Bodies in Equilibrium, elasticity and fracture

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To compress the volume of a steel block by 0.14 percent, a pressure of approximately 224 MPa is required, calculated using the bulk modulus of steel, which is around 160 GPa. This pressure induces a temporary volume change, as steel will return to its original shape once the pressure is released. However, if the pressure exceeds the yield stress of about 220 MPa in some low carbon steels, permanent plastic deformation occurs, resulting in a lasting volume change.
pupatel
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can anyone help me with this please...? :eek:

How much pressure is needed to compress the volume of a steel block by 0.14 percent?
 
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I'm not sure what units you are used to but I'll use SI here :

The bulk modulus of steel is about
G=160 * 10^9 N/m^2 = dP/(dV/V)
=>dP = G(dV/V)
=160*10^9*0.0014
=224 * 10^6 N/m^2
= 224 MPa

Of course, this change in volume exists only so long as the pressure is applied, and the steel springs back once the pressure is removed. However, in a very small number of low carbon steels, at about 220 MPa, you reach the yield stress and the steel will begin to plastically deform. Once this starts, the volume change becomes permanent.
 
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