Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa, Japan *Department fmechanical Engineering, Saga University, Hnjmachi, Saga, Japan ^YawataR&D Labratry, Nippn Steel Crpratin, Tbata, Kitakyushu, Japan Abstract A methd f detecting fatigue crack initiatin in sme weak sectin f a machine element is examined using a hled specimen under randm lad cnditins. Wavefrms f tw strain functins, that is hl=e,^+xe ^ and h2=s,-a.e ^ are successively bserved, e^and E are the strains in the vicinity f the hle and X, is the strain range rati Ac,^/Ae ^ The functin hi can be used t substitute fr the lad parameter and the wavefrm f h2 changes its shape after the crack initiatin due t the crack clsure behavir. Therefre, we can detect the fatigue crack initiatin at the hle by cmparisn f these tw wavefrms. 1 Intrductin In previus reprts^, we have prpsed a new detectin methd f the fatigue crack initiatin in a machine equipment during peratin. This called the strain interference methd. Generally, fracture f a machine cmpnent riginates in a fatigue crack initiatin frm a ntched r similarly weakened sectin"*. Metal fatigue prgresses with crack prpagatin leading t catastrphic failure. Many fatigue fractures culd thus be prevented if crack initiatin culd be mnitred in such weakened sectins. Thus, we cnsider the detectin methd f fatigue crack initiatin at a site weakened by a ntch. In previus reprts*^ using the specimen having a pit f 0.2mm diameter, we carried ut fatigue tests under cnstant and fluctuate stress amplitude. It was fund that the crack initiatin can be detected by the strain interference methd until the crack length, including pit diameter, reached 1mm. Hwever, in many practical cases, the applied stress n a machine element is a randm stress. The previus results were thus limited in these applicability. The previus methd is
842 Lcalized Damage applied t investigate the case f a randm lad cnditin in the present study. 2 Material and experimental prcedure The material used fr the test was 0.15%C lw carbn steel rund bar. Figure 1 shws the shape and dimensins f the specimen. The specimen width and thickness are 20mm and 4mm, respectively. A blind hle, which diameter is 2.15mm and depth 1.4mm, was cut in the center f test sectin by electric discharge machining. This hle acts as a crack initiatr and can be regarded as a ntch. A push-pull fatigue test was earned ut with a hydraulic fatigue machine under a randm lading cnditin. The wavefrm f applied stress is represented as fllws =2 max^ (RND-0.5)' (1) \ / where ^ is the maximum value f applied stress (=185MPa), RND randm number vanng frm 0 t 1. The calculatin f Eq.( 1) and cntrl f testing machine were carried ut using a persnal cmputer. The signal f Eq.(l) was transmitted by D/A cnverter frm the persnal cmputer t the cntrller f the testing machine with intervals f 0.1 secnds. The applied stress was varied randmly with a cycle f 102.4 secnds. Figure 2 shws the applied stress wavefrm at tw different time scales. The data sampling interval is 0.1 secnds which cincides with the interval f the randm lad. The crack initiatin and prpagatin were directly bserved by ptical micrscpe. The crack length c is defined the length measured frm hle bttm. Fr the purpse f detecting crack initiatin, tw element rsette strain gauges (gauge length is 1mm) were pasted n the center line f the specimen as shwn in Fig.3. E^. and & _. are defined the strains nrmal and parallel the lading directin, respectively, where the subscript i shws the measurement psitin (i=l,2). The dimensins f y 1 and y2 are 6.9mm and 3.6mm, respectively. Lading directin -Kl _/= 15 20 20-30 140 20 20 15 Detail f A Fig. 1 Gemetry f the specimen (mm)
