Brentwood, TN, August 28, 2013: A recent TV commercial on medical implants caught my attention. While touting the benefits of extensive laboratory testing, the fine print said that “…results of the testing have not been proven to predict clinical wear performance…” How true. Laboratory testing is rarely indicative of true wear and does not predict actual product reliability in the medical device industry. Read more
August, 20, 2013-VEXTEC ‘s Chief Technology Officer, Dr. Robert Tryon, and Dr. Animesh Dey, VEXTEC’s Chief Product Development Officer, will be making three presentations at the American Society of Mechanical Engineers (ASME) First Annual Conference on Frontiers in Medical Devices: Applications of Computer Modeling and Simulation, in Washington, D.C. September 11-13, 2013. Read more
In the race to get products to market, does risk-mitigation get enough time in the winner’s circle?
What do aerospace, medical device manufacturers, and auto racing all have in common? Answer: the need to minimize risk of premature/unexpected component failure while crossing the finish line first. While these industries each have vastly different stakeholders, goals, and success metrics, all look to avoid costly breakdowns in the field. And speed is key. Being the first across the finish line in auto racing gives you the largest share of the purse, not to mention first choice of lucrative endorsement deals. Being the first to market with an innovative or more reliable medical implant or a lighter aircraft component helps in marketing, product launch success, or company profitability and growth. However, pushing the design limits to gain this speed advantage must be weighed against the possible failure of the component in an unforeseen manner.
Speed in Design
Auto racing is one of the world’s most expensive sporting endeavors. A recent USA Today article puts the price tag of prepping and running a car in the Indianapolis 500 at nearly $1 million, and that is already assuming that the car is owned outright. While the bulk of this cost is sunk into parts, staffing, and off-track expenses, a not-insignificant 4.5% of that is spent on controlled testing. For example, one day at a rolling wind tunnel costs $35,000…more than the MSRP of the average production vehicle on US roadways today. While the finances of auto racing and the commercial automotive industry may differ, their goals are similar: to create lighter-weight components that will aid (or at least not hinder) aerodynamic performance. Designers are constantly being tasked with pushing the envelopes of their designs, while still attempting to maintain reliability and risk targets. These designs, in turn, lead to more expensive and detailed manufacturing/machining techniques and the use of more exotic material alloys. The uncertainties in every design usually manifest themselves as restrictive knock-down or safety factors that inevitably detract from performance. Governing bodies in the various auto racing categories (F1, NASCAR, drag racing, to name a few) place additional restrictions in the form of specification limits on components such as engines, body shapes, and spoilers to maintain competitive balance. Regardless of the type of restriction, if a way to reduce the uncertainty in a design is found, it can be advantageous. VEXTEC’s Virtual Life Management (VLM) simulation technology can be that solution. Through rigorous computational analysis of design, load-induced stress, and material, VLM can efficiently identify and quantify those design uncertainties. VEXTEC has provided VLM support to many of the industry’s leading manufacturers of heavy duty engine connecting rods, engine blocks, and turbochargers. This new insight has offered engineers the ability to understand where they really are on their design envelope, and how far they can push certain parameters, even before the first test piece is built.
Speed in Optimizing Maintenance
Weight savings and aerodynamics are, arguably, even more critical in the aerospace industry, where the civilian maintenance repair & overhaul (MRO) market is expected to be $56 billion this year. Engine maintenance alone will take up about 40% of this valuation. The cost of an unexpected catastrophic failure is much higher here than in the auto world. But in order to reduce this risk, aircraft must be maintained and repaired. And while they’re being maintained, they are not in the air delivering passengers, hauling freight, or making money. So minimizing the downtime is crucial to keeping viable profit margins. VEXTEC has partnered extensively with civil and military aircraft users, employing VLM on a multitude of issues including: unitized wing structures (US Air Force), certifying weld-repaired engine blades (EB Airfoils) and resolving premature bearing failure (American Airlines). The bearing study, for example, saved American Airlines about $4 million per year by avoiding the repair/replacement of their APU bearings. The results from these and other studies provide our clients with knowledge they would not have otherwise been able to acquire, and allow for sound financial decisions to be made on fielded components.
