Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 Fatigue life and cyclic elastic-plastic strain behaviur ahead f ntch f ntched specimen under cyclic plane bending K. Shingai epartment fmechanical Systems Engineering, Nagasaki University, 1-14 Bunkyumachi, Nagasaki 852-8521, Japan Email: shingai@net nagasaki-u. ac.jp bstract The fatigue test f ntched specimens under plane bending with the cntrl f bending deflectin have been cnducted t investigate the cyclic elastic-plastic strain behaviur near a ntch by using strain gauges Frm the cyclic strains measured, tw types f cyclic strain behaviurs near ntch rts have been fund: in ne type named as IS (Increasing Strain with an increasing cycles). the strain near ntches increases with an increasing cycles, and in ther type named as CS (Cnstant Strain with an increasing cycles), the strain near ntches remains cnstant with an increasing cycles. In case IS, the strain range at a ntch rt remains nearly cnstant with an increasing cycles until a prper number f cycles befre a fatigue crack initiatin and the mean strain increases with an increasing cycles until a fatigue crack imitatin In case f CS, the strain range and the mean strain at a ntch rt remain cnstant with an increasing cycles until a fatigue crack imitatin. In case f IS, it has been fund that thin surface layers f bth ntch rts extend tward the tensin strain with an increase f the number f cycles and Mansn-Cffin rule may be applied t the relatinship between the saturated strain range at a ntch rt and the number f cycles t a fatigue crack length f 1mm The mechanism f IS behaviur have been explained in detail frm the experimental result f a specimen with many strain gauges attached. In this paper these experimental results and their discussin are presented.
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Fracture Mechanics 1 Intrductin Fatigue strength f ntches during stress cntrl test has been estimated using the S^-N^ curve and the K-K^ relatin, where S% is the stress range and Nj is the number f cycles until smth specimens fracture, and K is the elastic stress cncentratin factr f ntched specimens and K^ is the fatigue strength reductin factr fr ntched specimens. Recently, the linear ntch mechanics has been presented t estimate the fatigue limit f ntched specimens by Nishitani [1]. Fatigue strength f ntches in lw cycle regin under the strain cntrl has been estimated using the e %-N^ curve and K e presented by Neuber [2] etc., where e ^ is the cyclic strain range and K e is the strain cncentratin factr f ntches. Crews [3] had investigated the cyclic strain at a ntch rt using strain gages t clarify the Neuber methd. In the fatigue test f ntches under the stress cntrl, Shingai[4] fund the tw types f cyclic strain behavirs ahead f ntches The authr has als fund in this paper that there are similar tw types f cyclic strain behavirs ahead f ntches under cyclic plane bending with the cnstant deflectin cntrl. 2 Specimens and Experimental Prcedures Chemical cmpsitins and mechanical prperties f the carbn steel annealed are shwn in Table 1 and Table 2 respectively. Specimens with ntches are shwn in Fig. 1 and plane bending fatigue machine is shwn in Fig. 2. The strain gage with gage length f.2 mm is attached t a ntch rt and strain gages with gage length f 1 mm are attached in frnt f a ntch at distance f 1 r 2 mm as shwn in Fig. 3. The test f cyclic plane bending fatigue have been cnducted by the fatigue machine f Fig. 2 and strains have been measured at prper number f cycles using the dynamic strain recrder. C.24 Table 1 Chemical cmpsitins (%) Si Mn P S Ni Cr.22.5.12.16.7.15 Ca.13 Table 2 Mechanical prperties Mdulus f elasticity 199 GPa Yield stress 273 MPa Tensile strength 457 MPa Elngatin 38%
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Practice Mechanics 331 L) _i \jy Slidmj./blck c. 2K7 h xial rd ^ j Specunen n, Bearing Crank Fixed blc! a. = 8, =24, B=72, K=1.48 Bearing b. p =12, =24, B=72,K=1.34 =fk = Mtr 1 c. p = 12, = 12, B= 5, K=1.37 Cam d p = 12, = 12, B= 6, K=1.49 e. = 4, = 2.5, B= 24, K=1.63 f. = 37.5, =25, B=72, K=1.2 g. = 8, =8, B=4, K=1.49 Bed ( ll dimensins except f K in mm ) Fig. 1 Specimens with ntches Fig.2 Fatigue machine Ntch Fig.3 Psitins f strain gages 3 Experimental Results 3.1 Relatin Between Saturated Strain Range at Ntch Rt and Number f Cycles t Fatigue Crack Length f 1 mm Fig. 4. a, b shw definitins f symbls and terms respectively. Fig. 5 shws the relatin between the saturated strain range at a ntch rt and the number f cycles t fatigue crack length f 1 mm btained by all specimens except f specimen g. The meaning f IS and CS in Fig. 4 are as fllws : IS ( Increasing Strain ) means that strains near a ntch increase with an increasing cycles, and CS ( Cnstant Strain ) means that strains near a ntch remain cnstant with an increasing cycles. The relatin between the saturated strain range at a ntch rt and the number f cycles t fatigue crack length f 1 mm in IS regin f 1M* cycles becmes straight line as shwn in Fig.5, and s Mansn-Cffin rule may be applied t these data.
