Assignment9

Problem 1

This repository contains a file data.csv that is actual data from a stress-strain test conducted in a standard test frame (MTS machine). The columns of data have the following format

time	Axial Displacement	Axial (engineering) Strain	Axial Force
(s)	(in)	(in/in)	(lbf)

Complete the function definition for the function named convert_to_true_stress_and_strain(filename::String). This function should take the name of a file (e.g. "data1.csv") as an string argument and return a tuple ($\varepsilon_T$, $\sigma_T$), where $\varepsilon_T$ is the true strain and $\sigma_T$ is the true stress.

Recall that the definition of engineering stress is

$$ \sigma_E = \frac {P} {A_o} $$

where $P$ is the axial force and $A_o$ is the original cross-sectional area of the sample. The cross-sectional area can be computed from the width and thickness that the function parse_width_and_thickness(filename::String) returns as a tuple. There is also a function read_data_file(filename::String) that will read the CSV file and return only the raw data as a two-dimensional Array of Float64s.

The conversion between engineering $\varepsilon_E$ and true strain is

$$ \varepsilon_T = \ln(1+\varepsilon_E). $$

The conversion between engineering and true stress is

$$ \sigma_T = \sigma_E (1+\varepsilon_E). $$

Use broadcasted operations to make your code compact and efficient. No for loops!

Problem 2

Complete the function compute_toughness(filename::String) to compute the materials toughness. Recall that toughness is the area under the stress-strain curve, i.e.

$$ \mbox{Toughness} = \int \sigma {\rm d}\varepsilon $$

Use the true stress and strain values computed in Problem 1, then use a trapezoid rule to do the integration. Again, you should use broadcasted operations for the computation.

Testing

To see if you answers are correct, run the following command at the Terminal command line from the repository's root directory

julia --project=. -e "using Pkg; Pkg.test()"

the tests will run and report if passing or failing.