f L £54.; (a? “(Y i ,' We “as same i ‘Ussswsméry E i‘ '~ \ This is to certify that the thesis entitled MACROSCOPIC AND MICROSCOPIC STRAIN-LIFE BEHAVIOR OF PEARLITIC MALLEABLE IRON presented by JOHN SAMUEL CUCCIO JR. has been accepted towards fulfillment of the requirements for MASTER MATERIALS SCIENCE degree in MZLM Major professor Date fiOI/f 9L 0-7639 MSU is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES .—3—. RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. '__‘ ___,.,_-..u-A MACROSCOPIC AND MICROSCOPIC STRAIN-LIFE BEHAVIOR OF PEARLITIC MALLEABLE IRON By JOHN SAMUEL CUCCIO IR. A 111E818 Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Metallurgy. Mechanics and Materials Science 1984 ABSTRACT MACROSCOPIC AND MICROSCOPIC STRAIN-LIFE BEHAVIOR OF PEARLITIC MALLEABLE IRON BY JOHN SAMUEL CUCCIO JR. Microscopic and macroscopic behavior for four hardness ranges of pearlitic malleable iron is correlated with the matrix preperties and the morphology of the graphite nodules. An analysis of the stress-strain and strain-life behavior is performed. The effects of microscopic discontinuities are characterized‘with an. interferometric strain gage that measured strains over gage lengths varying from 7'0 to 180 pm. The microstrains are used with Nueber's rule to determine stress concentrations produced by local regions of shrinkage pits and nodules. It was found that the macroscopic strain-life behavior for these four hardness groups is predominantly controlled by the stable cyclic stress-strain response of the matrix Stress concentrations fran the microscopic discontinuities were found to be relatively con- stant for the two extremes in hardness ranges. AKNOWLEDGEMENTS I would like to thank the people at General Motors Central Foundry for their assistance throughout this pro- gram. I would also like to thank Matt Melis and Barry Spletzer for their help. and for making it fun to work in the lab. My sincere thanks to my advisor and friend, Dr. john Martin, who helped push me to a new level of profes- sional ability. My deepest love and thanks to my wife who was always there when I needed her. ii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . iv LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 MATERIAL . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 3 STRAIN-LIFE TESTS . . . . . . . . . . . . . . . . . . 8 3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Observations . . . . . . . . . . . . . . . . . . . . . 9 3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 4 ANALYSIS OF STRESS CONCENTRATIONS . . . . . . . . . . 32 4.1 Test procedure . . . . . . . . . . . . . . . . . . . . 32 4.2 Remote and Local Behavior . . . . . . . . . . . . . . . 36 4.3 Nueber application . . . . . . . . . . . . . . . . . . 42 Chapter 6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . 46 LIST OF REFERmmS O O 0 O 0 O O O O O 0 O O O O O O O O O O O O 4 8 iii LIST OF TABLES Table Page 1 Specimen tested . . . . . . . . . . . . . . . . . . . . . 4 2 Strain-life data . . . . . . . . . . . . . . . . . . . . 15 3 Strain-life preperties . . . . . . . . . . . . . . . . . 31 4 Matrix hysteresis data . . . . . . . . . . . . . . . . . 37 5 Cyclic stress-strain parameters for the matrix . . . . . 39 6 Local strains, local stresses and stress concentrations around discontinuities . . . . . . . . . . 43 iv Figure 10 11 12 13 14 15 16 17 18 19 20 LIST OF FIGURES Etched and unetched microstructures . . . . . . Machined test surface . . . . . . . . . . . . . Microshrinkage . . . . . . . . . . . . . . . . Strain/time sine wave . . . . . . . . . . . . . Specimen schematic . . . . . . . . . . . . . . Failure surface . . . . . . . . . . . . . . . Schematic of a hysteresis loop with parameters Hysteresis loops from 250 and 230 BHN specimens Hysteresis loops fran 200 and 170 BHN specimens Log-stress/ log-plastic strain schanatic . . . Cyclic stress-strain curves . . . . . . . . . . Log-stress/log-plastic strain lines . . . . . . Schematic of strain-life curve with parameters Strain-life curve for 170 BHN specimens . . . . Strain-life curve for 200 BHN specimens . . . . Strainrlife curve for 230 BHN specimens . . . . Strain-life curve for 250 BHN specimens . Total strain-life curves . . . . . . . . . . . Elastic strainrlife curves . . . . . . . . . . Plastic strain-life curves . . . . . . . . . . Page 10 12 13 14 17 19 20 22 24 25 26 27 28 29 3O 21 22 23 24 25 26 27 28 Hysteresis loops recorded from interferanetric strain measurements . . . . . . . . . . . . . Test regions with indentations . . . . . . . Replicas of discontinuities with indentations . Schanatic of remote and local regions . . . . Cyclic stress-strain curve from the matrix . Micrograph of replicas from specimen tested at.t¢3$ e and $.145 e . . . . . . . . . . . . Hysteresis loops recorded near 1000 cycles . Theoretical stress concentrations fran an ellipsoidal cavity . . . . . . . . . . . . vi 33 34 35 36 38 40 41 44 CHAPTER 1 INTRODUCTION Extensive studies of the mechanical preperties of gray and nodu- lar cast iron have been performed(1-'). Very little fatigue data for pearlitic malleable iron has been produced. This thesis study presents a complete set of strain-life data for four hardness ranges (170, 200, 230 and 250 BHN) of pearlitic malleable iron. and charac- terizes the microstructural effects which produce this response. Some interest in studying cast irons is inherent in their microstructures. Cast irons are essentially steels with discontinui- ties. These discontinuities are graphite flakes or nodules, inclusions. and shrinkages. Many of the studies have been directed toward the graphite because it is the predominate discontinuity (by volume). and it's morphology can be controlled(‘). Since graphite has nearly no strength. as comparedmwith the matrix, it is modeled as a cavity. The effect the microstructure has on the mechanical preper- ties of cast irons can therefore be characterized by determining the mechanical pronerties of the matrix and the stress concentrations pro- duced by the graphite. The mechanical preperties of the matrix can be estimated by comparing it to a cast steel with a similar microstruc- ture and hardness. Stress concentrations produced by the graphite can be estimated brrcomparing the graphite morphology to a shape for which theoretical stress concentrations have been determined. Studies have been done to this effect for gray and nodular irons(5-7). In this thesis the effect that graphite nodules have on the mechanical preper- ties of pearlitic malleable iron are characterized by determining the matrix preperties and the stress concentrations. fron the graphite. with direct strain measurements. CHAPTER 2 MATERIAL Malleable iron is cast as a white iron. It is then heated into the austenite plus carbide region and held at this temperature until the large carbides have converted into graphite nodules. Fran this point the rate of cooling and subsequent heat treatments are dependent on the desired matrix structure("'). Specimens used in this progrmm were cast and.machined by General Motors Central Fbundary. After the specimens'were cast they were heated to more than.1700°F for 12 hours. The specimens were then oil quenched to lSO’F. Finally they were tempered at approximately 1200°F and held at this temperature for the time necessary to produce the desired hardness. Specimens*were received in hardness groups as tested by General Motors. They came in seven hardness lots according to the following Brinell hardness diameters, 3.8; 3.9; 4.0; 4.2; 4.3; 4.6; 4.7 mm. Due to the similarity of prOperties between the close hardness ranges, the specimens were regrouped into four hardness lots. The corresponding average Brinell hardness numbers were found for each Brinell hardness diameter range<1°). BHN values will be used for this thesis. Hardness ranges and the numtnr of specimens tested in each range are listed in Table 1. Table 1. Specimens tested BHD (mm) BHN HV (matrix) Specimens Tested 3.8-3.9 250 372 17 4.0 230 336 19 4.2-4.3 200 327 17 4.6-4.7 170 294 20 The Vickers microhardness of the matrix ‘was measured for each specimen. Table 1 has the average Vickers hardness for each range. Data presented in this thesis are grouped according to Brinell hardnesses. When the specimensrvere regrouped according to Vickers hardness values the results became more scattered. An etched and unetched microstructure of each hardness lot is shown in Figure 1. Unetched.microstructures illustrate the morphology of the graphite nodules. There is little difference between the nodule morphology of each hardness range. Nodules are compact and show only slight alignment. Both of these characteristics improve the mechanical prOperties. Etched.microstructures show the matrix to be martinsite. not pearlite, as it's name suggests. There is also little difference between the etched.microstructures, but this is expected since the only difference between these hardness lots is due to the degree of tempering. The surface of the specimens used for the strain-life tests were machined. The effect machining has on the surface of this material is shown in Figure 2. Cracking around the nodule is caused by machining. A second feature found in the surface of many of these specimens was microshrinkage. Figure 3 shows a common looking shrinkage. Many of the shrinkages had this type of circular symmetry, but