ASTM’s Symposium on Structural Integrity of Additive Manufactured (AM) Parts was held in the first week of November in Washington, DC. Being part of ASTM’s Committee Week, the symposium was sponsored by a number of ASTM Committees (F42 – Additive Manufacturing Technologies; E08 – Fatigue and Fracture; E07 – Nondestructive Testing) as well as national and international partners (NASA, NIST, European Structural Integrity Society, among others). Interest in this year’s AM symposium was so enthusiastic, ASTM needed to secure a larger venue and additional lodging to accommodate the 150+ attendees. As such, the symposium was held nearly a mile away from the main ASTM standards development meetings…and as anyone who has had to endure downtown D.C. traffic can attest, that’s a tough mile!

Over the three days of the meeting there were a number of very interesting presentations, as well as panel discussions on how AM is impacting nondestructive testing, medical device manufacturing, and the aerospace industry. VEXTEC’s symposium topic (“Probabilistic Computational Fatigue and Fracture Modeling of AM Components”) differed from the majority of presentations. ASTM’s focus on testing and test methods was reflected in most of the speakers’ content; few discussed the emergent issue of how to rapidly certify components manufactured using AM processes. VEXTEC’s VPS-MICRO® software, our virtual tool for evaluating material and component durability, efficiently uses probabilistic techniques to provide users with effective virtual supplements to physical testing of metallic components. This can have a large beneficial influence on the time and resources required for certification of these challenging AM technologies for critical-use applications.

VEXTEC looks forward to our current work in AM being included in a peer-reviewed ASTM Special Technical Publication (STP 1620) that is due to be published in the next year.

The history of customization is as ancient as the history of design. And there are three principles that have governed the need for customization – form, fit and function. Intimately intertwined with this quest for customization is the history of material development – mud, stone, wood, concrete, steel, superalloys, composite materials, ceramics, and so on. Keeping pace with these new materials has been the maturation of their manufacturing processes – for metals these include casting, forging, molding and now Additive Manufacturing (AM), which is the focus of this blog series.

Simply put, AM is an umbrella term that describes a “layer-by-layer” deposition process used to build an item, typically accomplished by a 3D Printing machine and a CAD model of the item. Depending on the industry and the raw materials used, the processing methods have specific nomenclature. For metals, Direct Metal Laser Sintering (DMLS) – and closely-related processes Selective Laser Sintering (SLS) and Selective Laser Melting (SLM) – have gained popularity since the mid-1990s, becoming particularly more sophisticated in this decade. Techniques such as these hold the promise of revolutionizing current paradigms in engineering design, manufacturing, and performance. Imagine: building components that are lighter-weight (form), geometrically-complex (fit), and structurally-equivalent/superior (function), all at a faster pace and with a smaller factory footprint. The Holy Grail is within our grasp, right? Well…not so fast.

To fully realize the potential of AM, significant advances are needed in both the process and performance modeling of additively manufactured materials and structures. The simulation of AM from “cradle to grave” is multidisciplinary in nature, involving multiple physics as well as multiple time and space scales. Interdisciplinary research efforts are therefore required in order to fully understand how everything fits together. Fortunately, the digital architecture of AM affords the possibility of efficiently integrating computational modeling with real-time measurements taken during the build process itself.

While AM as a technique might be new, it is being applied to traditional alloy chemistries. If you take the same alloy and run it through a selection of conventional processes (such as casting, forging, welding, heat treating), each path will give you a different microstructure. This, in turn, drives different performance properties (static strength, fatigue strength, etc.). The AM process creates its own signature in the material; any combination of changes in machine settings (laser power, scan speed, hatch spacing, layer thickness, etc.) will influence the resulting microstructure. Regardless of the manufacturing method, the mandate to produce a robust product with high reliability remains the same. And some of the unique challenges of AM, like finding those optimal machine settings, underscore the need for effective modeling of microstructural variability.

The physics-based probabilistic tools in VEXTEC’s VPS-MICRO® software, which are successfully predicting durability of conventionally-manufactured products, is being adapted at the microstructural level to meet AM head-on. In the second part of our blog series, we’ll show you how VEXTEC’s technology is being used in the cutting-edge world of additive manufacturing.

This is the first installment of a new blog series on the physics of fatigue.  It has been adapted from the upcoming Ph.D. dissertation of VEXTEC’s Robert McDaniels.

Fatigue can best be considered as a process, rather than an event [1, 2].  The fatigue process begins as soon as a component is manufactured and enters service, and proceeds through the life of the component in stages. From the perspective of modeling and simulation, there are 4 stages of the fatigue life of a component:

• crack nucleation: the number of fatigue cycles required to create a crack that spans one grain in a previously un-cracked specimen;
• short crack growth: the number of fatigue cycles required to grow a crack from the crack-nucleated grain until the crack is long enough to be modeled by bulk properties;
• long crack growth: the stage of life when bulk properties can be assumed and conventional linear elastic fracture mechanics (LEFM) is valid; and
• final overload: the stress intensity factor of the component exceeds the plane-strain fracture toughness of the material, and the component fails catastrophically in one additional cycle [2].

