The Effect of Void Size on the Strengthening of NMM
Oscar Nieto, Ioannis N. Mastorakos, Hussein M. Zbib
School of Mechanical and Materials Engineering, Washington State University
Introduction
Method
Computational studies of Nanoscale Multilayer Metallic
Composites(NMMC) were performed to improve the
properties of Copper(Cu) and Niobium(Nb) alloy. The
strength of Cu/Nb is much higher than the strength of
each material individually. Theoretically, by creating a
void in the Cu layer, the material’s strength will
increase.
•Molecular dynamics were used to study the
deformation behavior under uniaxial loading of Cu/Nb
structures with different void sizes varying from 1 to
6nm, while each layer thickness was kept constant.
Two structures were considered, one with a layer
thickness of 5nm and another with 8nm thickness.
Stress-Strain curves were ploted to obtain the strength
of each simulation.
Goal
The study of the effect of voids inside NMMC consisting
of alternating layers of Copper (Cu) and Niobium (Nb).
Key Materials
Dislocation: Imperfection in the crystal structure.
Results
The maximum strength is reached with a void of radius
of 2nm. Structures with voids with radius > or < 2nm
were weaker.
•Snapshots of Cu/Nb without voids during uniaxial deformation
Nb
B.
Dislocations in Cu/Nb alloy without any void
If the material contains dislocations they move inside the
material freely
A.
The three snapshots correspond to three different stresses, A=2GPa,
B=7GPa, and C=10GPa.
•Snapshot of Cu/Nb with a void of 2nm radius embedded in the Cu Layer
Nb
Cu
Cu/Nb with a void embedded in the Cu layer. As the dislocations try
to move across the material, the void acts as an obstacle against the
moving dislocations and makes the Cu/Nb alloy to have a greater
ultimate strength.
Layer thickness 8nm
2
0
0.5
1
1.5
2
2.5
3
Void Size(nm)
As we increase or decrease the void size from 2nm, the ultimate Yield
stress decreases and the material has a premature failure compare
with the case of 2nm. This either occurs because the void is too small
and it doesn’t have an effect against the dislocations or because the
void is too big and ends up covering most of the layer thickness
Increasing the layers’ thickness to 8nm
As the thickness of the layers increases, the distance
between each void increases.
1.00E+01
8.00E+00
6.00E+00
Layer 5nm, Void r=2nm
4.00E+00
Layer 8nm, Void r=1.5
2.00E+00
-2.00E+00 0
0.05
0.1
0.15
0.2
Strain
Cu
A.
C.
B.
The three snapshots correspond to three different stresses,
A=2GPa, B=7GPa, and C=10GPa
Stress-Strain Curve
1.40E+01
1.20E+01
Stress(GPa)
1.00E+01
8.00E+00
Void, Radius=2nm
No voids
6.00E+00
4.00E+00
2.00E+00
As dislocations
move to the right,
they are trapped
by the void.
4
0.00E+00
Cb/Nb with no void. When material is being loaded, dislocations
propagate inside the weaker layer, in this case the Cu layer. The
dislocations move freely, in this example, from left to right and make
the material weaker than if it had a void acting as a barrier against
the dislocations.
Nb
Layer thickness 5nm
0
C.
B.
Black lines are
dislocations
moving to the
right
The void acts as a barrier against existing moving dislocations
6
1.20E+01
Nb
Dislocation in Cu/Nb with a void
8
1.40E+01
Cu
Cu
10
C.
A.)Perfect crystal. B.)A half atomic plane is introduced in the
structure and causes the material to have dislocations. C.)Each circle
represents an atom and it shows the lattice mismatch where the
dislocation takes place.
Optimum
strength results
12
Stress(GPa)
A.
Stress at the maximum yield point(GPa)
Maximum stress resisted-Void size
0.00E+00
-2.00E+00 0
0.05
In a perfect crystal, as in the Cu/Nb
structure, a void makes the crystal
weaker and makes the structure reach
a premature yield point.
0.1
0.15
0.2
0.25
Strain
After the first Yield point many
dislocations are present in the Cu
layer. Now the void acts as an
obstacle to dislocations and increases
the material’s final strength.
Two structure were analyzed, one with a layer thickness
of 5nm and the other 8nm. As the distance between
the voids increases, the material’s ultimate yield point
decreases. This is because there is more space for the
dislocations to move around the void.
Conclusion
The voids increased the strength of the material with
existing dislocations. So the voids made the material
weaker before the first yield point. After that, many
dislocations had propagated and now the void starts to
act as a barrier against dislocations, increasing the
ultimate yield point. The best performance (in terms
of material strengthening) is achieved when a void of 2
nm of radius is introduced inside the Cu layer, while
each layer of Cu/Nb have a thickness of 5nm. Voids
with a radius greater than or less than 2nm decrease
the strength of the material, concluding that a void of
radius of 2 nm provides the optimum performance.
The voids show to improve the ultimate strength
results when the layer thickness is kept small around
5nm.
This work was supported by the National Science
Foundation’s REU program