Chapter 4 DIRECT AND BACK EFFECTS

4.1 General notions

4.2 Mechano-sliding fatigue.

4.2.1 Direct effect.

4.2.2 Back effect.

4.3 Mechano-rolling fatigue

4.3.1 Direct and back effects

4.3.2 Translimiting state

4.4 Effect of interaction conditions.

Self-test questions

Tasks for students' research

4.2 Mechano-sliding fatigue

4.2.1 Direct effect

Since direct effect is determined as changes of characteristics of resistance to fatigue due to the processes of friction and wear, its basic regularities are studied experimentally, from the standpoint of fatigue fracture mechanics (see pp. 1.3 and 3.3).

Let us design the simplest experiment observing the following basic principles:

·     a metal-to-polymer system is to be tested, i.e. the specimen (metal) and the counterspecimen (polymer) are made from the materials with contrasting mechanophysical properties of unlike origin;

·     the process of sliding friction occurs without any lubricating material, so the effect of the latter is ignored;

·     the metallic specimen experiences practically no wear during tests, hence only one component in the pair, viz. the counterspecimen, undergoes wear;

·     a linear state of stress appears in the working zone of the specimen during cyclic bending, i.e. they are the simplest conditions of tests for fatigue;

·     the process of friction locates in the zone of tension of the specimen in bending.

The following pieces were prepared for the tests:

·     cylindrical specimens from high-chrome steel 40Х (the ultimate strength in tension is 970 MPa);

·     counterspecimens from glass-filled (»25%) polyamide “Durethane” BKV-30H (the ultimate strength in compression is 170 MPa).

The configuration of the experiment causes some doubt. It seems apparent that the relatively soft counterbody cannot significantly affect the resistance of the quite hard steel to fatigue because no physical wear of the specimen is expected.

Fig. 4.1 shows the results of the experiments. From Fig. 4.1, а it follows that in the process of wear-fatigue tests of the metal-to-polymer system the durability of the steel specimen at the amplitude of stresses s_a = 200 MPa and contact pressure р_a = 8,5 MPa reduces ten times and the fatigue limit reduces by 32% (compared with common fatigue). If the amplitude of stresses diminishes to 150...160 MPa, the durability during wear-fatigue tests is approximately 10⁶ cycles, meanwhile the specimens do not fail at all during usual fatigue tests.

Thus, the processes of friction affect considerably the changes of characteristics of fatigue resistance (direct effect). Since no physical wear of the metallic specimen occurs in these test conditions, it may not be responsible for the above effect. In this case it is due to a complex of chemophysical phenomena in the friction zone. In particular, products of tribodestruction are known to possess the properties of surfactants. They accumulate in the contact zone and facilitate migration and multiplication of dislocations on the metallic friction surface (Rebinder effect, see p. 1.4.3). It causes acceleration of the surface fatigue damage. Also, as the contact pressure and duration of tests increase, the average temperature in the friction zone grows (to 70 °С in the conditions of the test) inducing thermal activation of many chemophysical processes so that the resistance of the specimens to fatigue becomes still less.

Fig. 4.1 – Results of wear-fatigue tests of steel 40Х / polyamide “Durethane” ВКV-30Н system: а – fatigue curves (1 – mechanical fatigue curve; 2, 3 – mechano-sliding fatigue curves at p_a = 5 and 8.5 MPa, respectively); b – fatigue limit as function of contact pressure (L A Sosnovskiy)

Fig. 4.1, b shows the fatigue limits as functions of contact pressure. The curve is the relation between s_–1р and p_a, so that according to this relation pressure rise leads to loss of fatigue resistance. The horizontal dotted line is the fatigue limit during mechanical fatigue that is definitely independent of the contact pressure.

The theoretical analysis yielded the following equation that satisfactorily describes the results of the tests (see the curve in Fig. 4.1, b):

where

According to equation (4.1) the mean fatigue limit s_–1р of steel specimens during mechano-sliding fatigue of the metal-to-polymer active system is governed both by the conditions of tests and by the complex of mechanophysical properties of the metal and the polymer. The fatigue limit with the account of temperature effect  (s_–1T) and the parameter of isotropy of steel (m_V) characterize integrally the conditions of testing for fatigue and mechanophysical properties. Nominal contact pressure (р_a), temperature variations of the polymer (DT), the scheme of contact interactions between the components of the system (b_S), relative damaged volume in friction (S_0.5g/S_к) describe the conditons of tests in sliding friction. Meanwhile, the mechanophysical properties of the polymer are rated by the destruction limit (p_d = U₀/g_p, where U₀ – the energy of breaking of interatomic bonds, g_p – the structurally sensitive coefficient), the parameter of the number of defects m_S, a single thermofluctuation stress  (k – the coefficient of Boltzman).

From equation (4.1) it follows that the effect of friction processes (described integrally by the function j_р) on fatigue resistance of the steel specimen is a damaging effect under these test conditions (it is predicted that s_–1 £ s_–1T always) and it is really due to the complex of mechanical and chemophysical phenomena described by the corresponding parameters and coefficients (see function (4.2) for j_р).

