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.
•Formulation combining the phase field approach for brittle fracture and the cohesive zone model.•Competition between crack penetration and crack deflection at an interface.•The role of the characteristic fracture-length scales of the two dissipative models is elucidated.•Explanation of complex fracture patterns observed in layered materials.
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.
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•Combined phase-field and cohesive zone model for fracture.•Transgranular and intergranular fracture in solar-grade Silicon.•Anisotropic phase field model for fracture.•Identification of polycrystalline Silicon mechanical parameters.
Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, in modeling the temperature ...dependency of the material functions in thermo-visco-elasticity, the standard time–temperature superposition principle is known to be ineffective in most of the cases (thermo-rheological complexity). In this work, a novel finite element formulation and numerical implementation is proposed for the simulation of transient thermal analysis in thermo-rheologically complex materials. The parameters of the visco-elastic fractional constitutive law are assumed to be temperature dependent functions and an internal history variable is introduced to track the changes in temperature which are responsible for the phase transition of the material. The numerical approximation of the fractional derivative is employed via the so called Grünwald–Letnikov approximation. The proposed model is used to numerically solve some test cases related to relaxation and creep tests conducted on a real polymer (Ethylene Vinyl Acetate), which is used as the major encapsulant of solar cells in photovoltaics.
Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin ...structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with ...coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to an operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.
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.
•A semi-analytical multi-physics formulation to study blistering in photovoltaic modules was developed.•A quantitative prediction of adhesion energy and critical bulge radius in four commercial ...products was reported.•Results of simulated standards accelerated tests and environmental exposure were compared.•Blistering is related to lamination defects.•Moisture diffusion and temperature govern blistering occurrence.
Backsheet blistering in photovoltaic modules is frequently reported but not yet thoroughly described. Visual inspection only identifies the presence of bubbles, while physical mechanisms leading to their occurrence need further theoretical investigation. To evaluate the effect of external (temperature, humidity) and internal (manufacturing defects) causes of blistering, we propose a semi-analytic model to describe this phenomenon in poly(ethylene-co-vinyl acetate)-based modules. The blistering occurrence is triggered by pressure exerted by partially vaporized moisture in existing defects. Vapor pressure in such defects, originated during module manufacturing, is related to moisture concentration profiles, governed by external conditions. Moisture also affects the adhesive fracture energy which plays a fundamental role in blistering activation. The proposed model predicts the critical pressure and the critical size of the initial defects causing blistering. This work represents an important step for the long-term reliability prediction of photovoltaic modules.
•A FEM formulation to study EVA thermo-photo-oxidation was developed.•A quantitative prediction of a 20-years outdoor exposure in different Köppen’s zones was reported.•Standards accelerated tests ...provided mismatching results.•Results of accelerated test can be improved by adding a UV source.•Environmental exposure affects EVA optical properties.
The increasing demand of photovoltaics installations, also in harsh climatic conditions, requires the accurate comprehension of module lifetime and durability. Accelerated environmental tests (damp heat, thermal cycling, and humidity freeze) are performed as pass/fail criteria to determine whether modules are suitable for sale, while do not accurate predict durability in all possible climates. Recently, we proposed a computational model to study the thermo-oxidative degradation of EVA encapsulant. This model was suitable to describe effects of temperature fluctuations on degradation, while neglecting dramatic changes of outdoor exposure in different climatic zones. To investigate the correlation between climatic zones and EVA degradation, we completed the existing degradation model by adding the UV exposure dependency. This model, for the first time, simulates EVA thermo-photo-oxidation in accelerated and environmental conditions. We compared results of simulated standard accelerated tests and outdoor exposure, observing a significant mismatch of results. The low prediction capability of standard tests pushed us to analyze modified accelerated tests, by adding an internal UV source. Modified test simulations show a better matching with outdoor long-term weathering. The modified setup will enable novel accelerated tests with predictive behavior of long-term EVA degradation and a more accurate PV module lifetime.
Thin ply laminates are a new class of composite materials with great potential for application in the design of thinner and highly optimized components, resulting in potential weight savings and ...improved mechanical performance. These new composites can stir the development of lighter structures, overcoming current design limitations as well as notably reducing the onset and development of matrix cracking and delamination events. This paper presents the application of two recent modeling methods for the failure analysis and strength prediction of open-hole thin ply laminates under tensile loading, which exhibit a brittle response upon failure: (i) the analytical coupled energy-stress Finite Fracture Mechanics (FFMs) technique, and (ii) the FE-based Phase Field (PF) approach for fracture that is incorporated into an enhanced assumed solid shell element. The predictions obtained using both strategies are compared with experimental data. These correlations exhibit a very satisfactory level of agreement, proving the robustness and reliability of both methods under consideration.
Among polymers used as encapsulant in photovoltaic (PV) modules, poly(ethylene-co-vinyl acetate), or EVA, is the most widely used, for its low cost and acceptable performances. When exposed to ...weather conditions, EVA undergoes degradation that affects overall PV performances. Durability prediction of EVA, and thus of the module, is a hot topic in PV process industry. To date, the literature lacks of long-term predictive computational models to study EVA aging. To fill this gap, a computational framework, based on the finite element method, is proposed to simulate chemical reactions and diffusion processes occurring in EVA. The developed computational framework is valid in either case of environmental or accelerated aging. The proposed framework enables the identification of a correspondence between induced degradation in accelerated tests and actual exposure in weathering conditions. The developed tool is useful for the prediction of the spatio-temporal evolution of the chemical species in EVA, affecting its optical properties. The obtained predictions, related to degradation kinetics and discoloration, show a very good correlation with experimental data taken from the literature, confirming the validity of the proposed formulation and computational approach. The framework has the potential to provide quantitative comparisons of degradation resulting from any environmental condition to that gained from accelerated aging tests, also providing a guideline to design new testing protocols tailored for specific climatic zones.
•A FEM formulation to study PV encapsulant degradation was reported.•A quantitative prediction of a 20-years environmental exposure was evaluated.•Accelerated tests provided higher degradation rates.•Degradation affects optical properties of encapsulant.
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