Characterization of fatigue crack initiation in α-brass by means of AFM and EBSP

Transcription

1 OS5W36 ATEM'3, JSME-MMD, Sep. -, 3 Characterizatin f fatigue crack initiatin in α-brass by means f AFM and EBSP Yshikazu Nakai and Ksuke Maeda. Department f Mechanical Engineering, Kbe University, Kbe, Japan. Sumitm Precisin Prducts C., Ltd., Fus-ch, Amagasaki, Japan Abstract: Slip-band frmatin and crack-initiatin prcesses in α-brass under cyclic shear stress were examined by means f atmic frce micrscpy (AFM), and the slip-directin was identified with electrn back scattering pattern methd (EBSP). Frm AFM bservatins, it was fund that slip-bands were nt always frmed alng the maximum reslved shear stress directins, and slip-systems culd be activated in the directin whse angles frm the surface were larger than. The depth f an intrusin increased linearly with the lgarithm f the number f cycles, and the increasing rate f the intrusin depth drastically increased with crack initiatin. By cmbining the intrusin depth and the slip directin, thse were measured with AFM and EBSP, respectively, the value f slip distance culd be evaluated, and the critical values f the slip distance fr the initiatin f transgranular crack was fund t be cnstant fr all crack initiatin sites, while the intrusin depth was nt cnstant. The critical value f the slip distance fr cyclic shear stress (trsin) was identical fr cyclic nrmal stress (bending). A unique relatinship between shear stress amplitude in the actual slip directin and number f cycles t failure was btained fr cyclic trsin and bending ladings. Key wrds: Fatigue, Crack initiatin, Cyclic shear stress, AFM, EBSP, Nantechnlgy, Maximum shear stress thery. INTRODUCTION It is well knwn that the fatigue prcess f metallic materials withut macrscpic defects can be divided int initiatin and grwth prcesses f cracks and final unstable fracture. Amng these prcesses, varius studies have been cnducted n the crack-grwth behavir, and that can be quantitatively analyzed based n the fracture mechanics []. The study n fatigue crack initiatin is especially imprtant fr fatigue damage evaluatin f micr-machine cmpnents because the fatigue life f these cmpnents is almst the crack initiatin life [, 3]. The initiatin cnditin f fatigue micr-cracks, hwever, still has nt clarified enugh, because n methd fr successive, direct and quantitative bservatin f the prcess had been devised. Fr cmpnents withut significant internal defects, free surface is nrmally the site fr fatigue crack initiatin, then micrscpic bservatin is the mst useful methd t clarify the mechanisms f fatigue prcesses in materials, and the prgress f metal fatigue study has strngly depended n the develpment f new micrscpic bservatin methds. With cnventinal micrscpes, such as ptical micrscpes, transmissin electrn micrscpes (TEM), and scanning electrn micrscpes (SEM), hwever, successive, quantitative three-dimensinal bservatins f the crack nucleatin site in the specimen surface culd nt be cnducted. Then, in mst f these studies, the crack-initiatin mechanisms were discussed qualitatively. Since the surface mrphlgy f materials can be bserved with atmic-scale reslutin, the scanning atmic frce micrscpy (AFM) is a pwerful technique t study the mechanisms f fatigue and fracture f slid materials. Nakai and his c-wrkers studied fatigue slip-bands, fatigue crack-initiatin, and the grwth behavir f micr-cracks in a structural steel [4], and α-brass [5-8]. They reprted fr fine grain α-brass that fatigue cracks were initiated nly frm the slip-bands. In a carse grain α-brass, hwever, they were initiated either frm the slip-bands r the grain bundaries. The depth f an intrusin drastically increased with crack initiatin, and with calescence f cracks, the width f cracks increased rapidly. The depth f an intrusin increased with the number f lading cycles, and when the depth reaches a critical value, a transgranular crack was initiated frm the intrusin. The critical value was given as a functin f the slip-band angle relative t the stress axis. Frm the AFM bservatins and gemetrical cnsideratin, it was fund that the critical value f the slip distance was independent f the slip-band angle relative t the stress axis, the stress amplitude, and the grain-size. Fr crack-initiatins frm grain bundaries, hwever, the value f the grain bundary depth at the crack initiatin was nt a unique functin f the grain bundary angle relative t the stress axis. In the present paper, slip-band frmatin and crack initiatin prcesses in α-brass under cyclic shear stress were examined by means f atmic frce micrscpy (AFM), and the slip-directin was identified with electrn back scattering pattern methd (EBSP) t elucidate fatigue crack initiatin cnditin. Crrespnding authr: Y. Nakai, nakai@mech.kbe-u.ac.jp

