The K Solution library module, PKSOL, contains the means to calculate the fracture mechanics stress intensity factor, K, for over 35 geometric cases. The module provides a means to generate a compliance function table for use in the MSC Fatigue fracture mechanics prediction module PCRACK where K is calculated as a function of crack size, stress history, and geometry.

The fracture mechanics stress intensity factor, universally known as K (or in fatigue), relates stress and crack size into a single parameter which is the driving force for the behavior of cracks in engineering materials in terms of fracture, stress corrosion or fatigue. Its use relies on the similitude concept which implies that, independent of geometry, if K is the same then the response is the same. The relationship may be viewed as a triangle in Figure 7‑1 in which if two are known the third can be derived. In this way, important decisions can be made regarding, for example, specified material toughness, NDT limits and inspection strategy, and operating stresses in engineering applications.

The three parameters are related by the general expression:

where Y, the compliance function embodies both the global geometry of the component or structure and the crack size, shape, and location. Consequently, many cases, or K solutions, are available in standard references ((Ref. 3.) through (Ref. 8.)) and more than 35 of the most significant solutions for engineering applications are coded into the PKSOL library module. They may be used to generate a compliance function table for a specific geometry and case, for all crack sizes.

As a specific example of using PKSOL to solve for one corner of the fracture mechanics triangle and its application to a crack growth analysis:

Suppose you want to be able to stop the analysis at a crack length that would cause a failure if the limit load occurred in the next cycle. Imagine you have a time history of random cycles varying between 1 and 3kips that represents a repeatable sequence, say one flight, but does NOT include the once per life 10kips limit load. The analysis would proceed to model the crack growth cycle by cycle including all the retardation, overshoot, and crack closure effects, but there are several ways of ending the process. One of them is to specify the final crack length.

The analyst would use the K solution library module (PKSOL), as a single shot solver, to calculate the crack size when the fracture toughness is exceeded at the maximum stress corresponding to the limit load. (It is also possible to calculate a final crack size when plastic collapse of the remaining section occurs rather than a KIC fracture). This crack size is then used to limit the crack growth process and effectively checks on a cycle by cycle basis "have I reached a crack size where the residual strength compromises the design limit strength?"

PKSOL may be accessed from the MSC Fatigue Solution Parameter form available from the main menu within MSC Fatigue Pre & Post or MSC Patran when the Analysis Type is set to Crack Growth, or it may be run outside of MSC Patran by typing the symbol pksol. A general description of the steps involved in a PKSOL session is shown in Table 7‑1 to calculate a missing corner of the triangle.

Once initiated, the PKSOL program will ask the user to select the crack length units to be used as in Figure 7‑3.

When first invoked PKSOL appears displaying two forms.

The top, small form is a generic form and allows for general program control. This is discussed in detail in Module Operations (Ch. 17) for the Motif driver.

Having defined the length units, the user will then be asked to define the type of calculation that he wishes to carry out. See Figure 7‑4.

The user must nominate one unknown on the fracture mechanics triangle (options 1-3), and over the subsequent few screens, supply the known data and define the specimens geometry.

For each group, another menu of specific geometric cases is given and selection from this leads to an input screen incorporating a graphic representation of the geometry highlighting unambiguously the required input dimensions. The various menus of specific cases and their geometries are shown in Figure 7‑6 through Figure 7‑13.

When a graphical image is presented for dimension input, the user must first use the mouse to select Define from the menu bar. He may then input the dimensions. Each parameter is input in turn and at the end of this sequence, alterations can be made if necessary using the syntax:

<parameter>=<value>

the default being <none> indicating no changes or no further changes. When all dimensions have been input, the user must use the mouse to select Calculate from the menu bar. To return to the non-graphic portion of PKSOL, click on Return.

To see graphical images of the different geometry options, press the F1 key while one of the options is highlighted (holding the mouse button down). A graphical display will appear. If all geometries do not show up in the graphical screen, click on Next or Previous to see the rest. Click on Return to return or Hardcopy if you wish to have a hard copy plot.

Once one of these geometries is selected, a graphical screen is displayed which allows for the definition of the local geometry dimensions. The main form (general options) is explained in Module Operations (Ch. 17). However, the Define, Calculate, and Return options on the main form are specific to this application.

If the user picks option A (user parametric definition) from Figure 7‑5, a form will be presented that asks for the constants in the equation:

This form allows the user to define a compliance function using a 5th order polynomial based on results from test or FEA, or from standard handbooks. The polynomial uses a non-dimensional crack size derived by dividing crack size (a) by total possible crack size (T).

By following the steps described in Table 7‑1 and the on-screen instructions, a results screen is reached. For example, when calculating a critical crack size, a result display, such as in Figure 7‑23, will result.

After successful completion of any of the options from Figure 7‑4, the user will be presented with some post-processing options as shown in Figure 7‑24. If options 1‑ 3 on the calculation menu (Figure 7‑4) are chosen, the postprocessing options in Figure 7‑24 will be presented. If option 4 is chosen, then the post-processing options in Figure 7‑25 will be presented.

When a plot is requested within PKSOL, a screen similar to the one below appears. Various utilities are available from the main form. These are explained fully in Module Operations (Ch. 17).