**Table of Contents**show

Generally, the S-N curves obtained through the manual are mostly the test results of standard specimens without notch, but the shape, size, surface state, working environment and working load characteristics of actual parts may be very different, and these factors have a great impact on the fatigue strength of parts.

The influencing factors of fatigue strength can be divided into three aspects: mechanics, metallurgy and environment.

These factors are interrelated, which makes it complex to comprehensively evaluate the influence of these factors in fatigue strength design and fatigue life prediction.

Among the three kinds of factors, the mechanical factor can be fundamentally attributed to the influence of stress concentration and average stress;

Metallurgical factors can be summarized as metallurgical quality, that is, material purity and material strength;

Environmental factors mainly include corrosive medium and high temperature.

For railway vehicle parts, most of them work in atmospheric and normal temperature environment, so generally, mechanical and metallurgical factors should be mainly considered.

They include the influence of notch shape, size, surface state and average stress.

For the empirical formula related to the specific data of the influence of these factors on the fatigue limit, refer to the relevant manuals and materials.

This paper mainly discusses some important influence laws or phenomena that need to be understood in fatigue strength design and fatigue life prediction, as well as precautions that must be or should be considered.

**1. Notch shape effect**

Parts or components often have so-called notches such as shoulder steps, bolt holes, oil holes, keyways, etc.

Their common feature is that the cross-sectional area of parts has a sudden change at the notch, and the stress at the root of these notches will rise sharply, which is called stress concentration.

The stress concentration at the notch is the main factor that causes the fatigue strength of components to decrease significantly.

The stress concentration makes the actual stress at the root of the notch much greater than the nominal stress, causing fatigue cracks at the notch, and ultimately leading to the failure or damage of the part.

The degree of stress concentration is described by stress concentration factor (also called theoretical stress concentration factor) Kt, and the expression is as follows:

Here, σ_{max} is the maximum stress, and σ_{0} is the average stress obtained by dividing the load by the net sectional area at the notch, also known as the nominal stress.

In a certain range, the smaller the curvature radius ρ at the notch root, the greater the stress concentration and the greater the reduction of fatigue strength.

However, for plastic materials such as low and medium carbon steel, when the curvature radius at the notch root is further reduced or even less than a few millimeters, the reduction of fatigue strength will become smaller and smaller, or even no longer reduce.

At this point, the stress concentration factor cannot truly reflect the impact of notch on fatigue strength.

Therefore, the fatigue notch factor K_{f} (formerly known as effective stress concentration factor) is often used to more directly reflect the true reduction of fatigue strength.

Here, σ_{w0} and σ_{w} are the fatigue limits of notched smooth specimens and notched specimens respectively.

The following figure shows the relationship between the stress concentration factor K_{t} and the fatigue notch factor K_{f} of steel.

It can be seen from the figure that for low and medium carbon steel, when the stress concentration coefficient is less than 2~2.5, K_{t} and K_{f} are basically the same, but when this value is exceeded, the growth rate of K_{f} is significantly slower.

For high carbon steel with high strength ratio, the linear increase of K_{f} with Kt keeps a long range.

It can be seen that the fatigue strength of high-strength steel is highly sensitive to the notch while that of low and medium-strength steel is less sensitive to the notch.

Generally, K_{f}<K_{t}, but for the sharp notch of high carbon steel, K_{t}>K_{f} may exist.

This phenomenon also exists for bolt parts, sometimes K_{t} is about 4 and K_{f }is 8~10.

This is mainly because the load shared by each thread is uneven, and even several loads are on a thread.

For smooth materials, surface heat treatment such as surface quenching, surface carburizing and surface nitriding can effectively improve their fatigue strength.

But for notched materials, these methods may become ineffective and even reduce the fatigue strength.

This is because the surface strength is improved by heat treatment, and the notch sensitivity is also increased.

The following figure shows the fatigue strength of notch materials of high-strength steel and low strength steel with good plasticity changes with the increase of stress concentration.

In the range of smaller stress concentration K_{t}, the fatigue strength of high strength steel is obviously higher than that of low strength steel.

However, with the increase of stress concentration factor, the fatigue strength of high strength steel decreases more rapidly than that of low strength steel, so that the fatigue strength of high strength steel is almost the same as that of low strength steel.

For welded components, because the welding heat affected zone is located at or near the structural notch in many cases, combined with the effect of welding defects and welding residual tensile stress, the fatigue strength may be significantly reduced by several times or even more than ten times.

The fatigue notch coefficient is also affected by the size of the parts.

Generally, with the same notch, the fatigue notch coefficient increases with the increase of the size.

Therefore, for notched materials or parts with notches, in order to improve their fatigue life, the most effective method is to reasonably carry out structural design and process selection to reduce or improve their stress concentration.

On the contrary, it may reduce the fatigue strength of components under the condition of rough surface and large size.

**2. Size effect of parts**

The diameter of the style used for fatigue test is generally in the range of 5~10mm, which is very different from the size of the actual parts.

Generally, for parts under bending and torsion loads, the fatigue strength decreases with the increase of size.

But for axial tension and compression load, the size has little effect.

The influence of size on fatigue limit is expressed by size influence coefficient ε.

Here, σ_{d} and σ_{d0} are the fatigue limits of smooth specimens of any size and standard size, respectively.

The size effect of high strength steel is larger than that of low strength steel, and the size effect of parts with rough surface is larger.

The size effect is mainly due to the influence of the structure state and stress gradient of larger size materials on the fatigue strength.

The larger the size of the material, the more difficult it is to control the manufacturing process, the poorer the compactness and uniformity of the material structure, the more metallurgical defects, and the larger the surface area, the more the number of these defects.

