ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR Final Report THE EFFECT OF SURFACE TREATMENTS ON THE FATIGUE RESISTANCE OF A HARDENED SAE 1065 STEEL C. A. Siebert R L. Jones Project 1685 ASSOCIATED SPRING CORPORATION BARNES-GIBSON-RAYMOND DIVISION PLYMOUTH, MICHIGAN August 1956

The University of Michigan * Engineering Research Institute TABLE OF CONTENTS Page ABSTRACT iii OBJECTIVE iv INTRODUCTION 1 EXPERIMENTAL METHOD 2 Material Tested 2 Heat Treatment 2 Fatigue-Specimen Preparation 2 Surface Treatments 3 Fatigue Testing 4 RESULTS 4 Heat Treatment 4 Polished Surface Condition5 Electrolytic Cyanide Surface Treatment6 Acid-Pickling Surface Treatment 6 Cadmium-Plating Surface Treatment 7 Parkerizing Surface Treatment 7 C ONCLUSIONS 8 APPENDIX. STATISTICAL EVALUATION OF FATIGUE DATA 19 Tests Pertaining to Differences in Means and Variance 20 REFERENCES 25 ii

The University of Michigan * Engineering Research Institute ABSTRACT The effect of surface alterations, resulting from several surface treatments, on the fatigue characteristics of a quenched and tempered SAE 1065 spring steel was determined by fatigue tests made with the R. R. Moore rotating beam machine. Fatigue tests were run on specimens which had been polished and then subjected to the following surface treatments: (1) as polished, (2) electrolytic cyanide cleaning, (3) acid pickling, (4) cadmium plating, and (5) Parkerizing. The spring steel was tested in the quenched and tempered condition. The average tensile strength of these specimens was 200,000 psi with an average hardness of 42 Rockwell "Co" The finite life fatigue data were analyzed statistically and average curves including 2aW limits were drawn for surface treatments one, two, and three listed above. The endurance limit was defined only within approximate limits. For the cadmium-plated and Parkerized surface conditions, between eight and ten specimens were used to estimate the S-N curve Cleaning by the electrolytic cyanide method caused a decrease in the high-stress fatigue life, but as the stress decreased and approached the endurance limit the difference in fatigue life became smaller until at the endurance limit the difference no longer existed. This cleaning method appeared to have little or no effect on the endurance limit. The acid-pickle cleaning method caused a general decrease in the finite fatigue life of this material. The decrease in life as represented by cycles to failure amounted to about 40 percent. The endurance limit appeared to be lowered by about 6 to 7 percent. Cadmium plating followed by a low-temperature heat treatment to remove the hydrogen appears to have lowered both the finite life and endurance limit from that of the polished condition. Parkerizing appears to have little effect on the finite fatigue life, but does appear to lower the endurance limit. iii

The University of Michigan * Engineering Research Institute OBJECTIVE The purpose of this investigation was to evaluate the influence of four surface treatments, electrolytic cyanide cleaning, acid pickling, cadmium plating, and Parkerizing, on the fatigue characteristics of anSAE 1065 highstrength spring steel iv

The University of Michigan * Engineering Research Institute INTRODUCTION It is well known that in almost all components, which have a metallurgical homogeneous section, failure by fatigue originates at the surface. Consequently, the influence of surface alterations as affected by various surface treatments has been studied quite extensively. A literature survey of this topic has been published under separate cover.1 Very little work has been done on steels having a tensile strength of 180,000 psi or higher. No information was found on the effect of electrolytic cyanide cleaning and only a small number of data were reported on the influence of acid pickling on the fatigue properties of steel. No data were found for the effect of Parkerizing on the fatigue characteristics of steel. A small amount of information was available on the influence of cadmium coatings on the fatigue properties of steel. Swanger and France2 found that the endurance limit of a quenched and tempered steel (tensile strength 168,500 psi) was lowered about 7.5 percent after pickling two minutes in an uninhibited hydrochloric acid solution (two parts water to one part hydrochloric acid), They also found decreases in the endurance limit up to 40 percent in three other steels, The change in endurance limit due to the acid pickling depended to a certain extent on the hardness and microstructure of the steels. Not enough information was available to evaluate the influence of the pickling treatment on the finite fatigue life of these steels, but the general trend was to lower the finite life values. Kehl and Offenhauer3 tested specimens pickled in an uninhibited 10-percent (weight percent) sulfuric acid solution at 149~F for 12 minutes followed by a hydrogen removal treatment of 72 hours at room temperature. The steel contained 0.54C and had a tensile strength of 136,000 psi. A 2-percent decrease in endurance limit and a 50-percent decrease in finite fatigue life were found, These investigators also found that exposure for normal periods of time to properly inhibited acid baths did not affect the fatigue properties of the steel. Frye and Kehl investigated the influence of pickling in a 5-percent sulfuric acid solution maintained at 150~F on the fatigue properties of a 0,50C steel of 115,700-psi tensile strength. The use of an inhibitor was not mentioned. They found a 10.5-percent decrease in endurance limit and about a 65percent decrease in finite fatigue life. Sopwith and Gough5 cadmium-plated fatigue specimens in a cyanide bath after anodically cleaning in a sulfuric-acid -potassium-bicarbonate bath at 100 amps per sq ft. Plate thickness was about 0.0005 inch. Only the effect on the endurance limit was investigated, and they reported a decrease of about 7 per1

