The fatigue strength of materials is very sensitive to various external and internal factors.

External factors include the shape and size of parts, surface finish and service conditions.

The internal factors include the composition, microstructure, purity and residual stress of the material.

The slight change of these factors will cause the fluctuation or even great change of material fatigue performance.

The influence of various factors on fatigue strength is an important aspect of fatigue research.

This research will provide the basis for the reasonable structural design of the parts, the correct selection of materials and the reasonable formulation of various cold and hot processing technologies, so as to ensure that the parts have high fatigue performance.

Table of Contents

**01 ****E****ffect of stress concentration**

The conventional fatigue strength is measured by carefully processed smooth specimens.

However, the actual mechanical parts inevitably have different forms of gaps, such as steps, keyways, threads and oil holes.

The existence of these notches results in stress concentration, so that the maximum actual stress at the root of the notch is far greater than the nominal stress of the part, and the fatigue failure of the part often starts from here.

**Theoretical stress concentration factor K****t****:**

Under the ideal elastic condition, the ratio of the maximum actual stress to the nominal stress at the root of the notch is obtained from the elastic theory.

**Effective stress concentration factor (or fatigue stress concentration factor) K****f****:**

Fatigue limit of smooth specimens σ- 1 and fatigue limit of notched specimens σ- 1 n.

The effective stress concentration factor is not only affected by the size and shape of the component, but also by the physical properties, processing, heat treatment and other factors of the material.

The effective stress concentration factor increases with the increase of notch sharpness, but it is usually less than the theoretical stress concentration factor.

**Fatigue notch sensitivity coefficient ****q****:**

The fatigue notch sensitivity coefficient represents the sensitivity of the material to the fatigue notch and is calculated by the following formula:

The data range of q is 0 ~ 1. The smaller the q value is, the less sensitive the characterization material is to the notch.

It is shown that q is not only a material constant, but also related to notch size

Only when the notch radius is larger than a certain value, the q value is basically independent of the notch, and the radius value is different for different materials or treatment states.

**02 ****The influence of size factor**

Due to the inhomogeneity of the material structure and the existence of internal defects, the increase of the size will increase the failure probability of the material, thus reducing the fatigue limit of the material.

The existence of size effect is an important problem in the application of fatigue data from small specimens in laboratory to large-scale practical parts.

Because it is impossible to reproduce the stress concentration and stress gradient of the actual size parts on the small samples, the results of the laboratory and the fatigue failure of some specific parts are disjointed.

**03 ****I****nfluence of surface processing state**

There are always uneven machining marks on the machined surface, which are equivalent to tiny gaps, causing stress concentration on the material surface, thus reducing the fatigue strength of the material.

The results show that for steel and aluminum alloy, the fatigue limit of rough machining (rough turning) is reduced by 10% ~ 20% or more than that of longitudinal polishing.

The higher the strength of the material, the more sensitive it is to the surface finish.

**04 ****The impact of ****loading ****experience**

In fact, no part works under absolutely constant stress amplitude.

Overload and secondary load will affect the fatigue limit of materials.

The results show that overload damage and secondary load training are common in the materials.

The so-called overload damage means that the fatigue limit of the material will decrease after the material runs for a certain number of cycles under the load higher than the fatigue limit.

The higher the overload, the shorter the damage cycle, as shown in the figure below.

Overload damage boundary

In fact, under certain conditions, a small number of times of overload will not cause damage to the material. Due to the effect of deformation strengthening, crack tip passivation and residual compressive stress, the material will also be strengthened, so as to improve the fatigue limit of the material.

Therefore, the concept of overload damage should be supplemented and modified.

The so-called secondary load exercise refers to the phenomenon that the fatigue limit of the material increases after a certain cycle of operation under the stress level which is lower than the fatigue limit but higher than a certain limit value.

The effect of the second load exercise is related to the performance of the material itself.

Generally speaking, for materials with good plasticity, the exercise cycle should be longer and the exercise stress should be higher.

**05 Influence of chemical composition**

There is a close relationship between fatigue strength and tensile strength under certain conditions.

Therefore, under certain conditions, all the alloy elements that can improve the tensile strength can improve the fatigue strength of the material.

Comparatively speaking, carbon is the most important factor affecting the strength of materials.

However, some impurity elements which form inclusions in the steel have adverse effects on the fatigue strength.

**06**** ****Effect of heat treatment on Microstructure**

Different heat treatment state will get different microstructure, so the effect of heat treatment on fatigue strength is essentially the effect of microstructure.

Although the same static strength can be obtained for materials of the same composition due to different heat treatments, the fatigue strength can vary in a considerable range due to different microstructures.

At the same strength level, the fatigue strength of flake pearlite is obviously lower than that of granular pearlite.

