In our last blog post of this series, I dive into how we can simulate cracked structures using Ansys simulation software, Ansys Mechanical. As before, if you’ve not read the previous two posts, go back and read ‘em!!! 

How Engineers Use Ansys Mechanical Software to Model Cracks 

Ansys Computer Aided Engineering (CAE) simulation software allows engineers to study cracks in structures via fracture mechanics, along with a host of other structural simulation needs. Ansys has a long history of simulation development since the 1970’s in creating tools for engineers to design and virtual prototype their products. As a quick note, Ansys is not limited to just structural physics either. Fluids, electromagnetics, systems and optics are some of the other fields Ansys offers in its portfolio of simulation capabilities. 

The options to create a crack in Ansys simulation software generally fall in two categories: either a) use a CAD surface that represents the crack, that overlaps with the structure or b) use the auto-generation tool in Ansys to add a crack at the mesh level. 

The former works well in all scenarios but is very useful when the crack is not a simple analytical shape, i.e., a penny-shaped crack. The latter is great for those simple, penny-shaped cracks, where the engineer can input two radii to define the shape, input where the crack is located, and they’re done. 

Here’s an example; take this simplified cast bearing/shaft support. The machinist finds a crack when machining the bearing support housing (outlined in the blue box). Perhaps this is caused by an incorrect casting process. 

Representative CAD Model, Crack Surface on Right 

When magnafluxed or cut open, the crack is not a simple shape. This is perhaps an extreme example, but it gets the point across. With a few inputs and clicks, Ansys overlaps the crack surface with the solid CAD, splits the mesh where these intersect, buffers the elements from the new crack mesh into the existing base mesh, and voila! The finite element model crack is ready to analyze.

Representative Finite Element Mesh of Structure with Crack Inserted: Back View on Left, Top View on Right (with red line indicating part boundary) 

What About Crack Growth? 

Ansys requires no special treatment of the crack to determine the relevant fracture parameters when evaluating a crack for simple comparison to material fracture toughness. The simplicity of the Ansys workflow mirrors the simplicity of what the engineer is after, i.e., a single value for Stress Intensity Factor. Using the methods described previously, engineers can model a crack and then mesh the structure with hexahedra, tetrahedra, or a mix of element shapes and get results for Stress Intensity Factor. 

For fatigue cracks, the requirements are greater. Engineers must provide the crack growth equation constants, i.e., the Paris constants C and m, then Ansys will do the rest. Ansys’ technology for general, 3D crack growth is quite extraordinary. This technology is referred to as SMART – Separating, Morphing, and Adaptive Remeshing Technology. To put it simply, automatic remeshing occurs as the crack grows in simulation. 

Representative Crack Growth Simulation Showcasing Automated Solution Remeshing 

For a nice overview of fracture mechanics in Ansys, you can watch an on-demand webinar on DRD’s website. In the webinar, I provide a brief overview of fracture mechanics and Ansys capabilities in fracture analysis, much like this paper. I also discuss damage tolerant design, material data acquisition, and Ansys CAE simulation of cracks in structures. 

Head over to DRD’s website for two on-demand webinars I conducted in October and November, ‘Simulating Crack Propagation Part 1 and 2.’ 

https://www.drd.com/resources-all/simulating-crack-propagation-part-1-webinar-recording/ 

https://www.drd.com/resources-all/simulating-crack-propagation-part-2-webinar-recording/ 

This concludes our 3-part series on fracture mechanics. We have a few other resources engineers can dig into on this topic, including the two on-demand webinars mentioned above. DRD has a fracture mechanics training course that I teach as demand requires, https://www.drd.com/project/ansys-mechanical-fracture-mechanics/. If you are interested in this course, please let us know at support@drd.com. 

Let’s continue our discussion on fracture mechanics with this second blog post, where I dive into the methods engineers have available to evaluate cracked structures. If you’ve missed part 1 of this blog series, go back and read it here. 