The University of Michigan * Engineering Research Institute cent for a 0.5C steel for both the 96,500-psi and 145,000-psi tensile-strength levels. Forsam arid Lunden6 investigated the influence of a 0.0002- to 0.0004inch cadmium plate on the fatigue properties of several steels. No details of the plating method were given. For steels having tensile strengths of 102,000 psi and lower, changes of the endurance limit ranged from 0 to an increase of about 4.5 percent. Decreases of endurance limit of 9.1 and 13.2 percent were detected for steels having 148,000-psi and 142,000-psi tensile-strength levels. However, it should be pointed out that the values reported in all these investigations are open to question since only five to ten specimens were used to establish each fatigue curve. It has been shown quite conclusively that many more tests are required to define adequately the fatigue characteristics of a material. EXPERIMENTAL METHOD MATERIAL TESTED In order to eliminate any possible heat-to-heat variation on fatigue properties, only one heat of SAE 1065 steel was used for this investigation. The steel and the analysis were supplied by the Associated Spring Corporation, and the material was received as 1/2-inch-diameter bar stock. The steel analysis is given below: Steel C Mn P S Si Fe SAE 1065 0.64 0.88 0.010 0,034 0023 Remainder HEAT TREATMENT Bars 1/2 by 3-5/8 inches long were heated for 1/2 hour at 1600~F and quenched into a violently agitated oil bath until cool. The quenched bars were tempered at 775~F for one hour and air-cooled. FATIGUE-SPECIMEN PREPARATION R. R. Moore type specimens were machined from the heat-treated bars. The specimens were standard, except for the minimum diameter of the reduced section. The fatigue machine available was not capable of producing the highstress level desired if the usual 0.250-inch-diameter specimen was used. It was therefore necessary to reduce this section size, and a 0.200-inch diameter was selected* The reduced section of the specimens was machined to about 0.002 incb 2

The University of Michigan * Engineering Research Institute oversize —the final cut removing about 0.002 inch. The specimens were then finished to size by polishing with 180 and 320 emery paper. After final polishing, the specimens were coated with a light oil film to protect them against corrosion. SURFACE TREATMENTS Five different surface treatments were tested in this investigation. The base or standard condition to which the four other surface treatments were compared was the polished condition. The polished specimens were tested after the oil film had been removed with acetone. The electrolytic cyanide cleaning, cadmium plating, and. the Parkerizing were done at the Barnes-Gibson-Raymond Division, and the acid pickling at the Wallace Barnes Division of Associated Spring Corporation. The surface treatments were as follows: 1. Electrolytic Cyanide Cleaning a. 5-minute alkali clean at 160~F (6 ounces of DuBois Alkon per gallon of water) b. cold-water rinse c. 10-minute cathodic cleaning in 60-percent sodium cyanide bath at 160~F (6 volts, 200 amps) d. cold-water rinse 2. Acid Pickling a. 20-minute cathodic alkali clean at 160~F (McDermitt, 6 ounces per gallon) b. cold-water rinse c. 30 —40second dip in 15-20-percent hydrochloric acid pickling bath d. cold-water rinse 5. Cadmium Plating a. 5-minute alkali clean at 160~F (6 ounces of DuBois Alkon per gallon of water) b. cold-water rinse c. 10-minute cathodic cleaning in 60-percent sodium cyanide bath at 160~F (6 volts, 200 amps) d. cold-water rinse e. cadmium plate to 0.0007-inch plate thickness f, cold-water rinse g. hot-water rinse ho spin dry i. heat for 1 hour at 300~F to remove hydrogen 4. Parkerizing a. 5-minute alkali clean at 160~F (6 ounces of DuBois Alkon per gallon of water) ----------------- 5 ----------------