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Fracture Mechanics max at ntch rt ^ (% turated strain range a. Symbls b. Terms i 3 Fig 4 efinitins f symbls and terms ^" a -, 1n irin Number f cycles t crack length f 1 mm N^ ( n * R824B72K1.48-IS R1224B72K1.34-IS * R1212B5K1.37-IS 3 R1212B6K1.49-CS/IS R42.5B24K1.63-IS C3 R42 5B24K1 63-CS K : Stress cncert tratin factr Fig. 5 Relatin between saturated strain range at ntch rt and fatigue life n e max-r= "f 6 e min-r= [] ~c * Q t max-r=1 cmin-r=1 P e max-r=3 jjh rff < c 2 - fl**l n"' V e min-r-3 fret & '5 -i nn - w p-i-i n ^ ^> K> ^ m 5? ggg -innnn-^.2.4.6.8 ^ 1 1.2 1.4 Number f cycles N ( X1* cycles ) a. e, e. vs N 5 - b ; v 4 - er cm C 3 - < 2 - c C -t '. 1 - irmrtur XX X r c i n' ' ) < n- $ ^' Fig. 6 Relatin between strains and number f cycles 3.2 Typical Examples f IS and CS n [ n.2.4.6.8 1 1.2 Number f cycles N ( X1* cycles ) b. R' ^ m ^ N The example f IS is shwn in Fig. 6. This specimen is a in Fig. 1 and its fatigue life is 1.59 X 1^ cycles n the cnditin f saturated strain range f 1.5 %. Fig. 6. a shws the relatin between maximum strains, minimum strains near a ntch in the regin frm a ntch rt t distance f 3 mm the number f cycles. Where, maximum strains crrespnd t ne at maxi and
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 mum bending deflectin and minimum strains crrespnd t ne at reversed maximum bending deflectin (r minimum bending deflectin ). Maximum strains and minimum strains at a ntch rt increase prgressively as the number f cycles increases, and strains near a ntch increases a little with an increasing cycles. Fig. 6 b shws the relatin between the strain range and the mean strain at a ntch rt and the number f cycles. Frm this, the strain range at a ntch rt keeps cnstant saturated value up t abut 6 cycles and increases after 6 cycles. The mean strain at a ntch rt increases initially frm t a certain saturated value and keeps cnstant value up t abut 6 cycles, and increases again after 6 cycles. This is the typical IS behavir. The example f CS is shwn in Fig. 7. This specimen is e in Fig. 1 and its fatigue life is 2.65 X1* cycles n the cnditin f saturated strain range f.42 %. Frm Fig. 7. a, maximum strains and minimum strains increase initially due t the cyclic wrk hardening f the material, but after then these strains remain cnstant as the number f cycles increases. Frm Fig. 7. b, the strain range at a ntch rt remains cnstant with an increasing cycles except f initial shrt perid f cycles due t the wrk hardening and the mean strain at a ntch rt keeps nearly zer with an increasing cycles. This is the typical CS behavir. H max-r= min-r- f 4 rrrrm L-Q Enn inn r me p max-r-3 L ) ( t (3 ( 8 & iinrrm tan ^ 5 1 15 2 25 3 Number f cycles N(X1* cycles) 12 1 - b X 8 n R cm % 6 f t rifff \»* TTTI mm nn etc c nnr* p " 2^ 4 gnrqa mnnrr r> 3 5 1 15 2 25 3 Number f cycles N ( X1* cycles) a., max' min N b. ^, e VS N Fig. 7 Relatin between strains and number f cycles n
