Stress vs strain is graph used to derive different engineering properties of materials like yield strengh
Basically there are two kinds of materials which are mainly used in engineering apllications namely ductile and brittle.
Ductile materials are those which can withstand load even after the elastic limit is reached. So the diagrams extends till breaking point after which the material fails.Mild steel is the best example for such behaviour and this accounts to its popularity in engineering.
Brittle materials fail as soon as the load reaches the ultimate strength capacity of the material.This is due to small grain size of the material, thereby increasing the hardness of the material.These materials are used were very tight dimensions are required to undergo smooth functioning.Eg:Glass
For further understanding the reasons, I suggest the following books
- Mechanics of solids by Beer and Jhontson
- Strength of materials by popov
- Engineering design by VK bhandari.
Engineering Magazine 
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