The University of Michigan * Engineering Research Institute b. cold-water rinse c. Parkerize dip (Parko compound 1A - 30 points acid) for 30 minutes d, cold-water rinse e. 1-minute dip in Parkoline solution (1.5 pints of Parkoline per 250 gallons of water) FATIGUE TESTING All specimens were tested on a single R. R, Moore machine run at a speed of 8000 rpm. The use of one machine eliminates possible variations in fatigue properties due to differences in testing machines. All samples which had not broken after 10 million (10 x 106) cycles of stress or longer were stopped and assumed to represent infinite life. To establish the finite fatigue life part of the S-N curve, five specimens were run at each of four stress levels for the "as-polished condition" and at each of three stress levels for the electrolytic cyanide and acidpickled surface treatments. Approximately 50 specimens are required to establish adequately the endurance limit. However, the scope of the investigation did not appear to warrant the cost of preparing and running this number of specimens. Therefore, in the above three cases about five specimens were used to locate approximately a range of stress for the endurance limit. For the cadmium-plated and Parkerized surface treatments, only eight to ten specimens were used to establish approximately the entire S-N curve. All fatigue specimens after testing were sectioned near the point of minimum diameter and tested for hardness to verify that the level of hardness was within the range chosen for this study. RESULTS HEAT TREATMENT The average quenched and tempered hardness of the heat-treated bars was 42 Rockwell "Co" Most all of the fatigue bars tested had a hardness within the range 41 to 43 Rockwell "C." The results from two tensile tests on bars having a hardness within this range are reported below: Tensile Re 0.1% Yield 0.2% Yield Reduction Strength Hardness Strength Strength Elongation of Area 199,500 43 169,000 176,000 (a) 36.2% 208,500 43 179,500 188,000 16.0% 39.2% (a) Broke outside gage length. 4

The University of Michigan * Engineering Research Institute The yield-to-tensile ratio is about 90 percent. Figure 1 shows the unetched structure of this steel at 100 magnifications. It will be noticed that a fair number of inclusions are present in this steel. Figure 2 shows the tempered martensite structure of the quenched and tempered fatigue bars at 100 and 1000 magnifications. The tensile results and metallographic examination indicate that complete hardening occurred in the oil quenching operation. POLISHED SURFACE CONDITION The machined and polished surface condition represents the standard or base condition to which the other surface treatments were compared. Figure 3 illustrates the smooth surface of these polished fatigue specimens. The fatigue data for this surface condition are presented in Table I. The individual test values, average values, x, and the 2at limits are given. An example of the statistical' calculations is given in the Appendix. Figure 8 is a semilog plot of the data given in Table I. The finitelife portion of the curve appears to be a straight line. The average expected life is 16,000 cycles at 150,000 psi and 90,000 cycles at 115,000 psi. Although the average value for fatigue life is 90,000 cycles at 115,000 psi, the 2at limits indicate that it is possible to obtain values of fatigue life between about 23,000 and 270,000 cycles for individual tests at this stress level. However, it should be pointed out that the use of 2Wa limits is not completely accurate when the average value, x,, has been established using a sample size of less than 30 specimens. Therefore, it would be expected that a certain variability of the average value, x, of samples of five tests exists and thus the 2aW limits established are not completely fixed. If 2a' limits based on the results of five tests are to be used, then great care should be exercised in making statements or conclusions based on these limits. The endurance limit is not as well defined as the finite life por'tion of the curve. At 110,000-psi stress one specimen did not fail upon the application of more than 107 cycles, two specimens broke at approximately 6 x 106 cycles, and two samples ran less than 5 x 105 cycles. This is a fair indication of the upper limit to the endurance region. At lower stresses, 105,00O psi and 102,500 psi, three samples broke before reaching 5 x 105 cycles and at 100,000-psi stress two samples exceeded 107 cycles of stress without failure. Therefore, the lower limit of the endurance range is at about 100,000-psi stress, and consequently a spread of about 10,000-psi stress is obtained for the endurance range. The estimated value of the endurance limit can be set at 105,000-psi stress. This value is approximately 50 percent of the tensile strength. ------------------ 5 —---------------

