Multi-scale modeling of elasto-plastic response of SnAgCu lead-free solder alloys at different ageing conditions: Effect of microstructure evolution, particle size effects and interfacial failure

In microelectronics applications, SnAgCu lead-free solder joints play the important role of ensuring both the mechanical and electrical integrity of the components. In such applications, the SnAgCu joints are subjected to elevated homologous temperatures for an extended period of time causing significant microstructural changes and leading to reliability issues. In this study, the link between the change in microstructures and deformation behavior of SnAgCu solder during ageing is explained by developing a hybrid multi-scale microstructure-based modeling approach. Herein, the SnAgCu solder alloy is seen as a three phase metal matrix composite in which Ag3Sn and Cu6Sn5 hard intermetallics play the role of reinforcements and Sn the role of a ductile matrix. The hardening of the Sn matrix due to fine intermetallics in the eutectic mixture is modeled by incorporating the mean field effects of geometrically necessary dislocations. Subsequently, a two level homogenization procedure based on micromechanical finite element (FE) models is used to capture the interactions between the different phases. For this purpose, tomographic images of microstructures obtained by Focused Ion Beam (FIB) and synchrotron X-Ray in different ageing conditions are directly used to generate statistically representative volume elements (RVE) using 3D FE models. The constitutive behavior of the solder is determined by sequentially performing two scales of numerical homogenization at the eutectic level and then at the dendrite level. For simplification, the anisotropy of Sn as well as the potential recovery processes have been neglected in the modeling. The observed decrease in the yield strength of solder due to ageing is well captured by the adopted modeling strategy and allows explaining the different ageing mechanisms. Finally, the effects of potential debonding at the intermetallic particle-matrix interface as well as particle fracture on the overall strength of solder are discussed based on simplified unit cell FE models and experimental observations. (C) 2016 Elsevier B.V. All rights reserved.

Microstructure-based modeling of the ageing effect on the deformation behavior of the eutectic micro-constituent in SnAgCu lead-free solder

John Botsis, Joël Cugnoni, Milad Maleki

The eutectic micro-constituent in SnAgCu solder governs the deformation behavior of the joint as it shows better deformation resistance than the Sn dendrites and occupies a high volume percentage of the whole solder. The main scope of this study is to develop a three-dimensional (3-D) homogenization model taking into account the microstructural evolution in the eutectic micro-constituent of SnAgCu solder in order to simulate the change in mechanical behavior of the joint caused by isothermal ageing. For this purpose, 3-D configurations of Ag3Sn and Cu6Sn5 intermetallic compounds (IMCs) in near-eutectic SnAgCu solder are visualized in the as-soldered condition and after ageing by focused ion beam/scanning electron microscopy tomography. The tomographic images are used to generate feature-preserving finite element meshes of the actual microstructures. The representative volume element size and constitutive behavior of the eutectic mixture in the two conditions are determined by a numerical homogenization procedure. The results show a considerable reduction in the yield stress level of the eutectic micro-constituent after ageing of the solder joint. It is shown that the increase in the interparticle spacing and decrease in the aspect ratio of IMCs due to ageing cause a significant change in the strain distribution in the tin matrix, which leads to a lower contribution of IMCs in load-sharing and yield strength of aged solder. The elastic plastic properties of as-soldered and aged eutectic mixtures are determined by nanoindentation. The results of homogenization are validated through comparison with experimental results and prediction of the dislocation detachment theory. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Elsevier2013

Isothermal Ageing of SnAgCu Solder Alloys: Three-Dimensional Morphometry Analysis of Microstructural Evolution and Its Effects on Mechanical Response

John Botsis, Joël Cugnoni, Milad Maleki

Due to the high homologous temperature and fast cooling rates, the microstructures of SnAgCu (SAC) solders are in a meta-stable state in most applications, which is the cause of significant microstructural evolution and continuous variation in the mechanical behavior of the joints during service. The link between microstructures evolution and deformation behavior of Sn-4.0Ag-0.5Cu solder during isothermal ageing is investigated. The evolution of the microstructures in SAC solders are visualized at different scales in 3D by using a combination of synchrotron x-ray and focused ion beam/scanning electron microscopy tomography techniques at different states of ageing. The results show that, although the grain structure, morphology of dendrites, and overall volume fraction of intermetallics remain almost constant during ageing, considerable coarsening occurs in the Ag3Sn and Cu6Sn5 phases to lower the interfacial energy. The change in the morphometrics of sub-micron intermetallics is quantified by 3D statistical analyses and the kinetic of coarsening is discussed. The mechanical behavior of SAC solders is experimentally measured and shows a continuous reduction in the yield resistance of solder during ageing. For comparison, the mechanical properties and grain structure of beta-tin are evaluated at different annealing conditions. Finally, the strengthening effect due to the intermetallics at different ageing states is evaluated by comparing the deformation behaviors of SAC solder and beta-tin with similar grain size and composition. The relationship between the morphology and the strengthening effect due to intermetallics particles is discussed and the causes for the strength degradation in SAC solder during ageing are identified.