The total fatigue life of a component (N_f) can be represented as the sum of the nucleation life (N_n), the short crack growth life (N_sc), the long crack growth life (N_lc), and the final overload cycle:

N_f= N_n + N_sc +N_lc +1

For any given alloy system, the relative fraction of a component’s life that is spent in each stage is controlled by the microstructure of the alloy, the geometry of the component, environmental factors (such as corrosion) and the load history of the component in question.

The Mechanisms of Fatigue Crack Nucleation

While there are as many different types of nucleation mechanisms as there are different types of microstructures, they can all be placed in a few broad categories:  fatigue crack nucleation in a material that is free of gross defects (like inclusions), and fatigue crack nucleation in a material that contains gross defects or defect-like features, like notches [3, 4].

For ductile materials (like face centered cubic [FCC] metals) without defects, cyclic stresses generate dislocations that move due to irreversible slip [3-6].  After continued cyclic loading, these dislocations tend to migrate and pile-up in structures known as persistent slip bands (PSBs). When PSBs migrate to the surface of a ductile metal, a series of extrusions and intrusions are formed.  These extrusions and intrusions become stress risers where cracks will eventually nucleate. Figure 1 is a transmission electron microscope (TEM) image that shows dislocation pile-ups that have accumulated to form PSBs [7, 8].   Figure 2 shows a schematic drawing that illustrates the formation of extrusions [5, 7].  Figure 3 shows two images of single crystal copper that have been cyclically loaded. There are PSB protrusions from the polished surface of the specimen, and there are also fatigue cracks that have nucleated and are about 5 micrometers long [9].  This is the nucleation mechanism that is most prevalent in FCC metals like copper (Cu), nickel (Ni), and aluminum (Al).

High strain materials, like pure alpha-iron (Fe) and other body centered cubic (BCC) metals, and hexagonal close packed (HCP) metals like titanium (Ti), display a somewhat different nucleation mechanism without defects [10, 11].  In these metals, dislocation motion is restricted, due to the lower number of easy slip systems that are available for these crystal structures.  Consequently, PSBs are much less likely to form, and cracks instead tend to nucleate at grain boundaries where there is strain incompatibility between adjacent grains [10, 11].

The third type of fatigue crack nucleation is crack nucleation at defects [10, 11].  These defects can take a number of different forms: non metallic inclusions, second phase particles, notches, pores, etc.  This mechanism is much more localized, due to the increased stress in the region around the defect due to its stress concentration. Cyclic loading can cause de-bonding between the defect and the matrix, or cracking of the defect itself [10, 11]. In aluminum alloy (AA) 7075-T651, a common aerospace alloy, there is a very large fraction of Fe-containing second phase particles. These particles are more prevalent at grain boundaries, and are of the same length scale as the grains in the L-S plane (which is the plane that has the slowest fatigue crack growth rate).  These particles come in many shapes and sizes, and most of them are already cracked after the T-651 strain aging heat treatment to which this alloy is subjected during initial processing.  Figure 4 shows two SEM images from a VEXTEC study of AA 7075-T651.  The images were taken from a specimen before fatigue testing began.  There are many observed cracks in the particles, and the representative crack length is nearly 10 micrometers.  This result has also been reported by others [8-20] and is found to be true for all 7XXX series and 2XXX series aluminum alloys.  It can therefore be assumed that components made from these aerospace alloys already contain cracks when they are manufactured, and therefore the fatigue crack nucleation life is zero. This is an important determination when it comes to fatigue life prediction, as well as evaluation of these materials’ capacities for damage tolerance.

 