not all. Figure 1. Etched and unetched microstructures Figure 3. Microshrinkage CHAPTERS! STRAIN- LIFE TESTS 3.1 PROCEDURE Standard strain-Life procedures were used(11) to produce the strain-life data. Data were produced fran strain controlled axial fatigue tests. An MTS closed loop, servo-hydraulic fatigue system was “584(13). Strain was induced into the specimen in the form of a con- stant amplitude. fully reversed, sine wave. shown in Figure 4. Each specimen was tested to failure or no less than 10‘ cycles. Stress-strain hysteresis leaps were recorded at convenient increments for data reduction purposes. The specimen configuration is given in Figure 5. This large test section was used to help homogenize the effects of the nearly macros- copic discontinuities and to utilize an available casting mold. +A6/2l— thne _A€ - /2 Figure 4. Strain/time sine wave / .75'l6 UNF _____ F5 ¢rr €i25 Figure 5. Specimen schematic 3.2 OBSERVATIONS Test frequencies fran .1 to 20 Hz were used. Low frequencies were necessary to prevent the large strain amplitude test specimens from overheating. The use of test frequencies of more than 20 Hz was inhibited by the loss of control caused by the large test section. Failures produced a classic fatigue fracture as seen in Figure 6. The well defined line between the fatigue and brittle fracture regions was observed in many of the specimens. Many of the surfaces could not be classified due to the compression of the surfaces by the hydraulic ram after shut downs In all but one of the preserved fracture sur- faces, a fatigue failure could be identified by a fatigue crack growth region. Approximately 40% of the failures. which could be examined. initiated at shrinkages. Several of the shrinkages that initiated failure were located by macroscOpic inspection before testing. All .7. 10 This may be attributed to the sur- failures initiated at the surface. 1n1ng_ face degradation produced by mach Failure surface Figure 6. 3.3 DATA Strain-life data are measured fran stress-strain hysteresis loops. The parameters which are derived fran a hysteresis loop are shown in Figure 7. Compressive and tensile moduli of elasticity (Ec and Et) are both measured because they are not the same for most cast irons. Stress amplitudes (Ac/2) and total strain amplitudes (As/2) are measured fran the hysteresis peaks. Elastic strain (Ace/2) is determined by dividing the stress amplitude by the average modulus of elasticity. Aee/Z = (Ao/2)/((Et+Ec)/2) = Aa/(Et+Ec) (Equation 1) Total strain is the sun of the elastic and plastic strains (Asp/2). Therefore. plastic strain is calculated as the difference between the total and the elastic strains. Asp/2 = Ae/2 — Ase/2 (Equation 2) As mentioned, the strain amplitude is held constant for strain-life testing. The stress amplitude will often change during a test. This material generally had a decreasing stress amplitude (cyclically softened) as it was cycled. Most of the change occurs early in the life of these specimens. Hysteresis loops recorded. 12 a a 13/5 r ECI- é ET L Aép Ace—.‘ r 13‘ Figure 7. Schematic of a hysteresis loop with parameters between one half of cycles to failure to near failure were considered stable for this material. The difference between the first hysteresis and the stable hysteresis for each hardness group tested. at t,3$ 8 can be seen in Figures 8 and 9. The 250 BHN group showed an average decrease in stress amplitude of 12%. while the 170 BHN group had an average increase in stress amplitude of 4%. Approximately half of the specimens in the 170 BHN group cyclically hardened and half cyclically softened. Stable leaps were used to calculate the data in Table 2. Included in the Table are the reversals te failure.(twe times the cycles. 2Nf) for each specimen. 13 (250 BHN) 1 (230mm) / aq /’ // I ——first loop ——steble loop Figure 8. Hysteresis loops from 250 and 230 BHN specimen 14 (200 BHN) (I70 BHN) 0 { 6 ——first leap stable loop Figure 9. Hysteresis leaps from 200 and 170 BHN specimen Table 2. 