2 OS5W36 ATEM'3, JSME-MMD, Sep. -, 3 d α α β s Slip plane Surface Table. Chemical cmpsitin (mass%). Cu Zn Fe Pb Fig. Slip plane and slip directin..% prf stress σ. (MPa) Table. Mechanical prperties. Tensile strength σ B (MPa) Elngatin (%) σ R 8 t = 3 σ (a) Uniaxial tensin stress (b) Shear stress Fig.. Maximum shear stress planes. 3 σ a =45 (MPa) σ a =69 (MPa) s=38 (nm) Fig. 3. Change f slip distance with stress cycles (R = ).. THEORY Cnditin fr the transgranular fatigue crack initiatin can be analyzed by a gemetrical mdel prpsed by Tanaka and Nakai [9,], which explains the relatin between the surface-step and the slip-directin. The surface-step, d, induced by a slip is d = s sin β cs α' () where the value f s is the slip distance in the slip-directin, the value f α' is the angle between the nrmal f the surface and the trace f the slip-band n the plane that is perpendicular t the surface and parallel t the lading-axis, and the value f β is the angle between the slip-directin and the slip-traces n the surface (see Fig. ). Althugh fatigue slip bands are nt steps like Fig., but they are intrusin and intrusins, Eq. () can be applied t fatigue slip bands because they are cnsequences f each step generated at each cycle. A slip usually takes place alng slip plane where the Fig. 4. Shape and dimensins f specimen (in mm). reslved shear stress exceeds the frictinal stress f dislcatin mtin. Fr istrpic hmgeneus material under uniaxial nrmal stress, lts f planes can be the maximum reslved shear stress plane whse nrmal has the angle f 45 frm the lading axis as shwn in Fig. (a). Then, in plycrystalline materials, there are many grains whse slip plane is very clse t the maximum reslved shear stress plane, and cracks are cnsidered t be initiated frm slip bands, which had slip systems in the maximum reslved shear stress directin [9,]. Fr slip-bands, where the reslved shear stress alng the slip-directin takes the maximum value, the fllwing relatinship shuld be satisfied. cs β = cs α () ct α + tan α' = (3) where the value f α is the angle between the lading-axis and the trace f the slip-band n the surface. The value f slip distance can be calculated frm the measured values f the depth f intrusin, d, and slip band angle, α, by substituting these values int Esq. (), (3), and Eq. (). The relatin between the slip distance and the number f cycles in uniaxial lading (bending) fatigue test is shwn in Fig. 3, where pen marks indicate data befre the crack initiatin, and slid marks shw data after the crack initiatin. The values f α are als indicated in the figure. The slpe f the line is changed with crack initiatin, and cracks are initiated frm slip bands when the slip distance reached a critical value. This critical value is 38 nm independent f stress amplitude. The value was als fund t be independent f stress rati and grain size [7,8]. 3. EXPERIMENTAL PROCEDURE The material fr the present study was 7-3 brass (α-brass). The chemical cmpsitin and mechanical prperties f the material are shwn in Tables and, respectively. After the specimens were made by an electric-discharge machining, they were heat treated at