Speed in Reliability
One of the fastest-changing industries is the medical device industry. Technology is racing forward, minimizing invasiveness is driving the miniaturization of implantable devices (especially in heart rhythm monitors), while manufacturing methods are still trying to catch-up. It seems that no other industry is as heavily scrutinized in terms of reliability and risk, at least in public perception. Medical implants are exposed to harsh internal environments, unpredictable stress and strain cycles, and oftentimes difficult installation procedures. Yet these devices are counted-on to reliably elevate our quality of life on a daily basis. The variability observed in material, vendor supply, and manufacturing all play a part in the reliability of the components that make up a medical device. Through industry-directed capability studies, the VLM technology pioneered by VEXTEC has effectively modeled these sources of variability, virtually tested millions of components, and delivered reliability answers to as many “what-if” scenarios as design and materials engineers saw fit to explore. The VLM approach reduces the number of blind alleys (ineffective combinations of material, design, and operational limits) that companies would have to travel down through the traditional design-build-test method, and focuses internal R&D resources on the combinations most likely to succeed in both manufacturing cost and operational reliability.
These three high-risk/high-reward sectors are not the only sectors that have benefited from VLM technology. Indeed, any company looking to speed-up their design phase, reduce their warranty reserves, or just wanting to make more-informed decisions on how their products can best be sourced, manufactured, and used would benefit from a conversation with us. The green flag has dropped…where are you in the field?
VEXTEC: Meeting the Need for Speed.
Over the last few weeks, VEXTEC has explored the two main philosophies of modern structural design: safe life design and damage tolerant design. Today we share with you a summary of these methods, including their benefits and limitations. We will also look at other considerations that are commonly encountered when implementing either method in a manufacturing environment, and how VEXTEC’s Virtual Life Management® (VLM®) technology can help.
Safe Life Design
Safe life design is a common method to predict the durability of a design in many industries, including automotive, pressure vessels, bearings, and portions of jet engines and aircraft landing gear. It is employed by manufacturers when it is understood that regular structural inspection of their products would not be possible or practical. Components are removed from service when their calculated safe life expires, regardless of the condition of the component.
Safe life is based on laboratory testing of simple specimens that are cyclically-loaded to create test points in a S-N curve. Damage initiates naturally within the material microstructure and grows to final failure. The resulting S-N curve has three major limitations: 1) due to the large scatter in lifetime, many tests must be performed to get a statistically-confident dataset; 2) the simple test specimens are not similar to the design of complex components (lack of similitude); and 3) the analysis usually considers only the peak stress that the component should see. The design method does not account for any unforeseen rogue flaws in the material, nor rare stress spikes in operation. Thus, large safety factors are applied to the design allowable life to theoretically ensure that any naturally-initiated damage will not pose a threat to the acceptable reliability for the life of the structure. The safety factors may be in terms of life or load, or in the case of pressure vessels, both life and load. While the goal of safety factors (or ‘knockdown factors’ or ‘margins of safety’, as they are also known) is admirable, their implementation is arbitrary at best. Using them leads to structures that are heavy and overly conservative, and add to the cost of manufacturing (in terms of necessary raw material, processing, and machining). There is no standardized way of implementing these factors across industries, because institutional knowledge will often trump hard physics when it comes to design.
Damage Tolerant Design
Damage tolerant design is a methodology which uses the physics-based principles of fracture mechanics (in particular, the stress intensity factor) to account for and measure the initiation and growth of damage in a structure in operational service. Industries which employ this methodology include military and civil aerospace and rotorcraft, heavy duty cranes, and bridges. Manufacturers who use this method can design lighter products or more severe loading cycles, as routine periodic inspection protocols are used to observe, detect, and repair fatigue cracks before reaching critical sizes.
Traditional fracture mechanics has less scatter in the developing of a S-N curve as opposed to safe life design, and can account for the geometry and stress distributions of complex designs. Residual stress can also be accounted for in the stress intensity factor, and complex load missions can also be assessed. The main limitation in damage tolerant design is that a crack must be assumed to be present in the component because fracture mechanics predicts the cycles for the crack to grow from one size to another. Linear elastic fracture mechanics, the most commonly used form of fracture mechanics, assumes the crack is large relative to the material’s microstructure. By assuming this initial crack size, the percent of the lifetime that would have actually been spent developing that initial crack in reality is not accounted for in the durability of the design. This conservative assumption can greatly reduce the design allowable life. Advanced fracture mechanics methods have been developed in recent decades to both reduce the size of the assumed initial crack and to understand fatigue crack closure effects. Additional testing to develop these methods can prove to be expensive, and the cost of these paired with the additional costs of routine end user inspections must be weighed during the design and manufacturing processes.