The University of Michigan * Engineering Research Institute ELECTROLYTIC CYANIDE SURFACE TREATMENT The data for the electrolytic cyanide surface treatment are given in Table II. The individual points, the average values, x, and the 2a& limits are presented in Fig. 9. Figure 4 shows in profile the surface condition of the fatigue specimens after the cleaning treatment. The surface shows a general roughening with occasional notches which may act as points for the initiation of a fatigue failure. As in the case of the polished surface condition, the finite life part of the fatigue curve appears to be a straight line. The upper limit of the endurance range appears to be at 110,000 psi, as indicated by results from three test specimens. At 105,000-psi stress, one specimen exceeded 107 cycles without failure, and at 102,500-psi stress, another specimen failed within 2 x 105 cycles of stress. At 100,000 psi, which appears to be the lower limit of the endurance range, a sample did not fail after reaching 107 cycles of stress, Therefore, it appears that the endurance limit is at about 105,000 psi with a range of about ~ 5000-psi stress. A comparison of Figs. 8 and 9 indicates that the electrolytic cyanide surface treatment has decreased the high-stress life of this material. As the stress decreases, the deleterious effect of this treatment also decreases until at stresses slightly above the endurance limit the fatigue properties seem to be about the same. Although it has not been proven conclusively, since only a small number of tests were used, it appears that this surface treatment has little or no effect on the endurance limit. ACID-PICKLING SURFACE TREATMENT Figure 5 illustrates the surface of the acid-pickled fatigue specimens. A slight roughening of the surface and a few notches can be seen. The data for the acid-pickling surface treatment are presented in Table III. The individual points, the average values, x, and the 2at limits are plotted in Fig. 10. The finite life part of the S-N curve is also a straight line for this surface condition. A comparison of Figs. 8 and 10 shows that this line is parallel to the straight-line part of the S-N curve for the polished surface condition, but is displaced to the left. This displacement amounts to about a 40-percent decrease in the finite fatigue life for the acid-pickled specimens There also appears to be a definite shift in the endurance limit to a lower value. From the data obtained, the upper limit of the endurance re6

The University of Michigan * Engineering Research Institute gion seems to be at 103,000-psi stress. The data are insufficient to locate definitely the lower limit of this region, but if the spread is assumed to be the same as that obtained for the other two surface conditions, the endurance limit can be placed at 98,000-psi stress. This amounts to a decrease of about 6.8 percent in endurance limit from the as-polished condition. The average lines of the S-N curves for the three surface conditions discussed above are presented in Fig. 11. The "t" test was used to determine if a statistical difference in the means could be detected between the aspolished condition and the electrolytic cyanide or acid-pickled conditions. This test indicated that both the cyanide and acid-pickled conditions produced real differences at the 150,000-psi and 130,000-psi stress levels. At the 115,000-psi level, the "t" test did not indicate a real difference. However, it should be pointed out that the "t" test is very useful in showing real differences, but the failure of the "t" test to show a real difference does not preclude the existence of a real difference. The "t" test calculations are included in the Appendix. CADMIUM-PLATING SURFACE TREATMENT Figure 6 illustrates the surface condition of the cadmium-plated specimens:. The surface of the steel shows a general roughening and is probably the best representation of the steel surface included in this report since the surface is supported by the cadmium plate and not rounded very much during the polishing operation. The bond between the cadmium plate and the steel appears sound and the surface of the cadmium plate is smooth. The average cadmiumplate thickness is about 0.0007 inch. The fatigue data are summarized in Table IV and plotted in Fig. 12. A curve has been drawn through these several points and at best represents a rough approximation to the average value as established for the first three treatments. The 2r' band established for the polished surface condition is included for comparison purposes. The fatigue results of the cadmium-plated surface condition all fall within the 2Wa band. It should be noticed that all these values lie on the lower side of the band. A statistical analysis of the cadmium-plate data cannot be made since only one specimen was run at each stress level. However, it seems rather improbable that all of the points would have fallen to the lower end of the 2crt band if no damage had resulted from the cadmium plating. There is some indication that the endurance limit has been lowered by cadmium plating. PARKERIZING SURFACE TREATMENT The surface profile of the Parkerized surface is shown in Fig. 7. The fatiguht specimens are presented in Table IV and are plotted in Fig. 13.

