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  • Micro Scale Modeling of Grain Boundary Damageunder Creep Conditions

    Oksana Ozhoga-MaslovskajaSupervisors: Holm Altenbach, Konstantin Naumenko, Manja Krger

    Oksana Ozhoga-Maslovskaja (OvGU) 1

  • Experimental Observation

    500 m

    Creep fracture at different scales: fractured creep specimen,micrograph of the copper specimen, tested at 550 C and 25 MPa

    Oksana Ozhoga-Maslovskaja (OvGU) 2

  • Creep Fracture

    Failed solder interconnection

    Overmold Metal pads

    Circuit Board

    Silicon Die

    Typical crack through solder joint interface. Scheme of solderinterconnection in an electronic assembly (Towashiraporn et al., 2005)

    Oksana Ozhoga-Maslovskaja (OvGU) 3

  • Creep in a Polycrystalline Solid 1

    Elastic stress concentration;

    Plastic flow-field;

    Diffusive flow-field of matter;

    Cavity formation in triplepoints and at grainboundaries.

    1Crossman and Ashby, 1975

    Oksana Ozhoga-Maslovskaja (OvGU) 4

  • Creep in a Polycrystalline Solid 1

    Elastic stress concentration;

    Plastic flow-field;

    Diffusive flow-field of matter;

    Cavity formation in triplepoints and at grainboundaries.

    1Crossman and Ashby, 1975

    Oksana Ozhoga-Maslovskaja (OvGU) 4

  • Creep in a Polycrystalline Solid 1

    Elastic stress concentration;

    Plastic flow-field;

    Diffusive flow-field of matter;

    Cavity formation in triplepoints and at grainboundaries.

    1Crossman and Ashby, 1975

    Oksana Ozhoga-Maslovskaja (OvGU) 4

  • Creep in a Polycrystalline Solid 1

    Elastic stress concentration;

    Plastic flow-field;

    Diffusive flow-field of matter;

    Cavity formation in triplepoints and at grainboundaries.

    1Crossman and Ashby, 1975

    Oksana Ozhoga-Maslovskaja (OvGU) 4

  • Creep in a Polycrystalline Solid 1

    Elastic stress concentration;

    Plastic flow-field;

    Diffusive flow-field of matter;

    Cavity formation in triplepoints and at grainboundaries.

    1Crossman and Ashby, 1975

    Oksana Ozhoga-Maslovskaja (OvGU) 4

  • Idea of the Study

    Aim of the StudyTo perform creep damage analysis of the polycrystalline material onthe micro scale in order to investigate the influence of chosenmicromechanisms on the creep curve of mesomaterial

    Considered mechanismsElastic deformation ofanisotropic grains;

    Power law creep;

    Grain boundary sliding;

    Grain boundary cavitation(Tvergaard 1984);

    Stiffness reduction due tocavitation.

    Other mechanismsDislocations and vacanciesmovement;

    Dislocation pile ups;

    Subgrains and slip bandsformation.

    Oksana Ozhoga-Maslovskaja (OvGU) 5

  • Collaboration

    Polycrystalline geometry:

    Oleksandr Prygorniev "Micromechanical simulation of deformationand fatigue of polycrystalline materials";

    Srihari Dodla "Experimental and numerical investigations oflamellar copper silver composites".

    Similar field researches:

    Shyamal Roy, Esmaeil Tohidlou, Dr.Ing. Rainer Glge.

    Oksana Ozhoga-Maslovskaja (OvGU) 6

  • Collaboration

    The uniaxial tensile creep tests under polycrystalline copper at550 C are performed in order to observe the micromechanismstaking place during creep.

    Prof. GariboldiDipartimento di Meccanica

    Politecnico di MilanoItalia

    Micrographs of the fractured specimens are performed withJun.-Prof. Dr.-Ing. Manja Krger assistance.

    Oksana Ozhoga-Maslovskaja (OvGU) 7

  • Geometrical Model of Polycrystal

    g1

    g2

    g3

    Crystalline material of the grain interiorex

    ey

    ez

    g1

    g2

    g3

    Grain boundary materialOksana Ozhoga-Maslovskaja (OvGU) 8

  • Linear Elasticity

    Elasticity law

    = 21(11 + 22 + 33)(ggg1 ggg1 + ggg2 ggg2 + ggg3 ggg3)

    + [1(11 22) + 2(11 33)]ggg1 ggg1 + [1(22 11) + 3(22 33)]ggg2 ggg2+ [2(33 11) + 3(33 22)]ggg3 ggg3 + 21212(ggg1 ggg2 + ggg2 ggg1)

    + 21313(ggg1 ggg3 + ggg3 ggg1) + 22323(ggg2 ggg3 + ggg3 ggg2)

