XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> LEFM Analysis of Lug
Set up a Crack Growth analysis now to determine if a crack will grow in the lug and to determine at what interval an inspection may be necessary. Set the General Setup Parameters as follows:
1. Analysis: Growth
2. Results Loc.: Node
3. Nodal Ave.: Global
4. F.E. Results: Stress
5. Res. Units: MPa
6. Jobname: lug_cg
7. Title: Crack Growth Analysis of Lug
Solution Parameters
Open the Solution Params... form. Before we can fill this form out completely we need additional information about the crack geometry, namely the compliance function. Run PKSOL (click the Compliance Generator button) and create a compliance function for a specimen with a double crack at a hole in tension where R = 15mm and W = 70mm. Call it LUG. These are the PKSOL steps:
1. Millimeters
2. Generate a Y function table
3. Output K-Solution Filename: LUG
4. Cracks a holes
5. Double crack at a hole in tension
6. Define
7. R: 15
8. W: 70
9. Changes: Carriage Return - no changes
10. Calculate
Select Plot Y function against crack ratio to see the graph of the crack ratio.
On the Solution Params... form set the following widgets and accept defaults for those not mentioned:
1. Select a Compliance Function: LUG
2. Initial Crack Length: 3
3. Final Crack Length: 55
Hint: | You can plot the compliance functions from the Solution Params... form (if you have done so from PKSOL first) by selecting a compliance function from the listbox and clicking the Plot button. To remove the plot, press the Unpost or Delete buttons. |
Material Information
Open the Material Info... form. Before filling the form out however, create a group with only Node 223 in it. Call the group far_field. Node 223 is chosen to indicate the area of nominal or far-field stress. It is not too close to the high stress gradient where the influence of the hole is dominant. LEFM theory is based on a nominal far-field stress.
The material again is BS4360-50D and the environment is air. The properties for this material are already in the materials database manager. On the Material Info... form set the cells of the spreadsheet as follows:
1. Material: BS4360-50D
2. Environment: air
3. Region: far_field
This group contains the node of the far field stress point only.
Loading Information
The load time history is identical to the previous two lug analyses.
Job Control
Open the Job Control... form and set the Action to Full Analysis and click the Apply button to run the job. Monitor the job form time to time until it is complete.
Results
Open the Results... form and with the Action set to List Results, click Apply to invoke PCPOST. View the Results summary page and the final a-N curve. Note that the crack takes over 150 years to grow to a critical size before total failure. Then close PCPOST.
The Damage Tolerant design philosophy would have us determine an inspection interval. Rerun the analysis by changing the Action to Optimize. Accept all the defaults on each setup screens presented to you by PCRACK. When the analysis begins you will notice that the crack grows, but fairly slowly. Therefore, you could feel good about a fairly long interval between inspections (say once a year).
When the analysis has completed, make your way back to the PCRACK Post Analysis main menu. It may be of interest to change the initial crack size to something less than 3 mm. We assumed a 3 mm initial crack length based on an engineering crack size from the initiation analysis. Use the Edit analysis parameters | local Geometry option to change the crack size to 2 mm. Then Recalculate. Do it again for 1 mm. Finally put in 0 mm which flags the code to calculate the minimum initial crack length valid for LEFM in this case. Note that the crack hardly grows for a long time. Growth of the crack is quite sensitive to the initial crack length. This could have been surmised from a plot of the compliance function which shows slow growth at first but very accelerated growth at a high crack ratio. Click the Abort button when you get tired of watching the crack grow.
