General Principles of Fatigue and Fracture, Part 1

The intent of this 3-part series is to expand the engineer’s understanding of the realities and opportunities in fatigue and fracture design. After reading this segment, the reader may have more questions than answers. This is not because the reader will not learn anything, but because they will better know the questions they should be asking.

Have Crack? What’s Next?

Have you ever had a crack in a structure or been called on to evaluate one? It can be rather unsettling. Cracks like the one in Figure 1 are pretty easy. We replace the segment of pipe. However, what if you have a crack like the one in Figure 2? Alternatively, the UT inspector tells you there is a crack inside a key portion of your structure that you cannot even see. Under these circumstances, the solutions become less obvious and more difficult. Complicating matters is the fact that there is nothing in the codes that guides the engineer in evaluating cracks, leaving a big hole in the engineer’s ability to assess them and provide recommendations for repair. Fortunately, there are ways to evaluate these challenges, which will be discussed in the next two articles in this series.

Figure 1

Figure 1. Rupture in a gas pipeline.

Figure 2

Figure 2. Crack in a steel truss.

It’s Complicated – and that’s OK

Embrace the complicated nature of cracks. The variables that influence fatigue and fracture behavior are truly legion. Figure 3 shows numerous inputs into fatigue and fracture design. It is certainly not complete, but it is a good start.

Figure 3

Figure 3. Inputs into fatigue and fracture design.

Fantasy vs. Reality

The greatest disservice we can do in our approach to fatigue and fracture design is to oversimplify things. Crack design is full of oversimplifications. Why? It makes the design easier – initially. Who would not like that? In the real world, the problem and solution are much more complex. Oversimplifying the problem results in the engineer missing important variables that affect performance.

By looking at the way engineer’s talk about fatigue and fracture, we see where fantasy distorts reality. The fatigue constant, Cf, is a common fixture in the fatigue design tables of the American Institute of Steel Construction (AISC), the American Association of State Highway and Transportation Officials (AASHTO) and the American Railway Engineering and Maintenance-of-Way Association (AREMA). However, it varies in each table. How can a constant have many different values? The mere fact we call Cf a constant shows we have room for improvement in the way we think about fatigue.

Two examples are illustrative of the fantasy in fatigue design. Let’s take a look at the S-N curve and the assumed crack in an eyebar.

Figure 4

Figure 4. Scatter in fatigue data.

S-N Curve

The textbook stress-number of cycles (S-N) curve is nice and smooth and comes complete with a threshold for steels. However, when we look at the test data represented in Figure 4, we see scatter – lots of it. Fantasy is a simple curve; if we keep our stresses low enough, we do not ever have to worry about cracks. Reality tells us there will be outliers that lead to cracks.

Figure 5

Figure 5. Assumed and actual crack locations in an eyebar.

Eyebar

The assumed crack location in an eyebar is at the pin, perpendicular to the bar length, illustrated in Figure 5. This makes a lot of sense and is a great place to start. However, if we only looked for cracks at the assumed location, we might miss all the other cracks. Reality shows us cracks do not just occur where we expect them to. Why? Let’s get into that.

Why Complicated?

So why is it so complicated? Mother Nature. Seriously.

Materials are not perfect, environments are not benign, and loads are never what we think. More specifically, the following profoundly affect crack formation, growth, and critical size:

  • Size
  • Location
  • Detailing
  • Grain Structure
  • Residual Stress
  • Corrosion
  • Load spectrum

These parameters are where many of the outliers originate. Laboratory testing simply cannot pick up all the variables that a structure will experience. This is unsettling if all we have available is a chart that tells us our structure will live forever if our stress is low enough.

So what should the design engineer do?

First, come to terms with the reality that cracks are complicated. As the engineer embraces all the parameters, it will become clear what is important and what needs additional attention. Second, use improved tools such as fracture mechanics to quantify the problem better. Third, use realistic material testing. Fourth, inspect. At some point, get out in the field and look at the problem. Observing the problem first-hand is the only way to know what is going on.

Finally, embrace the vast array of knowledge that is available. To this point, Pellini, while at the Naval Research Labs stated:

In summary, the present trends in fracture research emphasize an ever-increasing sophistication in the treatment of the problem – building upon rather than eliminating past knowledge. The great variety of fracture research evolves from the need for attention to widely different problems which have special features. Therefore, the engineer should not expect that fracture-safe design should ultimately evolve to a single generalized procedure, but rather to a variety of procedures that overlap and integrate into a coherent pattern. (Pellini 1969, p. 87)

More than a nice quote – it is wisdom for the ages.

Crack Growth Basics

Crack Growth Phases

Getting into some specifics, consider the following four stages of crack growth: nucleation, short and long growth, and final instability.

The first three phases are shown in Figure 6. The nucleation phase is the period required for a crack to form. Next, the short crack path depends heavily on grain structure, and often described as “tortuous”. The long crack phase is smoother, larger, and less influenced by grain structure. Final instability is often fast fracture, with the crack moving at the speed of sound in the material.