Stationary, Static and Fatigue Cracks 

When evaluating a structure with cracks, engineers have a few options with respect to the level of involvement in solving the problem. From least to most involved: 

• Stationary: review of status of crack, ignoring crack growth. 
• Static: review of status of crack under single, monotonically increasing load, crack growth is assumed. 
• Fatigue: review of status of crack under cyclic loading, crack growth is assumed. 

Stationary cracks provide an instantaneous view of the state of a crack in the structure. The engineer can only know one thing from this type of analysis: will the crack grow or not. No insight is provided into the second and third of the common questions asked in the previous section. Simple closed-form solutions are available for engineers to estimate the integrity of a cracked structure, and these can be found in literature reviews and textbooks. Many closed-form solutions take the resulting stress field caused by loading, the current crack length, and an empirically determined factor to determine stress intensity. A few examples are shown here, for plate geometry of varying sizes. 

Image Source: Elementary Engineering Fracture Mechanics, 4th Ed., Broek, pg. 85 

Static cracks allow the engineer to determine if a crack will grow and fast fracture, or if the crack will arrest. Static cracks are subjected to a single, increasing load, from unloaded to fully loaded. In this case, we are not interested in a time frame for the crack to grow or arrest; ultimately, engineers simply determine if the structure will break with the presence of the crack. 

Fatigue cracks, or fatigue crack growth, is the most complex case, both for understanding and to consider when designing a product. Fatigue crack growth considers the structure under cyclic loading, where the structure is repeatedly loaded and unloaded. There are variations to this load pattern as well, which we will not go into here. 

When it comes to fatigue cracks, there are additional test procedures to determine a crack growth rate versus the applied stress intensity. Engineers will typically see this abbreviated as da/dN vs. dK, i.e., the change in crack extension (da) over cycles per extension (dN) vs. change in stress intensity (dK). Like critical fracture toughness, every material will have a different crack growth curve. Examples of some different material curves are shown here. 

Image Source: Effects of ductile laminate thickness, volume fraction, and orientation on fatigue-crack propagation in Ti-Al3Ti metal-intermetallic laminate composites, Adharapurapa et al, 2005. 

The unique aspect of fatigue crack growth that harkens back to what Griffith found is the stress levels in the structure can be much less than those that would normally cause plastic collapse. Cyclically loading the structure will continue to grow the crack, under no threat of plastic collapse, and when the maximum stress intensity factor is less than the critical fracture toughness; we call this subcritical crack growth. 

Most crack growth data focus on this subcritical crack region, however, two other regions exist. Let’s limit the data shown in the previous graph to one material’s data set and expand the representative data out; we get a graph that looks like this. 

Image Source: A review of fatigue crack propagation modelling techniques using FEM and XFEM, Rege et al, 2017. 

The material data mentioned fits into the area marked ‘Region II’; on a log-log plot of crack growth rate versus change in stress intensity, this is commonly referred to as the Paris regime, and it is generally a straight line on this plot. A simple equation is used to describe this region, which takes the form of: 

where C and m are material constants determined via the graphed data. The other two regions, I and III, refer to the threshold and fast fracture regions, respectively. The threshold region describes when the crack grows slowly, either by small stress intensity or small crack size. Conversely, the fast fracture region describes rapid crack growth, which may result in surprise failure of the structure. Engineers use this crack growth data in damage tolerance assessment. 

In both the first and second blog posts, I’ve not touched on Ansys simulation to solve fracture mechanics problems. In the next blog post, I will discuss Ansys’ capability to model cracks and solve crack growth problems. 

Before we jump into the topic at hand, I’d like to introduce myself. My name is Alex Austin, and I am the Structural Team Lead at DRD Technology, an Ansys Channel Partner. I studied Mechanical Engineering at the University of Tulsa, OK, from which I graduated with a BS and MS in Mechanical Engineering a little over a decade ago (woo… it’s already been that long!). My graduate work was in the fatigue and fracture space. My primary area of expertise is structural mechanics; as many engineers may know, this is quite a large field of physics when we look at Ansys simulation capabilities. Fracture mechanics is a small part of that overall field, is relatively new in the world of engineering, and is very complex. 

