How To Handle Mechanical Failures During An Endurance Race – “cyclic loading” redirects here. For the term for soil liquefaction as a result of stress, see Soil liquefaction.
The surface of an aluminum crank arm from a bicycle is broken. The dark side (due to oil, dirt and stress) is a slow-growing fatigue crack and may have striations. The bright spot is caused by a sudden fracture.
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In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows by a small amount with each loading cycle, often causing striations on some part of the fracture surface. The crack continues to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, resulting in rapid propagation and usually complete fracture of the structure.
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Fatigue has traditionally been associated with the failure of metal components leading to the term metal fatigue. In the ninth century, the sudden collapse of metal railway axles was thought to be caused by metal crystallising due to the brittle nature of the fracture surface, but this has since been disproved.
To help predict the fatigue life of a part, fatigue tests are performed using coupons to measure the rate of crack growth by applying constant amplitude cyclic loading and averaging the measured growth. of a crack in thousands of cycles. However, there are also some special cases that need to be considered where the crack growth rate is significantly different compared to that obtained from the constant amplitude analysis, such as the reduced growth rate that occurs for small loads near at the threshold or after the application of an overload, and the increased rate of crack growth associated with short cracks or after the application of an underload.
If the loads are above a certain threshold, microscopic cracks begin to initiate at stress concretions such as holes, persistt slip bands (PSBs), composite interfaces or grain boundaries in metals.
The stress values that cause fatigue damage are usually lower than the yield strength of the material.
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Cycles to failure where stress is low and primarily elastic and low cycle fatigue where there is significant plasticity. Experiments have shown that low cycle fatigue also cracks.
Fatigue failures, both for high and low cycles, all follow the same basic steps: crack initiation, crack growth stages I and II, and finally failure. To initiate the process, cracks must nucleate within a material. This process can occur either at stress risers in metallic samples or at areas of high void density in polymer samples. These cracks propagate slowly initially in stage I crack growth along crystallographic planes, where shear stresses are highest. When the cracks reach a critical size, they rapidly propagate to phase II crack growth in a direction perpendicular to the applied force. These cracks can lead to ultimate failure of the material, usually in a brittle catastrophic manner.
The formation of initial cracks before fatigue failure is a discrete process consisting of four discrete steps in metallic samples. The material will form cell structures and stiffen in response to the applied load. This causes the amplitude of the applied stress to increase with new restraints on the strain. These newly formed cell structures eventually break down with the formation of persistt slip bands (PSBs). Slip in the material is localized at these PSBs, and the increased slip can now serve as a stress concntrator to initiate a crack. The nucleation and growth of the crack to a visible size defines the majority of the cracking process. It is for this reason that cyclic fatigue failures seem to occur so suddenly that most material changes are not detectable without destructive testing. Even in normally ductile materials, fatigue failures will resemble sudden brittle failures.
PSB-induced slip planes result in intrusions and extrusions in the surface of a material, which often occur in pairs.
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This slip is not a microstructural change within the material, but rather a propagation of dislocations within the material. Instead of a smooth interface, intrusions and extrusions will cause the surface of the material to resemble the edge of a deck of cards, where not all the cards are perfectly aligned. Slip-induced intrusions and extrusions create very fine surface structures in the material. With surface structure size inversely related to stress shortening factors, PSB-induced surface slip can cause fractures to initiate.
These steps can also be bypassed if cracks are formed in an existing stress concntrator such as from an inclusion in the material or from a geometric stress concntrator caused by a sharp internal corner or fillet.
Most of the fatigue life is quickly consumed during the crack growth phase. The growth rate is primarily driven by the range of cyclic loading although additional factors such as mean stress, vironmt, overload and underload can also affect the growth rate. Crack growth may stop if the loads are small and fall below a critical threshold.
If the growth rate becomes large, fatigue striations can be seen on the fracture surface. The striations mark the position of the crack tip and the width of each striation represents the growth from one loading cycle. The striations are the result of plasticity at the crack tip.
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When the stress intensity exceeds a critical value known as the fracture toughness, unsustainable rapid fracture will occur, usually through a process of microvoid coalesce. Prior to final fracture, the fracture surface may contain a mixture of fatigue and rapid fracture sites.
The American Society for Testing and Materials defines fatigue life, Nf, as the number of stress cycles of a specified character sustained by a specimen before failure of a specified nature occurs.
For some materials, notably steel and titanium, there is a theoretical value for the stress amplitude below which the material will not fail for any number of cycles, called the fatigue limit or the fatigue limit .
However, in practice, some bodies of work produced in greater numbers of cycles suggest that fatigue limits do not exist for any metals.
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Whether using a stress/strain-life approach or using a crack growth approach, complex or variable amplitude loading is reduced to a series of fatigue-equivalent simple cyclic loadings using a method such as algorithm in counting the flow of rain.
A mechanical part is often exposed to a complex, often random, sequence of loads, large and small. To assess the safe life of such a component using fatigue damage or stress/strain-life methods the following series of steps is usually performed:
Since S-N curves are generally used for uniaxial loading, some equivalence rule is needed if loading is multiaxial. For simple, proportional load histories (lateral load at constant axial ratio), the law of Sines can be applied. For more complex situations, such as non-proportional loading, critical plane analysis should be applied.
In 1945, Milton A. Miner popularized a rule first proposed by Arvid Palmgr in 1924.
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The rule, variously called Miner’s rule or the Palmgr–Miner linear damage hypothesis, states that where there are k differ magnitudes of stress in a spectrum, Si (1 ≤ i ≤ k), each will contribute by ni(Si) cycles, th if Ni( Si) is the number of cycles to failure of the constant return stress Si (determined by uni-axial fatigue tests), failure occurs when:
Usually, for design purposes, C is assumed to be 1. This can be thought of as assessing what proportion of life is consumed by a linear combination of stress reversals of various magnitudes.
The fatigue performance of materials is usually characterized by an S-N curve, also known as a Wöhler curve. This is often plotted using cyclic stress (S) against cycles to failure (N) on a logarithmic scale.
S-N curves are derived from tests on samples of the material to be characterized (often called coupons or specims) in which a regular sinusoidal stress is applied by a testing machine that also counts the number of cycles to in frustration. This process is sometimes referred to as coupon testing. For greater accuracy but lower generality component testing is used.
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Each coupon or compont test gives a point on the plot although in some cases there is a runout where the failure time exceeds that available for the test (see csoring). Fatigue data analysis requires techniques from statistics, especially survival analysis and linear regression.
The development of the S-N curve can be influenced by many factors such as the stress ratio (mean stress),
Is useful for studying the effect of stress ratio. The Goodman line is a method used to estimate the influence of mean stress on fatigue strength.
Also, in the presce of a steady stress superimposed on cyclic loading, the Goodman relation can be used to estimate a failure condition. It plots the stress amplitude against the mean stress with the fatigue limit and the ultimate strength of the material as two extremes. Alternative failure criteria include Soderberg and Gerber.
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Since coupons sampled from a homogeneous frame will show variation in their number of cycles to failure, the S-N curve should be more properly a Stress-Cycle-Probability