Lcalized Damage 843 Strain gauge * -p 0 20 40 Fig.2 Wavefrm f the applied stress xl Strain gauge Fig.3 Psitins f the strain gauge 3 Detectin f crack initiatin frm ntch bttm Cmpliance f a material varied after the crack initiatin due t the crack pening*. This behavir affected the lcal strain in the vicinity f the crack and the ntch. Therefre, the crack initiatin can be detected by analyzing the strain wavefrm. n the basis f this phenmena, the detectin methd f the crack initiatin, called the strain interference methd, was prpsed in the previus reprt^ and the crack initiatin culd be detected befre the crack reached 1mm under a cnstant stress amplitude. This methd is applying in the case f the randm lad in the present study. T detect the crack initiatin, the fllwing tw types f strain functin are used. hl=e,+x^ (2) hl=e^-^ (3) where E^ and E^ are any tw f the lcal strains measured at the psitins shwn in Fig.2 and X is the cefficient. Sensitivity is greatest if X is chsen the value clse t the strain range rati AE^/A E^. The best cmbinatin f the strains fr the strain functin are E ^ and E ^ and this case is discussed belw, i.e., E=e,, \=Ey (4) a yl' b y2 ^ ' In the present study, the cefficient X f Eq.(l) is chsen t be 1.0 because the rati AE,/A E ^ varied frm 1.1 t 1.3 during the testing. 3.1 bservatin f the wavefrm f the strain functin The wavefrms f the strain functin hi and h2 are shwn side by side in Fig.4 fr cmparisn, with hi n the left. Figure 4(a) is the case c=0mm, (b) the case c=0.28mm, (c) the case c=0.46mm and (d) the case c=0.62mm. The wavefrm f hi hardly changes its shape after the crack initiatin. n the ther hand, the wavefrm f h2 has nticeable change in shape by the time the crack length c
844 Lcalized Damage c=0mm x10-5 X10 0 20 0 20 40 (a) c=0mm 20 0 20 40 (b) c=0.28mm x10 20 0 20 40 20 0 20 40-1.2 (c) c=0.46mm (d) c=0.62mm Fig.4 Wavefrms f the strain functin hi and h2 reaches 0.46mm because f the variatin f the cmpliance f the material due t crack clsure behavir. Thus, the crack initiatin can be detected until the crack length c reach 0.5mm. Als, even if the cyclic stress is unknwn, we can detect the crack initiatin by cmparisn between the wavefrm f tw strain functin. 3.2 Detectin f crack initiatin by means f FFT In the present experimental case, the wavefrm f the strain functin h2 was varied after the crack initiatin. Hwever, in general case, we cannt ntice the change f the wavefrm unless the distinct change ccurs in its shape. Als, the subjective detectin is expected t be carried ut if we bserve nly the shape f the wavefrm. Thus, in general case, the crack initiatin is difficult t be detected by bserving the shape f the strain wavefrm under a randm lad cnditin. Therefre, the wavefrm analysis by the Fast Furier Transfrmatin (FFT) was
Lcalized Damage 845 carried ut t detect the crack initiatin, mre effectively. It is expected that the detectin can be carried ut withut the human subjectivity by the FFT methd. The spectrum analysis f the wavefrm was carried ut using the finitely dispersed Furier transfrmatin* by same methd as described in ur previus study^. The spectra f pwer Phi, Ph2 and PS crrespnding respectively t the strain functin hi, h2 and the nndimensinal stress a/a max are calculated. The spectra f Phi and Ph2 are shwn in Fig.5 with fur crack length cases. Figure 5(a) is the case c=0mm, (b) the case c=0.28mm, (c) the case c=0.46mm and (d) the case c=0.62mm. The pwer f Phi hardly changes its specrum independent f the crack length. n the ther hand, Ph2 gradually changes its spectrum with the crack grwth. We can detect the crack initiatin when c=0.46mm frm the variatin f Ph2 because the spectrum f Ph2 at this crack length can be distinguished frm that befre crack initiatin. Figure 6 shws the spectra f pwer Phi and PS after the crack initiatin, simultaneusly. The gd cincidence c=0mm xicr (D CM JZ 0 1 2 3 4 (a) c=0mm 1 2 3 4 5 (b) c=0.28mm 1 2 3 4 0 1 2 3 4 5 (c) c=0.46mm (d) c=0.62mm Fig.5 Variatin f the pwer spectrum f the strain functins
