Arthur Petron
Laboratory 6
Hashemi: Wednesday, L04
Abstract:
Plane strain fracture toughness and failure due to cracking were examined in this
laboratory module. Three tests were completed. The first was a fracture toughness test
with an ASTM CTS specimen of standard size, the second was a plastic failure collapse
test to show the dependence on crack length in failure versus collapse, and the last was a
cracked beam fracture test which was destroyed in a three-point-bending situation. It was
determined that materials will fail plastically before they fracture if the crack in the
material is of a small enough size. Also, in keeping with the premises of linear elastic
fracture mechanics, the beams that did fracture did so with little deviation from the linear
relationship between displacement and center-span load.
Introduction:
In this laboratory we performed tests with standard compact specimens in order to obtain
the plain strain fracture toughness of 7075-T6 aluminum. Using this value, we then
predicted and tested a crack containing structure of 7075-T6 in order to test the theory of
crack stress concentration experimentally. Ideally, the loading capacity of the structure
will be a monotone decreasing function of crack length (a), but for very small values of a,
the beam may go into full plastic deformation before fracture occurs. Because of this, we
must compare the predicted structural load carrying capacity to both the fully plastic
collapse condition as well as the fracture
condition suggested by the material’s
fracture toughness. The graph on the right
demonstrates the behavior of a beam with a
crack. As you can see, at certain small crack
lengths the beam plastically collapses before
it breaks due to fracture. Note: This graph is for
visualization purposes only. Any P values obtained from it will not
work with 7075-T6.
Methods/Experiment:
Firstly, a standard specimen – following ASTM standard E-399 of CTS geometry was
used in fracture toughness tests to determine KIC. Using this value, the fracture load of a
bar of 7075-T6 was predicted. The bar had dimensions B = 12.7mm, b = 38.1mm, and s
= 250mm. The sharp fatigue pre-crack length a was 12mm.
A fully-plastic load limit test was performed on an uncracked beam with the same
dimensions as the cracked beam (b = [38.1mm – 12mm] for consistency). This is done to
compare the relative magnitudes of ‘failure’ versus ‘collapse’ loads. With the uncracked
beam tested, a fracture test on the three-point-bend cracked specimen was performed and
compared to the experimentally predicted load capacity.
Results:
Numerical Results:
Q = 7.7
KIC = 38.3 MPa
Predicted Three-Point Cracked Failure: 9.41 kN (see appendix)
Predicted Three-Point Plastic Collapse: 18.4 kN (see appendix)
Experimental Three-Point Cracked Failure: 11.0 kN (from lab graph, see appendix)
Experimental Three-Point Plastic Collapse: 18.2 kN (from lab graph, see appendix)
Discussion:
The protocol for testing ASTM E-399 CTS samples involves a high frequency fatigue
cycle in order to ‘walk’ the crack out from the crack site. This is done to ensure that the
crack has as small a radius as possible, so that our ‘atomic radius’ theory will hold in
practice, which it seems to do very well.
The uncracked bend bar test showed extremely consistent results between the theoretical
predicted value and the experimental value.
Possible sources of error between the cracked three-point-bend beam experimental and
theoretical data include pre-stress on the beam before the test – which can include
anything from the crack ‘walking’ causing work hardening in the piece’ to heat stress
hardening to the beam being dropped – the radius of the crack being slightly larger than
atomic radius, and the force P not being perfectly directed over the crack site.
The cross-head displacement versus center-span load for the cracked beam in three-pointbending did not have a large deviation from linearity prior to fracture because the beam
was in the region where fracture would occur well before the beam had reached a fullyplastic state. Thus, the beam will tend to deflect much more elastically than plastically
prior to fracture, and this is consistent with the basic premises of linear elastic fracture
mechanics.
Appendix:
Matlab code used to find graphs and requested values:
start
sig_y = 462000000;
B = 12.7 * 10^-3;
b = 38 * 10^-3;
s = 250 * 10^-3;
k_ic = 38300000;
a = [0:.0001:.02];
% adjust this depending on the rage you want
% units are meters!
p_fail = k_ic ./ (pi .* a) .* ((4*B*b*b)/(6*s*5));
p_coll = ((sig_y*B/s) .* ((b - a) .^ 2));
plot(a ./ b, p_coll, 'red', a ./ b, p_fail, '--'); % specify what to
plot here
end