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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 93
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Paper 252

Comparison of Different Finite Element Models for the Simulation of the Ring-Ball on Ring Test

J. Barredo1, L. Hermanns2, I. del Rey2, A. Fraile2 and E. Alarcón2

1Centre for Modelling in Mechanical Engineering (CEMIM-F2I2),
2Department of Structural Mechanics and Industrial Constructions,
Polytechnical University of Madrid, Spain

Full Bibliographic Reference for this paper
, "Comparison of Different Finite Element Models for the Simulation of the Ring-Ball on Ring Test", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 252, 2010. doi:10.4203/ccp.93.252
Keywords: ball on ring test, monocrystalline silicon wafers, finite element model, shell elements, axisymmetry, solid elements, Weibull distribution, contact, anisotropy, large displacements.

The current trend in the photovoltaic industry is the use of thinner wafers which leads to a higher breakage rate in the cell production process. Strength characterization becomes necessary in order to optimize the process steps.

Studies of mechanical properties are usually carried out by means of tests and the development of numerical models simulating them [1,2]. For this study, the ball on ring test has been employed [2].

The simulation of the test has been carried out in different ways. It is important to take the anisotropic behaviour of monocrystalline silicon wafers into account. Moreover, the wafers present a non-linear behaviour during the test due to the large displacements and the contact between the sample, the ball and the ring.

The first method to analyze the test results consists of using analytical expressions taken from the literature. This method is inappropriate since the anisotropic behaviour and the non-linearities present in the test are not taken into account. However, it is a quick and easy way to analyze test results.

The finite element method has been employed for more realistic simulations. A three-dimensional model with shell elements has been developed. The calculation is quite fast and the results fit really well with the test. The information about stress distribution across the thickness of the wafer is very limited in this model.

An axisymmetric model permits much more information about the stress distribution in the wafer than the previous one. The anisotropy cannot be included in this model and circular shape of the sample has to be assumed. The highest value of the elastic tensor is taken as the Young's modulus [3], so the model behaves more rigidly.

A three-dimensional model using solid elements has been developed. This model takes into account all the features present in the problem. However, it takes a lot of time to complete the calculation.

In order to obtain an estimation of the error that can be expected in terms of characteristic fracture stress depending on the model chosen for the analysis, a Weibull fit has been made [1,2].

Results of all these methods and models in terms of calculation time, stress distribution, adjustment to the tests and fitting to a Weibull distribution are compared in the paper.

J. Barredo, A. Fraile, E. Alarcón, "Study of the Brittle Fracture of Monocrystalline Silicon Wafers", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 104, 2005. doi:10.4203/ccp.81.104
S. Schoenfelder, A. Bohne, J. Bagdahn, "Comparison of test methods for strength characterization of thin solar wafer", 22nd European Photovoltaic Solar Energy Conference, Milan, Italy, 2007.
S. Dumoulin, S. Gouttebroze, M. M'Hamdi, "Modelling of intergranular stresses during elastic deformation of multi-crystalline silicon", 23rd European Photovoltaic Solar Energy Conference, Valencia, Spain, 2008.

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