References

1. ASTM E 1823-13, “Standard Terminology Relating to Fatigue and Fracture Testing.” ASTM, (2013).
2. ASM HANDBOOK Vol 19 Fatigue and Fracture. ASM International. pp. 3-5. (1996).
3. Suresh, S. Fatigue of Materials. pp. 132-162. (1998).
4. ASM HANDBOOK Vol 19 Fatigue and Fracture. ASM International. pp.48-58. (1996).
5. Dieter, G. Mechanical Metallurgy. pp. 394-398. (1986).
6. Bannantine, J. Fundamentals of Metal Fatigue Analysis. pg. 244 (1990).
7. ASM HANDBOOK Vol 19 Fatigue and Fracture.  ASM International. pp.76-86. (1996).
8. Mughrabi, H., Ackerman, F. and Herz, K. “Persistent Slip Bands in Fatigued Fac-Centered and Body Centered Cubic Metals”, Fatigue Mechanisms, ASTM STP 675. pp.69-105. (1979).
9. Ma, B., and Laird, C. “Overview of Fatigue Behavior in Copper Single Crystals –I. Surface Morphology and Stage I Crack Initiation Sites for Tests at Constant Strain Amplitude”. Acta Metallurgica. Vol. 37, no 2. pp. 325-336. (1989).
10. Suresh, S. Fatigue of Materials. pp. 79-83. (1998).
11. ASM HANDBOOK Vol 19 Fatigue and Fracture. ASM International. pp. 96 -107 (1996).
12. ASM HANDBOOK Vol 19 Fatigue and Fracture. ASM International. pp. 153-158 (1996).
13. Kung, C.Y., and Fine, M.E. Fatigue crack initiation and microcrack growth in 2024-T4 and 2124-T4 aluminum alloys, Metallurgical Transactions A 10, 603-610 (1979).
14. Laz, P.J., and Hillberry, B.M. Fatigue life predicted from inclusion initiated cracks, International Journal of Fatigue 20, 263-270 (1998).
15. Merati, A. A study of nucleation and fatigue behavior of an aerospace aluminum alloy 2024-T3, International Journal of Fatigue 27, 33-44 (2005).
16. Weiland, H., Nardiello, J., Zaefferer, S., Cheong, S., Papazian, J., and Raabe, D. Microstructural aspects of crack nucleation during cyclic loading of AA 7075-T651, Engineering Fracture Mechanics 76, 709–714 (2009).
17. J., Hochhalter, J.D., Veilleux, M.G., Liu, M., Heber, G., Sintay, S.D., Rollett, A.D., Littlewood, D.J.,Maniatty, A.M., Weiland, H., Christ Jr., R.J., Payne, J., Welsh, G., Harlow, D.G., Waeryzynek, P.A., and Ingreffea, A.R.. A geometrical approach to modeling microstructurally small fatigue crack formation, part I: probablilistic simulation of constituent particle cracking in AA 7075-t651, Modeling Simulation Materials Science 16, 065007, 28 pp (2008).
18. Patton G., Rinaldi C., Bre´chet Y., Lormand, G., and Fouge`res, R. Study of fatigue damage in 7010 aluminum alloy, Materials Science and Engineering A 254 (1998).
19. Pearson, S. Initiation of fatigue cracks in commercial aluminum alloys and the subsequent propagation of very short cracks, Engineering Fracture Mechanics 7, 235-247 (1975).
20. Line, K., McDaniels, R., Pulikollu, R., and Tryon, R. Crack Nucleation Prediction through Surface Roughness Measurement, Phase II, VEXTEC Corp., Brentwood, Tenn., proposal to Defense Advanced Research Projects Agency (DoD). 2009.
21. Wood, W.A. Formation of Fatigue Cracks. Philosophical Magazine 3, no. 31, 692-699 (1958).

A turbocharger client of ours wanted to improve durability and reduce warranty costs on cast wheels made from a nickel superalloy with a radially-solidified (RS) microstructure. A significant portion of their previous field failures had been attributed to high cycle fatigue (HCF). Our client already had ideas about how to reduce these HCF failures by changing the wheel’s microstructure to an equiaxed (EQ) morphology. General representations of RS and EQ microstructures are shown here.

Since design changes like these would require a hefty amount of physical validation testing, they needed a way to predictively quantify the costs/benefits to the product line, should some of these proposed changes be implemented. So they turned to VPS-MICRO®. The VPS-MICRO simulation platform combines structural finite element analysis of the component (FEA, seen below) with a 3-D spatial model of the material’s microstructure to predict component durability risk. It is a probabilistic framework, accounting for variability in microstructure and strength properties, applicable damage mechanisms, and usage over time.

The primary inputs to VPS-MICRO are the design input file (stresses from the FEA and the corresponding stressed area in terms of elemental surface area) and the material input file. VEXTEC has developed plug-ins to extract the design input information from several commercial FEA software programs. The material input file contains all the relevant material properties of the component, from macro-scale to the microstructural level. These properties include those you would normally find in an FEA analysis (material modulus and Poisson’s ratio), but also microstructural properties such as grain size, population density of variously-sized inclusions/defects, and grain-level strength and energy parameters. It is the inherent variability of these microstructural properties that is a key factor of component-level fatigue life variability. The good news is that these properties can be statistically evaluated using industry standard (ASTM) tests.

Now, back to our client’s specific issue. Their RS material microstructure was originally developed to resist the onset of damage at high temperatures. The likelihood of initiating damage is low due to fewer grain boundaries. However once damage initiates, the failure probability goes up because there aren’t as many grain boundaries to arrest crack growth. Their proposed design change, using an equiaxed (EQ) microstructure instead for the turbocharger wheels, was thought to be more damage tolerant. The likelihood of initiating damage would be higher, but so would the opportunity for fatigue crack arrest (more grain boundaries). Using VPS-MICRO, our client was able to pursue a quantitative assessment of the risk of HCF failure versus grain type (radially-solidified vs. equiaxed), before any re-designed wheels were even produced or tested.

