Modelling constrained shrinking and cracking

Lead Research Organisation: University of Leicester
Department Name: Engineering

Abstract

INDUSTRIAL BACKGROUND: This proposal addresses a generic problem experienced in the manufacturing of following systems: (1) The solid oxide fuel cell manufactured by Rolls Royce Fuel Cell Systems Ltd (RRFCS) is a multi-layered ceramic system. Each layer is about 5-10 micrometres thick and has a different porosity and composition. The layers are screen-printed and sintered sequentially. (2) The TWI protective coatings, including optical coatings of indium-tin oxide, silica based protective coatings and anti-soiling coatings with fluorine incorporation, are made through a sol-gel and subsequent curing process. These coatings are typically less than 1.5 micrometres thick. (3) Piezoelectric films, between 1 and 50 micrometres thick, for micro electromechanical systems, are often made by first depositing fine powders using electrostatic spraying, inkjet printing or dip coating and subsequently sintering. PROBLEM DEFINITION: The problem is how to avoid cracking of the films during the drying, curing and sintering steps. Elevated temperatures are used to consolidate the films. As temperature increases, the porous and liquid-filled films shrink first due to liquid evaporation and subsequently due to sintering or curing. The line-shrinkage can be as large as 20%. However the films cannot shrink freely in the plane of the film surface because of their bounding with the substrate, and with each other in multilayered films. The shrinking is highly constrained which leads to stresses and hence cracking in the films. RESEARCH ISSUES: The current systems are far from being optimised. It is almost impossible to achieve the optimisation using trial and error experiments because there are too many material and processing variables involved. There is an urgent need to develop a computer modelling capacity for the constrained shrinking and cracking phenomenon. However such a capacity does not yet exist mainly because of two reasons: (a) The existing modelling technique (the finite element method) requires the viscosities of the film material. These viscosities depend strongly on the microstructure of the material which changes dramatically as the film shrinks. These data are too difficult to obtain experimentally. (b) The science of predicting multi-cracking is premature.THE PROJECT TEAM: Supported by RRFCS and TWI, this proposal brings together three research groups at Universities of Leicester, Surrey and Cranfield and a futher research group in Germany to address these issues and to develop and validate a computer modelling technique. METHODOLOGY: In a recently completed PhD project, the investigators developed a ground breaking technique to model time dependent shrinkage deformation without knowing the viscosities. The proposed project is to build on this success and to further develop the technique for constrained shrinking and to include multi-cracking. The difficulty to deal with multi-cracks will be addressed using a so-called materials point method. This method was initially developed for plastic deformation but has been successfully extended to the multi-cracking problem in our pilot studies. The computer models will be developed around three experimental case studies. Three different experimental techniques will be used at Surrey, Cranfield and Wurzburg to measure the material data required in the model and to validate the model predictions. PROJECT IMPACT: This project will make it possible to optimise the design, material selection and processing parameters for solid oxide fuel cells, coatings and piezoelectric films. More generally the project will make a major impact on modelling the multi-cracking of brittle materials. Such problems include ballistic impact of ceramic armour, missile or explosive impact of civil structures and safety concerns of all glass structures.
 
Description This project completed a comprehensive study on constrained shrinking and cracking of ceramic thin films.

Sintering of ceramic films on a solid substrate is an important technology to fabricate a range of products including solid oxide fuel cells, micro-electronic PZT films and protective coatings. Cracking is a major problem during constrained sintering of ceramic films. A local variation of density in a green film, referred to as a defect in this work, is the leading cause for cracking. The project studied the problem in the following three aspects:

Firstly, there is clear evidence that the constrained sintering process is anisotropic in nature. This project carried out a study of the constrained sintering deformation using an anisotropic constitutive law. The state of the material is described using the sintering strains rather than the relative density. In the limiting case of free sintering, the constitutive law reduces to a conventional isotropic constitutive law. The anisotropic constitutive law is used to calculate sintering deformation of a constrained film bonded to a rigid substrate and the compressive stress required in a sinter-forging experiment to achieve zero lateral shrinkage. The results are compared with experimental data in the literature. It is shown that the anisotropic constitutive law can capture the behaviour of the materials observed in the sintering experiments.

Secondly heterogeneities in a green film made from a powder compact is considered to be one of the major reasons for the generation of sintering cracks. Stresses are generated in a film due to the constraint of the substrate. Instabilities in the sintering process can occur at sites of these herogeneities resulting in the generation of multiple cracks, which can propagate through the thickness of the film. The classical finite element method is fundamentally ill-suited to studying this multiple-cracking problem. This project developed a simple and robust numerical method for the computer modelling of sintering and multiple-cracking. The method is based on the so-called material point method, which was initially developed for large deformation problems in plasticity. A parallel computing algorithm is implemented and a simple scheme for modelling the initiation and propagation of multiple-cracks is proposed. The numerical scheme is then validated by simulating a simple geometric problem for which an analytical solution can be obtained. Finally, the robust performance of the numerical method is demonstrated by modelling the sintering response of a film which contains different types of heterogeneities.

Thirdly a local variation of density in a green film, referred to as a defect in this work, is the leading cause for cracking. This project carried out analytical and numerical studies of the behaviour of such defects during constrained sintering. An interesting behaviour of de-sintering and healing of the defects is revealed. It is demonstrated that the healing process can be made to start earlier during sintering by using (a) larger particles, (b) lower sintering temperature and (c) lower initial density. However a uniform distribution of initial density in the film is shown to be the most effective means to avoid cracking. It is realised that most of the factors beneficial to defect healing are detrimental to sintering a film to high density, because the driving force for sintering also drives cracking. The analytical and numerical studies also offer some simple explanations to why thin films are less susceptible to cracking than thick ones. Finally, the constitutive model has been combined with a simple empirical failure criterion, to simulate the initiation and propagation of multiple cracks in a sintering film. The cracking patterns predicted by the simulations resemble those observed during sintering experiments.
Exploitation Route The numerical method that we developed needs to be implemented in commercial finite element code, so that these method can be used by the industry in their material design and process optimisation.
Sectors Aerospace, Defence and Marine,Electronics,Energy,Healthcare,Manufacturing, including Industrial Biotechology
 
Description Not by any industry yet but our results have made significant academic impact.