The following are the various mechanisms of strengthening metals and alloys: 1. Strengthening by Grain Refinement 2. Strain Hardening 3. Solid Solution Strengthening 4. Precipitation (or Age) Hardening 5. Dispersion Hardening 6. Particulate Strengthening 7. Phase Transformation Hardening.
1. Strengthening Grain Refinement:
Strength of a material is its resistance against deformation, especially, against plastic deformation or yielding. Yielding occurs due to movement of dislocations in metallic crystals. Movement of dislocation is stopped if some barrier or discontinuity comes in the path of dislocations.
To make dislocations move and thereby cause plastic deformation much more stress has to be applied over the material. This means the resistance of material against deformation or in other words, its strength is increased. Grain boundaries are regions where atoms are at higher energy level and also where atomic orientation changes.
Dislocations cannot glide past the grain boundaries easily. Hence, if there are more grain boundaries, there is more resistance to the movement of dislocations and hence an increase in strength. As indicated in the Fig. 3.38 (a) and (b), if there are more grains in a given amount of material, i.e., if the size of grains or crystals is smaller, there will be more grain boundaries compared to the case when the grains are larger.
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Hence, obviously the material with smaller grains or more grain boundaries will be stronger. Any process which tends to make the grains smaller (i.e., causes grain refinement) will increase the strength of the material. This is the mechanism of strengthening by grain refinement.
Yield strength a of a polycrystalline material is given by the equation-
This equation shows that yield strength increases as the crystal dia. ‘d’ decreases. Fine grains can be obtained by controlling the cooling rate of the solidifying metal or by adding some alloying elements which promote grain refinement. For example – in case of steel, micro alloyed steels have been developed by adding very small quantities of elements like Ti, V and Nb. The resulting grain size of such steels is about 2 to 3 pm. The yield strength is increased by as much as 50%.
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Effect of Cold Work on Ductility:
Fig. 3.39 (a) and (b) shows the relationship between grain size d and yield strength σy. Fig. 3.40 shows the effect of grain size on percent elongation (ductility) of metals. Smaller grains retard the movement of dislocations. This results in higher strength of materials. Deformation becomes easier in case of larger crystals and ductility, as measured in terms of percent elongation or percent reduction in area, increases. This effect is shown in Fig. 3.40.
Cold work increases hardness and strength due to the effect of strain hardening. As the degree of cold work increases (as expressed by percent reduction in thickness) ductility goes on decreasing. This is illustrated in Fig. 3.41.
Example:
Calculate the yield strength of poly crystalline iron with an average grain diameter of 0.1 mm. The constants in the Hall-Fetch equation are σi = 50 MN/m2 and k = 0.7 MN/m2.
(GATE)
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Solution:
Given: d =.0.1 mm, σi = 50 MN/m2, k = 0.7 MN/m2
Using Hall-Petch equation and substituting the values, we have
2. Strain Hardening:
We know that due to cold working of metals their yield strength, ultimate tensile strength and hardness increases; but the ductility decreases. The above changes during cold working are the result of strain hardening which occurs due to multiplication of dislocations according to Frank-Reed source. During plastic deformation there is a continuous increase in dislocation density and the stress necessary to move the dislocations continuously increases.
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This is described by the following equation:
i. This method is applicable only for ductile metals.
ii. The main disadvantage of cold working/strain hardening is the accompanying decrease in ductility. Cold working is also detrimental as it raises the ductile-brittle transition temperature of steels.
3. Solid Solution Strengthening:
Another technique to strengthen and harden metals is alloying with impurity atoms that go into either substitutional or interstitial solid solution. Accordingly, it is called solid solution strengthening.
Solid solution strengthening distorts the lattice, offers resistance to dislocation movement which is greater with interstitial elements which cause asymmetric lattice distortion, e.g., carbon in steel.
Mechanism:
Since no two elements have the same atomic diameter, solute atoms will be either smaller or longer in size than the solven atoms. Due to the difference in atomic size, lattice distortion is produced when one element is added to the other.
Smaller atoms will produce a local tensile stress field and larger solute atoms will produce a local compressive field in the crystal. In both the cases, the stress field of a moving dislocation interacts with the stress field of the solute atom. This increases the stress required to move the dislocation through the crystal.
The following factors affect solid solution strengthening:
(i) Atomic Size Difference:
With the increase in the atomic size difference between the solute and solvent the intensity of stress field around solute atoms increases. This increases the resistance to the motion of dislocations thereby increasing hardness and tensile strength. Therefore, more the atomic size difference, higher is the hardness and tensile strength.
(ii) Amount of Solute:
When the amount of solute or the number of solute atoms is more, greater will be the local distortion in the lattice and hence more will be the resistance to the moving dislocations. This will increase the hardness and strength of the material.
The increase in strength is proportional to C1/2 where C is the solute concentration. For dilute solutions, increase in strength with concentration is approximately linear.
