Napo Bonfoh

Micromechanical modeling of ductile damage of polycrystalline materials with heterogeneous particles

Abstract A two-level homogenization approach is applied in this micro-mechanical modeling of the ductile damage of polycrystals containing intracrystalline non-shearable particles. Voids nucleate around these second phase particles by interface debonding and thereafter, grow due to the plastic straining of the crystalline matrix. The equivalent behavior of the single crystal containing voids is derived from the description of the single crystal with particles. Moreover, this behavior is deduced from the classical formulation of the single crystal plasticity based on crystallographic gliding and Schmids law. At microscopic scale, void nucleation is possible when the elastic strain energy stored in the particle and released during debonding exceeds the energy of creation of new surfaces at the crystal-particle interface. The material pre-damage behavior is described by the hardening by intra-crystalline particles model proposed in Bonfoh et al. (2003).

Modeling of intra-crystalline hardening of materials with particles

Abstract A two-level homogenization approach is developed for the micromechanical modeling of the elastoplastic behavior of polycrystals containing intracrystalline non-shearable particles. First, a micro-meso transition is employed to establish a constitutive relation for a single crystal containing particles. The behavior of an equivalent single crystal with particles is derived from the classical formulation of plasticity of the single crystal based on the Schmids law and crystallographic gliding. Then, the transition to the macroscopic scale is performed with a self-consistent scheme to determine the elastoplastic behavior of the macro homogeneous material. The obtained global behavior is characterized by a mixed anisotropic and kinematic hardening related to an evolution of inter- and intra-granular material microstructure. Results have been analyzed in light of second and third order internal stresses developed during the plastic flow. Especially, yield surfaces have been determined for various preloadings and particle volume fractions.

Three-Dimensional Thermomechanical Simulation of Fine-Pitch High-Count Ball Grid Array Flip-Chip Assemblies

Flip-chip technology is increasingly prevalent in electronics assembly [three-dimensional (3D) system-in-package] and is mainly used at fine pitch for manufacture of megapixel large focal-plane detector arrays. To estimate the reliability of these assemblies, numerical simulations based on finite-element methods appear to be the cheapest approach. However, very large assemblies contain more than one million solder bumps, and the optimization process of such structures through numerical simulations turns out to be a very time-consuming task. In many applications, the interconnection layer of such flip-chip assemblies consists of solder bumps embedded in epoxy filler. For such configurations, we propose an alternative approach, which consists in replacing this heterogeneous interconnection layer by a homogeneous equivalent material (HEM). A micromechanical model for the estimation of its equivalent thermoelastic properties has been developed. The obtained constitutive law of the HEM was then implemented in finite-element software (Abaqus®). Thermomechanical responses of tested assemblies submitted to loads corresponding to manufacturing conditions have been analyzed. The homogenization–localization process allowed estimation of the mean values of stresses and strains in each phase of the interconnection layer. To access more precisely the stress and strain fields in these phases, two models of structural zoom, taking into account the real solder bump geometry, have been tested. The obtained local stress and strain fields corroborate the experimentally observed damage initiation of the solder bumps.

3D Modeling of high count fine pitch flip chip assemblies

Flip chip technology is increasingly prevalent in electronics assembly (3D System in Package), and is mainly used at fine pitch in the manufacture of megapixels large focal plane detectors arrays. To verify the reliability of these assemblies numerical simulations appear as the less expensive method. However, as very large assemblies contain an array of more than one million solder bumps, the repetitive simulation of such structures in optimization processes is inconceivable. To circumvent this difficulty, a model based on a micromechanical description of the effective thermo-elastic properties of the interconnection layer of the flip chip assembly is proposed in this study. The interconnection layer composed of solder bumps embedded in epoxy was replaced by a homogeneous equivalent material and the manufacturing process of the assembly was simulated. The homogenization method allows estimating mean values of local stress and strain in each constituent of the interconnection layer. To deduce the more accurate stress and strain fields in these phases, a structural zoom technique has been applied. The results attest stress concentration at the interface between solder bumps and substrate/chip, in accordance with experimental observations showing cracks initiation at this place. In order to validate the relevance of the proposed modeling, at the level of the flip chip assembly, numerical results were compared with experimental measurements in terms of macroscopic warpage. In view of obtained results, the simulation tactic proposed seems to be an adequate approach for improvement of optoelectronic components.

Thermomechanical characterization of electronic components

The main objective of this study is to validate the thermomechanical properties of materials used in some electronic components. The improved performance of HgCdTe infrared focal plane arrays requires reliability of the assembly at low temperatures down to 77K. Unfortunately, the thermomechanical behavior of most materials of these components remains to be clarified, particularly in a cryogenic environment. The present investigation is a part of a global study that aims to analyze the reliability of some electronic assembly, through numerical simulations combined with experimental measures. The relevance of this numerical modelling strongly depends on a precise characterization of the thermo-mechanical behavior of specific materials involved in the considered assemblies. Thus, through numerical simulations of a model of electronic chip, we determine the thermal and mechanical properties of materials such as indium, silicon, fused silica, by comparing these simulations results with the experimental measurements carried out on these same models of chips. This study enables us to have a complete database of the thermomechanical behavior of materials studied for the range of operating temperatures.