Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal

Subhasis Mukherjee, Bite Zhou, Abhijit Dasgupta, Thomas R. Bieler

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A multiscale modeling framework is proposed in this study to capture the influence of the inherent elastic anisotropy of single crystal Sn and the inherent heterogeneous microstructure of a single crystal SnAgCu (SAC) solder grain on the secondary creep response of the grain. The modeling framework treats the SAC microstructure as having several distinct length scales. The smallest length scale (Tier 0) consists of the Sn BCT lattice. The eutectic Sn-Ag micro-constituent, consisting of nanoscale Ag3Sn IMC particles embedded in the single crystal BCT Sn matrix, is termed Tier 1. The single-crystal SAC microstructure, consisting of Sn dendrites and surrounding eutectic Sn-Ag phase, is termed Tier 2. Dislocation recovery mechanisms, such as Orowan climb and detachment from nanoscale Ag3Sn particles, are found to be the rate controlling mechanisms for creep deformation in the eutectic Sn-Ag phase (Tier 1) of a SAC single crystal. The anisotropic secondary creep rate of eutectic Sn-Ag phase (Tier 1), is then modeled using the above inputs and the saturated dislocation density calculated for dominant glide systems during secondary stage of creep. Saturated dislocation density is estimated as the equilibrium saturation between three competing processes: (1) dislocation generation; (2) dislocation impediment caused by back stress from pinning of dislocations at IMCs; and (3) dislocation recovery due to climb/detachment from IMCs. Secondary creep strain rate of eutectic Sn-Ag phase in three most facile slip systems is calculated and compared against the isotropic prediction. At low stress level secondary steady state creep rate along (110)[001] system is predicted to be ten times the creep rate along (100)[0-11] system. However, at high stress level, secondary steady state creep rate along (110)[001] system is predicted to be ten thousand times the creep rate along (100)[0-11] system. The above predictions are in strong agreement with (1-4) orders of magnitude of anisotropy observed in steady state secondary creep response in SAC305 solder joints tested under identical loading conditions in experiments conducted by several authors. The above model is then combined with Eigen-strain methods and average matrix stress concepts to homogenize the load sharing between the Sn dendrites and the surrounding eutectic Ag-Sn matrix. The resulting steady state creep rates are predicted for a few discrete single crystal SAC305 specimens. Very good agreement is observed between the predicted steady state creep rate and the measured creep rates for two SAC305 single crystal specimens.

    Original languageEnglish (US)
    Title of host publicationAdvanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales
    PublisherAmerican Society of Mechanical Engineers
    Volume2
    ISBN (Print)9780791856895
    DOIs
    StatePublished - 2015
    EventASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, InterPACK 2015, collocated with the ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels - San Francisco, United States

    Other

    OtherASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, InterPACK 2015, collocated with the ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels
    CountryUnited States
    CitySan Francisco
    Period7/6/157/9/15

    Profile

    Creep
    Erythrocyte Inclusions
    Cardanolides
    Eutectics
    Addison Disease
    Enzyme Reactivators
    Employee Grievances
    False Negative Reactions
    Automobiles
    Muscle Contraction
    Microstructure
    Dendrites (metallography)
    Soldering alloys
    Anisotropy
    Recovery
    Carbamoyl-Phosphate Synthase (Glutamine-Hydrolyzing)
    Common Bile Duct Diseases
    Erythrocebus patas
    Anthralin
    Erwinia

    ASJC Scopus subject areas

    • Process Chemistry and Technology

    Cite this

    Mukherjee, S., Zhou, B., Dasgupta, A., & Bieler, T. R. (2015). Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal. In Advanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales (Vol. 2). American Society of Mechanical Engineers. DOI: 10.1115/IPACK2015-48710

    Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal. / Mukherjee, Subhasis; Zhou, Bite; Dasgupta, Abhijit; Bieler, Thomas R.

    Advanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales. Vol. 2 American Society of Mechanical Engineers, 2015.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Mukherjee, S, Zhou, B, Dasgupta, A & Bieler, TR 2015, Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal. in Advanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales. vol. 2, American Society of Mechanical Engineers, ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, InterPACK 2015, collocated with the ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels, San Francisco, United States, 6-9 July. DOI: 10.1115/IPACK2015-48710
    Mukherjee S, Zhou B, Dasgupta A, Bieler TR. Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal. In Advanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales. Vol. 2. American Society of Mechanical Engineers. 2015. Available from, DOI: 10.1115/IPACK2015-48710

    Mukherjee, Subhasis; Zhou, Bite; Dasgupta, Abhijit; Bieler, Thomas R. / Mechanistic modeling of the anisotropic steady state creep response of snagcu single crystal.

    Advanced Electronics and Photonics, Packaging Materials and Processing; Advanced Electronics and Photonics: Packaging, Interconnect and Reliability; Fundamentals of Thermal and Fluid Transport in Nano, Micro, and Mini Scales. Vol. 2 American Society of Mechanical Engineers, 2015.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    abstract = "A multiscale modeling framework is proposed in this study to capture the influence of the inherent elastic anisotropy of single crystal Sn and the inherent heterogeneous microstructure of a single crystal SnAgCu (SAC) solder grain on the secondary creep response of the grain. The modeling framework treats the SAC microstructure as having several distinct length scales. The smallest length scale (Tier 0) consists of the Sn BCT lattice. The eutectic Sn-Ag micro-constituent, consisting of nanoscale Ag3Sn IMC particles embedded in the single crystal BCT Sn matrix, is termed Tier 1. The single-crystal SAC microstructure, consisting of Sn dendrites and surrounding eutectic Sn-Ag phase, is termed Tier 2. Dislocation recovery mechanisms, such as Orowan climb and detachment from nanoscale Ag3Sn particles, are found to be the rate controlling mechanisms for creep deformation in the eutectic Sn-Ag phase (Tier 1) of a SAC single crystal. The anisotropic secondary creep rate of eutectic Sn-Ag phase (Tier 1), is then modeled using the above inputs and the saturated dislocation density calculated for dominant glide systems during secondary stage of creep. Saturated dislocation density is estimated as the equilibrium saturation between three competing processes: (1) dislocation generation; (2) dislocation impediment caused by back stress from pinning of dislocations at IMCs; and (3) dislocation recovery due to climb/detachment from IMCs. Secondary creep strain rate of eutectic Sn-Ag phase in three most facile slip systems is calculated and compared against the isotropic prediction. At low stress level secondary steady state creep rate along (110)[001] system is predicted to be ten times the creep rate along (100)[0-11] system. However, at high stress level, secondary steady state creep rate along (110)[001] system is predicted to be ten thousand times the creep rate along (100)[0-11] system. The above predictions are in strong agreement with (1-4) orders of magnitude of anisotropy observed in steady state secondary creep response in SAC305 solder joints tested under identical loading conditions in experiments conducted by several authors. The above model is then combined with Eigen-strain methods and average matrix stress concepts to homogenize the load sharing between the Sn dendrites and the surrounding eutectic Ag-Sn matrix. The resulting steady state creep rates are predicted for a few discrete single crystal SAC305 specimens. Very good agreement is observed between the predicted steady state creep rate and the measured creep rates for two SAC305 single crystal specimens.",
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