VEXTEC’s VLM technology can reduce assumptions and cost in either type of design, or can be used to combine the best aspects of safe life with damage tolerance to create a “total life” approach:
a) In safe life design, VLM can be used to predict the stress and strain vs. fatigue life (S-N curve) test results of simple test specimens, as well as components with complex geometry and loading. As VLM uses finite element methods, the simple and complex geometries drive the differences in the fatigue results (using the same set of empirical material parameters), so the similitude issue in safe life design is avoided. Virtual Life Management can be implemented without the need for large safety factors, as it has been shown to predict the mean and scatter in fatigue life of a final component’s design. Virtually testing many designs first can result in huge cost savings in money and time compared to manufacturing and testing of a multitude of “possible design” components.
b) The VLM approach can also be used in damage tolerance analysis methods without the need for the large initial crack assumption. The use of Monte Carlo statistical techniques advance fracture mechanics to predict actual fatigue response and its scatter. The method simulates fatigue crack growth starting at the naturally-occurring microstructural features (rather than an assumed large initial crack size) using the appropriate fracture mechanics processes (crack nucleation, short-crack growth, long-crack growth) to more accurately predict the fatigue durability of complex components experiencing complex loading. This analysis can provide a more realistic (and less-conservative) life prediction, providing more value to manufactured components.
c) By integrating safe life with fracture mechanics, VLM creates a total lifetime prediction from the initially unflawed component to final failure. VLM simulates the material at the fundamental level to include all of the individual grains, voids and inclusions that exist in the material microstructure of the component. As viewed under a microscope, the microstructure of each component and each location in the component is different. VLM uses probabilistic methods to capture these differences by representing the material as space filling 3-D statistical volume elements. Structural finite element analysis methods are used to capture the complex stress and temperature variations throughout the 3-D component along with geometry and residual stresses. The finite element stresses and temperatures are combined with the material volume elements to simulate damage as it initiates and grows through the component. This process captures the similitude needed for safe life and predicts the number of cycles spent initiating a crack for damage tolerance; all using probabilistic methods to capture the uncertainties that exist in a fleet of components, and thus predicting the true probability of when components fail in the field.
We hope you have found this series on structural design principles informative. Please contact us if you feel that your company could benefit from more-informed decision making capabilities in your products’ design process.
The damage tolerance approach to design has been employed by the aerospace industry for decades. In contrast to the safe life design method, damage tolerance explicitly accounts the fatigue crack growth process. This design approach takes advantage of the portion of service life a component can have with a growing fatigue crack. Crack inspection, detection and repair protocols are implemented to prevent fatigue cracks from growing too large and causing failure.
Advantages over Safe Life Design
The foundation of damage tolerance is the concept of fracture mechanics, and through its use, the determination of a stress intensity factor (SIF). This factor (which also can be denoted as K) governs the fatigue crack growth under a set of conditions (loading and geometry) for a given analysis. The fatigue crack growth rate can be determined by calculating the SIF and by experimentally-deriving parameters inherent in the material being examined. In contrast to the issues in similitude that are encountered in safe life design, the incorporation of loading and geometrical factors through fracture mechanics allows the damage tolerance method to achieve similitude for different loads, different crack sizes, and different crack shapes. This means that the only physical testing needed to assess the durability of different design geometries is simple coupon testing for the material parameters. Standard methods have been developed for determining the material parameters using far fewer test specimens than needed to create a S-N curve.
Inputs from finite element analysis are used with fracture mechanics to determine how the spatial stress distributions affect the crack growth rates, thereby providing a straightforward way to assess design changes in durability. This is a higher-fidelity analysis compared with safe life design, which only considers the peak stress in the component. The effects of fillets and other geometric features can be readily assessed using the damage tolerance approach. Residual stress can be directly incorporated into the stress intensity factor. The “sequencing” effect of variable cyclic load levels (e.g. “a high load followed by a low load” vs. “a low load followed by a high load”) can be assessed. Advanced techniques in fracture mechanics adjust the SIF with various energy terms to account for crack face interaction and other physical phenomena. With these methods, mean stress effects and complex load missions can be assessed.
While damage tolerant design can be very effective in improving similitude among varying loads, crack sizes and shapes, there are drawbacks. In most fracture mechanics methods, an initial crack must be assumed in the geometry. By assuming this initial crack, the percent of the specimen’s (or component’s) lifetime spent developing that crack is not accounted-for in determining the durability of the design; the total life of the design may thus be underestimated. In general, the higher the ultimate strength of the material, the higher the percent of lifetime is actually spent developing the initial crack. The initial crack is further assumed to be relatively large (commonly 1/32 inch or 0.8mm; at least one order of magnitude larger than typical size scales of the plastic zone and the material microstructure).
