The strength coefficient $=(80,000lb\frac{.}{i}{n}^2)$ and strain$-$hardening exponent $=(0\mathrm{.}30)$ for low$-$carbon steel used in a forming operation in which the work part is reduced in cross$-$sectional area by stretching. If the average flow stress on the part $=(40,000lb\frac{.}{i}{n}^2),$ determine the amount of reduction in cross$-$sectional area experienced by the part. You may take the value of the mathematical quantity, $e=2\mathrm{.}7183.$

Answer the following Questions:

$(1).$ The value of true strain $$ calculated to be $=0\mathrm{.}238$

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F

$(2).$ The value of true strain $$ calculated to be $=0\mathrm{.}448$

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F

$(3).$ The ratio of $(\frac{A_0}{A_t})=1\mathrm{.}579,$ where $A_0=$ Initial area of the Cross section and $A_f=$ Final area of cross section

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F

$(4).$ The ratio of $(\frac{A_0}{A_f})=1\mathrm{.}269,$ where $A_0=$ Initial area

of the Cross section and $A_f=$ Final area of cross section.

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F

$(5).$ The cross$-$sectional area reduction

experienced by the part $=21\mathrm{.}2\%$

$(6).$ The cross$-$sectional area reduction

experienced by the part $=6\mathrm{.}06\%$

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F

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F