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Fracture Mechanics 3.3 etail Mechanism f IS Behavir The careful measurement f strains has been cnducted under cyclic large bending deflectin in rder t investigate the detail f IS behavir. The specimen used is g in Fig. 1 and 1 strain gages are attached t this specimen as shwn in Fig. 8. Where, side f the specimen means the tensin side when the bending mment is laded initially at 1st cycle and the strain f e ^ crrespnds t ne f strain gage number f 1. The bending strain f e b at the minimum sectin is ne estimated frm e ^ by cnsidering the elastic stress cncentratin factr, rati f the mment arm length and the rati f the sectin mdulus. Fig. 9 shws the general mdels f the hysteresis lp and strain distributin in frnt f ntch. In this figure, ^ (r ^ in Fig. 4), e and e ^ mean the ttal strain range, the plastic strain range and the elas 1 (en) side side M B side Ntch Fig. 8 Psitins f strain gages and definitins f e, e e : Elastic-plastic strain at ntch rt e b : Elastic bending strain at e n : Elastic bending strain at n et Fig. 9 General mdels f hysteresis lp and strain distributin
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Fracture Mechanics 335 tic strain range respectively and sme symbls used in Figs 1, 11, 12, 13 are shwn. Fig. 1. a shws the relatin between maximum strains and minimum strains at bth ntch rts and the number f cycles. Fig. 1. b shws the relatin between strain ranges and mean strains at bth ntch rts and the number f cycles. The small difference between the strain f side and the strain f B side may be cnsidered due t initial yielding difference f the tensin side and the cmpressin side at 1st cycle. g n side max side- - B side B side-min. n ].9 B^ R : @«i * ' ^Tvd ' 5 1 15 2 25 3 35 Number f cycles N ( cycle )» * max- e vs N b. K' m vsn Fig. 1 Relatin between strains at bth ntch rts and number f cycles Fig. 11 shws changes f the strain distributin acrss the minimum sectin frm the ntch t the ntch B with an increasing cycles. Where, r f crrespnds t the ntch rt and r f 24 mm crrespnds t the ntch rt B. The large change f strain distributins is bserved. It is fund that the surface layers at bth ntch rts extend tward tensin strain with ) Q E i * b u g N2-c b= 3 N2- b= N2- b=( ) N2-e b= & 3 5 1 15 2 25 istance frm ntch rt r (mm ) a. at N= 2 cycles 6 <c9 N1- b=max 1 H N1-eb= N1- b=min, n- ' R i C < J 1 ~ E 4- c] R-R8K1.49 c) «m.r8ki.49 c 3.5- frb-r8k1.49 t < 3- c «mb.r8k1.49 ) 3 2.5- < * km BBS' I j Ji! 5? '! 1 i, 9 "5 1 5- w 1, G r.5-i # ' - 5) 1 15 2 25 3 Nu 35C mber f cycle N(cyc le) -1- " 5 1 15 2 25 istance frm ntch rt r ( mm ) b. at N= 1 cycles Fig. 11 Changes f strain distributin acrss minimum sectin at N cycles
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 336 amage and Fracture Mechanics I) N5- b= p N5-eb= max 1 4 N5- b= N5- b= min 4 5-i] j ] * >Q ' J I ((* jl _n «s«& 5 1 15 2 25 istance frm ntch rt r ( mm ) C ) 2_, Q C j> ~ -5- B " 5 8 E N1- b= N1-e b=max N1-eb= N1- b=min a S fi 2 n 6 1 15 2 25 istance frm ntch rt r ( mm ) c. at N= 5 cycles d. at N= 1 cycles Fig. 11 Changes f strain distributin acrss minimum sectin at N cycles an increase f the number f cycles because f an increasing f mean strains and the strain ranges at ntch rts remain nearly cnstant values with an increasing cycles. Fig. 12 shws all strain distributins at the maximum bending deflectin and at the maximum reversed ne with an increasing cycles and it is easy t knw shift f strain distributins. Fig. 13 shws changes f hysteresis lps at ntch rts and B with an increasing f the number f cycles. It is fund that the hysteresis lp shifts tward tensin strain with an increase cycles. This is the similar phenmena such as the cyclic creep ( r cyclic plastic defrmatin ) f the N2-rb-max N2-eb-mln 2 N1- e b-max 4 # N1- e b-mln 2 5 N3-e b-max? 2 N3-1 b-mln N5-1 b-max 1 5^C I + N5-1 b-mln N 1 - f b-max e 4«N1-t b-mln 5- + I ī ', * S 5-4 j*r -1 - " * 2 # * * ^ & S n 1 15 2 istance frm ntch rt r ( mm ) Fig. 12 Shift f strain distributin with an increase f number f cycles
