Problem $2$

Consider the raw tensile test data contained in the Excel file posted on the Moodle page called $"$HW$1$ Data". This

is raw force vs$.$ elongation data from a tensile test that was conducted on a specimen with a referential cross$-$

sectional area of ${0\mathrm{.}37500}^{\text{'}\text{'}}{0\mathrm{.}12500}^{\text{'}\text{'}}$ and a gauge length of $1\mathrm{.}25000".$ This data has had the toe$-$region corrected

for grip slippage.

At the first data point, when the load is $193\mathrm{.}09$ lbf and the elongation is measured as $0\mathrm{.}0184",$ the instantaneous

thickness of the specimen is measured as $0\mathrm{.}12454".$

Given this data, determine the following properties of the specimen providing documentation of your approach

and results. In order to receive credit for your answers you need to offer a proper justification $/$ explanation of

how you obtained them.

a$)$ Poisson's Ratio

b$)$ Yield Strength

c$)$ Ultimate Tensile Strength

d$)$ Ductility as measured via $\%$EL

e$)$ Modulus of Resilience

f$)$ Modulus of Toughness

g$)$ Strain$-$Hardening Exponent

Here is the supporting data:

Elongation $($in$)$ Load $($lbf$)$ Strain Stress

$1\mathrm{.}84$E$-02193\mathrm{.}091\mathrm{.}47$E$-024119\mathrm{.}253333$

$1\mathrm{.}84$E$-02200\mathrm{.}091\mathrm{.}47$E$-024268\mathrm{.}586667$

$2\mathrm{.}03$E$-02207\mathrm{.}091\mathrm{.}62$E$-024417\mathrm{.}92$

$2\mathrm{.}03$E$-02215\mathrm{.}091\mathrm{.}62$E$-024588\mathrm{.}586667$

$2\mathrm{.}14$E$-02222\mathrm{.}091\mathrm{.}71$E$-024737\mathrm{.}92$

$2\mathrm{.}14$E$-02229\mathrm{.}091\mathrm{.}71$E$-024887\mathrm{.}253333$

$2\mathrm{.}33$E$-02237\mathrm{.}091\mathrm{.}86$E$-025057\mathrm{.}92$

$2\mathrm{.}33$E$-02245\mathrm{.}091\mathrm{.}86$E$-025228\mathrm{.}586667$

$2\mathrm{.}42$E$-02252\mathrm{.}091\mathrm{.}94$E$-025377\mathrm{.}92$

$2\mathrm{.}42$E$-02260\mathrm{.}091\mathrm{.}94$E$-025548\mathrm{.}586667$

$2\mathrm{.}63$E$-02268\mathrm{.}092\mathrm{.}10$E$-025719\mathrm{.}253333$

$2\mathrm{.}63$E$-02276\mathrm{.}092\mathrm{.}10$E$-025889\mathrm{.}92$

$2\mathrm{.}73$E$-02285\mathrm{.}092\mathrm{.}18$E$-026081\mathrm{.}92$

$2\mathrm{.}73$E$-02293\mathrm{.}092\mathrm{.}18$E$-026252\mathrm{.}586667$

$2\mathrm{.}93$E$-02301\mathrm{.}092\mathrm{.}34$E$-026423\mathrm{.}253333$

$2\mathrm{.}93$E$-02310\mathrm{.}092\mathrm{.}34$E$-026615\mathrm{.}253333$

$3\mathrm{.}03$E$-02319\mathrm{.}092\mathrm{.}42$E$-026807\mathrm{.}253333$

$3\mathrm{.}03$E$-02327\mathrm{.}092\mathrm{.}42$E$-026977\mathrm{.}92$

$3\mathrm{.}22$E$-02336\mathrm{.}092\mathrm{.}58$E$-027169\mathrm{.}92$

$3\mathrm{.}34$E$-02345\mathrm{.}092\mathrm{.}67$E$-027361\mathrm{.}92$

$3\mathrm{.}34$E$-02354\mathrm{.}092\mathrm{.}67$E$-027553\mathrm{.}92$

$3\mathrm{.}64$E$-02363\mathrm{.}092\mathrm{.}91$E$-027745\mathrm{.}92$

$3\mathrm{.}63$E$-02372\mathrm{.}092\mathrm{.}90$E$-027937\mathrm{.}92$

$3\mathrm{.}74$E$-02381\mathrm{.}092\mathrm{.}99$E$-028129\mathrm{.}92$

$3\mathrm{.}74$E$-02390\mathrm{.}092\mathrm{.}99$E$-028321\mathrm{.}92$

$3\mathrm{.}94$E$-02400\mathrm{.}093\mathrm{.}15$E$-028535\mathrm{.}253333$

$3\mathrm{.}94$E$-02409\mathrm{.}093\mathrm{.}15$E$-028727\mathrm{.}253333$

$4\mathrm{.}03$E$-02419\mathrm{.}093\mathrm{.}22$E$-028940\mathrm{.}586667$

$4\mathrm{.}03$E$-02428\mathrm{.}093\mathrm{.}22$E$-029132\mathrm{.}586667$

$4\mathrm{.}24$E$-02438\mathrm{.}093\mathrm{.}39$E$-029345\mathrm{.}92$

$4\mathrm{.}24$E$-02447\mathrm{.}093\mathrm{.}39$E$-029537\mathrm{.}92$

$4\mathrm{.}34$E$-02457\mathrm{.}093\mathrm{.}47$E$-029751\mathrm{.}253333$

$4\mathrm{.}35$E$-02466\mathrm{.}093\mathrm{.}48$E$-029943\mathrm{.}253333$

$4\mathrm{.}55$E$-02475\mathrm{.}093\mathrm{.}64$E$-0210135\mathrm{.}25333$

$4\mathrm{.}54$E$-02485\mathrm{.}093\mathrm{.}63$E$-0210348\mathrm{.}58667$

$4\mathrm{.}64$E$-02494\mathrm{.}093\mathrm{.}71$E$-0210540\mathrm{.}58667$

$4\mathrm{.}64$E$-02503\mathrm{.}093\mathrm{.}71$E$-0210732\mathrm{.}58667$

$4\mathrm{.}83$E$-02512\mathrm{.}093\mathrm{.}86$E$-0210924\mathrm{.}58667$

$4\mathrm{.}83$E$-02520\mathrm{.}093\mathrm{.}86$E$-0211095\mathrm{.}25333$

$4\mathrm{.}95$E$-02528\mathrm{.}093\mathrm{.}96$E$-0211265\mathrm{.}92$

$4\mathrm{.}95$E$-02536\mathrm{.}093\mathrm{.}96$E$-0211436\mathrm{.}58667$

$5\mathrm{.}15$E$-02543\mathrm{.}094\mathrm{.}12$E$-0211585\mathrm{.}92$

$5\mathrm{.}15$E$-02550\mathrm{.}094\mathrm{.}12$E$-0211735\mathrm{.}25333$

$5\mathrm{.}24$E$-02557\mathrm{.}094\mathrm{.}19$E

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