The above figure compares crack growth data for 12 high strength steel specimens tested in rotating bend fatigue (Sasaki et al., 1987). The specimens were notched with a stress concentration factor (Kt) of about 3. This means that the surface stress at the center of the notch is about 3 times greater than the surface stress of a completely smooth specimen. The notched specimens were tested at a nominal stress amplitude (not adjusted for the stress concentration) of 58 ksi. The initial size for crack measurement is 0.8 mm, the lower limit for traditional fracture mechanics. Because the cracks grew quickly and caused failure not long after they reached 4 mm, the maximum allowable crack size in this experiment was set to 4 mm. Notice the limited scatter among the tests in the cycles to 4 mm. Of the 12 specimens, the quickest to 4 mm was 31,000 cycles while the longest to 4 mm was 43,000 cycles. This gives an average of about 37,000 cycles with a spread of about ±15%. On the other hand, the S-N curve for the notched specimens without an initial crack yields an average life of about 125,000 cycles. Herein lies the problem: the assumption of a crack, which is required in fracture mechanics, is conservative, ignoring 70% of the average lifetime in its estimate in this example.
Minimum lifetime is a different story. Because of better similitude and the conservative assumption of having a relatively large initial crack, it is common practice to use the average life in fatigue analysis using fracture mechanics; in this case, 37,000 cycles. The design-allowable life using the S-N curve (-3σ) is about 31,000 cycles. Therefore, even with the conservative assumption of the existence of a crack, better understanding of the physics using fracture mechanics could provide a higher design allowable life. Sometimes, the use of fracture mechanics does not give a higher life; this depends on the design and material of the component. It should be noted that in situations where components are inspected to assure safe operation, the inspection interval is often set to half of the average damage tolerance life. This gives an inspector two opportunities to discover the crack (and repair the location, if necessary) before failure.
If fracture mechanics could be extended to smaller and smaller crack sizes, a better estimate of the true lifetime could be predicted. This has been the goal of researchers for many years. The following figure shows the crack growth data for 12 high strength steel specimens tested in rotating bend in which crack growth is measured from an initial crack size of 0.2 mm (Sasaki et al., 1987). The average life here is about 115,000 cycles (ranging from 99,000 to 131,000 cycles with a similar spread of ±15%). This is more than three times the fatigue life than if an initial crack size of 0.8 mm is assumed. The problem is that traditional fracture mechanics is not applicable to this smaller crack size; the assumption that the crack is large compared to the plastic zone is violated, and the size of the crack is approaching the size of the material’s microstructural features.
In moving to smaller crack sizes, the above assumption violation has commonly been divided into two problems: the problem of the physically small crack and the problem of the microstructurally small crack. The physically small crack grows much faster than a large crack with the same stress intensity factor. The faster growth rate of the physically small crack is attributed to a cracked surface that is too small to have built up appreciable roughness. Long cracks have roughness/plastic strain-induced closure such that the crack tip is not opened until the applied stress exceeds a certain value; closure effectively reduces the stress amplitude. Thus the physically small crack, without the aid of closure, has higher stress amplitudes and therefore higher crack growth rates than long cracks. Several advanced fracture mechanics methods that adjust for this closure phenomenon have been developed over the past two decades (Newman, 2003). These methods require more and different testing than traditional fracture mechanics; therefore, they are more expensive to develop. But when considering the potential impact in the available design life, they can be a worthwhile investment.
Fracture mechanics for the microstructurally small crack has advanced down to the naturally-occurring microstructural features of grains, voids, and inclusions (Tanaka and Mura, 1981). Although fracture mechanics concepts are used, these features are so small that there is no well-defined crack; the term “microstructurally small crack” has therefore been replaced with microstructural crack nucleation. Similar to cracks, the microstructural features are discontinuities in the material matrix and, like cracks, can cause damage under loading. Unlike the typical fracture mechanics analysis assumption of a single crack, these features exist throughout the material; there are tens of thousands (if not millions) in any given component. Performing a fracture mechanics analysis of all of the microstructural features in a component to determine which ones nucleate damage, grow and coalesce with neighboring features to cause failure is a daunting task. To solve this problem, statistical methods have been combined with fracture mechanics to develop computational software that takes fracture mechanisms down to the true fatigue damage initiation size.
VEXTEC’s Virtual Life Management (VLM) Tool
Over the past 12 years, VEXTEC has developed a probabilistic computation tool called Virtual Life Management (VLM), which provides the algorithms that link the microstructural material properties and non-continuum mechanics. In this approach, the elements are defined as the individual microstructural features (grains, voids, and inclusions) of a polycrystalline aggregate (Tryon, 2005). Each feature is considered a single element with homogeneous (non-varying) properties. The properties vary from feature to feature. The macrostructure is modeled as an ensemble of these features. The material properties of this ensemble are defined using the appropriate statistical distributions for a given material.
