staggered solution scheme, it is also found that the QN monolithic solution scheme for the phase field modeling using enhanced strain shell formulation is very efficient without the loss of robustness, and significant computational gains are observed in all the numerical examples. In addition, to further reduce the computational cost in fracture modeling of large-scale thin-walled structures, a specific global–local phase field approach for solid shell elements in the 3D setting is proposed, in which the full displacement-phase field problem is considered at the local level, while addressing only the elastic problem at the global level. Its capability is demonstrated by the modeling of a cylindrical structure subjected to both static and fatigue cyclic loading conditions, which can be appealing to industrial applications

Análisis de la capacidad postpandeo de un panel rigidizado ante cargas de presión

X CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Algeciras los días 2, 3, 4 y 5 de julio de 2013En esta publicación se resumen los resultados obtenidos en el análisis experimental y numérico de un panel rigidizado cilíndrico ante cargas de presión superiores a la carga critica a la que se produce la inestabilidad del panel por abolladuras en la piel. En este trabajo se amplían los resultados presentados en el IX Congreso Nacional de Materiales Compuestos, [1]. El panel ensayado fue concebido y fabricado para su montaje en un avión real, ello es lo que justifica la geometría, material y laminados

Análisis de postpandeo de un panel rigidizado de material compuesto sometido a carga de presión

IX CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Girona, 5, 6, 7 y 8 de julio de 2011Para predecir el comportamiento de un panel curvo rigidizado ante una carga de presión por encima de la carga de pandeo se han realizado varias simulaciones numéricas con ABAQUS/Standard. Dada la influencia que las imperfecciones geométricas iniciales tienen en la citada evolución, se ha desarrollado una técnica que permite incluirlas en los modelos numéricos. El ajuste conseguido entre las predicciones numéricas y los resultados experimentales permiten validar el procedimiento