The University of Michigan * Engineering Research Institute An estimated curve is drawn through these points and the 2o" band of the polished condition is included for comparison. Most all the test points in the finite life region of the curve fall well within the 2&a band. Although the.2a' band is not well established, it is not reasonable to expect that the small changes of the 27' band that might occur if the average values, x, were more accurately established would cause any but the highest stress data point, in this case, to be shifted into or out of the 2a' band. It appears then that this surface treatment has little effect on the finite life fatigue properties of the steel. The data do indicate a decrease in endurance limit. It should be pointed out that any conclusions drawn from fatigue data based on the individual points from six to ten tests may be quite in error. If the individual points fall outside the 2Wa limits of the polished specimen condition, one can be fairly certain that these tests represent a condition different from the polished condition. On the other hand, if the test points fall within this 2Wa band, one cannot be sure that these tests represent a fatigue resistance which is the same as that of the polished condition. The reason for this is well illustrated by comparing Fig. 8 to Fig. 9 or 10. The 2&t band of either Fig. 9 or 10 overlaps considerably the 2ct band established for Figs 8 and consequently makes the interpretation of individual test results very difficult. CONCLUSIONS 1. The endurance limit of specimens in the polished condition was about 105,000 psi, or approximately 50 percent of the tensile strength. 2. Electrolytic cyanide surface cleaning resulted in a change of slope of the straight-line finite life part of the S-N curve. Lower life resulted at high stresses, but as the stress decreased, the difference in life, as compared to the polished condition, decreased. 3. Electrolytic cyanide surface cleaning produced no change in the endurance limit from that of the polished condition. 4. Acid pickling caused a 40-percent decrease in finite life at all stress levels, as compared to the polished surface condition. 5. Acid pickling caused a lowering of the endurance limit of approximately 6.8 percent compared with the as-polished condition. 6. Cadmium plating appears to lower both the finite fatigue life and the endurance limit from the values established for the as-polished condition. 7. Parkerizing seems to have little effect on the finite fatigue life but does appear to lower the endurance limit from the values established for the as-polished condition. I —--------------------- -------------------— 8

The University of Michigan * Engineering Research Institute TABLE I FATIGUE RESULTS ON THE POLISHED SURFACE CONDITION Stress, Fatigue Life, Hardness, Average, 2r' Limits, psi cycles Rc x cycles 13,000 39 13,000 41 150,000 15,000 42 15,500 9,985 to 23,000 15,000 43 21,000 43 140,000 22,000 42 35,000 43 36, o000 42 130,000 36,000 41 46,560 21,360 to 101,500 67,000 43 72,000 41 40,000 41 44,000 42 120,000 65,000 40 71,290 22,130 to 229,600 121,000 43 133,000 42 40,000 42 57,000 39 115,000 70,000 42 79,630 23,320 to 271,900 118,000 43 170,000 43 185,000 42 500,000 41 110,000 6,838,000 43 7,872,000 44 10,065,000 (a) 41 105,000 232,000 41 105,000 458,000 43 102,500 446,000 43 100,000 12,705,000 (a) 43 100,000 13,3835,000 (a) 41 -- (a) Test discontinued at this time. 9

The University of Michigan * Engineering Research Institute TABLE II FATIGUE RESULTS ON ELECTROLYTIC CYANIDE CLEANED SURFACE CONDITION Stress, Fatigue Life, Hardness, Average, 2a' Limits, psi _cycles Rc x cycles 4,000 42 5,000 40 150,000 9,000 43 6,946 2,891 to 16,700 9,000 42 10,000 43 140,000 33,000,o 44 15,000 39 21,000 42 130,000 25,000 43 25,900 10,920 to 61,440 37,000 43 40,000 44 120,000 54,000 43 41,000 37 58,000 42 115,000 60,000 43 80,020 21,500 to 297,800 125,000 43 184,000 44 284,000 43 110,000 1,614,000 43 10,003,000 (a) 43 105,000 11,800,000 (a) 44 102,500 209,000 40 100,000 10,000,000 (a) 44 (a) Test discontinued at this time. 10