Therefore, the greater the chance of fatigue and cracks on the surface of large size specimens.

All these can be attributed to the local stress concentration caused by metallurgical defects, which leads to the generation of fatigue cracks.

With regard to the influence of stress gradient, under the condition of bearing bending, torsion and other loads, the larger the size of the part is, the smaller the gradient of working stress is, the higher the average stress in unit area is, and the easier the fatigue crack is generated.

**3. Effect of surface condition**

The surface condition includes surface roughness, surface stress state, surface plastic deformation degree, surface defects and other factors.

In the test, the standard sample with polished (or polished) surface is used, but the actual surface of the parts is often the machined surface, forged surface and cast surface.

Machining will produce plastic work hardening on the surface of the part.

Cutting often produces a certain residual compressive stress on the surface of parts, which is beneficial to fatigue strength but has limited effect.

However, residual tensile stress, which is unfavorable to fatigue strength, is often produced during grinding.

On the other hand, the roughness on the micro scale of the machined surface causes stress concentration and reduces the fatigue strength.

As a result of the combined action of these factors, the fatigue strength is lower than that of the standard sample.

However, forged or cast surfaces generally have higher surface roughness, and there are surface work hardening layers and surface residual compressive stresses, which will significantly reduce the fatigue strength.

Therefore, formally, the rougher the surface processing method is, the greater the influence on the reduction of fatigue strength is.

The influence of surface processing conditions on fatigue strength is expressed by surface processing coefficient β.

Here, σ_{β} is the fatigue limit of the standard smooth sample in a certain surface state, σ_{β0} is the fatigue limit of the polished standard smooth sample, and abroad is the standard smooth sample with polished surface.

From the metallurgical point of view, rough machining has a greater impact on the fatigue strength of high-strength materials, so that high-strength steel may not play a role in improving the fatigue strength in the rough machining state.

This is mainly due to the high notch sensitivity of high-strength materials to rough surfaces, and the small work hardening effect of machining on the surface of high-strength steel.

There is little research on the influence of surface defects such as surface decarburization, surface bump marks and scratches on fatigue strength, but surface defects caused by these accidental reasons will have a great impact on fatigue strength.

Therefore, enough attention should be paid in the design, especially in the manufacturing process.

For smooth materials, surface heat treatment and other surface modification methods can improve the fatigue strength, but for materials with notches such as actual parts, these methods have little effect, even have the opposite effect.

Therefore, shot peening and rolling are often used to generate work hardening and residual compressive stress on the surface, thus improving the fatigue strength of components.

However, these two methods generally do not significantly improve the fatigue strength of parts with holes.

The latest research shows that the method of using a simple metal die to chamfer a small amount of the edge of the hole, so as to make the notch part residual local plastic deformation, has significantly improved the fatigue strength, and even can completely eliminate the impact of the notch to reduce the fatigue limit.

In the past, it was generally believed that the main reason for the surface plastic processing method to improve the fatigue strength was that residual compressive stress was generated on the surface to offset some of the working stress.

In fact, the compressive concentrated stress produced by the residual compressive stress at the notch offset the adverse effect of the notch;

The plastic deformation strengthens the tiny weak area in the structure near the notch, makes the structure performance more uniform, and improves the overall strength, thus improving the stress level that produces fatigue cracks.

At the same time, the residual compressive stress also makes the fatigue crack stop growing and become a stay crack.

**4. Effect of average stress**

As mentioned above, the root cause of fatigue failure is the dynamic stress component, but the static stress component, i.e. the average stress, also has some influence on the fatigue limit.

In a certain range of static stress, the compressive static stress increases the fatigue limit, while the tensile static stress decreases the fatigue limit.

It is generally believed that the residual stress has the same effect on the fatigue limit as the average stress.

For a material, a fatigue limit diagram can be drawn according to its fatigue limit results under various average stresses or stress ratios R.

The abscissa in the figure below is the ratio of the average stress σ_{m} (or residual stress) to the strength limit σ_{b}, and the ordinate is the ratio of the stress amplitude σ_{a} to the symmetrical cyclic fatigue limit σ_{-1}. Both are dimensionless quantities.

It can be seen from the figure that most test data points fall between straight lines and curves.

This line is called Goodman line; A curve is a Gerber parabola;

Soderberg line is obtained by replacing σ_{b} with yield limit σ_{s};

Morrow line is obtained by replacing σ_{b} with true fracture stress σ_{f}.

As follows:

Goodman line:

Gerber line:

Soderberg line:

Morrow line:

Goodman wire is a little conservative and simple for ductile metals, and is widely used in fatigue design.

Another commonly used method is called ideal improved Goodman diagram.

The following figure shows the ideal improved Goodman diagram of I-shaped steel butt beam under bending fatigue load.

The abscissa represents the minimum stress σ_{min}, the ordinate represents the maximum stress σ_{max}, and the linear equation is:

Where, m is the slope of Goodman line, b is the intercept of the line on the y-axis, and it is the fatigue limit of pulsation cycle when the minimum stress is equal to zero.

When the fatigue limit is expressed by the maximum stress, namely σ_{ w}= σ _{Max}, considering the stress ratio R= σ _{max}/ σ_{ Min}_{.}_{}

Morrow line includes:

The fatigue limit when the stress ratio is R can be obtained from the above formula.

The specific structure of the actual vehicle is much more complex than the test conditions when obtaining the S-N curve, such as the welding form and stress concentration, etc.

The American AAR standard provides us with valuable reference on the fatigue strength of many typical welding structures.

Therefore, b and m in the actual calculation are taken from the AAR standard.

The test results show that the influence of static load components on stress concentration coefficient, dimension coefficient and surface coefficient is small and can be ignored.