Saarstahl AG

Properties with static stress
Static stress is a permanent, vibration-free stress in a single or multi-axial direction. The calculation of static stress is based, for the most part, on data regarding the limit of elasticity and the tensile strength and, for particular requirements, also on the impact strength, elongation and necking. Generally, for constructions of which high demands will be made tempered steels where there is an optimum ratio for the limits of elasticity (limit of elasticity: tensile strength 100 in % c) are used . Furthermore, good toughness is achieved with tempered steels where sufficient hardenability in the core is ensured. With single cross sections and cases of stress (with bending or torsion), higher strength in the core is often not required since the neutral filaments are located there. However, there is often multi-axial stress where the properties at the surface and in the core should be more or less the same.

It must also be taken into account that hardness is in the inverse ratio to toughness. If the dimensions of a constructional component are to be reduced by increasing the hardness, it should be considered that this will bring about a reduction in toughness.

The above only relates to cases with purely static stress. If there is additional dynamic stress, the properties described are inadequate for carrying out the calculation.

Properties with dynamic stress
Dynamic stress is present where there is a pulsating or beating stress which may be single or multi-axial. Components which are subjected to constant vibration stress must have sufficient endurance fatigue strength (or, in short, fatigue strength). The term constant vibration stress is used to describe stress which constantly changes between a maximum stress s_o(s max.) and minimum stress s_u (s min.) It can be represented by a constant mean stress s_m and superimposed alternating stress with alternating stress amplitude ± s_a Therefore

s_d =s_m ± s_a

Fatigue strength is the stress which a part can just constantly withstand without breaking. It is defined as follows:

s_D =s_M ± s_A

The fatigue strength diagram according to Smith (figure 21) shows the cases of compression-tension stress and a diagram for constant stress.

The curves for s_o and s_u show the limit stress in the elastic range for various mean stresses. If s_m = O (i.e. the alternating stress amplitude fluctuates around the O-line), there is pure alternating stress.s_u = O represents pure pulsating stress.

The diagram applies to polished, un notched specimens. Apart from the tension-compression fatigue stress, depending on the type of stress, the terms fatigue strength with bending stresses and fatigue strength with torsional stresses are used.

For fatigue strength, a large number of influential values, depending both on the material and on the shape, are of importance. They can be divided into:

1. Metallurgical influences,
2. Technological infuences,
3. Mechanical influences,
4. Influences depending on the surface or shape,
5. Influences through manufacture of the specimens and testing conditions.

Metallurgical influences (such as the melting process and conduct of the heat, segregation and degree of purity) are of particular importance for steels with high levels of hardness. Therefore, steels melted in a vaccuum show great improvements in fatigue strength, particulary in a transverse directionally, compared to steels melted in air.

Cold working and heat treatment can both be considered as technological influences. Heat treatment, in particular, has a great influence on fatigue strength because of the type, distribution and evenness of the microstructure and due to the grain size and surface decarburization.

Mechanical influences (tensile strength, limit of elasticity and inherent stresses) along with the notch effect are of significant importance. Fatigue strength is proportional to tensile strength and the ratio of the limit of elasticity. However, it should be considered that, as the hardness increases, the notch sensitivity also increases. Figure 22 shows the influence of hardness on the fatigue strength with bending stresses depending on the surface finish.

It can clearly be seen that information regarding fatigue strength serves largely as a value for comparison and it is most practical to use only the values of polished specimens. The relation between fatigue strength and tensile strength can be represented by variousl approximation formulas with a scattering range of ± 20 %

Figure 21 (to elarge please klick to figure in question.)
Diagram showing constant stresses and an fatigue strength diagram (according to Smith) for tension-compression stress with mean tensile stresses.

Figure 22 (to elarge please klick to figure in question.)
Influence of surface finish, notches and corrosion on fatigue strength of points subjected to bending stresses (according to worksheet 1d. Special Committee for Machine Components b. VDI)

Approximation formulas for calculating fatigue strength:

Fatigue strength with bending stresses	= approx. 0.5 tensile strength
Fatigue strength with tension compression stresses	= approx. 0.46 . tensile strength
Fatigue strength with torsional stresses	= approx 0.28 . tensile strength

These values apply to polished and tempered specimens. No relation was ascertained between fatigue and impact strength and elongation at rupture and elongation at necking .

Inherent stresses change the fatigue strength depending on type, distribution and value. Whereas tensile stresses have a negative effect, compression stresses lead to increases in the fatigue strength. Therefore, with hardening of the surface (compressing, shotblasting), compressive stresses are created. Through nitriding, case and surface hardening, inherent compressive stresses are achieved and these result in an improvement in fatigue strength.

