Materials Science and Engineering A 427 (2006) 60–68 Modelling of Ag 3 Sn coarsening and its effect on creep of Sn–Ag eutectics Jicheng Gong ∗ , Changqing Liu, Paul P. Conway, VadimV. Silberschmidt Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, LE11 3TU, UK Received 9 August 2005; received in revised form 7 April 2006; accepted 11 April 2006 Abstract A new constitutive model, which can account for the solder’s microstructure and its evolution, is proposed to describe the creep behaviour of the Sn–Ag eutectic phase. In this model, the threshold stress, being a function of the particle size, volume fraction and distribution of Ag 3 Sn intermetallic compound (IMC), is introduced to build the relationship between the creep behaviour of the Sn–Ag solder and its microstructure. Evolution of the eutectic phase’s microstructure is accounted for in terms of the coarsening model. Both the creep strain rate and hydrostatic stress’s influence are taken into account in the IMC coarsening model. The proposed model is implemented into the commercial finite element code ABAQUS. The creep deformation due to the applied stress and IMC coarsening are discussed in the case of a flip chip solder joint. The obtained results show that the shape of the solder joint influences the particle distribution caused by heterogeneous coarsening. The solder joint is softened due to microstructure evolution over a long range of time. © 2006 Elsevier B.V. All rights reserved. Keywords: Pb-free solder; Constitutive model; Threshold stress; Coarsening; Finite elements 1. Introduction In the past five decades, the Sn–Pb solder has been the major material to assemble electronic components in the electronic industry. This has been mainly due to its low cost, good solder- ability, a low melting temperature and proper interfacial bonding reliability. However, the Pb and Pb-containing compounds are identified as the most toxic chemicals, and the Sn–Pb solder in the electronics is the main source of Pb contamination in the environment [1]. Under the new waste electrical and electronic equipment (WEEE) legislation, aimed to prevent environmental contamination with lead, the use of Pb in consumer electronics is banned after July 1, 2006 in the European Union [2]. Among the Pb-free alternatives, the Ag–Sn solder is one of the most promis- ing candidates because it can provide compatible properties with the Sn–Pb solder [3]. While the Sn–Ag solder shows better creep resistance and consequently higher fatigue performance than the Sn–Pb solder in the bulk specimen, it does not suggest that this material can provide better reliability in microscopic joints, because the characteristic size of its microstructure (e.g. grain size) can be comparable to the solder joint size, when it becomes smaller than 100 m in diameter. In this case, the creep and dam- ∗ Corresponding author. Tel.: +44 1509 227678; fax: +44 1509 227648. E-mail address: J.Gong@lboro.ac.uk (J. Gong). age behaviour shifts from polycrystals-based mechanisms to the intra-granular based ones. Few numerical studies have been done in this particular area. Hence a model that correlates mechan- ical integrity to the microstructure of micro-solder joints is of particular interest. The general numerical approach to reliability study of solder joints can be implemented in two steps: (i) finite element (FE) analysis and (ii) prediction of the fatigue life. In the first step, the material’s description, including a constitutive model for the solder material, are introduced into the geometry model. At the same time, the initial and boundary conditions are applied. Then the FE analysis is performed to calculate response of stresses and strains in the solder joints as well as a respective hysteresis loop. In the second step, a suitable fatigue model is chosen. The FE results are substituted into the fatigue model to predict the number of cycles to failure. The major drawback of this method lies in its assumption that the microstructure and corresponding properties of the solders remain constant during the entire load- ing process. So the analysed results of the FE analysis are usually for the forth loading cycle because they will reach a stable state at that stage. In fact, the stress response of solder materials to constant strain decreases under cycling load [4,5]. Thus, this approach underestimates the fatigue life of solder joints. The recently developed cohesive zone model [6,7] combines these two steps together and successfully predicts the damage accu- mulation in the solder joints. But it attributes degradation of 0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.04.034