15 Strain-life data Et Ec Ao/2 Ae/2 Ace/2 Asp/2 2Nf (10‘Psi) (lO‘Psi) (Ksi) 250 BHN 25.0 22.2 78.2 .00982 .00331 .00651 178 24.5 22.0 78.2 .00980 .00337 .00653 174 25.0 23.0 72.0 .00782 .00300 .00482 254 26 .8 23 .2 75 .0 .007 81 .003 00 .00481 202 24.8 23.8 62.3 .00485 .00257 .00220 1780 25.2 22.2 62.6 .00484 .00264 .00220 1300 26.2 24.0 56.4 .00284 .00225 .00059 16900 25.5 24.5 55 .4 .00284 .00222 .00062 11500 27 .0 26 .6 49.6 .00193 .00185 .00008 97 200 27.2 26.5 48.8 .00193 .00182 .00011 172800 27 .2 27 .2 42 .1 .00160 .00154 .00006 362000 27.0 27.0 41.8 .00157 .00157 .00000 618000 26 .5 26 .5 40 .5 .00153 .001£ .00000 356 000 26 .5 26 .5 39.3 .00148 .00148 .00000 404000 27 .5 27 .5 39.2 .00143 .00143 .00000 810000 27 .2 27 .2 38.6 .00142 .00142 .00000 8714000 230 BHN 24.0 23 .0 76.5 .00976 .00326 .00650 100 23 .5 22.5 71.8 .00782 .00312 .00470 170 26 .0 23 .5 67 .9 .00644 .00274 .00370 324 25 .2 23 .9 63 .2 .00484 .0025 8 .00226 2490 25.4 23.8 64.6 .00482 .00263 .00219 2090 25.2 25.0 58.6 .00359 .00233 .00126 6480 24.0 24.8 52.0 .002fi .00213 .00073 11100 26 .2I 25.0 50 .8 .00229 .00198 .00031 30200 25.1 25.2 49.5 .00206 .00197 .00009 73400 26 .8 25 .8 47 .8 .0 0188 .00181 .0 0007 182000 26 .2 26 .2 47 .2 .00187 .00180 .00007 194000 26 .5 26 .5 47 .4 .00187 .00179 .00008 111000 27 .5 27 .5 48.0 .00183 .00174 .00009 144000 26.0 26.0 46.1 .00180 .00177 .00003 131000 26.8 26.8 43.0 .00161 .00161 .00000 295000 25.8 25.8 41.2 .00160 .00160 .00000 706000 26.8 26.8 38.5 .00144 .00144 .00000 1620000 27 .0 27 .0 38 .0 .0 0141 .00141 .0 0000 43 1000 Table 2. continued 26.2 22.8 67.7 24.5 22.2 67.7 22.5 22.2 62.1 25.2 23.0 62.5 22.8 22.2 56.5 24.8 22.8 60.8 23 .5 21.8 56 .7 23 .2 19.9 56 .8 24.5 23.8 50.8 25.5 25.0 52.0 23.8 23.8 49.5 23 .2 22.8 48.5 27.0 26.2 45.5 27 .0 25.8 44.2 29.0 27 .2 43 .8 25.2 25.2 39.0 25.2 25.2 39.9 25.8 25.8 37.0 26.2 26.2 37.2 26.0 26.0 33.1 21.0 20.5 50.3 23.5 21.0 49.7 24.2 22.4 49.5 22.5 21.5 49 5 2445 23.2 47.0 24.2 23.7 46.7 22.9 22.0 40.8 23 .8 23 .0 44.2 23 .5 23 .5 42 .2 23 .8 23 .8 43 .8 24.2 24.0 43 .8 25.8 24.8 45.2 25.8 24.8 39.0 23.8 23.6 35.3 25.2 25.2 33.1 23 .5 23 .5 28.5 24.5 24.5 29.6 25.5 25.5 30.3 24.0 24.0 26.7 16 200 BHN .00983 .00276 .00707 156 .00982 .00290 .00692 88 .00783 .00278 .00505 346 .00780 .00259 .00521 380 .00587 .00251 .00336 686 .00551 .00256 .00295 1320 .00506 .00251 .00255 2120 .00503 .00263 .00240 3320 .00385 .00211 .00174 1950 .00380 .00206 .00174 830 .00300 .00208 .00092 9120 .00291 .00211 .00080 11000 .00191 .00171 .00020 73200 .00190 .00168 .00022 59400 .00163 .00155 .00008 87800 .00160 .00154 .00006 176000 .00157 .00157 .00000 538000 .00143 .0016 .00000 43 8000 .00142 .00140 .00002 357 000 .00127 .00127 .00000 610000 170 BHN .00798 .00242 .00556 92 .00592 .00219 .00373 268 .00490 .00220 .00270 600 .00442 .00224 .00218 1080 .00390 .00197 .00193 1560 .00353 .00195 .00158 4170 .00323 .00182 .00141 706 .00295 .00189 .00106 5700 .00270 .00180 .00090 3290 .00250 .00184 .00066 18200 .00242 .00182 .00060 16800 .00193 .00179 .00014 51600 .00175 .00154 .00021 60000 .00160 .00149 .00011 64600 .00134 .00131 .0 0003 263000 .00126 .0 0121 .0 0005 850000 .00121 .00121 .00000 1140000 .00119 .00119 .00000 937000 .00111 .00111 .00000 1200000 17 3.4 RESUETS A cyclic stress-strain curve is produced by connecting the tips of stablized hysteresis loops. The stress and plastic strain fran the cyclic stress-strain curve are linearly related en a log-leg scale. illustrated in Figure 10. The relationship can be written as: Ao/2 = K'(Aep/2)n' (Equation 3) The cyclic strain hardening exponent 01') and the cyclic strength coefficient (K') are determined by using the least squares method an the logarithmic values of stress and plastic strain. (leg-leg scale) Figure 10. Leg-stress/lag-plastic strain schematic 18 Cyclic stress-strain curves for each hardness group are given in Figure 11. The cyclic response of this material exhibits less change. with respect to hardness. than the monotonic response. The cyclic yield stress varied frcm 35 to 50 Ksi while the monotonic yield varied from 30 to 70 Ksi. The difference between the maximum and minimum monotonic yield stresses is 2.5 times greater than the difference between the cyclic yield stresses. The change in cyclic preperties did exhibit trends with respect to hardness. The average elastic modulus for each group varied from 24°10‘ Psi to 25.5-10‘ Psi. with increasing hardness. Also the cyclic strain hardening exponents and the cyclic strength coefficient increased*with increasing hardness. This can be seen in Figure 12 which has the leg-stress versus leg-plastic strain lines for each hardness group. 19 230 BHN 250 BHN ZOO BHN I7O BHN N 40 Ksi 4r Figure 11. cyclic stress-strain curves 20 a 23 H San: sandman»: \ueouualueq .o. .oo. 210 Oh. \ 21m CON 2% 03 \\ zrm.om~ .NH oceans l Ex 00. 