Fracture Toughness

1. Group InfoGroup 2MSE 527LRna WahebSiddhesh SawantDhaval Prajapati Pavan Kumar NanneRyan OhRameen Hassanzadeh

2. AbstractTwo samples of 7075 Aluminum were prepared for a fracture toughness investigation. The first, a compact tension specimen was prepared in accordance with ASTM E-399, was successfully tested under tensile load. The sample, starting with a 0.9in crack length, reached a maximum load of 4435 lbs before fracturing with a final crack length of 1.415 in. Using 95% of the slope of the linear fit of the linear regime of load vs crack-mouth opening displacement (COD), PQ was determined to be 2731 lbs, indicating a KQ of ~89 ksi in1/2. However, it was deterimied that this KQ value is invalid for being KIC due to the Pmax:PQ ratio. The second ssample, prepared as a single edge-notch bend sample, was tested under 3pt bend. It was found to fracture while still in the linear P vs COD regime, and to have an unmeasurable final crack length. It reached a maxium load of 4295 lbs.

Figure 1: Compact Tension Specimen

3. ProcedureIn this lab, two samples of 7075 Aluminum (E=68 GPa, YS = 70ksi, YS = 76ksi) were prepared in specific shapes for standardized testing (ASTM E-399) of their crack-induced fracture properties. The first was shaped as a standard compact tension specimen (Fig 1). The second was shaped as a standard single edge-notch bend specimen. The samples' dimensions were thoroughly measured. The formulas for stress intensity factors (K) for these shapes as a function of crack length (a) is well documented.Figure 2: Single Edge-Notched Bend Specimen

The compact tension sample was placed on a tension too, and tested under load (P). Prior to measurement, the compact tension specimen was pre-cracked under a small cyclic load, ~60% of an estimation of the estimated final fracture load (PQ) in order to extend the crack length to ~0.9 in, in order for the test method to be valid (W-a 15rIc). The edge-notch sample was tested under a 3-point bend tool/ The load was increased until the samples fractured, and the final crack lengths were measured (the final crack length for the single edge-notched sample was too small to be accurately measured).

4. Results and DiscussionThe formulas for determining the stress concentration for these samples is well document. For the compact tension specimen, the formula is as follows:

Where P is the load and a is the crack length. B and W are dimensions of the sample, as can be seen in Fig 1. f is the formula defined below:

Similarly, for the single edge-notched bend sample,

formula

formulaHere, S is the sample length as seen in Figure 2.

For the starting crack length values (0.9in for the compact tension sample, and 0.26in for the single edge-notch sample), K reduces to ~12*P and 7.7*P respectively.As mentioned in the methods section, the samples were tested under load until fracture. Figures 3 and 4 show the results of their load vs crack mouth displacement.

Figure 3: load vs crack mouth open displacement for the compact tension sample

Figure 4: Load vs crack mouth open displacment for the edge-notched sample, tested under 3pt bend.

As can be seen from the graphics, the compact tension sample showed a linear region up to COD ~ 0.02, after which the displacement rate vs load began to increase. The edge-notch sample fractured while still in a linear regime. The samples fractured once the increase in K due to the growing crack rank reached a critical point, after which the crack propagation went sonic, resulting in the complete fracture of the sample.For the compact tension sample, this critical crack length was found to be 1.415 in, and fractured at a load PMax = 4435lbs. The load at Similarly, the edge-notch sample fractured on a load of PMax = 4295lbs, though a could not be measured, and an accurate K cannot be established. The critical load (PQ) and fracture toughness (KQ) are determined by finding the slope of the linear regime of the load vs COD for the sample. Then, determining where a slope 5% less than that intersects with the load/COD curve (PV). This is illustrated below, in Figure 5.

Figure 5: The close-to-linear regime of the compact tension sample. The two lines give the linear fit of the regime (top) and Pv, which is 95% of that linear fit (bottom)

Using this method, PQ is found to be 2731 lbs. Using this value for P, and our final crack length, we can determine KQ.. We find this value to be ~89.1 ksi in1/2. However, this value for K is only valid (ie: is KIC) under certain conditions. Using our solve PQ, we can take another step in determining the validity of this test. For the test to be valid, the following formula would need to be true:

So, in order for our KQ to be our desired KIC, we need to check our load values. Plugging in our numbers, we get

Clearly, 1.6 is not less than 1.10. Unfortunately, this implies that our test is invalid, so our KQ is not a valid KIC.

In summary:SamplePre-test crack length (in)K(P) (ksi in1/2)Pmax (lbs)Final crack length (in)PQ (lbs)KQ (ksi in1/2)KIC?

Compact Tension0.912*P44351.4152731lbs89.1ksi in1/2No

Single Edge-Notch Bend0.267.7*P4295----

Table 1: Data summary for Compact Tension sample and Single Edge-Notch bend sample. The Edge-Notch sample fractured while still in a linear regime, and the final crack length was unmeasureable.

Errata to Report

In the case of the edge-notch bend sample, the discussion in this report is incorrect in some of its statements. Because the sample is Type 1, a 95% slope line is not required to find PQ. Instead, by definition, Pmax = PQ. This implies that KQ is calculable, using the Pmax value for the load. The results, using the measured pre-crack length as the post crack length (they were not significantly different for this sample), can seen below in Table 2.

SamplePre-test crack length (in)K(P) (ksi in1/2)Pmax (lbs)Final crack length (in)PQ (lbs)KQ (ksi in1/2)KIC?

Single Edge-Notch Bend0.267.7*P42950.26429533.1No

The question does this KQ represent KIC remains. The first check, taking the ratio of PQ and Pmax looks as follows.formulaTo summarize, it passes by definition. However, this is not only criteria that must be passed in order for this KQ value to represent KIC. The second is that a theoretical length, LQ must be small compared to the sample thickness and crack length.formulaFor the edge notch sample, B=W, and LQ resolves to the following.formulaThe resulting value is signifcantly larger than W and a from the sample, and therefore, KQ does not represent KIC.

References"Fracture Toughness Testing and Residual Load-Carrying Capacity of a Structure." Massachusetts Institute of Technology. 2004