846 Lcalized Damage x10-7 c=0.46mm 0.1 C 0 0 1 2 3 4 5 Fig.6 Cmparisn f Phi and PS 0 ' 0 1 2 3 4 5 Fig.7 Cherence f the strain functins was bserved between the distributin f these tw spectra, qualitatively. It is fund that the wavefrm f the strain functin hi has the same quality as that f cyclic stress a. Fatigue crack initiatin can als be mnitred by cmparing the tw spectra f Phi and Ph2. Befre the crack initiatin, the spectrum f Phi has many peaks at same frequencies with that f Ph2. Hwever, after the crack length c reached 0.46mm, the different distributin f the spectrum was bserved between the tw spectra f Phi and Ph2. This cmparisn can be carried ut mre effectively by cherence f the strain functin hi and h2 as shwn in Fig.7. The cherence at the time the crack length larger than 0.46mm is different frm that befre crack initiatin in the high frequency range. Therefre, the crack initiatin can be detected after the crack length c reaches 0.46mm under the randm lad cnditin. It is a merit f the present detectin methd that nly utput wavefrm f the strains are need fr the inspectin. Sme machines are designed such that ne can estimate the crack initiatin site t ease the subsequent mnitring f crack initiatin. In additin t regular inspectin fr fatigue cracks by a nndestructive methd, cntinuus mnitring at the weak sectin r ntched sectin f a machine cmpnent by a similar methd t the present study wuld decrease the incidence f fatigue - related fracture accident, assuming such a weakened sectin f the machine equipment can be determined. 4 Cncluding remarks The detectin methd f the fatigue crack initiatin during machine peratin was investigated. The experiments were carried ut with the hled specimens under randm lad cnditins. Tw types f the strain functin defined as fllws; hl= yl +^8 y2 and h2=e yl -A,E y2, where yl, and y2 e are the strains in the vicinity / f the hle and A, = 1.0. The main results btained are as fllws:
Lcalized Damage 847 (1) The wavefrm f the strain functin hi did nt change its shape till well after the crack initiatin and the pwer spectrum f hi cincides qualitatively with that f the applied randm lad. Therefre, the wavefrm f the strain functin hi can be used in substitutin fr that f the applied lad, qualitatively. (2) Crack initiatin frm a hle can be detected by the change f the wavefrm shape f the strain functin h2 after the crack reaches 0.46mm. This change reflects the variatin f the cmpliance f the matenal due t the crack clsure behavir. (3) The detectin f the crack initiatin can be carried ut mre effectively by analyzing the pwer spectrums and cherence f the strain functin hi and h2 with Furier transfrmatin. References 1. Makabe, C., Kaneshir, H., Itkazu, M. & hba, K., An inspectin f Fatigue Crack Extensin Based n Strain Infrmatin, Engineering Fracture Mechanics, 1993, 45, 655-662. 2. Makabe, C., Nishida, S. & Kaneshir, H., A Detecting Methd f Fatigue Crack Initiatin by Analyzing Strain Wavefrm, Jurnal f Testing and EvaWr/M, 1993, 21, 339-345. 3. Makabe, C., Kaneshir, H., Nishida, S. & Urashima, C., Detectin f 1mm Fatigue Crack Initiatin Using Strain Wavefrm, Jurnal f Engineering Maffnk aw 7fc&Wgy, 1994, 116, 483-487. 4. Nishida, S., Failure Analysis in Engineering Applicatin, Butter wrth Heinemann Ltd, xfrd, 1992. 5. Elber, W., The Significance f Fatigue Crack Clsure, ASTMSTP 486, 1971, 230-242. 6. Hm, M., Spectrum Analysis, Asakura-shten, Tky, 1977.