I understand that the engineering stress-strain curve of different material under tension test is different, but for the sake of simplicity the scope of this discussion will be for a general ductile material. If you have to pick a specify example, I think perhaps you can use steel or iron. There are various reference book out there that explains the stress-strain curve, but all of them vary from each other slightly. So I am a bit confuse and I would like to get some insight from here. There are many different points in a stress-strain curve, so I will list down in order base on my understanding: 1) Proportional Limit 2) Elastic Limit 3) Yield Point 4) Ultimate strength point 5) Fracture Questions: (i) Is the point of proportional limit same as the point of linearity limit? (ii) If my understanding is correct, elastic limit is the greatest stress the material can take without permanent deformation. Yield point is the point where the material starts to experience plastic deformation. So, is plastic deformation not exactly the same as permanent deformation? Is that means there are many kinds of permanent deformation and plastic deformation just one kind of permanent deformation? (iii) Does the nonlinearity starts at the elastic limit, yield point or the proportional limit? I have more questions actually, but it is more suitable to be asked after the above three have been answered. So I looking forward to your opinion. Any help is greatly appreciated.