3 OS5W36 ATEM'3, JSME-MMD, Sep. -, 3 ( µ m) A 3( µ m) (a) N = cycles (b) N =. 4 cycles (c) N = cycles (d) N = 4. 5 cycles (e) N = 6. 5 cycles (f) N = 8. 5 cycles Fig. 5. AFM images ( a = 4 MPa, Scanning area 3 µm 3 µm, vertical scanning range µm). 3 C fr 8 s. After the heat treatment, the grain size f the material was µm. Befre fatigue tests, surface f the specimens were electr-chemically plished. As shwn in Fig. 4, the specimen has a minimum crss-sectin f width 8 mm, and a thickness f 3 mm. The cyclic trsin fatigue tests were carried ut in a resnance type fatigue-testing machine (Shimadzu TB-) perated at a frequency f 33.3 Hz under fully reversed cyclic trsin. Denting by W and t, respectively, the width (8 mm) and the thickness (3 mm) f the specimen, and by T the trque applied t the specimen, the maximum shear stress ccurs alng the center line f the wider face f specimen, and is given by the frmula T = (4) kwt The value f k is.6 fr W/t=8/3 []. T cnduct a quantitative analysis f the develpment f fatigue slip-bands, the scanning atmic frce micrscpy (AFM) was emplyed fr the present study. The scanning area fr the bservatins was 3 µm 3 µm. Since it was very difficult t identify in advance where fatigue cracks wuld be initiated, replicas f the specimen surface were taken at the predetermined number f fatigue cycles. With resnance type testing machine, static lading was nt easy, then the AFM images were taken at the unlading state. The replica films were cated by gld (Au) befre bservatin. Althugh the height f the surface in the replica film was reversed frm the specimen surface, the height f the replica film in the AFM images was reversed by an image prcessing technique. Intrusin depth, d (nm) Fig x x 5 4.x 5 6.x 5 8.x Psitin ( µ m) Change f surface gemetry with stress cycles. 4. EXPERIMENTAL RESULTS AND DISCUSSION 4.. Crack initiatin prcess An example f AFM image f transgranular cracking prcess under cyclic shear stress (trsin) is shwn in Fig. 5, and the change f gemetry f crss sectin A, which is indicated in Fig. 5 (a), is shwn in Fig. 6. In bending tests, the bservatins were cnducted under maximum tensin stress, and it was very easy t identify the crack initiatin. In trsin tests, hwever, it was very difficult t bserve under lading cnditin, therefre, these figures were taken under unlading cnditin. In this case, fatigue crack initiatin is nt easy t identify frm these bservatins. Change f the depth f intrusin is shwn in Fig. 7

4 OS5W36 ATEM'3, JSME-MMD, Sep. -, 3 5 Intrusin depth, d (nm ) 4 3 s d Number f cycles, N (x 5 cycles) Maximum shear stress µ m Fig. 7. Change f intrusin depth with stress cycles. as a functin f the number f the fatigue cycles, N. The depth f intrusin increases linearly with lgarithms f number f cycles, and the increasing rate f the depth f the intrusin drastically increased at N = 3.5x 5 cycles. This change f the slpe may cme frm crack initiatin [7,8]. Fig. 8. AFM image. 4.. Crack initiatin cnditin In the thery fr uniaxial stress, fatigue cracks were cnsidered t be initiated frm slip bands, which had slip systems in the maximum reslved shear stress directin. In trsin lading, hwever, nly tw sets f planes can be the maximum shear stress planes as shwn in Fig. (b), and the actual slip bands had slight angle frm the maximum reslved shear stress directin as shwn in Fig. 8. Then the slip distance cannt be calculated thrugh the measurement f the slip depth by assuming that the slip plane is cincident with the maximum shear stress plane. Therefre, the directin f slip plane and the slip directin were experimentally measured by the electrn back scattering pattern (EBSP) methd. An example f the crystal rientatin btained by the EBSP methds is shwn in Fig. 9, where each clr indicates a specific rientatin. Fr the case f face-centered cubic (FCC) crystals, slip ccurs mst ften n {} planes and in <> directins. In all, there are slip systems (fur {} planes and three <> slip directins fr each {} plane). With the EBSP methd, ne f {} planes and ne f <> slip directin can be identified. Other planes and directins can be determined frm the gemetrical relatinships fr FCC crystal. Since a slip line n surface is an intersectin line f slip plane and surface plane, the actual slip plane can be identified frm EBSP methd and the actual slip line bserved by micrscpy. Slip directin, hwever, cannt be specified frm the methds mentined abve, then Schmid factr f each slip directin shuld be cnsidered. The mst reasnable assumptin may be that Schmid factr f the actual slip directin is larger than that f ther slip directins. Figure shws examples f slip distance estimated by the assumptin. Open marks