The occurance of surface cracking in the contact field without any macro slip has been investigated. The effects of the static normal load and the range of alternating tangential force on the crack initiation and growth have been made clear. It was also shown that the stress field may be useful to estimate the total effects of the applied forces even on the surface cracking and growth

Kisu Hiroyuki

Moritaka Hideshiro

Nakashima Akira

Ura Akira

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        Report of The Faculty of Engineering, Nagasaki University Vol. 15, No. 25, July 1985' 11           On the Surface Cracking and Crack Growth Due to           '                        ttt                    '           the Oscilated Tangential Force without Macro Slip                                                                                 ''                       '       '                                               by                             Hiroyuki KISU*, Akira URA*                                       tt t                                            '                Akira NAKASHIMA* and Hideshiro MORITAKA*                                                    tt                           '        The occurance of surface cracking in the contact field without any macro slip has been inve-    stigated. The effects of the static normal load and the range of alternating tangential force on the    crack initiation and growth have been made clear. It was also shown that the stress field may be    useful to estimate the total effects of the applied forces even on the surface cracking and growth.                                 '                  ･･ .1                                                        '                                         '                                   I. INTRODUCTION    It has become clear that the damage on the contact surface is much affected by the tangential forcei)'-4).However, it seems that its influence over the wide range of contact conditions still remains undefinitequantitatively. . '    In this study, some experiments were performed under the various unlubricated contact conditions of ahard metal sphere against a hard metal flat subjected to the oscilated tangential force with several staticnormal loads. The occurance of damage (especially cracking) on the surface in the contact field withoutany macro slip has been observed. The effects of the normal load and the range of oscilated tangentialforce on the occurance of the surface cracking and its advance have been investigated. It was also foundthat these effects can be explained using stress field.                                           '                                           '                                               '                                                '                                   II. EXPERIMENTAL    A rough sketch of testing machine is shown in Fig.1.' Specimens are set at A, where the upper oneis in directly contact with the lower one. The lower specimen is a ball for bearing (SUJ2) and the upperis an end of cylindrical roller for bearing (SUJ2). Dimensions of the specimens are shown in Fig. 2.The specimens are subjected to statical normal load P and reciprocated tangential force ±T. The tangentialforce is generated by centrifugal force of unbalanced weight on the pair of rotating spur gear as shown inFig. 1. The normal load P is determined using calibration curve of the relation between P and straingauge output. The tangential force T is evaluated by the calculation of the centrifugal force.  ･ All tests were carried out under the unlubricated condition without macro slip. The contaet conditionsin the experiments are shown in Table 1. At a proper interval of cycles, the upper specimen was taken                                           ,out and crack initiation and/or growth was checked by micro scope. Crack length was measured on thephotograph. Some of the specimens were re-loaded for the further experiments. .                  tt '                                                                                          ''            '    t t. .. .. .tt ..                                              'ngJFII60tlfiL5.fl8HMN ' ' ''･ '*Department of Mechanical Engineering ll ' 'i2ohs :,c kg dc kGs,hD hO l,d' i.i.g:ll".,..l--,,.,-:,lll,iSli   weight . ,., .''. .'' .i '9 .il .',' .'･ 17.. ,'' YP?iS '2 bimensi..L,9,)'!sS.r.,.,.,           Fig. 1. Testing Machine                                                       '                                         ''                      ･ Table 1 Contact Conditions in the Experiments                 '                                                 '                           Normal ' Herz ･ Radius of                            Load Pressure Contact Circle                             10kN ' 6.48 GPa O.858 mm                             15 7.42 ' ' ' O.982                                              '                             20 .8.17 1.081 ..,                             25 ' 8.80 '' 1.165                             30 ･ ' 9. 