What is Mechanical Metallurgy all about?
Let’s start by talking about what all is included in the study of mechanical metallurgy.
The mechanical engineer will deal with the loads that the structure faces. The mechanical metallurgist will focus on the materials used. The idea is to look at the materials under a microscope and find out why and how they behave under loading. Then use this information to design better. This is where a mechanical metallurgy is required.
You are to design a new material for some sensitive application like space exploration equipment or nuclear equipment. You need to know the exact behaviour of materials on varying loads and temperatures to design it well.
So you understand how the material responds to high temperatures or extreme loads and find out how it behaves and what causes this behaviour. Then you use these findings to improve your design.
Origin of Stresses
In equilibrium condition, if there are the external forces acting on the member, there will be some internal forces resisting the action of the external loads.
When you blow up a balloon, after you have tied the end, the air inside exerts a pressure on the surface of the balloon. Imagine the air pushing the surface of the balloon from inside. When you untie the knot and release the air, the balloon deflates and the force on the inner walls is reduced.
What pressure does to the balloon, the stress does to the metal. In that way, pressure and stress are analogous. But the difference is pressure comes into action because you apply force externally, whereas stress is the internal resisting opposing deformation. This also means stresses can be used to quantify the internal resistance.
You apply loads to get stresses. You don’t apply a stress!
Since pressure and stress are analogous, let us define stress the same way we define pressure i.e. load per unit area. This also implies that the internal force is stress times the area over which it acts. 1
Important Assumptions
It is very difficult to understand the behaviour of materials if you go about analysing the change at atomic levels. Let me give you an example.
Imagine a glass of hot water kept in front of you. At high temperature the molecules are very active and are vigorously vibrating because of the high energy. Now as you leave the glass to cool in air, the water cools down due to energy loss to surroundings.
You can use a thermometer and get a good estimate of how much the energy decreased (given by the temperature difference). However if you go about trying to measure the change in energy for each molecule, good luck to you!
What we did here is to approximate the change in energy with a change in temperature. Thus, the change is easy to measure and also good enough for most practical purposes. Similarly, for materials we make some assumptions to understand their behaviour.
We assume that the material is continuous, that is, it does not have and small voids or empty spaces. We also assume it is homogeneous and isotropic.
When we assume a material is homogeneous, what we mean is if we choose any random section of the material and compare it with its vicinity, the properties are identical.
Also, as metals solidify, groups of atoms may be oriented randomly or in one direction. This affects their variation in properties along a said direction. This is known as anisotropy. Again for simplicity, we neglect this and assume the material is isotropic.
So with these basic assumptions discussed, let’s see what is actually analysed.
Origin of Strains
In a typical experiment in which we wish to study the deformation behaviour, we wish to measure the stresses developed in the material as we keep “pulling” it in a given direction.
Let’s say you take a metal bar and clamp it at one end. Then you pull the free end by 1mm. Attached to the end is a meter which will give you the force required to pull by 1mm. Then you pull again by 1mm. So now, the displacement is 2mm total.
The force reading goes up, because as you pulled to 1mm stresses developed in the sample making it even more difficult to pull further. So you can imagine what will happen here.
For every additional pull of 1mm, the force required will keep on increasing because of the development of stress in the material. Also, if you keep pulling the sample, it will fracture and break off.
One way to figure out the what happens on loading the sample is to simply plot the force required vs the displacement. But this plot is not a very useful one. Recall that the internal resistance will be a function of area. This means if I have two different samples, one of area A and other of area 2A, I cannot directly compare their force-displacement curves because their areas are not the same.
If you remember from out earlier discussion, stress is calculated as load per area. This means stress is normalised with respect to area. 2 But our original plot was force vs displacement . If we normalise the force, we also need to normalise the displacement. This is where the idea of strains come into the picture.
Strain is defined as the ratio of change in length to the original length. Let’s denote strain by $e$. Therefore,
$\begin{equation}
\begin{split}
e & = \frac{\Delta L}{L}
& = \frac{L_{final} - L_{initial}}{L_{initial}}
\end{split}
\end{equation}$
So, now we have normalised both the force and the displacement from the original experimental setup.
If we have to two different samples, which vary in size and shape and we want to compare these two materials, we will first measure the load-displacement curve. Then we will normalise the force by dividing by the area of the sample and normalise the displacements by converting them to strains. This will result in two normalised plots of stress vs. strain for both the samples - and voila! we now have a way to compare the two samples.
Looking at the stress-strain curves, we can now start asking questions like, which of these two will fail easily or can this material be used to build a bridge? But for that we will have to get better at reading and interpreting the stress-strain curve.