The VLM software also recognizes the multiple stages of fatigue damage accumulation such as crack nucleation, small crack growth and long crack growth that lead to failure. Each stage is driven by different mechanisms and is distinctly modeled. The stages must be quantitatively linked because the crack successively grows from one stage to the next. In VLM, theoretical micromechanical models are used to determine the number of cycles necessary to nucleate a crack in the microstructure. A combination of models based on empirical observations and theoretical micromechanics are used to determine the number of cycles spent in the small crack regime to grow the cracks from nucleation to the long crack stage. Conventional fracture mechanics is then used to determine the number of cycles necessary for the crack to grow through the long crack regime to the critical crack size. Failure of the macrostructure is defined by the first VLM-simulated crack to nucleate and grow beyond the critical crack size. The statistical distribution of fatigue life for the macrostructure is determined using Monte Carlo simulation methods. This probabilistic model provides a direct quantitative link between the variations in the material microstructure and the scatter in the fatigue behavior.
The figure below compares the VLM predictions of a smooth titanium fatigue specimen with laboratory test data. The predictions were developed based on 1) data derived from typical monotonic material property testing, 2) a single fatigue specimen tested at 90 ksi, and 3) photographs of the material microstructure to measure the statistical distributions of the sizes and populations of the microstructural features. The solid circles represent laboratory test data; the hollow circles are the VLM predictions. Notice at each stress level there are many predictions. This is because Monte Carlo methods were used to simulate 20 specimens at each stress level. The simulation produced a unique microstructure for each specimen just like the actual specimens, and just like the actual specimens, each specimen has a different fatigue lifetime. Notice also that the predictions do a good job of capturing the change in fatigue lifetime with stress level. The predictions captured the increase in scatter as the stress is reduced, the “knee” (a discontinuity seen in some materials representing a fatigue transition point at higher cycles) of the S-N curve, and the “run-outs” (specimens which did not fail) at 1.E+08 cycles. The figure also shows that the VLM software does a good job of capturing the behavior of the notched fatigue specimen (solid diamonds represent laboratory test data; hollow diamonds are the VLM prediction), using not specimen data but just the geometry and local notch stress state derived from finite element modeling.
VLM is a powerful tool because the conservative fracture mechanics assumption of the existence of a large initial crack is not required, and the similitude issues of the S-N curve are avoided. Using typical fracture mechanics material testing and a few S-N tests of simple smooth specimens, the fatigue behavior of notches, fillets, and other geometric features can be assessed. The other major important aspect of VLM is that the scatter in the fatigue lifetime is predicted. This method has been applied directly to finite element models of complex components to predict the mean and scatter in fatigue life of the final component design. The application of VLM results in huge savings in cost and time compared to the manufacture and testing of actual components. Virtual Life Management has shown the ability to improve the accuracy and robustness of fatigue durability predictions.
Sasaki, S.K., Ochi, Y., Ishii, A., “Statistical Investigation of Surface Fatigue Cracks in Large-Sized Turbine Rotor Shaft Steel”, Engg. Fract. Mech., vol. 28, issues 5-6, pp. 761-772, 1987.
Newman, J.C., Jr., “Numerical Modeling of Fatigue Crack Growth”, Chapter in Comprehensive Structural Integrity, vol. 4, R.O. Ritchie and Y. Murakami, editors, Elsevier, 2003.
Tanaka, K., Mura, T., “A Dislocation Model for Fatigue Crack Initiation”, ASME J. Appl. Mech., vol. 48, pp. 91-103, 1981.
Tryon, R.G., “Using Probabilistic Microstructural Methods to Predict the Fatigue Response of a Simple Laboratory Specimen”, Chapter 42 in Engineering Design Reliability Handbook, E. Nikolaidis, D. Ghiocel, S. Singhal, editors, CRC Press, 2005.
The philosophy of safe life design is the preferred method for designing components for durable operation in the automotive industry. Under this method, the structure is operated at a stress far below the fatigue strength of the component. By doing this, the designer assumes that the structure will not form a detectable crack during its service life, thus reducing the risk of failure.
Safe life design uses an experimentally-determined S-N curve to evaluate operational limits. This curve relates the magnitude of the cyclic stress (S) on a test specimen to the number of cycles to specimen failure (N). The curve is dependent on many conditions, including the ratio of maximum load to minimum load (R-ratio), the type of material being examined, and the frequency at which the cyclic stresses (or strains) are applied. Typically, as the load decreases, the life of the specimen increases. The practical limit of experimental testing has been 106 or 107 cycles, due to frequency limitations of hydraulic-powered test machines. If the resulting component operates at stresses above the fatigue strength, it is said to be a life limited component. If the component operates at stresses below the fatigue strength, it is said to be an infinite life-designed component. Issues which continually hinder the creation of an appropriate S-N curve for safe life design are similitude and scatter.
