Stress Concentration Factor (2D)

Fall 2012 / Lab 6: Report (30 Points) / MAE 323
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Stress Concentration Factor (2D)

Problem Statement:

Determine the stress concentration factor of the two-dimensional part shown below (see lab 6 instructions for explanation and context). Do this by first creating an unstructured quadratic triangular mesh and ensuring that the maximum x-component stress has converged to within 3 percent.

Exercise 1. Stress Convergence

As pointed out in the problem statement, use quadratic triangles (Hint: Insert a “Method” to ensure that you get all triangles). Start with a ratio r/w2=0.05 (r=1mm) and insert a local mesh refinement scheme such that the x-component stress converges to within 3%. This only has to be done once (you may safely assume that mesh refinements for all subsequent fillet radii result in similarly converged results). Fill in the table below (Note: It may not take as much as four iterations. Depending on the mesh size you start out with in iteration 1, it could take as few as 2 iterations. However, it will have to be more than 1 in order to know whether the mesh has converged). (Hint: start with a local mesh refinement of (0.8) and body constant body size of 1mm)

Table 1 mesh refinement (8 Points)

Iteration / # of elements / #DoFs (total) / x / percent change
1 / --
2
3
4

Exercise 2:

With the converged mesh settings, modify the fillet radii shown in the figure (and discussed in the instructions) in order to estimate stress concentration factors according to the formula:

Where max is the maximum x-component stress and nominal is the nominal stress calculated according to:

More Tables

Obtain empirical or theoretical estimates for kt from an outside source and fill in the table below. Give your text or online reference (with table and page number if applicable).

Table 2 Kt from reference (to two decimal places) (4 points)

r/w2 / 0.05 / 0.1 / 0.15 / 0.2
kt

Reference:

Table 3 Kt from FEA (report all results to two decimal places) (8 points)

r/w2 / 0.05 / 0.1 / 0.15 / 0.2
x(max)
x(nom)
kt
% error

Questions:

How did the % error in kt compare with the 3 percent convergence criterion given in exercise 1 , any reasons for the differences if any?(Hint: If your kt came from an analytical estimate, they should be VERY close. However, there are some practical considerations which could affect this. 2 points)

Which representation (plane stress or plane strain) did you use to describe this part? Would the other representation have a made a difference to this study (Hint: Look at the lecture notes. 2 points)?

Figure 1: Converged Mesh (show me the mesh refinement for the smallest radius (1mm) used in the study). Give me the XY view only. 2 points

Figure 2: Loads and Boundary Conditions (2 points)

Figure 3: x-Component stress for 1mm fillet radius. (2 points)