## Steel performance analysis: about fatigue curve and basic fatigue mechanical properties

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Fatigue curve and symmetrical cycle fatigue curve

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Fatigue curve and fatigue limit

Fatigue curve is the relationship curve between fatigue stress and fatigue life, that is, S-N curve, which is the basis for determining fatigue limit and establishing fatigue stress criterion.

In 1860, Wöhler first proposed the concepts of fatigue curve and fatigue limit when solving the fracture of train axle, so later generations also called this curve the Wöhler curve.

For metal materials with general strain aging, such as carbon steel, ductile iron, etc., when the cyclic stress level drops to a certain critical value, the low stress section becomes a horizontal line section, indicating that the specimen can undergo infinite stress cycles without fatigue Fracture, so the corresponding stress is called the fatigue limit, denoted as σ-1 (symmetric cycle, r=-1). If this kind of material does not break after 10^{7} cycles of stress cycles, it can be considered that it will not break even after infinite stress cycles. Therefore, 10^{7} cycles are often used as the basis for determining the fatigue limit.

Another type of metal material, such as aluminum alloy, stainless steel, etc., has no horizontal part in the SN curve, but as the stress decreases, the cycle continues to increase. At this time, it can only be specified that a certain cycle cycle does not occur according to the use requirements of the material. The stress at break is regarded as the conditional fatigue limit, or the finite life fatigue limit.

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Determination of fatigue curve

The fatigue curve is usually determined by rotating bending fatigue test. The high stress (limited life) part of the SN curve is measured by the group test method, that is, the higher stress level of 3-4 is taken, and the data of about 5 samples are measured at each stress level, and then the data is processed and calculated The median (50% survival rate) fatigue life.

The σ-1 measured by the lifting method is used as the lowest stress level point of the S-N curve, and the result of the group test method is fitted to a straight line or curve, and the median S-N curve with a survival rate of 50% can be obtained.

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Fatigue limit under different stress states

The same material has different fatigue limits under different stress states, but there is a certain connection between them. The experiment determined that there is a certain relationship between the symmetrical bending fatigue limit and the symmetrical tension-compression and torsion fatigue limit.

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The relationship between fatigue limit and static strength

Tests show that the greater the tensile strength of a metal material, the greater its fatigue limit. For medium and low-strength steels, the relationship between fatigue limit and tensile strength is roughly linear.

- When σb is low, it can be approximately written as σ-1=σb;
- When σb is higher, this near-linear relationship will deviate. This is because when the strength is higher, the plasticity and fracture toughness of the material decrease, and cracks are easy to form and propagate.

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Fatigue diagram and asymmetric cycle fatigue limit

Many parts work under asymmetric cyclic loads, so it is necessary to determine the asymmetric cyclic fatigue limit of materials to meet the design and material selection requirements of such parts. Generally, engineering drawing method is used to obtain the fatigue limit of various asymmetric cycles from the fatigue diagram. According to different drawing methods, there are two fatigue diagrams:

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1. σa-σm fatigue diagram

Under the condition of different stress ratio r, the fatigue limit σr represented by σmax is decomposed into σa and σm, and the ABC curve is drawn in this coordinate system to obtain the σa-σm fatigue diagram.

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2. σmax(σmin)-σm fatigue diagram

The fatigue limit under different stress ratio r is expressed in the coordinate system with σmax (σmin) and σm respectively, and a fatigue diagram is formed. AHB is the fatigue limit σmax under different r. The fatigue limit increases with the increase of the average stress or stress ratio, but the stress amplitude a decreases.

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Anti-fatigue overload capacity

Metal parts are occasionally subjected to short-term overload, and the original fatigue limit of the material may not change or may be reduced. This depends on the overload stress of the material and the corresponding cumulative overload cycles.

If the metal is operated for a certain number of cycles under a stress level higher than the fatigue limit, its fatigue limit and fatigue life will decrease, which will cause overload damage. The ability of metal materials to resist fatigue overload damage is expressed by overload damage boundary or overload damage zone.

The overload damage boundary is determined by experiments. Different overload stress levels and the corresponding stress cycle cycles that start to reduce the fatigue life are measured, and different test points are obtained, and the overload damage boundary is obtained by connecting each point. The hatched area between the overload damage boundary and the high stress area of the fatigue curve (the stress cycle of fatigue fracture at each stress level of the line segment, called the overload persistence value) is called the overload damage area.

When the machine is overloaded and operated in this area, the fatigue limit of the material must be reduced to varying degrees, and the more the reduction is near the endurance value. The steeper the overload damage boundary (or the overload duration value) of the material and the narrower the damage zone, the stronger its ability to resist fatigue overload.

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Fatigue gap sensitivity

Due to the needs of use, mechanical parts often have steps, corners, keyways, oil holes, threads, etc. These structures are similar to notches, which will change the stress state and cause stress concentration. Therefore, it is also important to understand the influence of the stress concentration caused by the notch on the fatigue limit.

When evaluating materials based on fatigue notch sensitivity, two extreme situations may occur:

- Kf=Kt, that is, the stress distribution in the fatigue process of the notched specimen is exactly the same as the elastic state, and no stress redistribution occurs. At this time, the notch reduces the fatigue limit the most serious, the fatigue notch sensitivity qf =1, and the material’s notch sensitivity is the largest.
- Kf=1,σ-1=σ-1N, the notch does not reduce the fatigue limit, indicating that the stress has a great redistribution during the fatigue process, and the stress concentration effect is completely eliminated. qf=0, the material’s notch sensitivity is the smallest.

Therefore, the qf value can reflect the material’s ability to redistribute the stress during the fatigue process and reduce the stress concentration.

In high cycle fatigue, most metals are very sensitive to notch, while in low cycle fatigue, most metals are not very sensitive to notch, because the root area of notch in the latter is already in the plastic zone, resulting in stress relaxation and reduction of stress concentration.

Source: China Flanges Manufacturer – Yaang Pipe Industry Co., Limited (www.steeljrv.com)

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)

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