The concept of similitude is used in component design and testing, relating the similarity of the test specimen to the component that it is supposed to represent. This similarity is broken-down into three types: geometric similarity, kinematic similarity, and dynamic similarity. The higher the degree of similitude, the closer the test specimen is to the actual component. In most S-N curve testing, the specimens (coupons) are manufactured with a simplified design in order to be tested efficiently. However, this simple design will not typically reflect the actual geometrical and loading complexity of the component. Therefore, the empirical relationship derived in the coupon S-N curve testing cannot be directly applied to conditions outside this simple test specimen database. To account for this, large safety factors are included in the design’s predicted fatigue lifetime.
The above figure compares the S-N curve of smooth round bar specimens with notched round bar specimens tested in rotating bend fatigue (Nishijima et al., 1987). The steel material used to make the two different specimens is the same. The difference is in geometry: the notched specimen is created by machining a V-shaped groove into the center of a smooth specimen. The shape of this groove creates a stress concentration factor (Kt) of 3.5. This means that the surface stress at the center of the notched groove is 3.5 times greater than the surface stress of the completely smooth specimen. The Y-axis is the surface stress at the base of the groove for the notched specimens and the surface stress of the smooth specimens. Notice that there is not much similarity between the lives of the notched specimens and the smooth specimens with regard to surface stress. That means there is no similitude between the notched and smooth specimens. If the actual component to be designed has a notch or a fillet, the smooth round bar S-N curve is not applicable and a new S-N curve using notched round bars must be obtained. This process becomes expensive and time-consuming.
Further compounding this issue are the various geometries and loadings which can be tested. If notched bars with different Kt factors are tested, different S-N curves will be obtained. If the smooth bars are tested in axial pull fatigue instead of rotating bend fatigue, a different S-N curve will be obtained. If the bars are tested at a different mean stress, or if smooth bars with a larger diameter cross section are tested, different S-N curves will be obtained. It is evident that similitude breaks down very easily. In fact, the only method to determine the true S-N curve of a component is to test the actual component. This is very expensive and impossible to do until the component is designed and manufactured. Thus, S-N curves are used that are as similar as possible (given testing time and cost constraints) to th
e component being designed.
Scatter in the S-N Curve
Significant scatter can occur in the number of cycles to failure at any given stress level in a S-N curve. Let us return to the smooth round bar steel specimens tested in rotating bend fatigue, in the figure below. This figure shows only specimens tested to 107 cycles; if they did not fail by 107 cycles, they are test suspensions and are denoted by a triangle symbol.
Approximately 12 bars were tested at each stress level. Although each bar is meticulously prepared to be similar to the other bars and to have no pre-existing damage, and the testing is highly-controlled to minimize any variations, there is still considerable scatter in the data. This is because fatigue damage nucleates on a very small size scale governed by the microstructure of each bar. And although the bars are as similar as possible, when viewed under a microscope, the microstructure of each bar is not identical. There is a natural variation of microstructure from bar to bar, and even within the same bar.
This variation can have a significant effect on the allowable design stress. Assuming a component was designed to have a stress of 55 ksi, the S-N curve in the above figure indicates that the typical life of the component would be about 500,000 (5.E+05) cycles. However, components are not designed to a typical life (50% risk of failure) but are instead designed to some lower tail of the life distribution. The curve shows that the “1 out of 12” lifetime is about 100,000 (1.E+05) cycles, an 80% reduction in life compared to typical. However, 1 out of 12 failures is still high in the tail for allowable design risk in most cases. The “-3σ” failure (one in 370 specimens, assuming a normal distribution) is closer to what is typically used for allowable design risk. When a statistical analysis is performed on this data, the -3σ life is about 30,000 (3.E+04) cycles at 55 ksi, or a 93% reduction in life compared to typical.
Assuming the component was designed to have an infinite life, the S-N curve above would be used to determine the allowable stress. At 52 ksi, some of the bars did not fail at 1.E+07 cycles. As is typical engineering practice, a few bars were tested below 52 ksi. None of these bars failed, and thus the fatigue limit is found to be 51 ksi (the highest stress where no bars failed). The safe life “design allowable stress” would then be set somewhat below the experimental fatigue limit. While there is no standardized procedure, often the allowable stress will be set to a relatively high percentage of the experimental fatigue limit (say, 90%). In this case, 90% of 51 ksi is approximately 46 ksi, and so 46 ksi would be the design’s allowable stress.
