A piece of wire is stretched from length l1 to length l2 (step A), and then from

Question

A piece of wire is stretched from length l1 to length l2 (step A), and then from length l2 to length l3 (step B). (i) Write down an expression for the engineering strain associated with step A. (ii) Write down an expression for the engineering strain associated with step B. (iii) Write down an expression for the true strain associated with step A. (iv) Write down an expression for the true strain associated with step B. (v) Use the definition of engineering strain to write down an expression for the engineering strain associated with stretching the wire from length l1 to length l3 , and compare this with the result of adding your answers to (i) and (ii).

Explanation / Answer

i)

engineering strain step A =L2-L1/L1 =DELTA L /INTIAL LENGTH =e1

ii)

engineering strain step B =L3-L2/L2 =e2

iii)

Integrating from the initial length, Lo , to the current length, L, FOR STEP A

? = ?dL/L = ln(L2/L1 ).

This ?nite form is called true strain (or natural strain, or logarithmic strain).

iv)

Integrating from the initial length, Lo , to the current length, L, FOR STEP b

? = ?dL/L = ln(L3/L2 ).

This ?nite form is called true strain (or natural strain, or logarithmic strain).

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