21 Relationships have been made between strain and reversals to failure. These are illustrated in Figure 13. where total strain. plastic strain. and elastic strain are each plotted against reversals to failure. on a leg-lag scale. Elastic and plastic strains both have linear relationships on this scale. _ ' c . Asp/2 — ef(2Nf) (Equation 4) Ace/2 = (oE/EHZNf)b (Equation 5) The total strain is therefore: Ae/Z = (OE/EHZNf)b + e£(2Nf)° (Equation 6) The last parameter to be produced from the strain-life curve is the transition fatigue life (ZNt). This is the point where the clas- tic and plastic strains are equal. and is determined by equating Equations 4 and 5. The solution is: 2Nt = (s%-E/a£)1/(b_C) (equation 7) The stain-life curves for each test group are given in Figures 14 through 17. Each plat contains the total strain. plastic strain and elastic strain curves. with data points. Stress-strain data were measured from the stable hysteresis leaps as described in the data 22 (leg-leg scale) Plastic-f mus- l”— N z 2PM Figure 13. Schematic of strain-life curve with parameters section. Logarithmic values of plastic strain, elastic strain, and reversals to failure were used in a least squares formulation to pro- duce the elastic and plastic lines. The total strain curves were determined by summing the elastic and plastic strain values as indi- cated in Equation 6. The fatigue ductility coefficient (8%), fatigue strength coefficient (0}). fatigue ductility exponent (c) and fatigue strength exponent (b) were calculated fran the strain-life lines that were determined with the least squares method. The transition fatigue life was found with Equation 7. Values of these parameters are listed in Table 3, along with the cyclic strain hardening exponents and the 23 cyclic strength coefficients. Figure 18 has the total strain curves for each test lot. There is a small difference between these curves. Lower hardness groups failed at slightly shorter lives than the harder groups. The elastic strain lines in Figure 19, exhibit a similar trend. The Plastic strain lines given in Figure 20 have the least spread. Points on the strain-life plots exhibit a small degree of scattering, considering this material is a cast iron. The largest scatter is observed in the lower hardness groups. Specimens which failed far before their expected lives did not exhibit unusual voids or inclusions .but they often had low first cycle yield stresses. Although specimens tested with the low first cycle yield stresses gen- erally cyclically hardened to a cyclic stress-strain response similar to other specimens in their hardness range. the life of these speci- mensiwas usually much shorter. The large difference in monotonic stress-strain behavior within a hardness range indicates that the Bri- nell hardness test does not accurately predict the initial condition Of this material(1’). Another source of scatter is due to some speci- mens being put through more tempering cycles than other specimens in the same hardness range. The 170 BHN material showed the most scatter. with one failure close to an order of magnitude shorter than.expected. More scattering might be expected from this group since many of the specimens were cast from different lots on different days. 24 uneaweemm znm ova new e>u=e emmnnufiauam .Va eunwmm :3 now was mow vow mow Nor op —u- 4 ——d4 — —ddlq n ,—14D 4 —dqfi q ‘114 a dung . .L 4 u ‘ l L h eta-Ere 4 a caused I .ououlw a - AZIm Oh_v Poo. 25 ween—Moon» 2.5 can hem cargo eaglemauum .mn euemmm ZN GP or or or OP New or P quq - du—u uliqd— _ J ——uu — —O-d 1 ADH‘ 1 0.3-.an 4 0.7.0.on I .muoulw o A ZIm OON v 1111111 1 1 111114 So. 26 22:009.." zmm cmm hem metro eumaueuauum .3” 035mm Law New e2. me 43 mop we or P —44— 1Jq44 d ‘qd_ A —qq_ q —«fi« 1 —~«: ~ qdqq u 4 i i n so. 4 O <4 i O C L as 4 i o o H O 1 e In 5. ozouilo 4 i ozaaiuw I L .2316 o H IN: - so I 21m 0m N v .. 27 «seameemm z=m can Hem mo>u=e eumalemeuum .bH eunumm LZN sop mop new 43 mop N2. 3 F —1dd|«||und - 1“ AC ‘44— q —-— q dqu — quld q n So. 0 L U h 5. 022.36 4 . atesenc - .2076 o . . .wl I. wq m AZIm Ommv I —. 28 ue>u=e omamiumeua» fiuuph .mn oueumm az~ so, e2 we 48 m8 «2 S F —JI 1 d 1 — — — — q d H — W at — d 4 1 J] — u — _ u — — u i u — q fi u d zzm on .4. . 21m 08 H 8o zzm 0mm 95 08 h 5. LILJI ". 29 scene owneraaaua. oasusam .sH «Henna azw so? mop mop so. me. No. o— P I‘m-- a -q—_ u —_q a ---q q —-_ 1—_-J q d:—. A a ammo: r so. ormoo~ arm 08 2.. 0mm . l1 m .“ Fe. . N r owG m L P. nee: cumuluuuuuu 03qu .oa ouummu * 3O zm s2 so, m2 «2 m8 «8 S P 14$ 4 _.q_ . —a__ 4 d+__ . —.__ _ _i- 4 a... . zrm 0mm 21m 9.. . / 1 So. zxm 0mm zrm 08 r n S. l 1 11111 '1 Table 3. Strain-life preperties 31 Hardness groups (BHN) Property 170 200 230 250 n' .14 .15 .15 .15 x' (Ksi) 150 200 220 230 b -.079 -.091 -.084 -.086 c -u56 -»54 -.57 -.55 a} (Ksi) 90 115 115 120 a; .100 .100 .140 .140 2N 97s 1010 755 690 (BAPTER 4 ANALYSIS OF STRESS CONCENTRATIONS Nueber's rule(1‘) is applied to determine stress concentration factors based on strain measurements taken in the matrix and around discontinuities. 