Fig. 4.2 – Role of thermofluctuation stresses in wear-fatigue damage processes
(L A Sosnovskiy)

Fig. 4.2 illustrates the role of thermoactivating phenomena in the processes of mechano-sliding fatigue of the metal-to-polymer active system. The curve s_–1р(p_a) is borrowed from Fig. 4.1, b and represents the relation between ultimate stresses s_–1р and nominal contact pressure p_a. If thermofluctuation stresses are estimated in the polymer

that occured under the conditions of the experiment and the relation between the ultimate stresses s_–1р, and the value p_tf is plotted, then it turns out that thermofluctuation stresses exceed substantially (nearly two times) contact pressures. Hence, the effect of thermofluctuation processes both on the surface damage (or wear) of the polymer and generation of resistance to fatigue of steel specimens is governing during the tests. In other words, it is a convincing proof of the conclusion above that mechano-sliding fatigue of the active system in question is actually due to the chemophysical phenomena in the contact zone.

Let us consider again the results of tests of the metal-to-metal active system. Unlike the metal-to-polymer system the main distinction of the metal-to-metal system is that both components, i.e. the specimen and the counterspecimen, undergo physical wear in the process of fatigue tests. Curve in Fig. 4.3 depicts the relation of the fatigue limit of steel specimens and contact pressure in the steel 45 / iron active system (friction and lubrication with oil СУ), the horizontal dashed line represents the fatigue limit of the steel specimens during common fatigue tests (naturally, the limit does not depend on pressure). Comparison of the curves in Fig. 4.2, b and 4.3 enables to establish their principal difference, viz. the ultimate stress during wear-fatigue tests of the metal-to-metal system is higher within a relatively broad range of variations of contact pressure (from »1.05 MPa in Fig. 4.3) than the ultimate stress during common fatigue tests. In other words, these conditions of the processes of friction and wear do not cause damage, they lead, on the opposite, to hardening.

Fig. 4.3 – Ultimate stresses as function of contact pressures in steel 45 / pig iron active
system (V I Pokhmursky, et al.)

A similar abnormal behavior of the function s_–1(p_a) is explained by the ratio between the processes of hardening-softening and removal of surface impurities by friction.

The curve in Fig. 4.3 is satisfactorily described by the equation

where p_f – the ultimate value of pressure during sliding friction (the sliding fatigue limit); m_e – the parameter of strain hardening.

From the above it follows that it is not justifiable to consider friction and wear as some factors that are necessarily harmful for the active system. It is more opportune to imply some complex processes and results of interactions between two damaging phenomena, viz. mechanical fatigue and friction (including attendant wear). These interactions can lead to ambiguous consequences (while the effect of this or that factor is usually unambiguous. The fatigue limit of the specimen can either grow or fall or remain unchanged in response to the conditions of wear-fatigue tests and origin of contacting materials.

These are the basic regularities the direct effect established during the experiments performed, as it is noted above, from the standpoint of fatigue fracture mechanics. In fact, their understanding helps overcome the traditional limits of fatigue fracture mechanics and familiarize with tribo-fatigue as it has become clear and proved that friction and wear are the phenomena capable of mechano-physico-chemical interactions with the phenomenon of fatigue rather than the factors producing a simple effect on the resistance of materials to fatigue. It is the result of these interactions that complex wear-fatigue damage of the material occurs. Since it is complex, it is not just a simple sum of individual (particular) damages plus fatigue damages and damages due to friction and wear.

4.2.2 back effect

Since the back effect is defined as changes of the characteristics of friction and wear under the effect of the processes of fatigue damage, its basic regularities are studied by designing and performing experimental studies from the standpoint of tribology (see pp. 1.4 and 3.3).

The principles of experiment designing remained the same. A metal-to-polymer system steel 40Х (the specimen) / formaldehyde copolymer (the counterspecimen) was subjected to wear-fatigue tests: the ultimate strength at compression 56 MPa) at a constant contact pressure p_a = 5.7 MPa. However, this time the linear wear of the polymeric counterbody was measured in the process of tests. The result served to calculate the volume intensity of wear using the formula

where – the volume of the worn polymer; r – the steel specimen radius; n – the number of loading cycles.

Fig. 4.4 shows the relation between the wear intensity increment DI_s of the polymer and the amplitude of stresses s_a in the steel specimen. The value DI_s at a given contact pressure p_a = const was calculated using the results of measurements in the following manner:

Fig. 4.4 – Incrementations of wear intensity of polymer as function of amplitude of cyclic
stresses (alloyed steel 40Х / formaldehyde copolymer) (L A Sosnovskiy)

where – the wear intensity of the counterbody in the active system in which s_a > 0, i.e. during the wear-fatigue tests; I_V(n) – the wear intensity of the counterbody in a usual friction couple in which there are no cyclic stresses (s_a = 0).

From the data in Fig. 4.4 it follows that the amplitude of stresses in the steel specimen significantly affects the wear intensity of the polymeric counterbody. If cyclic stresses grow from 160 to 300 MPa, the wear intensity increment due to these stresses changes from 110 to 180% (versus the wear intensity in a common friction couple when s_a = 0). Hence, the durability of metal-to-polymer active system based on the wear criterion is governed by the back effect in many respects.