Seldom are a significant number of specimens tested at cycles greater than 1.E+07; it is simply too expensive and time-consuming. Nishijima et al. did test some specimens at lower stresses and higher cycles (see figure below).
If 12 specimens are tested out to 1.E+08 cycles, failures do in fact occur below the previous 1.E+07 fatigue limit of 51 ksi. Because many bars were tested, some of them failed before 1.E+07 cycles. At the previously-assumed safe design allowable stress of 46 ksi, 11 of the 12 specimens failed before 1.E+08 cycles. In reality, the experimental fatigue limit stress can only be determined to a finite number of cycles; the allowable stress for infinite life cannot be known. So, even if a small percentage of the experimental fatigue limit stress is used as the design allowable, the risk of failure is unknown.
Acknowledging these issues of similitude and scatter, reductions in the expected design life and allowable stress for infinite life must be made. These reductions take the form of safety factors (or “knockdown” factors) to assure safe and reliable designs, which culminate in excessive weight and manufacturing cost of the component. The S-N curves serve only as a baseline, with institutional knowledge taking the place of hard physics in designing against fatigue failures. Selected knockdown factors are based on past and related experiences. Also, different organizations have different experiences and therefore use different knockdown factors. This becomes problematic when a new design lies outside of the experience base. Increasing the knockdown factors and overdesign has to be weighed against the risk of failure in the field, none of which can be quantified.
Over the past 12 years, VEXTEC has developed a probabilistic computation tool called Virtual Life Management (VLM), which provides the algorithms that link the microstructural material properties and non-continuum mechanics. The VLM software platform can be used to predict the stress and strain versus fatigue life test results of simple test specimens, as well as components with complex geometry and loading. VLM can be used directly in the safe life analysis method without the need for large safety factors. The figure below compares the VLM-predicted fatigue lives with laboratory test data.
The exact same material model is used for both the smooth specimen and the notched specimen. Notice the good correlation between the predicted and actual data points. The model captures the notch similitude. This is significant because the notched specimen can be described by the notched specimen’s finite element model and the material’s mechanical properties that are determined by testing the smooth specimen. The additional tests to determine the notched S-N curve for each geometry can now be eliminated. The scatter in the fatigue lifetime is also predicted. The method has been applied directly to finite element models of complex components to predict the mean and scatter in fatigue life of the final component design. This can be a huge savings in money and time compared to the manufacture and testing of actual components.
In the next blog, we will explore the damage tolerance design methodology, and how VEXTEC’s Virtual Life Management (VLM) technology can be used to reduce the magnitude of the assumptions made and improve the accuracy and robustness of the DTA fatigue durability prediction.
Nishijima, S., Masuda, C., Abe, Komatsu, A., Ishii, A., Matsuyama, T., Sumiyoshi, T., Tanaka, Y., and Otsubo, S., “Statistical Fatigue Properties of Heat Treated JIS Steels S45C, SCM3, SNCM8, SK5, and SUS403 for Machine Use”, Trans. Natnl. Res. Inst. Met., vol. 19, no. 6, pp. 43-59, 1987.
Note: This post is the first in a series of blogs exploring industry-recognized structural design principles. This material originated in an internal white paper written by Dr. Robert Tryon, Chief Technology Officer at VEXTEC.
In the world of structural design, there are two main analytical techniques that are currently employed when attempting to predict the durability of components and systems: safe life design and damage tolerance analysis. Depending on the type of industry, one particular philosophy can be preferred over the other. We offer here an overview of these design philosophies.
The automotive industry commonly uses the safe life approach in designing and predicting the durability of their components. This approach dates back to the mid-1800s, when the repetitive loading on mechanical structures intensified with the advent of the steam engine. Engineers and academics began to understand the effect that cyclic stress (or strain) has on the life of a component (Wöhler, 1855); a curve was developed relating the magnitude of the cyclic stress (S) to the logarithm of the number of cycles to failure (N). This curve, known as the S-N curve, became the fundamental relation in safe life design. The curve is dependent on many conditions, including the ratio of maximum load to minimum load (R-ratio), the type of material being examined, and the frequency at which the cyclic stresses (or strains) are applied. Today, the curve is still derived by experimentally testing laboratory specimens at many different constant cyclic load levels, and observing the number of cycles to failure. Unsurprisingly, as the load decreases, the life of the specimen increases. The practical limit of experimental testing has been 106 or 107 cycles, due to frequency limitations of hydraulic-powered test machines. The load at which this high-cycle life occurs has come to be known as the fatigue strength of the material.