The University of Michigan * Engineering Research Institute TABLE III FATIGUE RESULTS ON ACID-PICKLED SURFACE CONDITION Stress, Fatigue Life, Hardness, Average 2a' Limits, psi_ cyles C cyclescycles 8,000 41 9,000 42 150,000 10,000 42 9,728 7,265 to 13,020 11,000 44 11,000 43 140,000 13,000 43 19,000 38 24,000 39 130,000 29,000 41 26,670 16,450 to 43,220 30,000 42 34,000 41 24,000 41 50,000 42 115,000 59,000 41 51,890 19,160 to 140,500 64 000 42 83,000 42 110,000 129,000 43 105,000 145,000 42 — 102,500 3,859,000 44 100,000 10,500,000 (a) 43 99,000 33,000 40 (a) Test discontinued at this time. 11

The University of Michigan * Engineering Research Institute TABLE IV FATIGUE RESULTS ON THE CADMIUM-PLATING AND PARKERIZING SURFACE TREATMENTS Cadmium Plated (a) Parkerized Stress, Fatigue Life, Hardness, Fatigue Life, Hardness, Ps _i ccycles Rc cycles c 150,000 11,000 44 8,000 42 140,000 15,000 43 26,000 42 130,000 21,000 42 54,000 42 120,000 43,000 42 63,000 40 110,000 66,000 41 236,000 41 105,000 71,000 4 102,500 184,000 44 252,000 42 101,000 11,650,000 (b) 44 100,000 54,000 42 549,oo000 41 100o,000 12,890,000 43 11,515,000 (b) 42 100,000 12,775,000 (b) 44 -- (a) Average cadmium-plate thickness = 0.0007 in. (b) Test discontinued at this time. 12

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The University of Michigan * Engineering Research Institute...-I_:::::: II i _:I 1 II_ _ 1:1 11......... Fig. 5. Surface profile of fatigue specimen after the acid-pickling surface treatment, unetched, X500. Fig. 6. Surface profile of fatigue specimen after cadmium plating, unetched, X500. Fig. 7. Surface profile of fatigue specimen after Parkerizing, unetched, X500O 15

The University of Michigan * Engineering Research Institute 150,000-,\;\ \ \ I I 1 * INDI.VIDUAL TEST RESULTS \ \ \ o STATISTICAL AVERAGE 140,000. \ - -- ---— 2 -' LIMITS \ \ ----- APPROXIMATE ENDURANCE RANGE \ I,,\ ~ -< SPECIMEN DID NOT FAIL \ \. 130,000 -0.- -- \ = 1 Cl) 120000 110,000 —------ SAE 1065 steel in the polished condition. 150,000 t\ I I s i \. I I t | * 1INDIVIDUAL TEST RESULTS I \I I I I I I 0 STATISTICAL AVERAGE 130,000\ - \ 0 m I I ~I I I I \ \ I)I20,000 110,000 1 -6 & \ ~ 100,000-... 90,000 3, 10000 100,000 oo000,000ooo 10,000,000 CYCLES OF STRESS, LOG. SCALE Fig. 8. S-N diagram for fatigue tests on SAE 1065 steel in the pol ishe d condition. 16

The University of Michigan * Engineering Research Institute 150,000 -— \150,0 \ * INDIVIDUAL TEST RESULTS \ \ \ ~ STATISTICAL AVERAGE 140,000 _\. ---— 2 a-' LIMITS --- APPROXIMATE ENDURANCE RANGE,\' \ - SPECIMEN DID NOT FAIL \ \ \ 130,000-'ra\,0 120,000 110,000 100,OO \ - -000- e"' \ \ 90,000 - - ___ I__- — _ I __I __ III 3,000 10,000 100,000 1,000,000 10,000,000 o AS-POLISHED SURFACE CYCS OF ELECTROLYTIC CYANIDE CLEANED 140,000 ---— ^ - ---- SURFACE * ACID - PICKLED SURFACE --— APPARENT ENDURANCE LIMIT 130,i000 co - 100,000 -_ 3,000 10,000 100,000 1,000,000 10,000,000 CYCLES OF STRESS, LOG. SCALE Fig. 11. Comparison of S-N diagrams for the average values of the fatigue tests on SAE 1065 steel in the as-polished, electrolytic cyanide cleaned, and acid-pickled surface conditions. 17