Shown below is the VPS-MICRO simulated fatigue life comparison of the current-state RS wheel, and the proposed EQ wheel (baseline average grain size = 2.7 mils). The comparison results are presented using a simulated S-N (Stress-Life) plot. The figure shows considerable variability at each stress level for both materials. Run-outs (the points on the right marked with arrows) are predicted at every stress level. A “run-out” means the simulated specimen did not fail within the number of cycles analyzed. These results indicate the RS wheel would have a lower endurance (fatigue limit) compared to the baseline EQ wheel. Generally speaking, this would seem to indicate that the EQ material is better than the RS material. These results appeared to correlate with published industry reports.

Because the wheel was a casting, there is an expected grain size variation throughout the part. Our client’s quality group thought they could maintain the EQ grain size between 1.7 and 3.8 mils, but acknowledged that sizes as high as 15 mils could occur. So they used VPS-MICRO in a different way: to evaluate the sensitivity of grain size to the risk of wheel failure. Their virtual analysis revealed that EQ wheels are not always better than RS wheels.  The figure below shows that failure probability is low for small EQ grains, but is very sensitive to grain size.  At a grain size of 15 mils, the EQ wheel is actually more likely to fail than the RS wheel (which has an average grain size of 87 mils). Probability of failure is not as sensitive to grain size for the RS wheel. Did the reversing trend make sense?

VEXTEC and our turbocharger client investigated this relationship between the grain size and HCF failure risk. After analyzing the output of the VPS-MICRO simulations, we determined that competing failure mechanisms were present:

• The area effect: it takes more small-sized grains to fill a given surface area compared to fewer, larger grains. A smaller average grain size means a statistically-higher probability of having a weaker grain in a given area. This is analogous to the “weakest link theory“, where increasing the number of links in a chain increases its probability of failure. This explains why larger grains are producing fewer failures compared to small grains (the downward trend of the figure above).
• The grain-level strength effect: as the grain size increases, an initiating fatigue crack has a larger size as well. These larger-sized starter cracks are more likely to grow (with minimal arresting) to final failure. Therefore, the local strength properties of the grains become key gatekeepers to either prevent or allow these cracks to propagate from their initial sizes.

The final conclusions reached by our client, with the assistance of VPS-MICRO, were

• Using EQ material (2.7 mils) would reduce turbocharger wheel HCF failures by at least 60%
• Not all EQ materials are equal; small changes in grain size yield large changes in durability
• The probability of wheel failure was not as sensitive to grain size for the RS material
• Replacing RS material with EQ material requires significantly-tighter production control

Our client could now make a more-informed decision about the proposed design change (producing and testing the EQ wheel). They knew they would have to cast the wheel in a production environment to capture realistic variations, and to assess their capability to hold tighter tolerance on grain size than what was previously required on the RS wheel.

We’ve said it before, and we’ll say it again:

This is the final installment of a four-part series on the history of fatigue analysis.  It has been adapted from the upcoming Ph.D. dissertation of VEXTEC’s Robert McDaniels. You can read Part 1 here, Part 2 here, and Part 3 here.

The 1950’s brought another of the seminal events in the history of fatigue.  The world’s first commercial airliner, the DeHavilland Comet, suffered a series of catastrophic crashes in 1953-1954 that resulted in the deaths of all of the crew and passengers [3, 16-18].   After a thorough investigation that included both the analysis of recovered aircraft, and the testing of an entire aircraft that simulated the pressurization and depressurization of the entire aircraft during flight, it was determined that the cause of the mishaps was fatigue cracks that had originated in rivet holes near the square portholes in the fuselage [3].  The cause of the crashes was found to be the stress concentration factor of the corners of the square portholes, along with the procedure used to manufacture the holes [3, 16-18].  The year 1954 saw two researchers, S.S. Manson and L.F. Coffin, simultaneously determine that fatigue damage is always the result of plastic strain [3, 6], which advanced the study of low-cycle fatigue, and led to the fatigue analysis model that bears their names.  The mechanisms of fatigue crack initiation that are now commonly understood were first proposed and identified in the late 1950’s by W.A. Wood [19, 20].

In 1957, George Irwin extended the previous work of Alan Griffith to include ductile materials, such as metals, using linear elastic fracture mechanics [3].  Irwin also introduced the concept of the Stress Intensity Factor [6, 14].  The pioneering work of Griffith and Irwin was fulfilled in 1961, when Paul Paris developed the fatigue crack growth law which bears his name [3, 6].  This revolutionized the field of fatigue research and analysis because it allowed engineers to analyze and assess the growth of cracks with only a knowledge of the far-field stresses and the material geometry [3]. Also in 1961 was the observation by P.J.E. Forsyth that fatigue crack growth can be divided into 2 separate phase, which he called Stage I and Stage II. [21]

