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Fatigue Overview Introduction to Fatigue Analysis

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Fatigue Overview Introduction to Fatigue Analysis Fatigue overview Introduction to fatigue analysis • Fatigue is the failure of a component after several repetitive load cycles. • As a one-time occurrence, the load is not dangerous in itself. Over time the alternating load is able to break the structure anyway. • It is estimated that between 50 and 90 % of product failures is caused by fatigue, and based on this fact, fatigue evaluation should be a part of all product development. What is fatigue? In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading (material is stressed repeatedly). Clients tous différents Routes de qualités variables Contraintes Fatigue Design in Automotive Industry Conception fiable PSA (Peugeot Citroën) Résistances 3s 3s Dispersion matériau Dispersion de production Fatigue • Fracture mechanics can be divided into three stages: 1. Crack nucleation 2. Crack-growth 3. Ultimate ductile failure Introduction to fatigue analysis • Fatigue is the failure of a component after several repetitive load cycles. • As a one-time occurrence, the load is not dangerous in itself. Over time the alternating load is able to break the structure anyway. • It is estimated that between 50 and 90 % of product failures is caused by fatigue, and based on this fact, fatigue evaluation should be a part of all product development. Historical background • In comparison to the classical stress analysis, fatigue theory is a relative new phenomenon. The need to understand fatigue arose after the industrial revolution introduced steel structures. Three areas were particularly involved in early failures: Railway trains, Mining equipment and Bridges. Historical background • 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test machine for conveyor chains used in the Clausthal mines. • 1839: Jean-Victor Poncelet describes metals as being tired in his lectures at the military school at Metz. • 1870: Wöhler summarizes his work on railroad axles. He concludes that cyclic stress range is more important than peak stress and introduces the concept of endurance limit. • 1910: O. H. Basquin proposes a log-log relationship for SN curves, using Wöhler's test data. • 1945: A. M. Miner popularizes A. Palmgren's (1924) linear damage hypothesis as a practical design tool. • 1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of plastic strain in the tip of cracks. • 1968: Tatsuo Endo and M. Matsuiski devise the rainflow-counting algorithm and enable the reliable application of Miner's rule to random loadings. Historical background • Fatigue theory is basically empirical. This means that the process of initiation of micro cracks that finally will form macroscopic cracks in the material is not accounted for in detail in the equations. • Fatigue properties must be treated by statistical means due to large variation during testing. • Virtually all mathematical equations dealing with fatigue are fitted to test results coming from materials testing. Fields of application & analysis considerations • Whenever a structure is subjected to time varying loads, fatigue must be taken into account. Typical structures subjected to time varying loads are for example: – Rotating machinery (pumps, turbines, fans, shafts) – Pressure vessel equipment (vessels, pipes, valves) – Land based vehicles, ships, air- and space crafts – Bridges, lifting equipment, offshore structures Fields of application & analysis considerations • In the design specification of the part there are some questions that must be answered, for example: 1. What is the expected number of cycles during the expected life time? 2. Shall the individual components be designed for infinite life or a specified life? 3. In case of a specified life time, what service/inspection intervals are needed? Fields of application & analysis considerations • Common Decisions for Fatigue Analysis • There are 5 common input decision topics upon which your fatigue results are dependent. These fatigue decisions are grouped into the types listed below: 1. Fatigue Analysis Type 2. Loading Type 3. Mean Stress Effects 4. Multi-axial Stress Correction 5. Fatigue Modification Factor Loading types When minimum and maximum stress levels are constant, this is referred to as constant amplitude loading. This is a much more simple case and will be discussed first. Otherwise, the loading is known as variable amplitude or non- constant amplitude and requires special treatment Loading types The loading may be proportional or non- proportional: - Proportional loading means that the ratio of the principal stresses is constant, and the principal stress axes do not change over time. This essentially means that the response with an increase or reversal of load can easily be calculated. - Conversely, non-proportional loading means that there is no implied relationship between the stress components. Typical cases include the following: Alternating between two different