1. SOLID SOLUTION STRENGTHENING
Strengthening due to addition of solute atoms as a result of their interaction with moving dislocations during dislocation glide is SSS.
Course Name: Mechanical Behaviour of Materials
Level(UG)
LO’s for prior viewing : NONE
Authors: R. Mridhula/A. Subhedar
Guide: Prof. P. Pant

2. Learning Objectives
After interacting with this Learning Object, the learner will be able to:
Visualise how addition of solute atoms to a metal or alloy enhances strength.
Explain how size of the solute atom in comparison to the solvent atom affects strengthening

3. 1 2 3 4 5 Definitions of the components/Keywords:
Solid solution: is a solid-state solution of one or more solutes in a solvent
Interstitial Solution: Solute atoms are appreciably smaller than the matrix atoms and occupy places between regular sites
Substitutional solid solution : Solute atoms are of nearly same size of the matrix atoms and substitute parent atoms in regular sites. 2 3 4 5 3

4. 1 2 3 4 5 Master Layout 1 : Stress field near substitutional site
Step 1: Size of substitutional atom is similar to that of matrix atom 2 3 4 5
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5. Step 1 Description of the activity Audio narration
Text to be displayed
Draw array of 7x5 circles as shown. Mark circle at center in red colour and all other in black colour. Join centers of circles by smooth curved line nearby red circle and by straight line on all other places.
Animation time : 2 seconds
Consider a lattice of black atoms. Assume that red atom is substituted in place of a black atom. If red atom is of nearly same size of black atom no stress is developed near the red atom.

6. 1 2 3 4 5 Master Layout 1 : Stress field near substitutional site
Step 2: Size of substitutional atom is smaller than matrix atom 2
v: Velocity of interface
∆T : undercooling 3 4 5
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7. Step 2 Description of the activity Audio narration
Text to be displayed
Draw array of 7x5 circles as shown. Mark circle at centre in red colour and all other in black colour. Ensure that size of red circle is 1/3 that of black circle. Join centres of circles by smooth curved line nearby red circle and by straight line on all other places.
Animation time : 2 seconds
Schematic represents
tensile strains imposed on parent matrix atoms by a smaller
substitutional atom. This happens because now bonds are stretched to connect bigger black atoms to smaller red atom.

8. 1 2 3 4 5 Master Layout 1 : Stress field near substitutional site
Step 3: Size of substitutional atom is larger than matrix atom 2
v: Velocity of interface
∆T : undercooling 3 4
Copyrighted image, should be redrawn 5

9. Step 3 Description of the activity Audio narration
Text to be displayed
Draw array of 7x5 circles as shown. Mark circle at centre in red colour and all other in black colour. Ensure that size of red circle is 2 that of black circle. Join centres of circles by smooth curved line nearby red circle and by straight line on all other places.
Animation time : 2 seconds
Schematic represents
compressive strains imposed on parent matrix atoms by a larger
substitutional atom. This happens because bonds connecting the bigger red atom to smaller black atoms are compressed.

10. 1 2 3 4 5 Master Layout 2 : Repositioning of solute atoms
Step 1: Stress field around edge dislocation 2 3 4 5

11. Step 1 Description of the activity Audio narration
Text to be displayed
Draw a inverted T shape inside a rectangle.
Animation time : 2 seconds
Edge dislocation is shown in the schematic as inverted T. Rectangle shows area near dislocation. Arrows show direction and magnitude of stresses qualitatively.
Note how matrix is subjected to compressive and tensile stresses, above and below the slip plane respectively.

12. Master Layout 2 : Repositioning of substitutional solute atoms1
Step 2: Substitutional atoms in random motion 2 3 4 5

13. Step 2 Description of the activity Audio narration
Text to be displayed
Draw 3 circles far from inverted T shape on top of previous figure
Animation time : 2 seconds
Consider solute atoms that are smaller in size than matrix atoms. These atoms under influence of stress field of matrix will continue to diffuse to reduce stress on them

14. 1 2 3 4 5 Master Layout 2 : Repositioning of solute atoms
Step 3: Stress field around edge dislocation 2 3 4 5

15. Step 3 Description of the activity Audio narration
Text to be displayed
Move the circles in the path shown(animator can choose any arbitrary path) and put them in position near to inverted T shape.
Animation time : 2 seconds
Substitutional atoms tend
to diffuse and relocate themselves around dislocations to reduce the overall strain energy.