The fledgling field of fracture mechanics research was further advanced in 1970, when Wolf Elder introduced the concept of crack closure [6].  In crack closure, the rate of fatigue crack growth is reduced due to the fact that the crack tip is wedged open by surface roughness in the fracture surface in the wake of the crack tip, or another mecanism, such as corrosion, or plastic deformation [3, 6].  A series of aircraft mishaps in the late 1960’s caused the study of fracture mechanics to gain new followers in the USAF [6], when an F-111 aircraft suffered a mishap after only 100 hours of flight due to a crack in the wing structure. The USAF then embarked on an extensive program to improve the durability of its aircraft structures [6].   The outcome of this program was a new set of specifications for all structural metals in the “Damage Tolerance Design Handbook”, and a series of conferences on “Structural Integrity” that have been held regularly since the 1980’s [6].  As a continuation and expansion of that work, the Defense Advanced Projects Development Agency (DARPA), a research organization within the Department of Defense (DoD), created a program called the Structural Integrity Prognosis System (SIPS).  The purpose of SIPS was to develop better ways to predict the fatigue durability of complex aviation structures.  VEXTEC was one of the companies that participated in the SIPS program [22-24].

The next significant contribution to fatigue research came in 1968, when Tatsuo Endo and M. Matsuishi first introduced the concept of rainflow counting [6, 19, 25, 26].  This would lead to another direction of research, which concentrated on variable loading, and the effects of the sequencing of loads, through such concepts as power spectral density, which expand on the work that resulted in Miners’s rule [6].  Another avenue of research that arose in the late 1970’s was the idea of multi-site fatigue damage, which is now called widespread fatigue damage [6].  This work took on new importance in 1988 after the mishap of Aloha Flight 243 [27].  In this incident, a Boeing 737 suffered a casualty in which a large section of the fuselage separated during flight, which resulted in the death of a flight attendant [27].  The investigation revealed that cause of the incident was multiple site fatigue damage in the skin panels near rivet holes at a lap joint [27].

This is not the end of the story of fatigue research.  In fact, this blog series has only illustrated the most historically-significant contributions that have been made in since Wilhelm Albert reported his first observations in 1838 [5, 6].  A brief search in a database of academic papers yields over 34,000 papers written on topics related to fatigue, nearly 17,000 of those being written just since the year 2000.  This illustrates the expanding interest in the many aspects of fatigue research, and the accidents and mishaps described in this short history demonstrates the importance of continuing this research, and how much more work needs to be done in this field.  As demands of fuel efficiency and environmental concerns increase, the need for lighter structures to carry more weight will put tremendous pressure on engineers and operators of all types of vehicles to design and maintain components that operate more economically, while simultaneously being safer.

REFERENCES

1. Turnbull, H.W. ed., The Correspondence of Isaac Newton: 1661-1675, Volume 1, London, UK: Published for the Royal Society at the University Press. p. 416 (1959).
2. “Wilhelm Albert”, Wilhelm Albert. Wikipedia. created 06 February 2016, accessed 31 Dec 2016.
3. Suresh, S. Fatigue of Materials. pp. 1-11 (1998).
4. Hansson, T.J. “Fatigue Failure Mechanisms and Fatigue Testing” NATO Science and Technology Organization Educational Notes. EN-AVT-207-14 (2012).
5. Albert, W. A. J. “Über Treibseile am Harz” Archive für Mineralogie Geognosie Bergbau und Hüttenkunde, vol. 10, pp. 215-34 (1838).
6. Schutz, W. “A History of Fatigue,” Engineering Fracture Mechanics, vol. 54. No. 2, pp. 263-300 (1996).
7. Bhat, S. and Patibandla, R. “Metal Fatigue and Basic Theoretical Models: A Review,” Alloy Steel -Properties and Use. Dr. Eduardo Valencia Morales, ed. (2011).
8. Mitchell, M.R. Fatigue, ASM Handbook, Vol. 19, 554-555. Materials Park, Ohio (1996).
9. Timoshenko, S.P. History of the Strength of Materials. pp. 162-173 (1983).
10. Bathias, C., and Pineau, A. Fatigue of Materials (2010).
11. “The Versailles Rail Accident,” Versailles Rail Accident. Wikipedia. Created 22 November 2016, accessed 31 Dec 2016.
12. ASM HANDBOOK. Vol 19, Fatigue and Fracture.  ASM International. pp.76-86 (1996).
13. “August Wohler,” August Wohler. Wikipedia. Created 21 October 2016, accessed 02 January 2017.
14. ASM dictionary, ASM International. p. 454 (1992).
15. “Sir James Alfred Ewing,” Sir James Alfred Ewing. Wikipedia. Created 05 August 2016, accessed 29 January 2017.
16. “de Havilland Comet,” de Havilland Comet. Wikipedia. Created 26 January 2017, accessed 28 January 2017.
17. “BOAC Flight 781,” BOAC Flight 781. Wikipedia. Created 09 January 2017, accessed 28 January 2017.
18. “South African Airways Flight 201,” South African Airways Flight 201. Wikipedia. Created 05 January 2017, accessed 28 January 2017.
19. Suresh, S. Fatigue of Materials. pp. 132-162 (1998).
20. Dieter, G. Mechanical Metallurgy. pp. 394-398 (1986).
21. Bannantine, J. Fundamentals of Metal Fatigue Analysis. pg. 244 (1990).
22. Papazian, J., Agnagnostou, E., et al. Structural Integrity Prognosis System (SIPS) Final Report. Northrup Grumman Corporation (2009).
23. Line, K., McDaniels, R, Pulikollu, R, Tryon R. Crack Nucleation Prediction Through Surface Roughness Measurement Phase I Final Report. VEXTEC Corporation (2008).
24. Tryon, R., McDaniels, R., Oja, M., Matthews, R.  Crack Nucleation Prediction Through Surface Roughness Measurement Phase II Final Report. VEXTEC Corporation (2011).
25. Hertzberg, R.W. Deformation and Fracture Mechanics of Engineering Materials. pp. 570-572 (1996).
26. Bannantine, J. Fundamentals of Metal Fatigue Analysis. pp. 189-196 (1990).
27. National Transportation Safety Board Summary Report on Aloha Flight 243 (June 14, 1989).

