Advance (also called Constantan) has a strain sensitivity SA=2.1 for strain as large as 8%. Determine the amount of contribution due to the change in specific resistance to SA in the elastic region (Poisson's ratio v=0.30) and plastic region (Poisson's ratio v=0.30).

Respuesta :

Answer:

[tex]\frac{dP}{P} = 6.25[/tex]

Explanation:

Given data:

Sa = 2.1

[tex]R = \frac{pl}{A}[/tex]

[tex]\frac{dR}{R} =\frac{dP}{P} +\frac{dL}{L} (1_2V)[/tex]

[tex]\frac{dR}{R} =\frac{dP}{P} +\epsilon (1_2V)[/tex]

[tex]Sa = \frac{\frac{dR}{R}}{\epsilon} =\frac{\frac{dP}{P}}{\epsilon} +\frac{\epsilon (1_2V)}{\epsilon}[/tex]

[tex]Sa = (1+2v) + \frac{\frac{dP}{P}}{\epsilon}[/tex]

change in specific resistance is given as [tex]\frac{dP}{P}[/tex]

[tex]\frac{dP}{P} = \frac{Sa -(1-2v)}{\epsilon}[/tex] ........2

where v  is elastic range = 0.30

[tex]\epsilon = 0.08[/tex]

[tex]\frac{dP}{P} = \frac{2.1 -(1-2\times 0.30)}{0.08}[/tex]

[tex]\frac{dP}{P} = 6.25[/tex]