16. 1 2 3 4 5 Master Layout 2 : Repositioning of solute atoms
Step 4: Stress field around edge dislocation 2 3 4 5

17. Step 4 Description of the activity Audio narration
Text to be displayed
Put a circle on center vertical line of inverted T shape and put other circles on either side of it in the path that shown (Note that this path should not be random but in parabolic shape).
Also take care to draw circles above horizontal line of inverted T shape
Animation time : 2 seconds
Once Substitutional atoms reach the vicinity of dislocations, stress field readily directs them to a place where they will have compressive stresses acting on them.
In the case of edge dislocation smaller Substitutional atoms can be found adjacent to the extra half plane and above the slip
Plane. Note also that this reduces the overall stresses.

18. 1 2 3 4 5 Master Layout 2 : Repositioning of solute atoms
Step 5: Repositioning of larger atoms 2 3 4 5

19. Step 5 Description of the activity Audio narration
Text to be displayed
Again draw inverted T shape inside a rectangle. Draw two cirlces (with radius 2 times of the circles drawn in the previous steps) below horizontal line of inverted T shape
Animation time : 2 seconds
Similarly when substitutional atoms have size larger than matrix atoms they will relocate themselves below slip plane to reduce overall strain energy.

20. 1 2 3 4 5 Master Layout 3 : Strengthening of material
Step 1: Distribution of Substitutional atoms 2 3 4 5

21. Step 2 Description of the activity Audio narration
Text to be displayed
Inside a rectangle draw 4-5 “T” shapes at random positions. Draw circles of two sizes(one twice as large as other)
and put them around T shapes. Also draw these circles at few other random postions.
Animation time : 2 seconds
Distribution of Substitutional atoms is shown in the schematic. Note that most dislocations are surrounded by them. During plastic deformation when dislocations are in motion, their strain interactions with Substitutional atoms will occur so as to lower the total strain energy. Hence more stress is required to cause the plastic deformation. This process is known as solid solution strengthening.

22. Master Layout 4 : Quantification of Solid Solution Strengthening
Step 1: strength dependence on solute atom concentration
= Increase in yield strength
= concentration of the solute atoms
= Burgers vector magnitude
= Lattice strain due to solute atom
= Shear Modulus 22

23. Step 2 Description of the activity Audio narration
Text to be displayed
Write the equation as shown. Below the equation display symbols used in the equation with their definition.
Animation time : 2 seconds
It is clear from the equation that solid solution strengthening varies as square root of solute concentration. Here c is the concentration of the solute atoms, G is the shear modulus, b is the magnitude of the Burger's vector, and is the lattice strain due to the solute.

24. Questions
a. Parent matrix atom experience compressive stresses by subtitutional atom when size of subtitutional atom is
Same as parent matrix atom
Larger than parent matrix atom
Smaller than parent matrix atom
b. Solid solution strengthening does not depend upon
1. Shear modulus of solute atom
2. Shear modulus of parent matrix atom
3. Concentration of solute atoms
c. As the solid solution strengthening formula suggests material can
be strengthened to arbitrary high value by increasing concentration of solute atoms. True or False?
d. Smaller substitutional atoms tend to occupy a position that is above
dislocation slip plane. True or False?

25. Answers Larger than parent matrix atom
2. Shear modulus of parent matrix atom
3. If the concentration of the solute exceeds a critical point then new phase might get precipitated.
4. True, this way total strain energy of system can be reduced.

26. Links for further reading
Reference websites: 1.
Books:
1.G. Dieter, Mechanical Metallurgy, Third Edition(1986), McGraw Hill Book Company.
2. W. Callister, Materials Science and Engineering - An Introduction, Seventh Edition(2007), John Wiley & Sons, Inc.
Research papers:

27. Summary
Relative size of the Substitutional atom determine kind of stresses generated at the substitutional site.
Substitutional atom tend to occupy sites that are close to dislocations.
Strengthening occurs because dislocations need to overcome stress fields in order to move