This is the third of a four-part series on the history of fatigue analysis.  It has been adapted from the upcoming Ph.D. dissertation of VEXTEC’s Robert McDaniels. You can read Part 1 here, Part 2 here, and Part 4 here.

The beginning of the 20^th century saw the introduction of metallurgy to the study of fatigue. In 1903, Sir James Alfred Ewing and his colleagues in Scotland were the first to observe and describe slip bands.[3, 6, 15]  Ewing also invented the term “hysteresis.”[3, 6, 15]  While his discovery was initially limited to electromagnetism, it was later extended to many other phenomena, including mechanical fatigue.  The idea of dislocations was first introduced by Michael Polyani in 1934.[6]  Another important discovery in the analysis of fatigue data was made by Olin Basquin in 1910, when he observed that when fatigue data (in terms of stress and number of cycles to failure) is plotted in log space, there is a linear relationship between stress and fatigue life over a large range of stress.[3]  Work and study into fretting fatigue was begun by E.M. Eden and his colleagues in 1911.[3]

The period from the 1920’s through the 1940’s saw rapid growth in the field of fatigue research.[3]  The first book devoted to the study of fatigue, “The Fatigue of Metals” was published by Herbert Gough in 1924 in the U.K. and another book with the same title was published by Herbert Moore and Jesse Kommers in the U.S. in 1927.[3, 6]  The influence of surface roughness on fatigue life was first discussed in Gough’s book.[6]  Also in this period, the effects of corrosion and heat treatment on fatigue behavior were first studied.[3]  The study of fracture mechanics, which describe the physics and mathematics behind the growth of cracks in brittle solids, was begun by Alan Griffith in 1920.[6]

The next major advance in the statistical treatment of fatigue data occurred with the work of Waloddi Weibull in the late 1930’s.[6]  The first damage accumulation model was proposed by Arvid Palmgren in 1924, then extended and improved by M.A. Miner in 1945.[3, 6]  During the period of 1924-1956, one of the most important contributors to fatigue research was August Thum.  He authored or co-authored over 500 papers on nearly every aspect of fatigue, including:  stress-concentration factors, the effects various factors on the fatigue limit of metals, the effect of heat treatments on fatigue, corrosion fatigue, fretting fatigue, fatigue at cryogenic temperatures, welded joints, and many other diverse aspects of fatigue.[6]

References

1. Turnbull, H.W. ed., The Correspondence of Isaac Newton: 1661-1675, Volume 1, London, UK: Published for the Royal Society at the University Press. p. 416. (1959)
2. “Wilhelm Albert”, Wilhelm Albert.Wikipedia. created 06 February 2016, accessed 31 Dec 2016.
3. Suresh, S. Fatigue of Materials. Pp. 1-11. (1998).
4. Hansson, T.J. “Fatigue Failure Mechanisms and Fatigue Testing” NATO Science and Technology Organization Educational Notes. EN-AVT-207-14. (2012)
5. Albert, W. A. J. “Über Treibseile am Harz” Archive für Mineralogie Geognosie Bergbau und Hüttenkunde, vol. 10, pp 215-34 (1838)
6. Schütz, W. “A History of Fatigue,” Engineering Fracture Mechanics, vol. 54. No. 2 pp 263-300 (1996).
7. S. Bhat and R. Patibandla. “Metal Fatigue and Basic Theoretical Models: A Review”, Alloy Steel -Properties and Use, Dr. Eduardo Valencia Morales (Ed.), (2011).
8. Mitchell, M.R. Fatigue, ASM Handbook, Vol. 19., 554-555. Materials Park, Ohio. (1996).
9. Timoshenko, S.P. History of the Strength of Materials. Pp. 162-173. (1983).
10. Bathias, C., and Pineau, A. Fatigue of Materials.,  (2010)
11. “The Versailles Rail Accident”, Versailles Rail Accident. Wikipedia. Created 22 November 2016, accessed 31 Dec 2016.
12. ASM HANDBOOK Vol 19 Fatigue and Fracture.  ASM International. pp.76-86. (1996).
13. “August Wöhler”, August Wöhler. Wikipedia. Created 21 October 2016, accessed 02 January 2017.
14. ASM dictionary, ASM International. pg,. 454. (1992)
15. “Sir James Alfred Ewing”, Sir James Alfred Ewing. Wikipedia. Created 05 August 2016, accessed 29 January 2017.