4 .1 TEST PROCEDURE An interferanetric strain gage (ISG) was used to measure strains over short gage lengths in both remote and critical regions. This system monitors interference patterns formed by the reflection of coherent light from two Vickers microhardness indentations. The dis- tance beuveen the fringes is inversely prepertional to the distance between the indentations. Therefore. the fractional change in dis- tance between the fringes is a measure of strain between the indentations. Detailed explanations of the system have been published(1"“). Five testsw_ere run. One to check the calibration of the 186 and four to obtain data. Fran these four tests two were run on 170 BHN specimens and two on.250 BHN specimens. These tests were also run under constant amplitude. sine wave, strain control. Both hardness groups were tested at two strain ranges. £35 a and *.14‘5 e. The strain monitored to control these tests came fran an extensometer. Each specimennwas cycled until a crack (uncroscopically visible) was produced. A copy, of a series of hysteresis leaps recorded from 186 32 33 measurements. taken fran indentations around a nodule is given in Fig- ure 21. Gage lengths fran 75 to 180 nm were used for strain measuranents. These strains were measured around nodules. near shrinkages, and in the matrix away fran the discontinuities. One example of each is shown in figure 22. The position of the indentations around nodules was varied to find locations with large strain concentrations. Because sane shrink- ages were close to 300 pm in diameter. indentations could be put closer to the notch root. Six sets of indentations and respective discontinuity. are shown in Figure 23. These are micrOgraphs of replicas made fran test locations. 5? s Figure 21. Hysteresis loops recorded fran interferanetric strain measuranents 34 Figure 22. Test regions with indentations 35 Figure 23. Replicas of discontinuities with indentations 36 4.2 Remote and Local Behayiar In general. stress concentrations are determined by comparing a defined ranete response to a local response at the most highly stressed regions of a material. The location of remote and local regions is illustrated in Figure 24. In the following analysis the remote response is the response of the matrix away fran discontinui- ties and the local response is measured near the discontinuities. .— remete (As, Ae) Oo————local (A0, A6) Figure 24. Schematic of remote and local regions. Characterization of the matrix preperties of a cast iron have been done by comparing the structure and hardness of the matrix to a cast steel with a similar structure and hardness. Matrix properties will be determined here by direct strain measurements and corrected stress measurements. Stresses recorded during these tests were determined by dividing 37 the measured load by the crossectional area of the specimen. It is assured that the matrix supports the entire load. Therefore the stress in the matrix was calculated by dividing the load. by the cros- sectional area of the specimen.minus the crossectional area of the nodules. The area of the nodules was measured fran a micrograph. Data obtained fran the stress-strain response of the matrix are listed in Table 4. Corrected stress values are included. Table 4. Matrix hysteresis data 170 BEN 250 BHN Specimens Specimens Aa/2 (extensometer) .0014 .0030 .0014 .0030 E (10" Psi) 27 27 29 23 Act/2 (Ksi) 33 46 34 49 Ae/Z (corrected) 38 53 39 57 Ae/Z .00126 .00265 .00117 .00215 Ase/2 .00118 .00169 .00115 .00177 Asp/2 .00008 .00096 .00002 .0003 8 In section 3.4, a method for determining cyclic stress-strain curves was described. That method is not used here because there are only two sets of points to be used in a least squares calculation. Instead. the cyclic stresrstrain curves in Figure 25 were derived fran the stable hysteresis loeps recorded fran the matrix. The per tien of the hysteresis loep fran the compressive peak. clockwise. to the tensile peak was used. One half of the stress and strain values 38 measured fran these curves were replotted to produce the cyclic stress-strain curves. 250 BHN I70 BHN ZOKm .002 5 Figure 25. Cyclic stress/strain curves from the matrix As mentioned, there is a linear relation between the log-stress and log-plastic strain values from cyclic stress-strain curves. An equation for plastic strain can be produced by rearranging Equation 3. Asp/2 = (Aa/ZK')1/n' (Equation 8) The total strain can be written as the sum of the elastic and plastic strains. 