Figure 6

Figure 6. Crack growth phases.

Crack Modes

There are three modes of crack loading: opening (Mode I), sliding (Mode II), and tearing (Mode III). In Mode I, cracking is characterized by stresses and displacements normal to the crack surfaces. In-plane shearing stresses with associated crack displacements in the plane of the crack, and perpendicular to the crack leading edge, produce Mode II cracking. Mode III cracking is caused by out-of-plane shear with displacements also in the plane of the crack, but parallel to the crack front.

Crack Growth Mechanisms

While fracture mechanics is interested in dealing with the critical crack size and how fast a crack will reach this size, it tells us nothing about how the crack originated. Without understanding how the crack formed, one can only superficially deal with the crack. However, when the processes of cracking (the physics of failure) are understood, the crack can be treated in a holistic manner. This results in a safer, more reliable structure.

A broad range of mechanisms cause cracks and influence a crack’s potential propagation and propagation rate. Figure 3 lists many of the factors that affect both crack nucleation and growth. As seen from the table, the causes of cracks and influencing factors on propagation are intermingled. Focusing on one variable, as is so often the case with stress, and not considering other factors will likely result in a design that is unconservative, possibly by orders of magnitude.

Constraint

We hear from seasoned engineers to avoid over-welding joints. Why? It certainly has an economic and environmental impact, but, more importantly, it reduces constraint. Reduced constraint increases toughness and energy absorption.

Constraint refers to the materials inability to deform because the surrounding material restrains it. When a material is constrained, a tensile stress is created in both directions perpendicular to the applied stress (Y and Z directions if X is in the direction of applied stress) due to Poisson’s effect, illustrated in Figure 7. Triaxial stress states reduce the principal shear stresses in materials. This, in turn, diminishes plastic deformation, which occurs on planes of principle shear stress due to slip. To come full circle, the reduction in a materials ability to plastically deform reduces its toughness, or ability to absorb fracture energy.

Figure 7

Figure 7. Triaxial stress states due to a notch.

Fracture Toughness

Toughness is to the boxer as strength is to the weightlifter. Toughness is a measure of the amount of abuse a material can take. More technically, fracture toughness measures crack resistance.

Figure 8

Figure 8. Conceptual material property variation with change in size (source: Introduction to Structures, P. W. McMullin, J. S. Price, 2016, Routledge).

Toughness Trends

Fracture toughness and all structural properties are influenced by size. As size increases, toughness – and strength, stiffness, and stability – decrease, as shown in Figure 8. As we move from a test specimen to component test to full-scale performance, there is a general trend of decreasing properties.

Unique to fracture toughness, as the material gets thicker, the toughness decreases. After a certain point, the toughness remains the same – known as the plane strain fracture toughness.

Toughness is also highly influenced by temperature. Figure 9 shows the transition curves for a Charpy and Dynamic Tear Test. As temperature decreases, so does fracture toughness. Note how the test type changes the location of the curve. The curve to the right is a 1-inch thick specimen, while the Charpy curve is based on the standard one-half inch thick specimen. If the material was ½-inch thick and relied on the Charpy test, we would grossly miss the actual transition temperature. This was the case in the Liberty Ship failures during World War II.

Figure 9

Figure 9. Temperature and specimen size effect on fracture toughness (source: Principles of Structural Integrity Technology, 1976, Office of Naval Research).

Finally, strain rate affects fracture toughness. As the strain rate increases, the toughness decreases. It is worth considering this for impact type loads.

Toughness Tests

Characterizing fracture toughness is key to good fracture design. We will briefly look at Charpy, Drop Weight Tear, and Fracture Mechanics type tests.

The reader may remember the Charpy test from mechanics lab where a ½-inch thick specimen is notched in the middle and a weight swings through it. The amount of energy the specimen absorbs is the toughness. Charpy tests should only be used for quality control, not a direct correlation to structures with a thickness greater than ½-inch thick.

Fracture Mechanics type tests take us from general correlations to direct analysis of crack behavior. The most common specimen is the plane strain, compact test specimen that determines KIc. To conduct this test, the specimen is pre-cracked so that it reflects the conditions of an actual crack. Then the specimen is loaded until the crack unstably propagates. Using a stress-intensity solution, we can calculate the fracture toughness and then apply it to design.

This article has introduced some fundamental concepts in fatigue and fracture design. Hopefully, the reader is beginning to develop some questions. The next article presents details of AISC and Fracture Mechanics-based fatigue design.▪

About the author  ⁄ Paul W. McMullin, Ph.D., S.E.

Paul McMullin, Ph.D., S.E. is a Founding Partner at Ingenium Design in Salt Lake City. He is an Adjunct Professor and the lead editor of the Architect’s Guidebooks to Structures series. Paul can be reached at Paulm@ingeniumdesign.us.

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