the Methodology of Tribo-Fatigue

• Introduction
• Objects of Studies
• Method of Studies
• Processes and Phenomena
• Objectives and Tasks
• Interactions between Scientific Disciplines
• Interests of Tribo-Fatigue
• Bibliography

Method of studies

Another essential attribute of each scientific discipline is the methods of studies of objects (Table 1). Let’s begin our analysis with experimental methods (Fig. 6) [11, 12].

Table 1

Figure 6 – Development of methods of wear-fatigue tests: MRF – mechano-rolling fatigue, MSF – mechano-sliding fatigue, FF – fretting fatigue

Figure 7 – Typical methods of wear-fatigue tests: 1, 1a, 1b – specimen; 2 – test apparatus spindle; 3, 4 – counterspecimen; Q – bending load; F_N – contact load; w₁, w₂ – speed of rotation of specimen, counterspecimen

Specialists in the mechanics of fatigue fracture elaborate and apply the methods and machines or testing structural elements under various conditions of cyclic loading. Fig. 6 shows one such method for rotation bending of a cylindrical specimen. Fig. 7, c shows the tests scheme. Tribologists elaborate and apply the methods and machines for testing friction pairs under various conditions of contact interactions. Fig. 6 shows all three methods, Fig. 7, b and 7, d show the schemes of tests under rolling and sliding friction. Specialists in tribo-fatigue elaborate the methods and machines for complex wear-fatigue tests of models of active systems. Fig. 6 shows three methods of the tests, Fig. 7, a and 7, e show the schemes of tests for mechano-sliding and mechano-rolling fatigue. They are  the combination of test schemes implemented by specialists in tribology and strength. The difference is the following. Machines for friction tests do not allow to investigate the resistance of structural elements to fatigue. Machines for fatigue tests do not allow to investigate the friction and wear processes. Meanwhile SI series machines for wear-fatigue tests allow to investigate both, as it should be, but it is more essential that they allow to carry out complex tests under any combination of cyclic and contact loads acting simultaneously. Naturally it becomes possible to obtain fundamentally new experimental results.

Fig. 8 shows an example of the results of the tests of the active system, such as carbon steel 45 (the cylindrical specimen) / alloyed steel 25ХГТ (the roller), for mechano-rolling fatigue [5, 13, 14].

Figure 8 – Multicriterial diagram of limiting states of active system in mechano-rolling fatigue (SPW — surface plasticity waves)

The ABCD diagram is plotted in the coordinates of pressure р₀ in the center of the contact area (the x-axis) and amplitude s_а of cyclic stresses in bending (the
y-axis).

The point A is the fatigue limit s_–1 of steel 45 specimens, it is determined by common mechanical fatigue tests of the scheme shown in Fig. 7, c. The criterion of the limiting state is disintegration of the specimen into two parts due to the growth of the main fatigue crack in the dangerous section. Hence, this point implies the mechanics of fatigue fracture. Generally the y-axis s_а is the scale of strength: the results of fatigue tests of any structural elements of any materials may and should lie within this scale.

The point D is the critical pressure p_f under rolling friction without slippage, it is determined by common friction tests. The criterion of the limiting state is the appearance   of pittings of critical  density  along  the  rolling  path. Hence, this point implies tribology. Generally the x-axis р₀ is the tribological scale: the results of tests of any friction pairs with the elements of any materials may and should lie within this scale.

The curves ABCD are a diagram of limiting states of an active system under mechano-rolling fatigue. The diagram is plotted using the results of wear-fatigue tests of the scheme shown in Fig. 7, a. Hence, it is tribo-fatigue.

The limiting state within the portion AB is predominantly due to the growth of the main fatigue crack when the processes of pitting are attendant. Direct effect occurs in this case, which is satisfactorily described by the expression

where m_р = 0.92 is the contact hardening parameter.

On the contrary, the limiting state within the portion CD is determined by the critical density of pittings, meanwhile the evolution of mechanical fatigue cracks is an attendant damage. Back effect occurs in this case, which is satisfactorily described by the equation

where m_s = 0.65 is the cyclic hardening parameter.

The portion BC is transient, hence it is of particular interest since the kinetic processes of interactions between friction phenomena (together with wear) and mechanical fatigue take place here at a very high level of loading parameters s_а and р₀. In these test conditions it is stated that surface waves of plasticity emerge along the rolling path, though the profile radius of the counterspecimen (the roller) remains practically perfectly smooth. Appearance of the waves is another attribute of the limiting state since impermissible vibrations are generated in the system.

Analysis of the ABCD diagram allows to make the following basic conclusions.

1. Fatigue limit of a specimen increases 1.5—1.6 times providing the process of rolling friction comes into effect simultaneously (the direct effect — AB portion). The direct effect coefficient advanced in tribo-fatigue

is in reality the characteristic of strength; in experiments its maximum is K_Dmax = 268/165 = 1.62. Coefficient (4) is naturally included into equation (2).