35 ' ' 'L 238'                                   Range of Tangential Force                                     1 O.35 kN - O.8o kN                                                           '                                              ttt                                   '                                      t tt                             III. RESULTS AND DISCUSSIONS     1. Damage Appeared on the Contact Surface                                                                    ,The state of the contact surface after the tests are typically shown in Photo 1 (a)-(d). There exists anannular region extending to the edge of the contact area where fretting has arised, A wide locked regionin the central part -of the circle also exists. This affords guarantee that no macro slip has been occured.Crack has initiated at the intersection of the contact circle and a line through the center of the circle par-allel to the tangential force on the surface. Crack begins to extend to the direction perpendicular to thatof･tangential force and grows drawingalocus of circular arc as sho, wn in the Photoes. ･ ' ･                                                           '                                tt t2. 0n the Crack lnitiation ' ' '' ' ' ' ' '  ' Figure 3 (a), (b) shows the typical relation between the alternating tangential force range and loadingcycles to crack initiation. Tt is recognized that the relation between the range of tangential force andcycles to the onset of crack is similar with the S-' N' curve in fatigue as already shown by Hirano and Gotoi).That is, the !arger the tangential force range, the less is the cycles, and there is the endurance limit of'the tangential force. However, if the normal load become increase, the line shifts to the left as the similarrelation has been kept as shown in Fig. 4.' Tn other words, the fatigue life to surface cracking is reducedby the increase of statical normal Ioad. It is indicated that stress distributiQn.. should be made clear inorder to estimate the total effects of the normal load and the range of tangential force on'the fatigue li{e., .   Hamilton and Goodman5) have already derived the stress field induced by the normal as well as by the,'Hiroyuki KISU     'Akira URA Akira          ' NAKASHIMA(a) P = 28.1 kNT = O.62 kN2×104 cycles                (c) P = 17.6 kN                     T = O.71 kN                     7×104 cycles                            Photo 1 Surfacetangential traction of Hertz-type. Since there existsof tangential traction may be slightly differentcontact. Nevertheless it seems that these solutions                    'field of the present problem provided that the resultant    Using stress field on the surface calculatedapplied stress Aa (maximum principal stress) andshown in Fig.5. It should be emphasized that da-NThis dependence, however, seems to be explainedis alternating as schematically described in Figtangential force is alternating as shown in Fig.compared with the tangential force in order to preventto the present caseand Hideshiro MORITAKA(b) P == 28.1 kNT = O.62 kN105 cycles13*More suitable stress field                     s･iiiti･{f- x20                 (d) P = 8.36 kN                     T = O.71 kN                     105 cycles  Cracking and Propagation  ' the locked region in the actual contact, the distribution  from Hertz-type which materialize in the case of sliding      can be used as a first step to approximate the stress        of shear traction is the same.*  from these solutions, the relations between the range of   cycles to the onset of crack (N) have been obtained as      relations are still dependent on the static normal load.    by mean stress. As a matter of fact, the applied stress  . 6 (a) under the present contact conditions, although  6 (b). This is because the normal load is rather large        macro slip, consequently mean stress becomes high.(finite body) is being investigated by numerical method.14 On the Surface Cracking and Crack Growth Due to the Oscilated Tangential Force without Macro SlipAzxv-qc)tu-y£ru-t'9is!6¢acUecAzxv'<ese£ru-u.9g6¢acUcrO.8O.6O.4O.2O.8O,6O,4O.2moNormatLoad30KNX:NoCrackA:lnitiationPointO:CrackExistsx xuxxwwxxxoox>o    1Number of        Fig.         10Cyctes, N3 (a)(xlo4)1OOx-NormatLoad20KNxxp X:NoCrackA:InitiationPointO:CrackExistsxXzNOXxxxXX×<Xx--×-Fig        1 10    Number of Cyctes, N            Fig. 3 (b).3 Number of Cycles to Crack(xl04)Initiation1OOIt can be suspected from these that the fatigue life has been much affectedalternating stress. The effects of the mean stress can be easily expressed by theThe limit diagram of the specific cycles was obtained as shown in Fig. 7 in thethat the diagram is similar with the one for non-contact fatigue.by the mean stress am ofenduranee limit diagram.present cases. It is foundHiroyuki　KISU，　Akira　URA，　Akira　NAKASHIMA　and　Hideshiro　MORITAKA 152こ三〇．8旨62£　　0．6石359厚04もΦ◎σ¢1O一△r●口 Normd　L◎αd030kNo ∠9　ロ △25●20o △●一ロ@　　ロロ100　　4◎8 9b8口● ●8　　　　　1　　　　　　10　　　　　10◎　　　　　Number◎？Cycles、　N（xlOる》Fig，4　Effect　of　the　Normal　Load　on　Cracking　0．75ゐ89℃級0．5総窪巴00．25＆§些　　　0口口0oQ◎　△　○　　　　　○▲　△　▲　△　　　▲　　ムロ　　　　▲　　　口o010kN●15△20▲25ロ30O　oロ　ロ臼。△口　　　　　　　　　　　　1　　　　10　　　．100　　　　　　　　Number◎f　Cycles、　N（x104）Fig．5　Relations　between　the　Range　of　Stress　and　Number　of　Cycles誘2筋△6● ●　　　　● o6m　　　TimeFig．6（a）Cyclic　Alternation　of　ApPlied　　　　Stress8bL護国呂易←TimeFig．6（b）Cyclic　Alternation　of　ApPlied　　　　　Tangential　Force16 On the Surface Cracking and Crack Growth Due to the Oscilated Tangential Force without Macro SlipGea1.o'VN().i 1$9.e--ut O,5'og,goct''t'''1t1t'tt111'''111-11111'  21/bAu  /i O ',i A     moAo  oA1 o45xlo42xl o58CyclesFig. 