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 amage and Fracture Mechanics 337 slde-n2 S-i slde-n1 side-n5 4- side-n1 side M25 # 3-?- ft, d v 4* < r 5 1 - ] f'c 3 i* ( - % ^ <bi tb' (M c C -1 - [ [ C c: ( ^^ -.25 -.2 ^-.15 -.1 -.5.5.1.15.2.25 Bending strain c (%) Fig. 4 35 3-2- 1 5-5- - -5- -1- < &* j \ I fit ' f I i I * ^ Bside-N2 Bside-NI B side-n5 Bside-N1 Bside-N25 % ^ q ^ [ ( L i ( b L [ rrr i r^rj 3 -.25-.2-.15-.1-.5.5.1.15.2.25 Bending strain e (%} a. at ntch rt b. at ntch rt B 13 Shift f hysteresis lp with an increase f number f cycles smth specimen under large stress. Cffin[5] presented the equivalent fatigue test under the cntrl f strain t find the estimatin methd f the fatigue life under the cntrl f stress. Recently the authr [4] has fund that the cyclic creep is ccurred at the ntch surface layer f ntched specimens under the cyclic stress. nd the authr has fund in this paper that the cyclic creep is als ccurred at the ntch surface layer f ntched specimens under the cyclic plane bending with the cntrl f bending deflectin. The authr thinks that these findings give the meanigful suggestin t cnsider the better estimatin methd f lw cycle fatigue f ntched specimens. 4 Cnclusins Frm the experimental data and their discussin abve, the fllwing cnclusins can be drawn. 1 Tw types f cyclic strain behavirs near ntch rts have been fund in ne type named as IS, the strains near ntches increases as the number f cycles increases, and in ther type named as CS, the strain near ntches remains cnstant as the number f cycles increases. 2. It is fund in case f IS that the surface layers at bth ntch rts extend
Transactins n Engineering Sciences vl 19, 1998 WIT Press, www.witpress.cm, ISSN 1743-3533 338 amage and Fracture Mechanics tward tensin strain with an increase f the number f cycles because f an increasing f mean strains and that the strain ranges at ntch rts remain nearly cnstant values with an increasing cycles. 3. Mansn-Cffin rule may be applied t the relatin between the saturated strain range at a ntch rt and the number f cycles t fatigue crack length f 1 mm in IS regin f fatigue life 4. The cyclic change f strain distributins acrss the minimum sectin between bth ntch rts and the cyclic change f hysteresis lps at bth ntch rts have been presented in detail t understand the mechanism f IS behavir. cknwledgment The authr wishes t thank Mr. M. Maeda in ur department fr his supprt n prepairing specimens etc.. References [1] Nishitani, H., Linear Ntch Mechanics as an extensin f linear fracture mechnics, Rle f Fracture Mechanics in Mdern Technlgy, Elsevier, msterdam, pp.25-37,1987 [2] Neuber, H., Thery f Stress Cncentratin fr Shear Strained Prismatical Bdies with rbitrary Nn-Linear Stress Strain Law, J. pplied Mechanics, pp. 544-55, 1961 [3] Crews, J. H., Elastplastic Sress-Strain Behavir at Ntch Rts in Sheet Specimens under Cstant-mplitude Lading, NS, TN -5253, 1969 [4] Shingai, K, Cyclic Elastic-Plastic Strain Behavir ahead f Ntches under Cyclic Tensile Lad and Fatigue Life, dvances in Fracture Research, 9th Internatinal Cnference n Fracture, Vl. 3, Pergamn, pp. 1421-1428, 1997 [5] Cffin, L. F, The Stability f Metals under Cyclic Plastic Strain, J. Basic Engineering, Vl. 82, pp. 671-682, 196