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.
Typical S-N curve showing fatigue strength of material (image courtesy www.ami.ac.uk)
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.
References
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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