2. The critical (limiting) pressure under rolling friction increases 1.2—1.25 times providing cyclic stresses are induced in the specimen simultaneously (the back effect — BC portion). The back effect coefficient advanced in tribo-fatigue

is in reality a tribological characteristic; in experiments its maximum is K_Bmax = 2200/1760 = 1.25. Coefficient (5) is naturally included into equation (3).

3. Within the optimum range of contact pressures (р » 400–1300 MPa) the process of wear under rolling results in significant improvement of the reliability of a system based on the criterion of fatigue resistance, hence any tendency towards wearless friction in this case is unjustifiable.

4. Tensile stresses under cyclic loading within the optimum conditions (s_а » 50–100 MPa) are positive significantly improving the reliability of a system based on the criterion of rolling friction resistance.

Better characteristics of the limiting state s_-1р and р_fs in the process of wear-fatigue tests compared with the characteristics under rolling friction (р_f) and mechanical fatigue (s_-1) can be explained from the standpoint of mechanics by the following major causes:

·     addition of stresses with opposite signs (contact and bending), which leads to shifting the mean stress of the cycle towards negative values and therefore leads to the reduction of the maximum cycle stress;

·     hardening of the working portion of the specimen by surface plastic deformation;

·     appearance of favorable residual compressive stresses;

·     healing  primary fatigue cracks during elastoplastic deformation in the process of rolling friction.

The governing parameter of wear-fatigue damage (see Fig. 8)

has the critical value

This critical value separates the spheres of direct and back effects in the diagram of the limiting states of an active system. If m_sp < m_k, the CD curve is obtained. If m_sp > m_k, the AB curve is obtained. m_sp = ¥ corresponds to the point A (pure mechanical fatigue), and m_sp = 0 corresponds to the point D (pure rolling friction).

Hence, only methods of wear-fatigue tests allow to obtain a number of characteristics which truly reflect (describe) the serviceability of a real active system as the object studied by tribo-fatigue. Naturally the methods of tests for friction and the methods of fatigue tests reflect (describe) the performance of friction pairs (the object studied by tribology) and the structural elements (the objects studied by the mechanics of fatigue fracture), respectively. Yet, from Fig. 8 it follows that characteristics of serviceability determined experimentally within the frameworks of the reviewed disciplines should not be opposed. On the contrary, the point A (pure fatigue) and the point D (pure friction) naturally belong to the ABCD diagram of limiting states (wear-fatigue damage) so that the characteristics s_–1 (in the point A) and р_f (in the point D) are basic for tribo-fatigue (see also equations (2), (3) and coefficients (4), (5), (6a)).

Now let’s examine the methods of theoretical studies (see Table 1). The theory is known to rely upon experience. Hence, tribologists use their own experience to elaborate primarily the mechanics of contact interactions. Specialists in strength use their experience to elaborate the mechanics of deformation and fracture. Of course, specialists in tribo-fatigue use both as an inseparable entity. Yet, in order to study a more extensive object new approaches are to be sought for investigating complex phenomena.

Hence, a non-traditional approach towards the analysis of contact problems and the problems of the mechanics of deformation and fracture is being developed recently in tribo-fatigue. The approach is based on using a statistical model of the deformable solid with a dangerous volume (DSDV model) [15–17]. According to this model the strength of a specimen (including its surface strength) is determined by the region of finite dimensions containing the critical level of stresses. This region is termed as the dangerous volume.

The concept of the approach advanced in tribo-fatigue is the following [18, 19].

Assume the steel shaft is cyclically bended by moment M, so that in some region of the shaft the field of normal stresses s is a damaging one. It means that a dangerous volume V_pg > 0 (cases F in Fig. 9), limited by the condition s ³ s_–1min, where s_–1min is the lowest value of the dispersion of fatigue limits, is formed on the surface of the shaft.

Assume the process of rolling friction or sliding friction is realized in the dangerous zone of the shaft. Assume that the field of contact pressures p in the (shaft – counterspecimen) active system is such that it produces a dangerous volume S_pg (cases T in Fig. 9) in the contact region. In case of sliding friction this dangerous volume S_pg = S_WP is formed within a fine surface layer of the shaft (case T-1). In case of rolling friction the dangerous volume S_pg = S_WP (case T-1) and / or S_pg = S_VP (case T-2) is formed both on and under the surface. In all these cases it is limited by the damaging level of tangential stresses t ³ t_-1min, where t_-1min is the lowest value of dispersion of fatigue limit in shear (or torsion of thin-walled tubes).

Assume wear-fatigue tests are a combination of cyclic bending and friction (sliding or rolling). Then two situations are possible when dangerous volumes appear (the right column in Fig. 9). First, volumes V_pg and S_pg combine on the surface (case FT-1). Second, they combine under the surface (case FT-2).

