Finite-Elemente-Methode (FEM)

The Finite-Element Analysis enables a design in the fore field of the construction of a Component. The FEA decompose all material sections of the considered components in infinitesimal small pieces and allocate them material properties, depending if it is metal, ceramic, plastics or brazing material.

Alumina Systems GmbH disposes about an own ANSYS-Workstation, which is able to simulate the whole brazing joint including the braze. As internal stress is the brazing process itself simulated (="joining" stresses) and if needed the joining stresses are superimposed with external stresses like thermal or mechanical loads. The single steps are shown in Pic.1. The challenge is to replace a cap made from NiFe42 by a cap made from Ni 99,6%. The Youngs Modulus of the Ni 99,6% is higher by about 30% in comparison to NiFe42.

Grafik1Pic 1: Creating a model fort he FEA calculation (simplified)


The calculation results in a stress distribution for ceramic, metal and braze. For the prediction several material models are applies like linear-elastic behavior (ceramic) and stabilization of the metal and braze. The load of metals is estimated by a Mises comparison stress, this is not possible for ceramics, because the failure criteria referring to Weibull contains a tensile component, i.e. this requires a complete summation of the tensile stressed volume. This leads after applying the Weibull laws to a failure probability F, which is able to compare the failure probability of variants of the considered components. Within the existing model it is possible to exchange materials or change the construction itself. As a result you receive an optimized construction, without producing one part. This saves iteration loops and at the end development costs.

Grafik2Pic 2: Result for 1st variant of feedtrough.


Aus der Berechnung ist erkennbar, dass 24 von 1.000 Keramiken nach dem Löten versagen würden. Ebenso weist die metallische Hülse eine Dehnung von rund 3,06% auf, welches nahe an der Beanspruchungsgrenze liegt. Anpassungen an der Keramik als auch an der Hülse führen zu einer Variante die eine um den Faktor 17 niedrigere Bruchwahrscheinlichkeit aufweist.

Grafik3Pic 3: Optimized braze joint


The ceramic shows now a fracture probability of F="0,14%," what is better than factor 17 compared with Pic.1. Even the metal strain is reduced to a plastic strain of 2,28%.

In principal this solution is better, but due to the change of the ceramic diameter a new ceramic pressing tool is needed, what will raise the costs too. In a new construction this would be used from start on.