The described back effect in the metal-to-polymer active system is due to additional intensification of kinetic processes of breakup of polymeric molecules by cyclic stresses in the actual contact spots. This breaking is much due to the phenomenon of thermodestruction of the polymer because of intensive heat emission in the contact. It intensifies due to non-elastic cyclic deformation of the surface layer on the steel specimen during tests for fatigue. Effective transfer of the polymer to steel observed visually during tests is an indirect proof of this assumption.

Fig. 4.5 – To analysis for back effect

Let us examine Fig. 4.5 in order to answer the question, from the standpoint of mechanics, why the wear of the polymeric counterbody strongly intensifies when cyclic stresses are excited in the conjugated steel body. The body is shown as rotating disk 1 with smooth working surface and the counterbody as fixed single indentor 2. During usual tests for friction (Fig. 4.5, а) only the contact load q_r is operative, indentor 2 statically bends (in the direction opposite to rotation w₁), so the deformable zone on the working surface of the disk looks like a strip (a friction path). During wear-fatigue tests (Fig. 4.5, b) additional cyclic deformation ±e_z(s) is excited in the disk. Small deformation of the working surface of the disk in the direction z makes the friction path over the surface look zigzag and the indentor is subjected additionally to cyclic bending (in the direction z). The wear process of both components naturally intensifies in accordance with the magnitude of the cyclic stresses ±s_z. If the indentor is polymeric, while the disk is steel, only the wear of the polymer as a softer material intensifies. If the indentor is steel too, the wear of both components may intensify.

Thus, during such conditions of wear-fatigue tests the back effect may lead to two phenomena: wear accelerates in one and the other component under the effect of cyclic stresses excited in only one component of the active system.

Theoretical analysis has yielded the following formula to estimate the wear intensity I_V(s) of the polymeric counterbody with the allowance for both the amplitude of stresses s_a and the complex of the mechanophysical  properties of steel and the conditions of tests for fatigue:

where I_V – the wear intensity of the polymer without any cyclic stresses in the steel specimen (i.e. in the common friction couple); – the coefficient known a priori and making allowance for the conditions of fatigue tests;  – a relative dangerous volume of the cyclically deformable steel specimen;  – relative temperature of the metallic specimen in the friction zone; m_T – the parameter of temperature activation of the processes of  fatigue damage; s_–1min and s_W – the parameters of the function of distribution of fatigue limits of steel specimens in the form of the law of Waybull; m_V – the parameter of steel isotropy.

Equation (4.5) predicts the damaging effect of cyclic stresses: the value  and , hence, .

Experimental studies thus show (cf. Fig. 4.4) that the value I_s depends strongly non-linearly on the conditions of cyclic deformation. It means that the resulting wear in the active system is not just a simple sum of usual wear (in a friction couple) and additional wear due to cyclic stresses. Therefore, it is another confirmation of the main assumption that wear-fatigue damage results from an intricate interaction between the phenomena of fatigue and friction (together with wear). Since the effect is complex, it is represented by the non-linear function (4.5) of individual (particular) damages.

The principal distinction between two notions – wear-fatigue damage and fatigue wear – should be outlined now. In this connection it is opportune to quote the corresponding definitions in the Standards:

·     wear-fatigue damage is damage due to kinetic interactions between the phenomena of fatigue, friction in any its manifestations, wear and (or) erosion (GOST 30638–99);

·     fatigue wear is mechanical wear resulting from fatigue fracture when microvolumes of the material in the surface layer undergo re-deformation (GOST 27674–88).

The following formula has been obtained for estimating the wear intensity of the shaft in the metal-to-metal system crankpin / connecting-rod end (with a sliding bearing):

where  – linear wear intensity in the common friction couple (when s_a = 0) and the function Ф depends on the size of the crankpin (the ratio between length and radius: L/R), the design of the unit (the ratio between half-width of the contact strip and radius: a/R), the coefficient of sliding friction f, the Poisson coefficient n and the elasticity moduli of contacting metals:

The loading parameter  makes allowance for both cyclic (s_a) and contact (p_a) stresses in the friction zone. Since, according to formula (4.8), Ф > 1 always, equation (4.7) predicts like (4.5) the damaging effect of cyclic stresses, i.e. . Equation (4.7) describes the wear of the shaft as one manifestation of the back effect.

Understanding of the back effect enables to go beyond the traditional frame (this time the frame of tribology) and come close thus to tribo-fatigue, on the other hand. In fact, it turns out that the wear intensity can be controlled non-traditionally by exciting cyclic stresses in one component of the friction couple. This control is highly effective: the wear intensity can change tens or even hundreds of per cent. If it is borne in mind that according to the experimental data, certain wear can exceed significantly the reliability of an active system, it becomes clear that we go beyond the common approach to ensuring the reliability of mechanical systems based on individual criteria of fatigue or wear resistance. We approach the complex problem of control over the reliability of active systems in modern machinery based on the criterion of wear-fatigue damage. In other words, it has become clear that tribo-fatigue should be created on the verge of tribology and fatigue fracture mechanics.