load cases, An alternating load superimposed on a static load , Nonlinear boundary conditions . Terminology Consider the case of constant amplitude, proportional loading, with min and max stress values σmin and σmax: The stress range Δσ is defined as (σmax- σmin) The mean stress σm is defined as (σmax+ σmin)/2 The stress amplitude or alternating stress σa is Δσ/2 The stress ratio R is σmin/σmax Fully-reversed loading occurs when an equal and opposite load is applied. This is a case of σm = 0 and R = -1. Zero-based loading occurs when a load is applied and removed. This is a case of σm = σmax/2 and R = 0. Stress life theory • General: – The stress life (SN) analysis estimates the time spent to initiate and grow a crack until the component breaks into parts. – The model takes the stress variation and makes a look-up in a material graph to find the corresponding number of cycles to failure. – Historically this is the first mathematical model developed for lifetime calculations, and the one with the most readily available material data. – The analysis requires stress results from a linear static analysis as input. • Suitability and limitations: – The method is applicable for components failing after more than 10.000 to 100.000 cycles (HCF). – For higher loadings with a shorter fatigue lifetime local plasticity is probably considerable not only at the crack tip, but locally on the structure as well. – Such cases should be analysed using the Strain Life Method instead as the stress life method gives overly conservative results here. Stress life theory Material data – When doing test on stress range versus fatigue life and plotting the results on two logarithmic axis, the results tends to be linear. – Gustaw Wöhler observed this when doing bending test on railroad shafts, illustrated below. – Later Basquin formulated this mathematically in a power law. The curve may consist of several linear pieces. Two parameters for each of the curves in Basquin's law are needed as input: Starting point S and slope b. s The properties are usually found for zero mean stress and a uniaxial stress state on polished specimens. Stress life theory • Metals typically experience infinite fatigue life for low stress ranges. • This is modelled as a flat curve at a cut-off stress ΔSe and above Ne cycles. • Ne is usually between 1 and 5 million cycles and Se is typically half the ultimate strength Rm. The plateau tendency may not be present for other metals, such as aluminium or stainless steel. • As explained, Basquin is not valid in the low cycle fatigue region, so caution should be used if the calcu- lated life is low – as illustrated with the dashed line in the figure below. Stress life theory • The material curve on previous page may describe the fatigue strength of a base material, but it may also be describing the fatigue strength of a whole component, such as a welded T-joint. • Alternatively the material curve to be used may be dictated by a design standard, based not only on the material but also as a function of geometry, failure consequences and inspection intervals for example. Stress life theory Basquin's law Basquin's law calculates the number of cycles to fracture as: Nf = ƒ (S, S0, N0, b) Nf = Number of cycles to failure S = Applied stress range = Δσ = 2σa (N0, S0) = Point on the material curve b = Fatigue strength exponent (Slope of material curve) Basquin's law is usually presented as: However, usually So = Se and No = Ne, thus making Basquin's law: Stress life theory Basquin’s law In lack of fatigue material data, the following guidelines can be used (although other methods exist to predict this): 6 Se=0.5×Su at Ne = 10 3 S =0.9×Su at N = 10 Su = Rm (ultimate tensile stress) Stress life theory Mean stress correction Since the fatigue properties given are valid for zero mean stress only, one must do corrections if mean stresses are not equal to zero in the actual load history. Compressive mean stresses are good for fatigue life, while mean tensile stresses are bad. The three load histories to the right all have equal stress amplitudes, but different mean stresses. As such they will experience different fatigue life also. This is not covered by Basquin’s formulae. We will now look at a method to account for this so that Basquin still can be used. Stress life theory Mean stress correction A number of models exist to compensate for mean stresses, four are incorporated in ANSYS Fatigue module. - Goodman (England 1899) - Soderberg (USA 1930) - Gerber (Germany 1870) - Mean Stress Curves The three first models work in the same manner: The stress amplitude that is to be used in Basquin’s law is corrected according to the mean stress σm and yield or tensile stress σy or σu. The three models are shown graphically below: Stress life theory Mean stress correction The last model does not use any correction formulae, but instead have several material curves input - each corresponding to its own Stress Ratio (R): Tests yield results between that predicted by the Goodman and Gerber models.
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