(a) Limit of Proportionality:
Imagine pulling a rubber band gently. Initially, it stretches proportionally to the pulling force. This linear relationship between stress and strain defines the elastic region. The limit of proportionality, represented by a point on the graph, marks the transition from this linear region to a slightly curved region. Beyond this point, the material starts to deform slightly more than expected for the applied stress.
(b) Yield Point:
Continue pulling the rubber band harder. At some point, it suddenly stretches significantly even with a small increase in force. This abrupt jump on the graph is the yield point. It signifies the onset of plastic deformation, where the material begins to deform permanently even after the stress is removed.
(c) Ultimate Tensile Strength (UTS):
Keep pulling the rubber band relentlessly. It continues to stretch, but at a slower rate as its internal resistance builds up. Eventually, it reaches a peak point on the graph, the ultimate tensile strength (UTS). This represents the maximum stress the material can withstand before finally breaking.
(d) 0.1% Proof Stress:
Not all materials have a distinct yield point. In such cases, we use the 0.1% proof stress. Imagine pulling the rubber band slightly again and measuring its length after releasing the force. If the permanent elongation reaches 0.1% of its original length, the stress at that point is called the 0.1% proof stress. It serves as a practical measure of the material’s yield strength in the absence of a clear yield point.
Visualising the Graph:
Think of the graph as a mountain trail. We start walking on a flat (elastic) path, then encounter a slight incline (limit of proportionality), followed by a steeper climb (yield point), reaching the peak (UTS), and finally, the trail drops off before we fall (fracture). The 0.1% proof stress would be like stopping at a certain point on the slope and checking how far down the path we’ve permanently slid.
Understanding these terms and their visual representations is crucial for selecting materials appropriate for different engineering applications. Knowing their limits helps us design components that can safely handle expected loads and deformations without compromising their integrity or performance.