39 Ae/2 = Ace/2 + Asp/2 = Ae/2E + (Ad/2K')1/n' (Equation 9) The cyclic strain hardening exponent and the cyclic strength coeffi- cient were again calculated using the least squares method. The values of these parameters. for both hardness groups, are listed in table 5. Table 5. Cyclic stress-strain parameters for the matrix 170 BHN 250 BHN K' 187 213 n' .18 .17 Fourteen local regions were monitored in the t,145 3 tests. Strain amplitudes recorded fran these regions are given in the next section. Data from the 1.3$ e tests are not included because crack growth was observed throughout the test life of these specimens and this study is only concerned with a continuoum approach for determin- ing stress concentration factors. Because of crack growth. the strain 19991385 from the tu3fi 2 tests were largely a measure of crack apening and closure. The number of crack sites and the extent of crack growth is illustrated in Figure 26. In each test the strains measured in the matrix were less than the strains measured from the extensometer. and strains measured across discontinuities were larger than both. A copy of a hysteresis loop recorded from each location is given in Figure 27. Figure 26 . 40 Micrographs of replicas from specimens tested at $.37) 13 and $.14!» e 41 10 Ksi~~ AL— .00 1 5 c / L6 e e .+ e°® a“, x9 . F230 60 $9 6° (5' Qfi" $0 (:30 Figure 27. Hysteresis loops recorded near 1000 cycles 42 4.3 NUEBER APPLICATION Nueber's rule has been applied to fatigue studies of notched materials. This rule accounts for the effect of plastic deformation in notched members. The stress concentration factor is related to the remote and local stresses and strains. The relationship between these parameters is given in this equation. Kt = [(Aa-Ae)/(As.Ae)]l/2 (Equation 10) The application of the Nueber's rule was used here to determine the stress concentrations produced by microscopic discontinuities. that are a part of the materials microstructure. fran directly meas- ured remote and local strains. Remote stresses and strains were determined. Local strains were directly measured. Local stresses were calculated by putting the local strain values into Equation 9, along with the apprepriate con— stants from Table 5. The measured strains and calculated stresses for the discontinuities are listed in Table 6. All of the parameters, necessary to detenmine the stress concentrations around the discon— tinuities using the Nueber relationship. (Equation 10) have been directly measured or calculated. The stress concentrations for the corresponding discontinuity are also listed in Table 6. 43 Table 6. Local strains. local stresses and stress concentrations around discontinuities Discontinuity Ae/2 Ao/2 Kt 170 BHN specimen shrinkage .00272 54 1.75 nodule .00210 49 1.47 nodule .00175 44 1.27 nodule .00175 44 1.27 nodule .00230 50 1.55 nodule .00170 44 1.25 nodule .00202 48 1.42 nodule .00200 47 1.40 nodule .00190 46 1.35 250 BHN specimen nodule .00155 47 1.26 nodule .00150 46 1.23 nodule .00155 47 1.26 nodule .00170 50 1.36 nodule .00155 47 1.26 44 Theoretical stress concentration factors (Kt) for ellipsoidal cavities(17) are illustrated in Figure 28. These values are for a cavity in an infinite body in tension. The ellipsoid is defined by two radii, r and t. The stress concentration is plotted against the ratio of the two radii t/r. If the shape of the nodules or shrinkages is approximated by an ellipsoid, the ratio of t/r would vary from 1 to 3, as determined from microscopy. The corresponding theoretical stress concentrations‘would be between 2 and 3. These values are nearly twice the values experi- mentally determined in this study. _ r— p. - t/: Figure 28. Theoretical stress concentrations from an ellipsoidal cavity 45 The difference between the theoretical and experimental values may be partially attributed to the location of the indentations. The minimum gage length used (75 um) was not small enough to place the indentations at the notch root of the graphite nodules. This can be seen in Figure 23. The shrinkages were larger so the indentations were closer to the notch root. Stress concentrations measured near the shrinkages were closer to the theoretical values than those meas- ured around the nodule. CHAPTER 5 CONCLUSIONS Strain-life behavior of four hardness ranges of pearlitic malle- able iron have been determined. Peralitic malleable iron is generally a cyclic softening material between the hardness ranges of 170 and 250 BHN. All hardness ranges soften except the lowest hardness range which slightly hardens. Because of this. the difference in stress-strain response between hardness ranges, decreases as this material is cycled. This causes the strain life preperties to be less sensitive to hardness than the monotonic preperties. waever. this material does exhibit a trend in which the strain-life becomes shorter with decreasing hardness. This trend is observed at all strain apmli- tudes unlike common steels which have strain-life curves. for different hardness ranges. that cross