Figure 9 – Scheme of emergence of dangerous volumes during friction tests (S_pg > 0), fatigue tests (V_pg > 0) and wear-fatigue tests (W_pg > 0)

In both these cases a combined dangerous volume W_pg > 0 appears as a function of volumes V_pg and S_pg, i.e.

where j_SV is the function of interaction; it can be assumed that in some cases it is enough to treat this function as the parameter of interaction.

The formulas for determination of dangerous volumes using any component of normal s and tangent t stresses are given in Table 2. Applying the DSDV model to mechanical fatigue and friction it is easy to derive the conditions of failure-free operation and / or the conditions of damage and fracture if suitable measures of damage w are introduced (S₀ and V₀ are the working volumes in friction and fatigue, respectively). All the solutions are easily expandable to cover the case of complex wear-fatigue damage.

Table 2

Moreover, the problems of reliability, strength, wear resistance and life are solved with the account of the fundamental relationship between the relevant characteristics and the scale of damaged areas of an object (i.e. the size of its dangerous volume).

For example basic results of the assessment of the indicators of reliability of metal-to-polymer active system (see Fig. 7, e) under mechano-sliding fatigue can be shown. It has been established that the probability of failure of the metal-to-polymer system is determined by the function:

where Y(s, p) is the function of interactions between the phenomena of friction, wear (under the effect of contact pressure p) and mechanical fatigue (under the effect of cyclic stresses s).

According to (8) the probability of failure of the metal-to-polymer system under mechano-sliding fatigue increases with growth of the number of defects in the metal and the polymer (the parameters of isotropy m_V and m_S), the sizes of dangerous areas of deformation under cyclic loading and friction (the dangerous volumes V_pg and S_pg), effective cyclic (s > s_–1min) and contact р < р_d stresses, temperatures of the metal and polymer (Т_M and DT_p). It also depends on the shape of the bodies, the configuration of their contact interaction, the method of cyclic deformation of the body (the coefficients C_V and C_S), geometrical dimensions of the contacting solids (the working volumes V₀ and S₀), the mechano-physical properties of the polymer (the destruction limit р_d and singular thermofluctuating stress ) and the metal (the parameters s_–1min and s_w of the function of distribution of durability limits), thermal activation of the chemico-physical processes of fatigue damage (the parameter m_T).

After performing relevant limiting transitions function (8) yields the formulas for predicting two more indicators of the wear-fatigue damage (see Fig. 3). First, a formula to calculate the average value  of the fatigue limit of the metallic shaft with the account of the effect of the friction and wear processes under contact pressure p (the direct effect):

where  is the average value of the fatigue limit of the shaft with the account of temperature Т_M, b_S – the coefficient. According to formula (9) usually  in the metal-to-polymer system during mechano-sliding fatigue, the bigger is the contact pressure p the smaller is the value .

Second, a formula for calculating the average wear rate  of the polymeric counterbody with the account of the effect of cyclic stresses s in the conjugated metallic specimen under the effect of contact pressure p (the back effect):

where  is the average wear rate in a similar friction unit (in which s = 0), b_V is the coefficient. It follows from formula (10) that  is always observed in the metal-to-polymer system under mechano-sliding fatigue under equal contact pressures in the friction unit and the active system.

According to (10), wear rate can be controlled in a non-traditional manner by exciting cyclic stresses in one of the elements of the friction unit. Experimental studies have confirmed that such control is highly effective. To exemplify it Fig. 10 shows the results of MSF (see Fig. 7, e) tests of the alloyed steel 40X (the specimen) / formaldehyde copolymer (the counterspecimen) system under constant contact pressure р_а = 5.7 MPa. If the amplitude of cyclic stresses increases from 160 to 300 MPa, an incriment in the wear rate due to these stresses grows from 110 to 180%.

It should be noted that s_–1р > s_–1 in case of the mechano-rolling fatigue of the metal-to-metal system (see Fig. 8 and equation (2)), on the contrary, in case of the mechano-sliding fatigue of the metal-to-polymer system it turns out that s_–1р < s_–1 in accordance with equation (9). The latter regularity is well corroborated by the experimental data. Fig. 11 exemplifies it by showing the back dependence of the limiting stresses on the contact pressure in the alloyed steel / polymer system. It means that the regularities of the direct effect can be highly variable.

Figure 10 – Dependence of the increment of polymer wear rate intensification on amplitude of cyclic stresses (active system is alloyed steel 40X / formaldehyde copolymer)

Figure 11 – Dependence of limiting stresses  on nominal contact pressure in the active system of chromium steel 40X (specimen) / glass-filled (~25%) polyamide Duretan                           BKV-30H (counterspecimen)

Equations (9) and (10) approximate sufficiently well the experimental data (the points in Fig. 10 and 11). One of the causes is that both these equations are constructed with the account of the DSDV model. Equation (9) contains the value S_pg/S₀, meanwhile equation (10) contains the value V_pg/V₀.