(iii) Nature of Distortion:
Hardness and tensile strength are also affected by the nature of distortion produced by solute atoms. Spherical distortion produced by substitutional solute atoms is much less effective than non-spherical distortion produced by interstitial solute atoms, this is shown in Fig. 3.42.
The figure shows that the element Cr, Ni, Mo, Mn and Si are less effective in increasing the yield strength (YS) of iron than the elements like C and N. This is owing to the fact that C and N form interstitial solid solutions and produce tetragonal distortion in the lattice whereas the other elements form substitutional solid solutions and produce spherical distortion.
Disordered solutions are less harder and stronger than ordered solid solutions.
4. Precipitation or Age Hardening:
In case of some alloys there is increase in hardness with time at room temperature or after heating to slightly higher temperatures. This type of hardening is called precipitation or age hardening.
It is observed in alloys such as Al = 4.5%, Cu, Al = 6%, Zn = 2.5% Mg, Cu = 2% Be, Ni = 17%, Cu = 8% Sn, Ti = 6%, A1 = 4%, etc.
The conditions for precipitation or age hardening to occur in any alloy system are:
(i) The solubility of solute in the solvent must decrease with decrease in temperature.
(ii) The precipitate that separates out from the matrix should be coherent otherwise the material will not be hardened. There is no true interface between the precipitate particle and the surrounding matrix. Since the solute atoms are of different sizes from the solvent atoms, large amount of elastic distortion is observed around the precipitate particle.
These coherent precipitate particles are powerful obstacles to the motion of dislocations. This is because the large elastic distortion of the matrix around the particles interacts strongly with the stress field of dislocations. In some systems like Mg-Pb, Al-Mn and Al- Mg decrease in solubility is observed with decrease in temperature, but the precipitate is not coherent and hence the alloys from these systems cannot be hardened by the above process.
The general steps involved in age/precipitation hardening are:
(i) Heating (solutionizing),
(ii) Quenching, and
(iii) Ageing.
5. Dispersion Hardening:
The resistance to motion of dislocations, in this strengthening mechanism, is increased by introducing finely divided hard particles of second phase in the soft matrix. The increase in hardness and tensile strength is due to the interaction of the stress field around the particles with the stress field of a moving distortion and also due to physical obstruction by the hard particles to the moving dislocation.
The extent to which strengthening/hardening is produced depends upon the following factors:
i. The amount of second phase particles;
ii. The characteristics and properties of second phase;
iii. The particle size, shape and distribution.
The maximum strengthening, hardening is observed at some intermediate spacing of particles, not too less and not too more. The optimum properties are usually observed at a concentration of particles from 2 to 15 percent (by volume), their size between 0.01 and 0.1 μm, and a spacing of 0.1 to 1.0 μm between particles.
The increase in yield strength due to very hard and inert particles is given by the relation:
The above equation, truly speaking, gives the stress necessary to move a dislocation line of length I pinned at both ends with Burger’s vector of b, i.e., to operate a Frank- Reed source of length I through a matrix of shear modules C.
The dispersed particles are normally oxides, carbides, borides etc. The main advantage of dispersion hardened materials is their ability to maintain high strength and creep resistance at elevated temperatures of the order of 80 percent of the melting point of the matrix.
Common examples of this type are:
i. Sintered aluminium powder,
ii. Thoriated polycrystalline tungsten.
The common method of manufacturing dispersion hardened material is powder metallurgy.
6. Particulate Strengthening:
The particulate strengthened systems differ from dispersion strengthened ones in the size of the dispersed particles and their volumetric concentration. In the former systems the particles are 1 μm or more and of concentration of 20 to 40 volume % whereas in the latter systems the particle size is usually less than 0.1 μm. It is very important that the particles should be small, properly distributed and of uniform size.
Particulate composites are made mainly by powder metallurgy techniques that may involve solid or liquid state sintering or even impregnation by molten metal.
Examples:
Tungsten-nickel-iron system obtained as a liquid-sintered composite and the tungsten-nickel copper system.
7. Phase Transformation Hardening:
Phase transformation is a change in the number and/or character of the phases that constitute the microstructure of an alloy, e.g., in steel conversion of austenite into martensite.
Martensitic transformation occurs in steels when austenite phase is cooled rapidly (i.e., cooled exceeding the critical cooling rate) to room temperature or below room temperature. Due to rapid cooling, austenite (FCC) gets transformed to a Body Centered Tetragonal (BCT) martensite by a diffusionless process.
Martensite is a supersaturated solid solution of carbon in BCC iron with BCT structure and is formed from austenite by shear mechanism. Martensite is a hard phase and its hardness depends on the carbon in the austenite or steel.
Because of the formation of BCT structure from FCC structure, the lattice gets distorted and the intense stress field around the carbon atoms in martensite effectively hinders the motion of dislocations. Martensite transformation is very important for controlling the properties of steels.