Fracture Toughness Measurement Experiment Report

1. Introduction

Aluminum alloy 2011-T6 is known for its high mechanical strength and excellent machinability, making it suitable for various applications. This alloy is often referred to as a "free machining alloy" due to its compatibility with automatic lathes. To assess the fracture toughness (KIc) of this alloy, we utilized notched round bar (NRB) specimens, which are designed to evaluate plane-strain fractures. The KIc value obtained for this alloy through NRB testing was found to be 27.9 MPa√m, demonstrating a high degree of accuracy with only a 6.

8% discrepancy compared to the average value of 26.0 MPa√m determined from 67 tests using the ASTM E399 standard. Additionally, we introduced a new geometric correlation based on ρ, D, and d to extrapolate Kπ values measured with various NRB specimen geometries to a single KIc value.

2. Experiment

A total of 9 specimens were used in this experiment, comprising 3 specimens for each of 3 different values of ρ (root radius of the notch). All specimens, both tensile and notched, were manufactured in compliance with Australian Standard AS 1391 to ensure consistency.

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The only variation among the notched specimens was the root radius profile, with three different values of 0.5 mm, 0.8 mm, and 1.2 mm, each cut at an entry angle of 60°. Three specimens were prepared for each root radius to replicate the experiment three times.

The aluminum alloy material was supplied as a 3-meter-long solid rod, which was cut to the required sizes using an electric circular saw, leaving additional length for lathe gripping. A total of twelve parts were cut, including three for tensile testing and three for each root radius of the notch.

To machine the notches to precise dimensions, a special diamond-shaped cutting tool with a holder was used. The aluminum rods were placed in a lathe equipped with a cutting tool, and the lathe's software code was employed for machining. After machining, all specimens underwent a thorough dimensional inspection using a vernier caliper to verify size consistency and accuracy.

Furthermore, unpainted tensile specimens were prepared to collect material properties. Two strain gauges were attached to each of the three specimens: one in a vertical orientation and the other radially. Finite Element (FE) analysis was conducted to establish the relationship between the nominal stress applied and the stress concentration factor in the plastic zone near each notch. An axisymmetric 2D model was developed using 8-node quadrilateral elements to optimize computational efficiency. Due to symmetry, only a quarter of each bent round bar needed to be meshed. The analysis involved both linear elastic and elastic-plastic analyses, with the latter considering the varying cross-sectional area during the test. A convergence analysis indicated that a mesh size of 0.05 mm at the notch was acceptable. The fracture stress was determined as the mean of the highest stress values among the three specimens.

3. Observation and Results

For each root radius of the notch, an elastic analysis was conducted to determine the maximum normal stress in the vertical direction and calculate the stress concentration factor (SCF). SCF is defined as the maximum stress at the root of the notch divided by the applied stress at the top of the specimen. The following table shows the relationship between the notch radius and the stress concentration factor:

It is evident from the table that as the root radius of the notch decreases, the stress concentration factor increases. Sharp notches result in higher maximum stress compared to blunt notches. To visualize this relationship, we have plotted a graph with notch radius on the X-axis and stress concentration factor on the Y-axis.

Next, we examined the effect of the root radius on the size of the plastic zone. The table below presents the relationship between the notch radius and the size of the plastic zone:

As evident from the table, the size of the plastic zone increases with an increase in the root radius of the notch. We have represented this relationship through a graph, with notch radius on the X-axis and the size of the plastic zone on the Y-axis.

Finally, we determined the fracture toughness (KIc) for each notch radius. The following table illustrates the relationship between the notch radius and the fracture toughness:

It is important to note that in the case of a simple cut in a plane (zero notch radius), the stress distribution at the tip of the cut exhibits a stress singularity with potentially infinite stress values. However, when a non-zero notch radius is introduced, the cumulative stress becomes finite. To address this, we evaluated the stress distribution slightly ahead of the crack or notch tip and extrapolated the results.

4. Conclusion

We employed the least square method to fit a straight line to the data points, allowing us to extrapolate the KIc value for Al 2011-T6 to be 27.9 MPa√m when ρ /D = 0. This value closely aligns with the median value of 26.0 MPa√m determined from previous tests using the ASTM E399 standard, with only a 6.8% difference. This demonstrates the reliability and accuracy of the Notched Round Bar (NRB) testing method.

Our findings suggest that NRB testing offers a cost-effective and practical alternative to testing generic pre-cracked planar specimens. The tests performed in this experiment were found to be slightly non-conservative compared to the ASTM standard norm. Future research could involve testing specimens with the same root radii but varying outer specimen diameters (D) and inner neck diameters (d) to further validate the proposed geometric correlation. If successful, the NRB testing method may become standardized in the future, similar to the Stark-Ibrahim CNT process. However, the size specifications for unnotched NRB geometry must be calculated using finite element analysis.

5. References

[1] G.G. Vanian, A.K. Hellier, K. Zarrabi, and B.G. Prusty, "Fracture toughness determination for aluminum alloy 2011-T6 using tensile notched round bar (NRB) test pieces."

[2] ASTM Standard E399 (2009), "Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials."