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In materials science, fatigue is the progressive, localised, and permanent structural damage that occurs when a material is subjected to cyclic or fluctuating strains at nominal stresses that have maximum values less than (often much less than) the static yield strength of the material. The resulting stress may be below the ultimate tensile stress, or even the yield stress of the material, yet still cause catastrophic failure. A practical example of low-cycle fatigue would be the bending of a paperclip. A metal paperclip can be bent past its yield point (i.e., bent so it will stay bent) without breaking, but repeated bending in the same section of wire will cause the material to fail. Characteristics of fatigue failures The following characteristics are common to fatigue in all materials: Timeline of early fatigue history
High-cycle fatigue Historically, most attention has focused on situations that require more than 104 cycles to failure where stress is low and deformation primarily elastic. The S-N curve
Probabilistic nature of fatigue As coupons sampled from a homogeneous frame will manifest variation in their number of cycles to failure, the S-N curve should more properly be an S-N-P curve capturing the probability of failure after a given number of cycles of a certain stress. Probability distributions that are common in data analysis and in design against fatigue include the lognormal distribution, extreme value distribution and Weibull distribution. Complex loadings In practice, a mechanical part is exposed to a complex, often random, sequence of loads, large and small. In order to assess the safe life of such a part: Miners rule In 1945, M. A. Miner popularised a rule that had first been proposed by A. Palmgren in 1924. The rule, variously called Miner's rule or the Palmgren-Miner linear damage hypothesis, states that where there are k different stress magnitudes in a spectrum, Si (1 ≤ i ≤ k), each contributing ni(Si) cycles, then if Ni(Si) is the number of cycles to failure of a constant stress reversal Si, failure occurs when: C is experimentally found to be between 0.7 and 2.2. Usually for design purposes, C is assumed to be 1. This can be thought of as assessing what percentage of life is consumed by stress reversal at each magnitude then forming a linear combination of their aggregate. Though Miner's rule is a useful approximation in many circumstances, it has two major limitations: Low-cycle fatigue Where the stress is high enough for plastic deformation to occur, the account in terms of stress is less useful and the strain in the material offers a simpler description. Low-cycle fatigue is usually characterised by the Coffin-Manson relation (popularised by L. F. Coffin in 1979 based on S. S. Manson's 1960 work): -where: Fatigue and fracture mechanics The account above is purely phenomenological and, though it allows life prediction and design assurance, it does not enable life improvement or design optimisation. For the latter purposes, an exposition of the causes and processes of fatigue is necessary. Such an explanation is given by fracture mechanics in four stages. Factors that affect fatigue-life Magnitude of stress including stress concentrations caused by part geometry. Quality of the surface; surface roughness, scratches, etc. cause stress concentrations or provide crack nucleation sites which can lower fatigue life depending on how the stress is applied. For example, shot peening puts the surface in a state of compressive stress which inhibits surface crack formation thus improving fatigue life. Other surface treatments, such as laser peening, can also introduce surface compressive stress and could increase the fatigue life of the component. This improvement is normally observed only for high-cycle fatigue. Little improvement is obtained in the low-cycle fatigue régime. The most recent development in the field of surface treatments utilises ultrasonic energy to create residual compressive stresses that surpass those achieved by shot peening, laser peening, and other legacy methods. Ultrasonic Impact Technology operates within the harmonic frequency range of metals, allowing energy to be delivered deep into the material. Low amplitudes ensure that the metal is not overworked. Surface defect geometry and location. The size, shape, and location of surface defects such as scratches, gouges, and dents can have a significant impact on fatigue life. Significantly uneven cooling, leading to a heterogeneous distribution of material properties such as hardness and ductility and, in the case of alloys, structural composition. Size, frequency, and location of internal defects. Casting defects such as gas porosity and shrinkage voids, for example, can significantly impact fatigue life. In metals where strain-rate sensitivity is observed (ferrous metals, copper, titanium, etc.) strain rate also affects fatigue life in low-cycle fatigue situations. For non-isotropic materials, the direction of the applied stress can affect fatigue life. Grain size; for most metals, fine-grained parts exhibit a longer fatigue life than coarse-grained parts. Environmental conditions and exposure time can cause erosion, corrosion, or gas-phase embrittlement, which all affect fatigue life. Design against fatigue Dependable design against fatigue-failure requires thorough education and supervised experience in structural engineering, mechanical engineering, or materials science. There are three principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication: Versailles accident On May 8, 1842 one of the trains carrying revellers on their return from Versailles to Paris, having witnessed the celebrations of the birthday of Louis Philippe, derailed and caught fire. Though the resulting conflagration mutilated the dead beyond recognition or enumeration, it is estimated that 53 perished and around 40 were seriously injured. The derailment had been the result of a broken locomotive axle and Rankine's investigation highlighted the importance of stress concentration for the first time. De Havilland Comet Metal fatigue came strongly to the notice of aircraft engineers in 1954 after three de Havilland Comet passenger jets had broken up in mid-air and crashed within a single year. Investigators from the Royal Aircraft Establishment at Farnborough in England told a public enquiry that the sharp corners around the plane's window openings (actually the forward ADF antenna window in the roof) acted as initiation sites for cracks. All aircraft windows were immediately redesigned with rounded corners. Others See also | |||||||||||
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