Mechanical stability of BaTiO3-based PTC thermistor components: experimental investigation and theoretical modelling

Barium titanate based positive temperature coefficient (PTC) thermistors, especially high power switching devices, can suffer major mechanical damage if inhomogeneous heating occurs under an applied electrical voltage. The main mode of mechanical failure, known as delamination fracture, manifests itself by cracking of the ceramic disc along a plane approximately parallel to the electrodes. This damage results from the build-up of thermal stresses, the amplitude of which is governed by a large number of geometrical, electrical and thermo-elastic parameters. For an experimental investigation, a measurement device was set up to observe the electrical behaviour of PTC-components during the switching process. To interpret specific aspects of the observations, a mathematical model was developed to simulate the electrical, thermal and thermo-elastic behaviour. In addition to the resistance/temperature characteristics considered by other authors, the varistor-effect (i.e. the non-linear isothermal current-voltage behaviour which is thought to make a significant contribution to the development of the mechanical stresses inparticular) is also taken into account. By doing a non-linear analysis with one and two dimensional models, and taking all relevant temperature dependencies of the material properties into account, a qualitative and quantitative agreement with the experimentally determined electro-thermal and failure statistical behaviour could be achieved. It is shown that in addition to the resistance/temperature characteristics, it is very important to account for the varistor-effect when modelling the build-up of the mechanical stresses during the switching process.