This is the second of a four-part series on the history of fatigue analysis.  It has been adapted from the upcoming Ph.D. dissertation of VEXTEC’s Robert McDaniels. You can read Part 1 here, and Part 3 here.

While early and important work was being done by Wilhelm Albert, Jean-Victor Poncelet, William Rankine, and other researchers in the growing field of fatigue in the 1800’s, by far the most influential person at the beginning of the systematic study of fatigue was August Wöhler.  His influence on early fatigue research is so great that an entire section of Walter Schutz’s paper on the history of fatigue [6] and an entire section of Stepan Timoshenko’s book “History of Strength of Materials” are dedicated to Wöhler’s work [9].  Wöhler was a railroad engineer who worked his way from the machine shop manager to the head of all rolling stock and machine shops of the railroad in Frankfurt, Germany [9, 13].   During his long and influential career he established materials specifications for the metals that were used in railroad applications, fostered the creation of a network of material testing laboratories in Germany, and standardized those labs’ testing and reporting procedures [9].  He also designed and built many different types of fatigue testing machines, and performed many different types of tests [6].  He was the first to understand the importance of both stress amplitude and mean stress on the fatigue life of components [6].  He differentiated between safety factors for components that had finite-design lives and components that were designed for infinite life [6].  Wöhler was also the first researcher to seriously consider the effect of residual stresses on fatigue [9].  He also published the results of his rotating bend fatigue test results in tabular form, and he is generally credited as the originator of the concept of the “endurance limit” [3].  His influence was so great that many years later, this rotating bend fatigue data (and other fatigue data) were presented as curves that his successors called Wöhler curves in his honor [6].

The next significant contributor to our understanding of fatigue was Johann Bauschinger [6].  His main contribution was the discovery and description in 1886 of the effect which bears his name.  The Bauschinger effect is the effect whereby induced strains beyond the elastic limit in one loading direction decreases the elastic limit in the opposite direction [3, 14].  This was an important discovery because it led the way to the theories of L.F. Coffin Jr. and S.S. Manson in the 1950’s, and for understanding both the low cycle fatigue phenomena and damage accumulation theories that are still used today [6].

REFERENCES

1. Turnbull, H.W. ed., The Correspondence of Isaac Newton: 1661-1675, Volume 1, London, UK: Published for the Royal Society at the University Press. p. 416 (1959).
2. “Wilhelm Albert”, Wilhelm Albert. Wikipedia. created 06 February 2016, accessed 31 Dec 2016.
3. Suresh, S. Fatigue of Materials. pp. 1-11 (1998).
4. Hansson, T.J. “Fatigue Failure Mechanisms and Fatigue Testing” NATO Science and Technology Organization Educational Notes. EN-AVT-207-14 (2012).
5. Albert, W. A. J. “Über Treibseile am Harz” Archive für Mineralogie Geognosie Bergbau und Hüttenkunde, vol. 10, pp. 215-34 (1838).
6. Schutz, W. “A History of Fatigue,” Engineering Fracture Mechanics, vol. 54. No. 2, pp. 263-300 (1996).
7. Bhat, S. and Patibandla, R. “Metal Fatigue and Basic Theoretical Models: A Review,” Alloy Steel -Properties and Use. Dr. Eduardo Valencia Morales, ed. (2011).
8. Mitchell, M.R. Fatigue, ASM Handbook, Vol. 19, 554-555. Materials Park, Ohio (1996).
9. Timoshenko, S.P. History of the Strength of Materials. pp. 162-173 (1983).
10. Bathias, C., and Pineau, A. Fatigue of Materials (2010).
11. “The Versailles Rail Accident,” Versailles Rail Accident. Wikipedia. Created 22 November 2016, accessed 31 Dec 2016.
12. ASM HANDBOOK. Vol 19, Fatigue and Fracture.  ASM International. pp.76-86 (1996).
13. “August Wohler,” August Wohler. Wikipedia. Created 21 October 2016, accessed 02 January 2017.
14. ASM dictionary, ASM International. p. 454 (1992).

This is the first of a four-part series on the history of fatigue analysis.  It has been adapted from the upcoming Ph.D. dissertation of VEXTEC’s Robert McDaniels.  You can read Part 2 here.

