Image analysis of polycrystalline solar cells and modelling of intergranular and transgranular cracking

Infuso, Andrea; Corrado, Mauro; Paggi, Marco

doi:10.1016/j.jeurceramsoc.2013.12.051

Cited by 29 publications

(10 citation statements)

References 18 publications

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“…In addition to the previous considerations, the development of numerical methods (especially finite element (FE)-based formulations) to predict fracture onset, propagation and branching in engineering components has been a matter of intensive research during the last decades, to tackle problems that cannot be solved by analytical methods. Most of the extensively used techniques to trigger quasi-brittle and ductile fracture events fall into the following general categories: (i) Continuum Damage Mechanics (CDM) models accounting for a smeared crack representation [19], which in their local version suffer from mesh dependency that has been partially alleviated by using integral-based non-local and gradient enhanced procedures [20,21,22,23,24]; (ii) extended FE strategies with nodal kinematic enrichment (extended-FEM, X-FEM) that rely on Partition of Unity Methods (PUM) [25,26,27] and element enrichment formulations (enhanced-FEM, E-FEM) [28,29,30,31]; (iii) adaptive insertion of cohesive interface elements during the computation or their prior embedding along all the finite element edges [32,33,34,35,36,37,38]; (iv) thick-level set approaches [39,40]. Although these strategies have been successfully applied to many different fracture mechanics problems, they all present limitations with regard to predicting crack initiation, crack branching, and crack coalescence for multiple fronts.…”

Section: Introductionmentioning

confidence: 99%

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

Paggi

Reinoso

2017

Computer Methods in Applied Mechanics and Engineering

210

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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 this investigation, this problem is revisited in view of the recent progresses on the phase field approach to 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 the characteristic fracturelength scales of the dissipative models are 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 opens new research perspectives for the simulation and understanding of complex fracture patterns.Keywords: Crack penetration or deflection at an interface; Bi-material systems; Phase field approach to fracture; Cohesive interface; Finite element method.

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Section: Introductionmentioning

confidence: 99%

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

Paggi

Reinoso

2017

Computer Methods in Applied Mechanics and Engineering

210

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“…Image analysis has been proposed in the work of Infuso et al to process real solar cell pictures, identify grains and grain boundaries in polycrystalline silicon, and generate finite element meshes. More recently, a phase‐field approach has been combined to the cohesive model to study intergranular and transgranular fracture in solar‐grade silicon with a finite element–based technique …”

Section: Introductionmentioning

confidence: 99%

Micromechanical modeling of cohesive thermoelastic steady‐state and transient cracking in polycrystalline materials

Geraci

Aliabadi

2018

Numerical Meth Engineering

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In this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady-state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.In polycrystalline materials, the modes of fracture are well recognized and can be categorized as follows: brittle intergranular and transgranular cracking, ductile failure, and, at high temperature, creep has to be taken into account. It is worth noting, however, that Blendell and Coble 3 have measured stress development due to TEA in Al 2 O 3 and showed that the microstructure does not experience any stress relaxation until at very high temperature, close to annealing. Thus, in this work, the effect of creep has not been considered since thermal loading has been applied within the range of temperatures that guarantees no stress relaxation. Moreover, still from the experimental findings in the work of Blendell and Coble, 3 the authors have extrapolated the stress-free temperature, from which it is possible to approximate analytically the maximum local stress due to differential thermal expansion. Results in the present work will be shown in good agreement with these literature results.Experimental methods may be used for such investigations, even though, sometimes, they might be expensive and time consuming due to specific required techniques. Experimental results on grain size dependence and TEA were presented by Rice et al 4 and Rice and Freiman, 5 as well as spontaneous cracking in the work Rice and Pohanka. 6 Experiments and simulations were run by Yousef et al, 7 where residual stresses due to cooling from stress-free status have been investigated. TEA has been studied also in the work of Sridhar et al, 8 where the effect of microcracking due to a local thermal expansion mismatch has a substantial influence on the damage evolution in the polycrystalline aggregate.A popular and powerful approach to investigate such mechanisms is the use of computational micromechanic models. The finite element method (FEM) has been widely used due to the availability of commercial software. Intergranular failure has been studied by modeling grains' interfaces as cohesive surfaces. Two-dimensional (2D) models o...

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“…In reality, it is reasonable to expect intermediate configurations where cracks may partially conduct depending on the relative crack opening displacement at crack faces. A complete modelling of the phenomenon should therefore consider the following steps: (i) simulation of crack nucleation and propagation according to a computational approach based on the cohesive zone model (CZM) 18 19 20 , where cohesive tractions opposing to the relative displacements of the crack faces are decreasing functions of opening and sliding; (ii) analysis of thermal effects by augmenting the basic mechanical CZM to take into account the additional thermal resistance of cracks 9 ; (iii) modelling of the electric response of the cell. For this last item, localized series resistances dependent on crack opening might be postulated in correspondence of cracks, in addition to the distributed series resistance.…”

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confidence: 99%

Fatigue degradation and electric recovery in Silicon solar cells embedded in photovoltaic modules

Paggi

Berardone

Infuso

et al. 2014

Sci Rep

Self Cite

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Cracking in Silicon solar cells is an important factor for the electrical power-loss of photovoltaic modules. Simple geometrical criteria identifying the amount of inactive cell areas depending on the position of cracks with respect to the main electric conductors have been proposed in the literature to predict worst case scenarios. Here we present an experimental study based on the electroluminescence (EL) technique showing that crack propagation in monocrystalline Silicon cells embedded in photovoltaic (PV) modules is a much more complex phenomenon. In spite of the very brittle nature of Silicon, due to the action of the encapsulating polymer and residual thermo-elastic stresses, cracked regions can recover the electric conductivity during mechanical unloading due to crack closure. During cyclic bending, fatigue degradation is reported. This pinpoints the importance of reducing cyclic stresses caused by vibrations due to transportation and use, in order to limit the effect of cracking in Silicon cells.

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Image analysis of polycrystalline solar cells and modelling of intergranular and transgranular cracking

Cited by 29 publications

References 18 publications

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

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

Micromechanical modeling of cohesive thermoelastic steady‐state and transient cracking in polycrystalline materials

Fatigue degradation and electric recovery in Silicon solar cells embedded in photovoltaic modules

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