Problem $1(40$ points$).$

Given: An Excel file $($projectdata$.$xls$)$ is attached with time, force, displacement, and strain data obtained during

the Fall $2006$ semester. The sample tested was $6061-$T$6$ aluminum and a strain rosette was used to collect

strain data through auxiliary inputs $1,2,$ and $3$ that correspond to gages a$,$b$,$ and c$,$ respectively.

Auxiliary input $1$ corresponds to the x$^(\text{'})-$axis and auxiliary input $3$ corresponds to the y$^(\text{'})-$axis with the $2^("$nd $")$

auxiliary input $45$ degrees in the middle of both. The overall x $-$axis is the axial axis of the dogbone

sample.

Find: $1.$ Produce a plot of axial stress versus axial strain.

Produce a plot of the absolute value of transverse strain versus axial strain.

Determine Young's modulus and Poisson's ratio for each sample by fitting a linear equation to

each of the above using the following strain range $($linear regression analysis$)$:

$-$Strain range: mu epsi

What is the percent error between the Young's modulus and Poisson's ratio versus tabulated

values for this material?

What is the smallest angle $(+$ or $-)$ between the x$^(\text{'})-$axis and x$-$axis?

$-$calculate the average value obtained over the same strain range as above and report the

standard deviation and coefficient of variation on this angle over this range

Operator Information

FSW WORK ORDER#

SPECIMEN NUMBER $/$ TYPE

WIDTH $($mm$)$

THICKNESS $($mm$)$

STRAIN RATE $($ mm$//$min $)$

OPERATOR

Operator Information End

Data Acquisition

the axial stress and strain were early attempts at trying to get it$,$ there is no initial length given, how am i supposed to solve for it$,$ and what should it look like. i think the axial stress is right