Project Name: Compact Tension Specimen Analysis
Program: ABAQUS
Year: Spring 2020
For this project a compact tension specimen and the relevant stresses and deformations is analyzed using ABAQUS. The purpose was to study the stress at the crack tip and measure the critical load. This can then be used to determine the fracture toughness of the specimen and create a model that is accurate to the exact stress intensity factor. This model was created by dividing the specimen using 1000 nodes. This has been done by strategically placing nodes throughout the specimen in order to create the most accurate model with the constraints given.
Model Illustration
The figure displays the compact tension specimen model, load, and boundary conditions. The original model has been separated along the x axis because the top and bottom of the specimen are symmetrical. The origin of the model is at the crack tip. This is to make modeling and meshing easier later in the finite element process. “P” is a concentrated force located at the top of the circle. The distance “a” was dependent on each student. For my particular case, P is 100 kN/m and a is 0.027 m.
Sectioned Mesh with Load and Boundary Conditions
Mesh Plot
Mesh Plot, Crack Tip Region
Deformed Mesh Plot
Deformed Mesh Plot, Close Up
Stress Contour Plot
Stress Contour Plot, Close-Up
Summary
The goal of this project was to create a model to accurately study the stress intensity factor. Doing so was a challenge due to the limitation of only utilizing 1000 nodes. Because of this, the mesh had to be carefully planned to have small elements near the crack tip and larger ones while radiating outward. This transition had to be made gradually to ensure an accurate result. I decided to use a mesh that is similar to the focusing/spider webbing method. This can be seen in figure 4. This was accomplished by creating a semicircle around the crack tip and then a rectangle around that to appropriately increase the element size slowly to get the most accurate results possible.
However, the results on accuracy were different depending on the method used to test it. The first method is calculating the stress intensity factor (KI) using different methods. The first method uses the reaction force at the crack tip and displacement of the first node to the left of the tip. This yielded a relatively accurate result with 7.64% error. The next method also calculated KI, but using the displacement of the nodes to the left of the tip. Using this method yielded a much more accurate result for the model with an average percent error 0.4%. The last method using KI calculated the stress intensity factor based on the stress of the nodes to the left of the tip that are around 10° to 50°. This yielded strange results with error ranging from 3% to 11%. The error increased as the node moved further away from the tip, which was expected, but did so in a very erratic manner. I believe this is due to the nodes being at different y distances away from the origin. Since the formula involves using the opening stress and displacement of the node to calculate KI, the nodes chosen might have been too far away from the crack tip to get accurate results.
The final method for testing accuracy used was the behavior of the opening stress around the crack tip. This method compares the normalized stress of points surrounding the crack tip using two different approaches. The first using the displacement and the exact KI and the second using just the angle of the nodes. Figure 11 shows these results and it is easy to observe that the values do not line up. I believe this is a fault with the mesh not having perfect squares as the element shape around the crack tip. This results in the displacement being slight off for each node and therefore the normalized stress is incorrect as well.
The mesh structure of the model is very accurate, but could be improved more to lower the percent error even more. If I were to do this again without the 1000 nodes limit, I would have a dense small element section around the crack tip similar to what I have done, but with the transitions from small to large elements being more gradual. Also, the elements would be more uniform in shape. With both of these changes the model would be much more accurate and allow for a better mesh.
More specifics about this paper can be read here