In the safe life method, the S-N curve is used to design a component in such a way that it will not fail within a pre-determined number of cycles. For example, if a test specimen (or coupon) has not failed by the typical limit of 107 cycles, it is assumed that the specimen would never fail before 107 cycles in the safe life design. Subsequently the component’s durability is estimated, first by evaluating the highest operational stress on the component using hand calculations or finite element methods, and then comparing the component’s highest operational stress to the stress scale on the test specimen’s S-N curve. If the stress of the component is below the fatigue strength on the S-N curve, the component is said to be designed for infinite life. If the stress of the component is above the fatigue strength (e.g. stress S1 in the figure above), the component is life limited (in the example figure at S1, the life is limited to between 105 and 106 cycles). In the latter scenario, the structure of the component should not fail during its operational “safe life.” To ensure that the component does not fail, it should be removed from service at the end of this safe life regardless of its condition. Significant safety factors are often applied to ensure that catastrophic failures will not occur during operation in the safe life regime.
Not to be confused with safe life is the fail safe design philosophy. This method differs from safe life in that fail safe assumes that a component will fail, and therefore the component is designed to fail in a safe manner. The techniques that are typically used in this method include attempts to reduce the likelihood of single-point failures by creating redundancies. If, for example, a structure is loaded using multiple beams and one fails, the load is re-distributed among the remaining members. The overall system does not fail, but the failed member can be detected and repaired or replaced. Another core tenet of fail safe design is damage tolerance analysis, or DTA for short, and is widely used in the aerospace industry.
Damage tolerance has its foundation in fracture mechanics, a branch of physics first developed in the 1920s (Griffith, 1921) that evolved to be applied to fatigue of metallic structures in the 1960s (Paris et al., 1961). Fracture mechanics provides a physical basis for a crack growing in a structure. It quantifies the energy the crack has in a value called the stress intensity factor (SIF). This factor is a function of the applied cyclic load (the same loading used in aforementioned safe life analysis) as well as the morphology of the crack. The SIF determines the size and shape of the “plastic zone” ahead of the crack’s tip. This plastic zone size is directly related to the available energy (and the energy, in turn, related to the applied stress) for continued crack growth. Without sufficient energy, the formed crack can arrest (stop growing). Damage tolerance analysis therefore assumes that fatigue cracks can (and will) nucleate in a component during operational life, and that growth of these small cracks in fatigue will occur if sufficient energy exists in the system.
Two fundamentally-different “small crack” sizes are defined for this analysis: the physically small crack and the microstructurally small crack. These cracks operate in the material’s microstructure, which, for most metals, consist of grains: the building-blocks of the material. The microstructurally small crack is typically considered to have a size range between 1 and 5 grains, while the physically small crack is closer to 10 grains in size. The physically small crack grows much faster than a large crack with the same SIF, whereas the microstructurally small crack grows in a much more unpredictable way due to its smaller size. Growth of cracks of this size is varied and highly dependent on the local variability of the material and the aspect ratio of the individual grains (Lankford and Davidson, 1986). For example, some cracks may arrest upon reaching barriers such as inclusions (particles that are chemically different than the majority of the microstructure) or boundaries of grains. Once cracks grow to a size of 10 grains (on the order of a physically small crack), this variation tends to converge.
As opposed to the safe life method, modern DTA employs finite element methods to determine how the stress in a component is spatially distributed. Rather than using a single peak component stress (as in safe life), a stress distribution can be applied to the crack’s growth rate. Subtle changes in design (fillet radius, residual stress, etc.) can lead to varied and important differences in a DTA durability prediction. The effect of sequencing variable cyclic load levels (e.g. a high load followed by a low load vs. a low load followed by a high load) can also be evaluated using this method.
In the coming blogs, we will further explore these two main structural durability prediction methods. Also, we will see how VEXTEC’s Virtual Life Management (VLM) technology can be implemented in either paradigm to both reduce the amount of necessary assumptions and increase the effectiveness of the designs’ results.
Wöhler, A. “Theorie rechteckiger eiserner Brückenbalken mit Gitterwänden und mit Blechwänden”, Zeitschrift für Bauwesen, vol. 5, pp. 121-166, 1855.
Griffith, A. A., “The phenomena of rupture and flow in solids”, Philosophical Transactions of the Royal Society of London, A 221, pp. 163–198, 1921.
Paris, P. C., Gomez, M. P., and Anderson, W. E., “A rational analytic theory of fatigue”, The Trend in Engineering, vol. 13, pp 9-14, 1961.
Lankford, J., and Davidson, D. L., “The Role of Metallurgical Factors in Controlling the Growth of Small Fatigue Cracks”, Small Fatigue Cracks, Ed., Ritchie, R. O. and Lankford, J., The Metallurgical Society, Warrendale, PA, pp. 51-71, 1986.
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