Arthur Petron (L04)
Lab Report #2:
Abstract:
Tensile test methods were used to help determine Young’s modulus, the
tensile yield strength, tensile strength, and true strain to necking in 7075-T6
Al, 2024-T3 Al, 6061-T6 Al, and 304L stainless steel. Further calculations to
identify a power-law strain hardening exponent (n) were completed on
the stainless steel sample. A sample of polymer was tested for fun.
Figure 1: examples of two test section
layouts
The 2024-T3 was done with a rectangular cross-section dog-bone tensile
test specimen, while the 7075-T6, 6061-T6, and 304L tests were done with
round tensile test specimens similar to the first example in figure 1.
The tension tests showed a lack of distinction between two of the Young’s
modulii of the aluminum samples. More distinct were changes involving
the yield point, percent elongation (deformed area change), and
ultimate tensile strength. Because of its material properties, the steel
increased in length much more than the aluminum, showing that it is a
much more ductile material. It is also interesting to note that nonmagnetic stainless steel becomes magnetic after strain testing.
Introduction:
The purpose of this lab is to get a better understanding for different types
of metal and how they compare to each other on the level of
categorical mechanical properties. This will become very important when
designing mechanisms in the future. In order to explore this fully, both the
elastic and the plastic region of the material curve is analyzed, whereas
before only the elastic curve was fully defined. By analyzing the plastic
curve as well, the material’s behavior at yielding can be more accurately
defined. This will aid in the design of manufacturing processes that may
involve this type of metal.
Methods/Experiment:
The tension tests were performed on both hydraulic and mechanical
tension testing machines. In all three cases (as the 6061-T6 was already
done) an extensometer as well as the normal cross-head sensor were
used to measure the elongation of the specimen during testing.
Care was taken not to test the sample too quickly, as this would cause it
to get hot and alter the test results. The measurements taken by the
sensors on the tensile testing machine were plotted real time to a
computer where they would later be saved to Excel spreadsheets. Each
specimen was tested to failure, and the failure diameters were measured
and recorded for use in data processing.
Results:
Figure 2: 7075-T6
Figure 4: True Al Stress curves
Figure 3: 2024-T3
Figure 5: 6061-T6
Figure 7: 304ss tension data
Figure 6: 304ss Strain hardening curve
Note: σTS arrows on figures point to point of εU.
Table 1:
E (GPa)
σy (MPa)
σTS (MPa)
εU (%)
Aluminum Tension Test Properties
2024-T3
6061-T6
73.5
67.9
436
266
596
316
3.256
9.952
Table 2:
Steel Tension Test Properties
304Lss
E (GPa)
305
σy (MPa)
554
σTS (MPa)
739
εU (%)
30.63
7075-T6
61.0
589
664
10.11
Discussion:
The aluminum alloys tend to be similar on some parts of the curve and
different on others. For example, the plastic regions near necking of 7075
and 2024 look very similar, however 7075 has a much higher yield point,
whereas 2024 and 6061 have closer E values (from the data) than to 7075.
2024 and 6061 also have a very smooth yielding point whereas 7075’s
seems very sharp in comparison.
From the data plotted in figure 6, it can be estimated that n = 1.3e-4 and
K = 267300.
n and εU are very different from each other, almost reciprocals.
References:
Matlab help.
Note: I spent a very, very long time on this lab, but not on the report itself.
I was developing a Matlab tool that will quickly interpret tension test data,
creating all the graphs you see in this report simply by specifying a
filename that contains the data you’d like to process. I invite you to look
over the code here:
function mat_analysis(strs, strn, lin_range)
lregress_strn = strn(lin_range); % MAKE SURE THIS IS IN THE RANGE OF
lregress_strs = strs(lin_range); % THE LINEAR REGION OF THE DATA!!
yfit = polyfit(lregress_strn,lregress_strs,1);
mod_E = yfit(:,1)
b = yfit(:,2)
yield_strs = mod_E * (strn - .2) + b;
data
% Finds E of data set
% Sets E value
% For Yield calcs
% Calculates the yield line
UTS = max(strs);
% Finds UTS. That makes things easy.
UTS_strn = strn(find(strs == UTS));
UTS_strn = UTS_strn(1);
% Sometimes find returns multiple values
cutoff1 = 1;
for cutoff2 = 1:length(yield_strs) % Cuts off yield line at the right
place
if yield_strs(cutoff2) < 0
cutoff1 = cutoff2;
% For bottom
end
if yield_strs(cutoff2) > UTS
% For top
break;
end
end
diff = [10000 0 0]; % Storage variable
figure;
hold on;
% Plots the initial data
plot(strn, strs, strn(cutoff1:cutoff2), yield_strs(cutoff1:cutoff2));
ylabel('MPa');
axis([0,strn(length(strn)),0,UTS + 20]);
if max(strn) > 5
legend('Engineering Stress vs. Strain', 'Yield Line', 'Location',
'Best');
title('2.002 Lab data: Tension Engineering Stress vs. Engineering
Strain');
% CHANGE THIS FOR NEW TITLE
xlabel('percent');
else
legend('True Stress vs. Strain', 'Yield Line', 'Location', 'Best');
title('2.002 Lab data: Tension True Stress vs Trues Strain');
%
CHANGE THIS FOR NEW TITLE
xlabel('log scale');
end
text(UTS_strn, (UTS - 30), strcat('\uparrow \sigma_T_S:
',num2str(UTS),'MPa'));
% ignore the man behind the curtain doing tricky functions
holder(500) = 0;
for pnt = 100:600
% REALLY simple least squares analysis, but works
well
holder(pnt - 99) = (strs(pnt) - yield_strs(pnt))^2;
end
fgh = find(holder == min(holder));
diff(2) = strs(fgh(1) + 99);
diff(3) = strn(fgh(1) + 99);
plot(diff(3), diff(2), '*')
% Puts a * on the yield point
text(diff(3), diff(2), strcat('\leftarrow \sigma_y:', num2str(diff(2)),
'MPa'));
ptr = lin_range(floor((length(lin_range) / 2)));
if (diff(2) / 2) > strs(ptr)
ypos = diff(2) / 2;
ptr = find(strn == diff(3));
else
ypos = strs(ptr);
end
text(strn(ptr(1)), ypos, strcat('\leftarrow E:', num2str(mod_E),
'MPa/%'));
% More text stuff, labels sig_y and E
hold off;
And an example of how to run the function:
M = dlmread('6061.txt');
strn = M(:,1);
strs = M(:,2);
trstrn = log(1 + strn);
trstrs = strs .* (1 + strn);
mat_analysis(strs, strn, [50:300]);