at the transition fatigue life. The strain-life behavior of pearlitic malleable iron is more reliable than many cast irons. The scatter in these data was small for a cast iron. Much of the scatter. that was observed. was produced by inaccurate nondestructive methods of categorizing this material. Microshrinkages often initiate failures but they do not appear to sub— stantially shorten the fatigue lives. The variation in strains between microstrucural discontinuities and the matrix have been measured. The macroscopic cyclic behavior of pearlitic malleable iron is produced by the strength of the matrix, combined with the stress concentrations caused by the discontinuities. This is verified by the strain measurements which show the macrOSCOpic 46 47 strains to be greater than the strains measured in the matrix but less than the strains measured around discontinuities. Stress concentrations have been calculated for micrOSCOpic discontinuities in this material. using direct strain measurements. Table6 shows these stress concentrations to be small and consistantly small for all regions tested and for both hardnesses extranes tested. The strainrlife behavior of pearlitic malleable iron is a product of the composite response of the matrix and the graphite nodules. This material has a more stable cyclic stress-strain response. with respect to changes in hardness. than a monotonic response. Graphite nodules produce relatively low stress concentrations. The high quali- ty of the castings combined *with these properties produce a strainrlife response which has low scatter and is relatively insensi- tive to hardness. In conclusion, pearlitic malleable iron has excellent strain-life behavior for a cast iron. 10. 11. 12. LIST OF REFEREJCES Gilber, G. N. 1.. "Review of Recent Properties of Nodular Cast Iron," Foundagy Trade Journal. May 19, 1966, pp. 667-672. May 26, 1%6, pp. 713-723. Testin, R. A.. "A Review of the Mechanical Properties of Nodular Cast Iran with Special Reference to Fatigue." T. A. M. Report No. 2. Department of Theoretical and Applied Mechanics. Univer sity of Illinois. Urbana. Illinios, 1972. Secie, D. F.. Fash, J. W.. and Downing, S. D., "Fatigue of Gray Iron." T. A. M. Report No. 44. Department of Theoretical and Applied Mechanics. University of Illinois, Urba- na. Illinios, 1982. "Properties and Selection: Irons and Steels ." Metals Handbook. Anerican Society of Metals,9th Ed.. Vol. 1, Metals Park, Ohio. 1982. pp. 57-73. Mitchell. M. R.. "Effects of Graphite Morphology. Matrix Hard- ness and Structure on the Fatigue Resistance of Gray Iron," T. A. M. Report No. 14. Department of Theoretical and Applied Mechanics. University of Illinois. Urbana. Illinois, 1974. Testin, R. A.. ”Characterization of the Cyclic Defenmation and Fatigue Behavior of Nodular Cast Iron." Fracture Mechanics Report No. 371, Deparnnent of Theoretical and Applied Mechanics. University of Illinois, Urbana, Illinios, 1973. Ikawa. E.. Ohira. G.. "Fatigue Properties of Cast Iron in Rela- ion to Graphite Structure." American Foundagy SocietyI Cast Metals Res. _.T_._. Vol 3, 1976, pp. 11-21. "Malleable Iron Castings," Mal leable Founders Society. Cleveland. Ohio, 1%0, 57—75. Angus. H. T.. "Cast Iron: Physical and Engineering Properties." Butterworths Inc.. Boston. Massachusetts, 1976, pp. 187-199. "Nondestructive Inspection and Quality Control." Metals Handbook. American Society of Metal 3, 8th Ed.. Vol. 11, Metals Park. 0hio,1976, p. 426. Feltnei; .C. E.. Mitchell. M. R.. "Basic Research on the Cyclic Deformation and Fracture Behavior of Material s," ASTM STP 465 , American Society of Testing Material 8. 1x9, pp. 27-66. Hirschberg. M. E.. "A Low Cycle Fatigue Testing Facility." Manual pp Low gale Fatigue. ASTM STP 465, American Society of Testing Material s. 1%9. pp. 67-86. 48 13. 14. 15. 16. 17. 49 Webster. J. T.. "An Investigation to Determine the Reliability of the Brinell Test and Some Nondestructive Tests in Quality Testing Gray Iron-Castings." M. S. Thesis. Department of Mechanical Engineering. Michigan State University. 1964. Topper. T. E.. Wetzel. R.M.. and Morrow. J. "Neuber's Rule Applied to Fatigue of Notched Specimens." Journal 9; Materials. Vol. 4. No. 1. March 1%9. pp. 200-209. Bofferding. C. H. III. "A Study of Cyclic Stress and Strain Concentration Factors at Notch Roots Fatigue Life." M. S. Thesis. Department of Metallurgy. Mechanics and Materials Sci- ence. Michigan State University. 1980. pp.4-18. Sharpe. W. N. Jr.. "A Short Gage Length Optical Gage for Small Strain."§gpeximental Mechanics. Vol. 14. No. 9. 1971, pp. 373-377. Peterson .R. E.. Stress Concentration Factors. Wily, New York. 1974. pp.l39—141. 219. “iuwmmmmuwarunjmmagmflmw“