Isaac Newton wrote to Robert Hooke “If I have seen further, it is because I have stood on the shoulders of giants.”[1]   Since the first research on metal fatigue began in the 18^th century, a very large number of researchers from all over the world have contributed to the knowledge base that has been amassed.  Some workers have contributed to the characterization of fatigue failures, the discovery of the mechanisms of fatigue, and the testing of materials. Other researchers have contributed by adding to the theoretical and mathematical models that allow us to make predictions about how components will behave in the future when subjected to periodic loading under different conditions.  Fatigue research is truly a multidisciplinary field that incorporates:

• Mechanical engineering expertise to understand the stresses and strains to which components are subjected;
• Materials science expertise to understand how the stresses and strains affect, and are affected by, the microstructure of the components; and
• Statistical expertise to recognize and mathematically describe the microstructures, loads, and geometries of the components that are all inherently variable, and how these variabilities will affect the fatigue behavior of an individual component, or a fleet of components.

The first person to observe and report what we now know as metal fatigue was a German mining administrator named Wilhelm Albert.[2]  He investigated the failure of mine hoist chains.  He then built a machine which subjected lengths of chain to repeated loads of up to 100,000 cycles.[3]  He authored the first paper on metal fatigue in 1838.[4-6]

The importance of fatigue in transportation was well established by the 1850’s.[6]  The failure of axles of both horse drawn and railroad carriages were investigated by Arthur Morin in France, and William Rankine and J.O. York in Great Britain.[6]  The actual usage of the term “fatigue” has been attributed to most often to Jean-Victor Poncelet [7-9], but also to Morin, Frederick Braithwaite, and his colleague Mr. Field.[3, 6]  Whoever coined the term, the historical record is clear that by the mid-19^th century, it was already well-established that fatigue was a significant problem in all modes of transportation, and in many industries as well.

Unfortunately, it is often catastrophic accidents that provide the impulse and direction of fatigue testing and research.  One of the first accidents that spurred the growth and direction of fatigue research was the famous railroad mishap that occurred in 1842, on the railroad from Versailles to Paris, France.[3, 6, 7, 10, 11]  While transporting revelers back to Paris from King Louis Phillipe I’s birthday celebration at Versailles, a locomotive suffered an axle failure, which caused a derailment.  The trailing carriages ran into the engine, and they all caught fire.[11]  The crash killed over 60 people, and was the one of the worst railroad accidents that occurred during the 19^th century.[7]  A failure analysis investigation was conducted by Rankine, who found brittle cracking of the shaft.  Railroad mishaps, many caused by fatigue failures, were so commonplace that newspapers in Great Britain were reporting “the most serious railway accidents of the week” even into the late 1880’s.[6, 12]  By the mid 1800’s, several engineers in the British railroad industry had conducted tests of axles and members used in railroad bridges, and had already determined that even a load of half the ultimate strength of iron and steel components was sufficient to cause failure of metal components.  They had also created a predecessor to what engineers now call the endurance limit or “safe life” of components used in the railroad industry.[9]  In addition, they also identified sharp notches and corners as locations where cracks were likely to form, a precursor to the modern concept of stress risers, and had begun to investigate the idea of microstructural changes in the metal, [9] although they were decades too early to be able to explore microstructure the way that we currently can.

References

1. Turnbull, H.W. ed., The Correspondence of Isaac Newton: 1661-1675, Volume 1, London, UK: Published for the Royal Society at the University Press. p. 416. (1959)
2. “Wilhelm Albert”, Wilhelm Albert.Wikipedia. created 06 February 2016, accessed 31 Dec 2016.
3. Suresh, S. Fatigue of Materials. Pp. 1-11. (1998).
4. Hansson, T.J. “Fatigue Failure Mechanisms and Fatigue Testing” NATO Science and Technology Organization Educational Notes. EN-AVT-207-14. (2012)
5. Albert, W. A. J. “Über Treibseile am Harz” Archive für Mineralogie Geognosie Bergbau und Hüttenkunde, vol. 10, pp 215-34 (1838)
6. Schütz, W. “A History of Fatigue,” Engineering Fracture Mechanics, vol. 54. No. 2 pp 263-300 (1996).
7. S. Bhat and R. Patibandla. “Metal Fatigue and Basic Theoretical Models: A Review”, Alloy Steel -Properties and Use, Dr. Eduardo Valencia Morales (Ed.), (2011).
8. Mitchell, M.R. Fatigue, ASM Handbook, Vol. 19., 554-555. Materials Park, Ohio. (1996).
9. Timoshenko, S.P. History of the Strength of Materials. Pp. 162-173. (1983).
10. Bathias, C., and Pineau, A. Fatigue of Materials.,  (2010)
11. “The Versailles Rail Accident”, Versailles Rail Accident. Wikipedia. Created 22 November 2016, accessed 31 Dec 2016.
12. ASM HANDBOOK Vol 19 Fatigue and Fracture.  ASM International. pp.76-86. (1996).