If it does not return to its original shape, we say that it has been plastically deformed. The critera for this, is that it exceeds the yield stress.
Your second question, whether it would snap depends on many things, like the speed of loading, but the simplest measure is ultimate tensile stress. There's typically one more stress you should worry about, fracture stress.
The ultimate tensile stress describes the most force a material will take. At that point it will start necking (reducing in area), until it snaps at the fracture stress.
Mild steel = Low carbon steel.
I like AISI's standards. So I'm going to use 1018 steel.
The way the metal is formed is also important, whether it has been cold rolled versus hot rolled, quenching, tempering, etc.
I'm going to use the numbers from here:
http://www.matweb.com/search/DataSheet.aspx?MatGUID=3a9cc570fbb24d119f08db22a53e2421for Cold rolled 1018
The yield stress is 370 MPa and the ultimate tensile stress is 440 MPa.
Know that there are variation in these numbers, and that they are tested in tension, not bending.
This is your case: cantilever bending.
The important part is the maximum bending moment
M=PL
The stress for bending is then
=IMz
z is the distance from the neutral axis... I'm just going to take it as half the thickness because I'm lazy...
and I is the second moment of area, which you can find here:
http://en.wikipedia.org/wiki/List_of_area_moments_of_inertiaI=12bh3
h = 1 mm
b = 10 cm
L = 1 m
P = (200 kg)*(10 m/s^2)= 2000 N
z = .5 mm
M = 2000 N * 1 m = 2000 m N
I = 8.33 mm^4
sig = 120 GPa
This is pretty huge stress and would mean it would just snap.