What is Fracture Mechanics? 

When engineers evaluate stress in a structure, the common, simple equation that comes to mind is stress = force/area. This equation carries several assumptions: static equilibrium, uniform cross-sectional area, uniaxial stress, to name a few. With the introduction of a crack to the structure, the state of stress at the crack tip is not uniaxial. Cracks are sharp corners, or notches. In the computer simulation (finite element) world, we call these singularities. In fact, singularities are locations where the theoretical stress is infinite. A strength of materials approach does not account for these singularities. When a crack exists, we need a method to analyze it. Fracture mechanics is that method. Fracture mechanics is the study of crack propagation in materials. 

Image Source: Wikipedia 

Motivation for Fracture Mechanics 

Often, cracks naturally form during the manufacturing process, either through casting or machining methods. Cracks can exist in a product and never cause issues with the working of the structure. In fact, cracks may be invisible to the naked eye. However, when this is not the case, what happens? 

Let’s say we’ve designed and manufactured structure that is currently out in the field, and our customer notices a crack… is this a problem? Let’s say a customer reported cracks popping up on some rotating machinery housings and they simply asked, ‘Is this a problem?’ though, the more likely case is no questions and, ‘Please fix this!!!’. What is the engineer typically tasked with determining? The common questions we ask are: 

1. Will the crack grow? If so, 

1. How quickly will the crack grow? And then, 

1. Will the structure fail catastrophically? 

As stated, the customer absolutely thinks the presence of a crack is a problem. This is commonly the case when the customer is not an engineer, and even if they’re an engineer, they had no insight into the design and manufacture of the product. Answering the above questions will directly determine if the crack is or is not a problem. 

What about the case where the engineer designs a structure and during the design process must consider a structure that has cracks? This is a common practice in regulatory bodies, namely, the FAA (Federal Aviation Administration). In this case, the engineer assumes a crack or cracks exist in the designed components and must design for this potential failure mode. This is referred to as Fatigue and Damage Tolerance. The engineer establishes inspection intervals for components based on this analysis. The maintenance crew knows how many hours the component can be used before it needs to be checked for integrity and possibly replaced. 

In the next blog post, we will discuss the methods to evaluate cracked structures. 

In many situations, we have seen customers ask for ways to output custom results from ANSYS Mechanical. The usual results like Total Deformation, Equivalent Stress or Equivalent Plastic Strain may not be enough for your needs. Depending on the requirements (say a specification you are designing a part to), you can create a User Defined Result to output the needed result. ANSYS already outputs various quantities via User Defined Results that can be viewed in the Worksheet. Here is a quick look at some of what is available:

These quantities are used to create your own results output. User Defined Results can be operated on in several ways. Here is an excerpt from the ANSYS Help documentation (Mechanical Applications > Mechanical User’s Guide > Using Results > User Defined Results > User Defined Results Expressions):

Just as a simple example, say Total Deformation is required and is not output automatically (it is, just an example). If you add an UDR to the results, then type in the expression sqrt(Ux^2+Uy^2+Uz^2), keeping in mind these expressions are case sensitive, you get to resultant deformation from all three component values. Compare this to Total Deformation.

One can also do something more complex, say safety factor calculations. If your specified safety factor is not directly related to the Yield Strength or Ultimate Strength of the material, but some factor of, an UDR can be used; constants can be created and used just like any User Defined Result in the Worksheet. An example is shown here, where a safety factor is calculated based on a value of 6,200 psi. The safety factor looks at the First Principal Stress output, computes the safety factor, then caps the display at 7. Values less than 0 psi (compression when looking at the First Principal Stress) are set to the highest safety factor allowed (7 in this case).

