Question

For a bronze alloy, the stress at which plastic deformation begins is 267 MPa and the modulus of elasticity is 115 GPa. (a) What is the maximum load (in N) that may be applied to a specimen having a cross-sectional area of 377 mm2 without plastic deformation? N (b) If the original specimen length is 127 mm, what is the maximum length (in mm) to which it may be stretched without causing plastic deformation?

Answer 1

Answer

given,

Stress for plastic deformation =  267 MPa

modulus of elasticity = 115 GPa

cross sectional area = 377 mm²

a)    maximum load (in N) that may be applied to a specimen

= σ x A

= 267 x  10⁶ x  377 x 10⁻⁶

= 100659 N

b)   modulus of elasticity = stress/strain

     115 x 10⁹  =$\dfrac{267 \times 10^6}{\dfrac{\Delta l}{L}}$

        L = 127 mm

      115 x 10⁹  =$\dfrac{267 \times 10^6}{\dfrac{\Delta l}{127}}$

      $\dfrac{\Delta l}{127}=\dfrac{267 \times 10^6}{115\times 10^9}$

    Δ l =   0.295 mm

maximum length after the stretched = 127 mm + 0.295 mm

                                                            = 127.295 mm