1. High temperature deformation of polycrystalline MgO
- Lower mantle rheology
Flow Law of Polycrystal
Flow law of polycrystal
𝜀 = 𝛢
𝜎 𝑛
𝑑 𝑝 𝑒
−
𝑄
𝑅𝑇
𝜀 : strain rate A : proportional constant 𝜎 : differential stress
n : the stress exponent p : the grain size exponent d : grain size
Q : activation energy R : the ideal gas constant T : absolute temperature
Viscosity
𝜼 =
𝝈
𝜺
Abhijeet SONI
Earthquake Research Institute, University of Tokyo
Indian Institute of Technology Kharagpur, INDIA
Introduction
Experimental details
Fixed
Cylinder
SiC Road
SiC
SiC
Alumina
Alumina
Deformed
sample
Composition of Earth's mantle
in weight percent of MgO is
37.8
Lower Mantle
mantle
(polycrystal)
Earth’s interior
Reference
sample
Reference
KG258
Vertical
Deformed
KG258
Reference
KG259
Vertical
Deformed
KG259
Reference
KH96
Vertical
Deformed
KH96
Results and Discussion
10 μm
9.7 mm
• Stress exponent is similar between polycrystal at lower
stress level.
• Grain size is sensitive to dislocation creep.
• Dislocation creep leads to reduction in grain size
Summary
From our experiments,
We obtained a relationship
of
𝜀 𝛼
1
𝑑 𝑝
where p = 1.4
Which shows Grain size is sensitive to
dislocation creep
Shear Modulus of MgO is 10
GPa.
By Graph, Strain should be
10E-7.
And from the result i.e. 10E-4.
Hence in this experiment
grain size is sensitive to
dislocation creep.
Original and SEM image of the sample
before deformation
Experimental Setting
Thermocouple
furnace
Microstructures
Creep Experiments
Temperatur
e
Grain size Differential
Stress
(Mpa)
Strain
Sample No. D
Referenc
e
D
Horizontal
D
vertical
KG258 7.88 8.69 6.23
*30-100
0.059
KG259 NA NA NA
*30-100
0.202
KH96 15.35 NA 12.48
*50-80
0.415
20
30
40
50
60
70
80
90
100
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
-200 0 200 400 600 800 1000 1200 1400
KG258 Stress and Strain vs Time
Stress (N/mm2) Strain
0
20
40
60
80
100
-0.02
0
0.02
0.04
0.06
0.08
0.1
-5000 0 5000 1 10
4
1.5 10
4
2 10
4
KG259 Stress and Strain vs Time
Stress(N/mm2) Strain
0
20
40
60
80
100
120
140
160
-0.05
0
0.05
0.1
0.15
0.2
-1000 0 1000 2000 3000 4000 5000
KH96 Stress and Strain vs Time
Stress (N/mm2) Strain
10
-8
10
-7
10
-6
10
-5
0.0001
0.001
10 100
Log (stress) VS Log (Strain rate)
KG 258, T 1400
KG 259, T = 1350
W & KT T = 1500
W & KT, T = 1300
Mariani et al, T = 1400
10-6
10
-5
0.0001
6 8 10 12 14 16
Grain size vs strain rate
At constant stress of 50 MPa
10-7
10
-6
10
-5
0.0001
0.001
0.00056 0.00058 0.0006 0.00062 0.00064
1/ T vs Strain rate
100 MPa
30 MPa
50 MPa
y = 0.0004x-1.356
y = 3E+13e-65706x
y = 3E+07e-48100x
y = 6E+09e-59139x
ൗ𝑄
𝑅 = 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓
1
𝑇
𝑣𝑠 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 𝑐𝑢𝑟𝑣𝑒
Where, Q – Activation energy and R is
universal gas constant.
KH96, T=1450
W & KT, T = 1400
Mariani et al.,2009
Microstructure evolution and
recrystallization during creep of
MgO
Wolfenstine et al., 1988
Creep of MgO single crystals
(W & KT)
Grain size
Strainrate
1/Temperature
StrainRate
Log (Stress)
Log(StrainRate)