micro scale modeling of grain boundary damage under …ozhoga... · micro scale modeling of grain...

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


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)


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


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.


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.


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.


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


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

]


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


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


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


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


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


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.


Thank You for attention!


Experimental ObservationConstitutive ModelingResultsSummary

micro scale modeling of grain boundary damage under …ozhoga... · micro scale modeling of grain...

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