A small note on the equation written in the graphic, in order to display a constant value (0 or 7 in this example), it must be multiplied by the identity matrix (matrix of 1’s). If you are just using a constant for equation manipulation, the identity matrix is not required.

User Defined Results can be a powerful tool if the output from Ansys Mechanical isn’t quite tailored to your needs.

‘Restarting’ the process in ANSYS Mechanical Products by which a model is solved starting from a previously solved point. The previously solved point contains data for all nodes/elements in the model; there is no results mapping and interpolation when a restart is performed. This is the most accurate method for starting an analysis from a previously solved point.

By default, restarts are not kept when a simulation finishes. The user must modify the Analysis Settings in ANSYS Mechanical to keep the restarts points that will be needed. Those options are shown below:

Restarts do have limitations. For instance, modification of loads in a step before a restart point is to be used invalidates that restart point. Several tables in the ANSYS Help documentation characterize what happens to restart points if objects in the model tree are changed. This section can be found in Mechanical Applications > Understanding Solving > Solution Restarts, as shown.

Here’s one of the tables showing where restarts can be used followed by common questions we related to restarts.

What can solution restarts be used for?
For cases where some subset of the loads does not change and only a few loads change/vary. This is commonly referred to as load case modeling. ANSYS Mechanical FEA can do load case modeling.

Can you give an example of load case modeling?
A model that solves bolt pretension in the first several steps and then locks them in place. Commonly, service loads are applied after the bolt tightening is simulated. The service loads can represent multiple load cases, say one load case is a pressure load, another is a force load.

Another example is a ROPS (Roll Over Protection System) analysis, where loads are sequentially applied on a structure until some criteria is met (usually energy dissipated by the structure). Once the criteria are met for one load case, the load is removed and another load is applied. This process can also be done via restarts.

Why would we do this?
This saves time on solving models. Using the example above, without restarts, the bolt pretension steps would need to be solved every time a load case is added/modified. With restarts, loads can just be activated/deactivated in a step following the bolt pretension and the bolt pretension final step used as the restart point.

Things to know before attempting this method:
All of the load cases that will be solved should be known beforehand. The restart analyses require that ALL loads are defined in the initial model. In ANSYS Mechanical, loads cannot be added to the model tree without invalidating the previous results (ignoring the ability to use restarts).

Newly added loads also will not be applied in a restart analysis as the restart method does not create new elements for these new loads.

If bolt pretension is to be used, any loads defined for a load case should be applied in a step after the final bolt pretension, as usual.

Also, if bolt pretension is used, a step after the final pretension occurs IS REQUIRED. If this is not included, ANSYS assumes the last bolt pretension will be Loaded and not Locked. This means that ANSYS would modify the pretension to maintain whatever preload you have assigned, rather than applying the service loads as a working load on the bolt. Physically, it would be like tightening/loosening the bolt as the service loads are applied.

Method:
The general steps to this method are as follows:

1. Set up a model with all of the loads applied to the structure. This includes bolt pretensions and any loads that need to be simulated for the load cases. Set up the Analysis Settings as required for the analysis (multiple load steps, Large Deflections, etc.).
2. Modify the Restart Controls to keep all restart points once the model is solved.
3. Modify the loads for the load case studies to be inactive.
4. Solve the model.
5. Duplicate the analysis, sharing the Engineering Data, Geometry and Model cells. This guarantees the model setup remains the same for all models.
6. In the new system, activate the load for the first load case study.
7. Use the Tools > Read Results File… and locate the file.rst from the previously run analysis. This imports the results data into the model.
8. Modify the Restart Analysis options in Analysis Settings to restart from the end of the first simulation (the final bolt pretension loading, for example).
9. Solve the model.

Example:
The example shown here uses an oil field fluid end model with bolt pretensions applied. There are two load cases: 1) a pressure load on the cylinder bore, 2) a force load applied on one side of the fluid end body.