Springer2014

Microstructure of single crystal Ni-based superalloys during blade manufacturing process and creep deformation

Stéphane Pierret

The aim of the thesis is to obtain more understanding about the influence of plastic deformation on the microstructural changes observed in single crystal (SX) Ni-based superalloys using diffraction techniques. This work was organised around two main problematics: (1) rafting in turbine blades after the manufacturing process and (2) rafting and mosaicity evolution in two SX alloys with different composition during creep deformation. SX Ni-based superalloys are first choice materials for turbine blade application in land-based gas turbines and aero-engines. Superior mechanical properties of these materials at high temperatures are achieved due to the optimisation of the alloying composition and the microstructure. SX Ni-based superalloy turbine blades solidify by dendritic solidification with dendrites aligned along the directions of lowest Young modulus (interdendritic spacing around 300μm). At the end of the manufacturing process, the microstructure consists of high volume fraction of cubic γ’ precipitates (around 500nm) coherently embedded in the γ matrix. However specific parts of engine-ready turbine blades exhibit directionally coarsened γ’ precipitates in a preferred direction (rafting) without the influence of an applied load. It is of prime importance to understand the origin of rafting prior to the introduction of the blades in the engine since rafting can alter the mechanical properties of the alloy. Chemical segregations and the introduction of plastic deformation prior to thermal treatments were identified as potential driving force for rafting during load-free high temperature annealing. Most of the SX Ni-based superalloys used in the current blade production in Alstom contain significant amount of refractory elements which are expensive and increase the density of the alloy. To answer the demand of cheaper and lighter components, Alstom launched a development program to design novel SX superalloys. One of these projects led to the production of a Re-free superalloy, so-called MD2. Extensive mechanical investigations on MD2 are on-going and compared to the behaviour of the MK4HC alloy (3wt% Re) currently used in turbine blade production. One of the major differences in terms of mechanical properties between Re-containing and Re-free SX alloys is the faster kinetics of coarsening and rafting during creep deformation at high temperature in the latter alloys. It prevented so far their application in the hottest areas in gas turbines. It is therefore of utmost importance to acquire more knowledge about the mechanisms associated with the microstructure evolution during creep of the new MD2 SX alloy in comparison with the MK4HC alloy. The evolution of the lattice parameter misfit in different directions with respect to the applied load during creep deformation was associated with the evolution of the microstructure from cubic to elongated γ’ precipitates It could be shown that rafting occurs after the cooling stage following the solution heat treatment (SHT) during the manufacturing of the blade with investigations of the microstructure. The influence of chemical segregations on rafting was excluded with the investigation of the blade alloy composition in different parts of the blade cooled from the SHT and diffraction measurements in stress-relieved combs prepared from the same blade. The formation of a rafted microstructure during the manufacturing process was associated with the formation of plastic strains during cooling after the SHT. This was confirmed after gathering results from investigations of the microstructure, simulation of the cooling stage and neutron diffraction measurements on the blade. The investigations of the microstructure performed on the engine-ready blade revealed an inversion of the γ’ raft orientation below (parallel to [001]) and above the platform of the blade (perpendicular to [001]). This was attributed to an inversion of the sign of residual strain between the previously mentioned positions as revealed by neutron diffraction measurements performed along the airfoil of the blade cooled after the SHT. Microscopy also showed that the rafted microstructure was more pronounced below the platform (long γ’ rafts) than above the platform (shorter γ’ rafts with retained cubic precipitates). The concept of the threshold plastic strain necessary to induce rafting during annealing subsequent to plastic deformation was used to describe the difference in rafted microstructure. It is suggested that plastic strains largely exceed the threshold below the platform leading to fully formed rafted microstructure. On the other side, plastic strains of the order to the threshold strain are suggested above the platform in order to explain the partially formed rafted microstructure Neutron diffraction measurements revealed that the lattice parameter misfit was larger in the MK4HC than in the MD2 alloy at 20°C in the unloaded state. The larger misfit in the MK4HC alloy was attributed to the larger concentration of elements dissolving in the γ phase and to the presence of Re. During creep deformation, coherency stresses are relieved at the γ/γ’ interface in the γ channels perpendicular to the applied load by dislocations. On the other hand, dislocations increase the internal stress at the γ/γ’ interface in the γ channels parallel to the applied load. This leads to the rafting of the γ’ precipitates perpendicular to the applied load. This was observed in the MK4HC. The absence of clear misfit evolution in the MD2 alloy was attributed to the anomalous microstructure at the beginning of the creep deformation. The mosaicity of the MK4HC and MD2 alloys revealed crystallographic misorientation between neighbouring dendrites up to 0.5°. The misorientation was associated with the presence of dislocations in the regions between the dendrites formed during the dendritic solidification of the alloys from existing work. It was shown that the composition of the SX alloys and short periods at high temperature in the unloaded state had only little influence on the misorientation between neighbouring dendrites. Upon creep loading to 180MPa, the mosaicity markedly changed in the two SX alloys independent of the creep temperature. In particular, the number of single misoriented domains measured by X-ray diffraction decreased. This was attributed to the fast propagation of the dislocations present in the interdendritic structure inducing a rotation of the individual dendrites. During creep deformation, the mosaicity increased as visible from the broadening of the maximum spread in misorientation. The formation of inhomogeneous plastic strain fields in the γ/γ’ microstructure is believed to create new mosaic blocks in the dendritic structure of the alloys leading to the observed broadening of the mosaicity. The influence of plastic deformation on the evolution of the mosaicity was demonstrated. The mosaicity significantly changed during creep of the MD2 at 1050°C/180MPa and 1000°C/180MPa whereas no significant evolution could be measured during creep at 950°C/180MPa. This was attributed to a temperature dependence of the yield strength of the MD2 alloy. It therefore induces difference in dislocation propagation at 950°C compared to 1050°C and 1000°C which retards the broadening of the mosaicity during creep at 950°C. Furthermore, the mosaicity formed during creep deformation was retained upon unloading and cooling of the SX samples to room temperature.

EPFL2012

Microstructure of single crystal Ni-based superalloys during blade manufacturing process and creep deformation

Stéphane Pierret

EPFL2012