shw data befre crack initiatin, slid marks indicate thse after crack initiatin, and the value f λ is the angle between the surface and the slip directin determined by the maximum Schmid Fig. 9. Grain rientatin btained by EBSP. factr criterin. Fr λ = (Fig. 7 (a)), the slip distance at crack initiatin is 38 nm, which is identical t that btained fr bending tests. Fr λ = 4 (Fig. 7 (b)), and λ = 8 (Fig. 7 (c)), the distance is abut 3 µm and µm, respectively. Surface bservatins f slip bands with AFM, hwever, did nt supprt such large discrepancy acrss the slip line. Generally, fr the values f λ smaller than, the estimated slip distance was unrealistically large. In the bservatins f slip bands frmed under uniaxial stress fatigue, the value f λ smaller than 8 was nt appeared [7,8], then the slip system may nt be activated if it is almst parallel t the surface. In the cnsideratin f slip mtin, image frce des nt act n the dislcatin mtin in the parallel directin f surface, but in the nrmal directin f the surface that perates t enhance the dislcatin mtin, i.e., dislcatins can mve nrmal t the surface by smaller frce than in the parallel directin. The xidatin f newly created surface may be anther factr t cntrl the directin f dislcatin mtin. When the slip directin is parallel t the surface, there is n slip step, and fresh surface is nt frmed. Then reversible mtin f slip plane is pssible in reversed cyclic lading. On the ther hand, by the absrptin f xygen atms n the fresh surface, slip mtin cannt ccur in the same plane between tensin ging part and cmpressin ging part f the fatigue cycle, and intrusins and extrusins can easy t be frmed. By assuming fr λ smaller than that the slip directin shuld be the secndly large Schmid factr directin, the estimated slip distance is shwn in Fig. 8. The estimated slip distance at the crack initiatin is 38 nm

5 OS5W36 ATEM'3, JSME-MMD, Sep. -, λ = s=38(nm) 5 6 λ = 4 (a) λ = 5 6 λ = 8 (b) λ = (c) λ = 8 Fig.. Change f slip distance with stress cycles. (Slip directin: Maximum reslved shear stress directin.) independent f the slip bands angle, and this value is identical t that fr bending fatigue tests S-N curve One f the mst difficult tasks in fatigue is t translate the infrmatin gathered n the uniaxial fatigue t applicatins invlving cmplex states f cyclic stress. The multiaxial appraches have been based n the fllwing three criteria: (i) maximum principal stress, (ii) shearing energy (vn Mises yield cnditin), and (iii) λ λ s = 38 (nm) 5 6 Fig.. Change f slip distance with stress cycles. (Slip directin: Secndary large shear stress directin fr λ <, and maximum reslved shear stress directin fr λ.) Stress amplitude, a (MPa) Number f cycles t failure, Fig.. Trsin Bending S-N curves. (cycles) maximum shear stress (Tresca yield cnditin). If the fatigue damage f metallic materials cme frm slip mtin f dislcatins and it is cntrlled by the shear stress n the slip plane, the fatigue strength shuld be given as a unique functin f cyclic shear stress amplitude. Experimental results n multiaxial fatigue, hwever, des nt always supprt the maximum shear stress (Tresca) criterin. Nisitani and his c-wrkers reprted that the rati f fatigue limits f trsin and bending is larger fr istrpic steels (.68) than that fr anistrpic steels with lamellar structure (.58) [-4]. They als reprted that the rati is much larger (.77) fr steels with small defects [5]. They discussed the difference f crack initiatin site and strain cncentratin in ferrite grain in the materials, but it is still unslved why the maximum shear stress criterin is nt applied even fr hmgeneus istrpic material. Kitamura and his c-wrkers pinted ut that the maximum shear stress evaluated by the frmulae fr the hmgeneus istrpic materials cannt explain the lcal shear stress f plycrystalline metals, and they calculated the lcal shear stress in each grain by FEM analysis fr anistrpic bdy [6]. The bservatin f slip directin in the present study, hwever, des nt supprt such maximum shear stress criterin, but the N f