The smaller the cementite particles are, the higher the fatigue strength is.

The effect of microstructure on the fatigue properties of materials is not only related to the mechanical properties of various structures, but also related to the grain size and the distribution characteristics of the structures in the composite structure.

Grain refinement can improve the fatigue strength of the material.

**07**** ****Influence of inclusions**

The inclusion itself or the hole produced by it is equivalent to a tiny notch, which will produce stress concentration and strain concentration under the action of alternating load, and become the crack source of fatigue fracture, which has adverse effect on the fatigue performance of materials.

The influence of inclusions on fatigue strength depends not only on the type, nature, shape, size, quantity and distribution of inclusions, but also on the strength level of materials and the level and state of applied stress.

Different types of inclusions have different mechanical and physical properties, and have different effects on fatigue properties.

Generally speaking, plastic inclusions (such as sulfides) which are easy to deform have little influence on the fatigue properties of steel, while brittle inclusions (such as oxides, silicates, etc.) do great harm.

Inclusions with larger expansion coefficient than the matrix (such as sulfide) have less influence due to compressive stress in the matrix, while inclusions with smaller expansion coefficient than the matrix (such as alumina) have greater influence due to tensile stress in the matrix.

The compactness of inclusion and base metal also affects the fatigue strength.

Sulfide is easy to deform and closely combined with base metal, while oxide is easy to separate from base metal, resulting in stress concentration.

Therefore, from the type of inclusions, sulfide has less influence, while oxides, nitrides and silicates are more harmful.

Under different loading conditions, the effect of inclusions on the fatigue properties of materials is different.

Under the condition of high load, no matter whether there is inclusion or not, the external load is enough to make the material produce plastic flow, and the influence of inclusion is small.

However, in the fatigue limit stress range of materials, the existence of inclusions causes local strain concentration and becomes the controlling factor of plastic deformation, which strongly affects the fatigue strength of materials.

In other words, the existence of inclusions mainly affects the fatigue limit of the material, but has no obvious effect on the fatigue strength under high stress condition.

The purity of materials is determined by the smelting process. Therefore, the use of purification smelting methods (such as vacuum smelting, vacuum degassing and electroslag remelting) can effectively reduce the impurity content in steel and improve the fatigue performance of materials.

**08**** ****Influence of surface property change and residual stress**

In addition to the surface finish mentioned before, the influence of surface state also includes the change of surface mechanical properties and the influence of residual stress on fatigue strength.

The change of __mechanical properties__ of the surface layer can be caused by different chemical composition and microstructure of the surface layer, or by deformation strengthening of the surface layer.

Surface heat treatment, such as carburizing, nitriding and carbonitriding, can not only increase the wear resistance of parts, but also improve the fatigue strength of parts, especially the corrosion fatigue and pitting resistance.

The effect of surface chemical heat treatment on fatigue strength mainly depends on the loading mode, the concentration of carbon and nitrogen in the layer, the surface hardness and gradient, the ratio of surface hardness to core hardness, the depth of the layer, and the size and distribution of residual compressive stress formed by surface treatment.

A large number of tests show that as long as the notch is machined first and then treated by chemical heat treatment, generally speaking, the sharper the notch is, the more the fatigue strength is improved.

The effect of surface treatment on fatigue properties is different under different loading modes.

Under axial loading, because there is no uneven distribution of stress along the depth of the layer, the stress on the surface and under the layer is the same.

In this case, the surface treatment can only improve the fatigue performance of the surface layer, because the core material is not strengthened, so the improvement of fatigue strength is limited.

Under the condition of bending and torsion, the stress distribution is concentrated on the surface layer, and the residual stress formed by surface treatment and the external stress are superimposed, which reduces the actual stress on the surface

At the same time, due to the strengthening of the surface material, the fatigue strength under bending and torsion conditions can be effectively improved.

Contrary to chemical heat treatment such as carburizing, nitriding and carbonitriding, the fatigue strength of the material will be greatly reduced if the surface strength of the part is reduced due to decarburization during heat treatment.

Similarly, the fatigue strength of surface coatings (such as Cr, Ni, etc.) decreases due to the notch effect caused by the cracks in the coatings, the residual tensile stress caused by the coatings in the base metal, and the hydrogen embrittlement caused by the immersion of hydrogen in the electroplating process.

By induction __quenching__, surface flame quenching and shell quenching of low hardenability steel, a certain depth of surface hardness layer can be obtained, and favorable residual compressive stress can be formed on the surface layer, so it is also an effective method to improve the fatigue strength of parts.

Surface rolling and __shot peening__ can form a certain depth of deformation hardening layer on the surface of the specimen and produce residual compressive stress on the surface, which is also an effective way to improve the fatigue strength.