The surface finish and shape of the component are of particular importance. Rough, scarred surfaces with tool marks have an negative effect on the fatigue strength as a result of the notch effect. When designing components, sharp edged transitions, mould notches and profile changes which have a negative effect on stresses are to be avoided. The surface can be improved by grinding, polishing, blasting etc.

Fatigue strength is generally calculated according to the Wöhler method whereby several specimens of the same type are tested as the same mean or minimum stresses in various stress phases. The number of cycles till rupture is calculated. This gives us the curve known as the Wöhler curve which is shown in figure 23.

Fatigue strength is the stress which has not lead to rupture after 10⁷ cycles (characterized by the horizontal course of the curve). The area up to the number of cycles is known as the finite life fatigue strength. In this area, the specimen withstands an increased load for only a limited period of time. The area of finite life fatigue strength is divided into two sections by the damage curve:

Below this line, a specimen can be overloaded for a limited time without starting to rupture. Above the line (between damage line and Wöhler curve) the specimen does not rupture for some time after overloading but it does show damage in the form of several small tears. The damage line shows after how many cycles, how much damage to the specimen occurs without rupture occurring. Therefore, when a component is exchanged at regular intervals, the load within the finite life fatigue strength area below the damage line can be used (e.g. for transport cables).

The finite life fatigure strength and damage line are not sufficient to assess the life of components where there are large and frequent fluctuations in the amount of stress during operation. In such cases, fatigue strength under operating stresses is calculated for the components concerned under load conditions which are close to those experienced in practice.

Although fatigue strength is of essential importance for design calculations, exact data for the individual steels in not available. It is necessary to make do with reference values calculated for polished specimens. The reason for this is the large number of factors influencing fatigue strength, in paticular, the shape of the component and its surface finish. Any statements regarding figures for the component would have to be calculated exactly through testing under operating conditions.

Figure 23
Wöhler Line and Damage Line
for tests with constant mean stresses s_m [s_D = s_m ± s_A ]
or constant minimum stresses s_u [ s_D = ( s_u + s_A ) ± s_A ]

Fatigue fracture
The type of fracture which occurs most in practice is fatigue fracture. It is the result of fatigue in the material and arises after constant vibration stress which is at a level above the fatigue strength. This stress can be lower than the limit of elasticity which is sufficient for static loads and, if there is not a high level of mean stress, it occurs suddenly, without external distortion (also in soft steels). For components which are subjected to vibration stress, fatigue strength therefore forms the basis of the calculations.

Fatigue fracture (figure 24) has a typical appearance. Starting from the tearing point, there is a fine, silky fracture microstructure over a large area, characterized by a number of lines of rest running approximately concentric to the tearing point and showing the zones where the tear has occaisonally come to a standstill during its development. The other part of the fracture area shows a granular, slightly distorted, veined structure which has come about as a result of the force of the fracture.

As a result of the fracture´s specific appearance, significant conclusions can often be drawn as to how it was caused.

Appropriate design for shape
Often cases where damage has been caused by fatigue fracture are the result of inadequate design. In components subjected to dynamic stresses, care should be taken that there are no notch effects at transitional points in the cross section or unacceptably high tension peaks. In shafts and bolts, for example, grooves should be made in the transition points in the cross section and, at the same time, the surface should be free of tool marks. Sharp edged transitions are to be avoided at points which are at risk (Figure 25).

With constant vibration stresses, component connections such as screwed, clamped or shrink connections can cause damage to the surface due to reciprocal friction and seizing which, in turn, can be the start of fatigue fracture. This can be avoided through appropriate design and careful manufacturing.

If there is widespread frictional corrosion, surface hardening or nitriding can largely prevent seizing. At points which are subjected to greater stress or which are more at risk of rupturing, suface hardening can reduce this. This is due to an increase in the inherent compression stresses on the surface.

For designing components with a risk of fatigue fracture so that they are safe in operation, it is important to take not only the choice of material into account (tensile strength, limit of elasticity, notch sensitivity and optimum tempered condition) but also the shape of the oomponent and the surface finish: (avoidance of tension peaks, notch effects, tool marks and scars on the surface, with no decarburisation and possibly using a process for achieving surface compression stresses). Only if all the factors which have an influence are taken into account can safe operaion be guaranteed as far as possible for parts which are subjected to dynamic stresses.

Figure 24
Fatigue fracture

Figure 25
Design suited to the purpose
Transitions