6 OS5W36 ATEM'3, JSME-MMD, Sep. -, 3 slip directin shuld be cnsidered. S-N curves f the present material fr bending and trsin fatigue are shwn in Fig. by circular marks, where the value f a is the amplitude f maximum shear stress evaluated by the frmula fr hmgeneus istpic materials. The relatin fr trsin fatigue des nt agree with that fr bending fatigue, and fatigue strength is nt cntrlled by the maximum shear stress amplitude. Open triangular marks shw the relatin fr the trsin fatigue where the shear stress amplitude is that in the actual slip directin that was evaluated in last sectin, where the average value f Schmid factr was emplyed. By taking the assumptin, the relatin fr trsin is almst identical t that fr bending. Actually, the fatigue life is the sum f crack initiatin life and prpagatin life, and in mst metals, the latter is mre dminant than the frmer. In mst cases, the fatigue crack prpagatin rate is cntrlled by the mde I cmpnent f the stress intensity factr, and fatigue life may be cntrlled by the maximum principal stress. Then the rati f shear stress amplitude f cyclic uniaxial stress amplitude and the cyclic shear stress amplitude fr the same fatigue crack prpagatin life may be :.5. On the ther hand, the rati was :.55 fr crack initiatin life by assuming that slip ccurred in the secndly large Schmid factr directin. In the present material, the rati is almst the same fr crack prpagatin life and crack initiatin life, then as a result, the cnsideratin nly fr crack initiatin can be explain the fatigue life f cyclic uniaxial stress and cyclic shear stress. Shrt crack prpagatin life is mre imprtant fr fatigue life analysis. Then the crack prpagatin law f shrt cracks under mixed mde shuld als be cnsidered [7]. 5. CONCLUSIONS Slip-band frmatin and crack-initiatin prcesses in α-brass under cyclic shear stress were examined by means f atmic frce micrscpy (AFM), and the slip-directin was identified with electrn back scattering pattern methd (EBSP) t elucidate fatigue crack initiatin cnditin. The fllwing results were btained. () Fr transgranular cracking, the increasing rate f intrusin depth and slip distance drastically increased with crack initiatin. () When the slip distance reached a critical value, fatigue cracks were initiated frm the intrusin. The critical value fr trsin fatigue is identical t that fr bending fatigue. (3) Slip system, which is almst parallel t the surface, cannt be activated even if Schmid factr f the slip system is largest in that directin. In this case, slip system with secndary large Schmid factr may be activated. (4) T emply the shear stress in the actual slip-directin, the relatin between shear stress and fatigue life fr trsin is almst identical t that fr bending. Acknwledgement: The authrs wuld like t appreciate Prfs K. Tanaka and Y. Akiniwa, Dr. H. Kimura, Nagya University, and Prf. H. Tanaka, Kbe University fr prviding the pprtunity t measure the grain rientatin with EBSP. REFERENCES. K. Tanaka,, JSME Int. J., 3 (987), pp.-3.. Y. Nakai, C. Hiwa, T. Imanishi, and A. Hashimt, Prceedings f Asian-Pacific Cnference n Fracture and Strength '99 (999), SM. 3. A. Hashimt, and Y. Nakai, Materials Science fr the st Century, Vl. B, The Sciety f Meterials Science, Japan (), pp Y. Nakai, S. Fukuhara, and K. Ohnishi, Int. J. Fatigue, 9 (997), pp.s3-s Y. Nakai, K. Ohnishi, and T. Kusukawa, Trans. JSME, 65A (999), pp (in Japanese). 6. Y. Nakai, K. Ohnishi, and T. Kusukawa, Small Fatigue Cracks: Mechanics and Mechanisms, Elsevier (999), pp Y. Nakai, T. Kusukawa, and N. Hayashi, Fatigue and Fracture Mechanics: 3nd Vlume, ASTM STP 46 (), pp Y. Nakai and T. Kusukawa, Trans. JSME, 67A (),pp (in Japanese). 9. K. Tanaka, Y. Nakai, and O. Maekawa, J. Mat. Sci., Japan, 3 (98), pp K. Tanaka, M. Hj, and Y. Nakai, ASTM STP 8 (983), pp F. P. Beer and E.R. Jhnstn, Jr., Mechanics f Materials, McGraw-Hill Inc. (98), p.39.. H. Nisitani and T. Fukuda, Trans. JSME, 57A (99), pp (in Japanese). 3. H. Nisitani, T. Fukuda, Trans. JSME, 59A, (99), pp.86-8 (in Japanese). 4. H. Nisitani, T. Fukuda, Trans. JSME, 6A (994), pp.75-8 (in Japanese). 5. T. Tanaka, H. Nisitani, W. Fujisaki, T. Teranishi, and Y. Tanaka, Trans. JSME, 6A (996), pp (in Japanese). 6. T. Kitamura, T. Sumikawa, and K. Ohishi, Trans. JSME, 68A (), pp.4- (in Japanese). 7. T. Hshide, Materials Science Research Internatinal, l3 (997), pp.9-4.