7 Range        O,5 1,O    Mean Stress, dm (G Pa)of Stress-Mean Stress Relations for the1.5Specific Cycles     3. 0n the Crack Propagation   As shown above, crack extends outer the contact circle. However, it was found that crack growth tothe depth has almost not been recognized at 105 cycles despite that the growth on the surface has alreadysaturated as shown in Photo 2. This indicates that crack propagates, in the beginning, along the shallowlayer on and beneath the surface. Propagation of this shallow crack on the surface has also been investigatedthrough an identical specimen. Figure 8 shows the typical relation between the amount of crack extensionon the surface and number of cycles. In the early period after the crack started to grow, the crack lengthhas increased so rapidly, but as the crack encircle the contact circle in the further several tens of thousandsof cycles its increasing has saturated. Us;ng the solutions of stress field mentioned above, it is found thatthe applied stress is higher near the initial cracking point than that of the side of contact circle. It isconsidered that the crack growth rate da/dN is also affected by the applied stress (range of the maximumprincipal stress).Photo 2 Crack   (P=28enExtension to.1 kN, T=theO.62Depth'kN lo5    'cycles)ffeeHiroyuki KISUA    1.2EEvs.,.,caS O.8xvsv   O.4     o'Akira URA          'AkxxxiraxNAKASHIMA and Hideshiro MORITAKA      x xxxxxxNormat Load:30KNT;angentiat FOrce:O.8KN10017TOH× 15Assvts105Fig.A     1 10   Number of Cyctes, N (xlO`)8 Crack Extension on the Surface       Norrnat Load:30 KN                  A : Contact Circte                  B:O.6KN                  C: 1.2 KN                  D: 1.8 KNBcD                            s                           Tangentiat Force                       o                         O 5 10 15                                                    X (mm) × 10'i                 Fig. 9 Prediction of the Path of Crack Propagation on the Surface                                                                           '   Path of the propagating can be predicted using the present stress solutions as shown in Fig. 9.Provided it is assumed that the crack extends to the direction perpendicular to that of the maximum principalstress. As indicated by the experiments, the locus has not varied so much even if the range of tangentialforce increase by three-times. '                                  IV. CONCLUSIONS   Conclusions can be summarized as follows'                                        '    From the experiments;(1). Crack initiation occurs at the ends of a diameter of contact circle parallel to the applied tangential(2). Relation between the range of tangential force and cycles to the surface cracking is similar with the  18 On the Surface Cracking and Crack Growth Due to the Oscilated Tangential Force without Macro SlipS-N curve in fatigue. '(3). Increase of statical normal load reduces the cycles to the cracking, although the similar relation withthe S--N curve is kept.(4). Crack begins to extend to the direction perpendicular to that of the tangential force and grows draw-ing a locus of circular arc.(5). Rate of growth on the surface is rather high in the beginning, but it becomes slow by degrees andsaturates finally. .(6). It is indicated that this propagating crack on the surface is a shallow crack and that the growth tothe depth is not so much before the growth on the surface saturates. -                                                                       '(7). Increase of the range of alternating tangential force cause that of the range of alternating appliedstress, consequently the fatigue life is reduced.(8). Increase of the statical normal load cause that of the mean stress of alternating stress, consequentlythe fatigue life is reduced under the present contact conditions.(9). The crack growth rate is affected by the range of alternating stress.(10). It seems that path of the propagation can be predicted on condition that crack extends perpendicularto the direction of the maximum principal stress. The path is not much affected by the tangential force norby the normal load. .                                       REFERENCES                                   '  1)Hirano, F. and Goto, S.; Fatigue Cracks of Bearing Metals Caused by Reciprocating Rubbing, Inter-    national Mechanical Engineering 181-30 (1967), p.108. .  2)Goto, S. and Hirano, F.; Surface Failure of Carburised Steel Caused by Alternating Tangential Stress    (in japanese), Journal of Japan Society of Lubrication Engineers 20-2 (1975), p.90.  3)Goto, S. and Hirano. F.; Fatigue Cracks of Rolling Bearing Steel Caused by Alternating Tangential    Force (in japanese), Journal of Japan Society of Lubrication Engineers 20-7 (1975), p.489.  4)Waterhouse, R. B.; Fretting Fatigue, (1981), Applied Science Publishers  5)Hamilton, G.M. and Goodman, L.E.; The Stress Field Created by a Circular Sliding Contact, Journal    of Applied Mechanics 33 (1966), p.371. '

On the Surface Cracking and Crack Growth Due to the Oscilated Tangential Force without Macro Slip

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On the Surface Cracking and Crack Growth Due to the Oscilated Tangential Force without Macro Slip

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