    Grain interior21 = 125 GPa

    a

    1 = 2 = 3 = 12.3 GPa12 = 13 = 23 = 62.3 GPa

    aChang and Himmel, 1966

    Grain boundary21 = 600 GPa

    1 = 2 = 3 = 12.3 GPa12 = 13 = 23 = 62.3 GPa

    Oksana Ozhoga-Maslovskaja (OvGU) 9

  • Creep Behavior

    Creep strain rate evolution equation

    c =

    12

    an1eq

    {

    [

    1(11 22) + 3(11 33)]

    (

    ggg1 ggg1 13

    III)

    +[

    2(22 33) + 1(22 11)]

    (

    ggg2 ggg2 13

    III)

    +[

    3(33 11) + 2(33 22)]

    (

    ggg3 ggg3 13

    III)

    + 6[

    1212(ggg1 ggg2 + ggg2 ggg1)

    + 1313(ggg1 ggg3 + ggg3 ggg1) + 2323(ggg2 ggg3 + ggg3 ggg2)]

    }

    Equivalent stress

    2eq =

    12

    [

    1 (11 22)2 + 2 (22 33)

    2 + 3 (33 11)2]

    + 3[

    12212 + 23

    223 + 13

    213

    ]

    Oksana Ozhoga-Maslovskaja (OvGU) 10

  • Material Parameters Identification

    Idea of the numerical testTime

    Ave

    rage

    dcr

    eep

    stra

    in

    Material model parametersParameter Grain interior Grain boundary

    A, (MPa)n

    s 4 1015 6 108

    n 9.4 41, 2, 3 1 0.212, 23, 13 0.2 0.3

    Oksana Ozhoga-Maslovskaja (OvGU) 11

  • Material Parameters Identification

    Idea of the numerical testTime

    Ave

    rage

    dcr

    eep

    stra

    in

    Material model parametersParameter Grain interior Grain boundary

    A, (MPa)n

    s 4 1015 6 108

    n 9.4 41, 2, 3 1 0.212, 23, 13 0.2 0.3

    Oksana Ozhoga-Maslovskaja (OvGU) 11

  • Material Parameters Identification

    Sliding strain in the loading directionTotal strain [-]

    Slid

    ing

    stra

    in[-

    ]

    Material model parametersParameter Grain interior Grain boundary

    A, (MPa)n

    s 4 1015 6 108

    n 9.4 41, 2, 3 1 0.212, 23, 13 0.2 0.3

    Oksana Ozhoga-Maslovskaja (OvGU) 11

  • Model Application

    IIII

    II300

    Creep curves of the axial and torsional strains of the non-proportional loading tests of

    Murakami and Sanomura (1985) with the principal stress direction rotation at 30

    Oksana Ozhoga-Maslovskaja (OvGU) 12

  • Model Application

    Time, [h]0 5 12

    x

    y

    z

    Non-proportional loading Proportional loadingLoadingdirection

    Stress,[MPa]

    Time,[h]

    Loadingdirection

    Stress,[MPa]

    Time,[h]

    x 30 012 x 30 012y 15 05 y 15 012z 15 512 z 15

    Oksana Ozhoga-Maslovskaja (OvGU) 13

  • Model Application

    Non-proportional loading testProportional loading test

    Time [h]

    Ave

    rage

    dto

    tals

    trai

    n[-

    ]

    Evolution of the total strain in the xdirection with time for the case of proportional and

    nonproportional loading cases

    Oksana Ozhoga-Maslovskaja (OvGU) 14

  • Model Application

    Y

    XZ

    a) b)

    damaged stateundamaged state

    Distribution of damage in the crosssection of the unit cell after 9 hours of creep

    testing under a) nonproportional loading and b) proportional loading

    500 m

    Copper microstructure after creep testing at 25 MPaOksana Ozhoga-Maslovskaja (OvGU) 15

  • Summary

    The copper microstructure is simulated by means of the unit cell.

    The material model parameters are determined from the elastic and creeptensile tests on the single crystal copper.

    The grain boundary sliding is validated by means of the experimental data.

    The creep cavitation and stiffness reduction models are implemented tointroduce the tertiary creep stage.

    The developed model is able to reflect the following phenomena observed on theaveraged creep curve of the unit cell, tested under nonproportional loading test:

    On the averaged strain diagram the strain rate decrease is detected afterthe principal axes rotation;

    On the crosssectional diagram of the unit cell the cavitation of the grainboundaries orthogonal to the maximum principal stress is noticed;

    The prolongation of the time to rupture for the non-proportional loadingcase is observed. This can be explained by the fact, that after the principalaxes rotation another grain boundaries are involved in the cavitationprocess.

    Oksana Ozhoga-Maslovskaja (OvGU) 16

  • Thank You for attention!

    Oksana Ozhoga-Maslovskaja (OvGU) 17

    Experimental ObservationConstitutive ModelingResultsSummary

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