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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