Marco Paggi

A multi-physics and multi-scale numerical approach to microcracking and power-loss in photovoltaic modules

Abstract A multi-physics and multi-scale computational approach is proposed in the present work to study the evolution of microcracking in polycrystalline Silicon (Si) solar cells composing photovoltaic (PV) modules. Coupling between the elastic and the electric fields is provided according to an equivalent circuit model for the PV module where the electrically inactive area is determined from the analysis of the microcrack pattern. The structural scale of the PV laminate (the macro-model) is coupled to the scale of the polycrystals (the micro-model) using a multiscale nonlinear finite element approach where the macro-scale displacements of the Si cell borders are used as boundary conditions for the micro-model. Intergranular cracking in the Si cell is simulated using a nonlinear fracture mechanics cohesive zone model (CZM). A case-study shows the potentiality of the method, in particular as regards the analysis of the microcrack orientation and distribution, as well as of the effect of cracking on the electric characteristics of the PV module.

On the Stress Singularities at Multimaterial Interfaces and Related Analogies With Fluid Dynamics and Diffusion

Joining of different materials is a situation frequently observed in mechanical engineering and in materials science. Due to the difference in the elastic properties of the constituent materials, the junction points can be the origin of stress singularities and a possible source of damage. Hence, a full appreciation of these critical situations is of fundamental importance both from the mathematical and the engineering standpoints. In this paper, an overview of interface mechanical problems leading to stress singularities is proposed to show their relevance in engineering. The mathematical methods for the asymptotic analysis of stress singularities in multimaterial junctions and wedges composed of isotropic linear-elastic materials are reviewed and compared, with special attention to in-plane and out-of-plane loadings. This analysis mathematically demonstrates in a historical retrospective the equivalence of the eigenfunction expansion method, of the complex function representation, and of the Mellin transform technique for the determination of the order of the stress singularity in such problems. The analogies between linear elasticity and the Stokes flow of dissimilar immiscible fluids, the steady-state heat transfer across different materials, and the St. Venant torsion of composite bars are also discussed. Finally, advanced issues for the stress singularities due to joining of angularly nonhomogeneous elastic wedges are presented. This review article contains 147 references. DOI: 10.1115/1.2885134

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

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.

Partial-slip frictional response of rough surfaces

If two elastic bodies with rough surfaces are first pressed against each other and then loaded tangentially, sliding will occur at the boundary of the contact area while the inner parts may still stick. With increasing tangential force, the sliding parts will expand while the sticking parts shrink and finally vanish. In this paper, we study the fractions of the contact area, tangential force and tangential stiffness, associated with the sticking portion of the contact area, as a function of the total applied tangential force up to the onset of full sliding. For the numerical analysis randomly rough, fractal surfaces are used, with the Hurst exponent H ranging from 0.1 to 0.9. Numerical simulations by boundary element method are compared with an analytical analysis in the framework of the Greenwood and Williamson (GW) model. In both cases, a universal linear dependency between the real contact area fraction in stick condition and the applied tangential force is found, regardless of the Hurst exponent of the rough surfaces. Regarding the dependence of the differential tangential stiffness on the tangential force, a linear relation is found in the GW case. For randomly rough surfaces, a nonlinear relation depending on H is derived.

A consistent interface element formulation for geometrical and material nonlinearities

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.

A unified interface constitutive law for the study of fracture and contact problems in heterogeneous materials

A unified interface constitutive law for the description of contact and decohesion at bi-material interfaces is proposed. To this aim, a synthesis of the nonlinear models pertaining to Fracture and Contact Mechanics is presented. The issues pertinent to the implementation within the FE discretization framework are also discussed in detail. Finally, a numerical example of fatigue modeling at the mesoscopical level in a fiber-reinforced composite is provided.

Thermomechanical deformations in photovoltaic laminates

Recent experimental results based on the digital image correlation technique (U. Eitner, M. Köntges, R. Brendel, Solar Energy Mater. Solar Cells, 2010, 94, 1346–1351) show that the gap between solar cells embedded into a standard photovoltaic laminate varies with temperature. The variation of this gap is an important quantity to assess the integrity of the electric connection between solar cells when exposed to service conditions. In this paper, the thermo-elastic deformations in photovoltaic laminates are analytically investigated by developing different approximate models based on the multilayered beam theory. It is found that the temperature-dependent thermo-elastic properties of the encapsulating polymer layer are responsible for the deviation from linearity experimentally observed in the diagram relating the gap variation to the temperature. The contribution of the different material constituents to the homogenized elastic modulus and thermal expansion coefficient of the composite system is also properly quantified through the definition of weight factors of practical engineering use.

A coupled cohesive zone model for transient analysis of thermoelastic interface debonding

A coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive cracks. Traction-displacement and heat flux–temperature relations are theoretically derived and numerically implemented in the finite element method. In the proposed formulation, the interface conductivity is a function of the normal gap, generalizing the Kapitza constant resistance model to partial decohesion effects. The case of a centered interface in a bimaterial component subjected to thermal loads is used as a test problem. The analysis focuses on the time evolution of the displacement and temperature fields during the transient regime before debonding, an issue not yet investigated in the literature. The solution of the nonlinear numerical problem is gained via an implicit scheme both in space and in time. The proposed model is finally applied to a case study in photovoltaics where the evolution of the thermoelastic fields inside a defective solar cell is predicted.

Size-Scale Effects on Plastic Rotational Capacity of Reinforced Concrete Beams

A complete numerical algorithm that assumes a strain localization in concrete, both in tension and compression, is proposed for modeling cracking and crushing growths during the loading process of reinforced concrete beams in bending. With this algorithm based on nonlinear fracture mechanics models, it is possible to investigate the effects of the main mechanical and geometrical parameters on the rotational capacity with particular regard to the reinforcement percentage and the element size. A comparison with experimental results demonstrates the effectiveness of the proposed approach for a wide range of reinforcement percentages and beam depths. The obtained results show that the prescriptions concerning the admissible plastic rotations provided by the existing design formulas are not conservative in the case of large structural sizes. To overcome such a drawback, a new design diagram is proposed for practical purposes.

Are the Paris’ law parameters dependent on each other?

The question about the existence of a correlation between the parameters C and m of the Paris’ law is re-examined in this paper. According to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter C to m and to the governing variables of the fatigue phenomenon is derived. Then, from the observation that the Griffith-Irwin instability must coincide with the Paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. A fair good agreement is found between the proposed correlation and the experimental data concerning Aluminium, Titanium and steel alloys.