The University of Michigan * Engineering Research Institute 150,000 - - \\ \ * ~ INDIVIDUAL TEST RESULTS \~\ \.. —— 2' LIMITS OF THE POLISHED 1 \\ooo - _ \ CONDITION o _ _ O O-'_ -- -- APPROXIMATE ENDURANCE RANGE \\ \\ \ _ OF THE POLISHED CONDITION 3as-\ ~ - SPECIMEN DID NOT FAIL 130,000 -- 06 32,OO00 IOOO \ I \I 120,000 _ _ mt- \ \ | ~~~I-~ \ \ 110,000 --- \ O I00:..... JI 100,000 -— ~ — --- -— x ----— _ — - ------.__ — -— ^ 90,000 -- 3,000 10,000 100,000 1,000,000 10,000,000 CYCLES OF STRESS, LOG. SCALE Fig. 12. S-N diagram for fatigue tests on cadmium-plated 1065 steel. 150,000 -,- --- ~* INDIVIDUAL TEST RESULTS \\ --— 2 -'LIMITS OF THE POLISHED CONDITION 140,000 - --- - -_S^ —-- - -- APPROXIMATE ENDURANCE RANGE OF'THE POLISHED CONDITION'\ <'\ -~ SPECIMEN DID NOT FAIL 130,o000 u 120,000 110,000 I00,000 90,000 3,000 10,000 100,000 1,000,000 10,000,000 CYCLES OF STRESS, LOG. SCALE Fig. 13. S-N diagram for fatigue tests on Parkerized 1065 steel, 18

The University of Michigan * Engineering Research Institute APPENDIX STATISTICAL EVALUATION OF FATIGUE DATA With the number of samples used in this investigation, only the finite-life part of the fatigue curve can be analyzed statistically. Recent studies )'89 indicate that most of the scatter observed in fatigue testing is an inherent characteristic of the material and does not necessarily indicate poorly adjusted equipment or improper testing techniques. The distribution of fatigue life of groups of similar specimens is quite varied but has been found in several instances to approximate closely a logarithmic normal distribution. The following calculation will serve to illustrate the method used to determine the average value of fatigue life and the variability of this value from a sample of five specimens tested at the same stress. The data from tests run on the "as-polished condition" at 115,000Opsi stress will be used for this example. The following values apply: Test No. of Cycles Log xijLog x (Log xi-Log x))2 No. to Failure (xi) Log (xi) = A log x = (A log x)2 1 40,000 4.60206 - 0.29901 0.0894069801 2 57,000 4.75587 - 0.14520 0.0210830400 3 70,000 4.84510 - 0.05597 0.0031326409 4 118,000 5.07188 + 0.17081 0.0291760561 5 170,000 5.25045 + 0.32938 0.1084911844 24.50536 0.2512899015 Log =. log (i) 4.5 90107 no. of tests 5 x 79,630 For a normal type of distribution of test values, the standard deviation of a small sample (e) is defined as A^ g xi j-log )2 ^ / /0. 2'12899015 = 19

The University of Michigan * Engineering Research Institute The symbol a, the standard deviation of a small sample, is only a poor estimate of the standard deviation of the universe, ac. To obtain a more accurate estimate of the universe standard deviation, a, the following definition is given: A a* = a where C2 = 0.8407 for a C2 sample of 5 0.2242 01 0.2242 = 0o..2667 0.8407 If 20& values are taken as limits, then the following values apply: 20' limits = log X ~ 2t' 4.90107 + 0.5334 = 5.43447 and 4.36767 = 271,900 and 25,320 cycles It has been a general practice in many investigations to plot x and the 2a' limits established with small samples. However, it should be pointed out that the conclusions drawn from the use of 2a' limits are not completely accurate when the average value, 3X, is established using a sample size less than 30. Since the sample size used for this investigation was five, it can be assumed that the average value x is- a fair estimation of the universe average value but not the actual value. This simply means that if another sample of five fatigue specimens were run at a given stress, the X established would probably be different from that found from the first set of five, but the difference expected would not be too great. To define statistically the endurance limit, a refined technique based essentially on the log-normal distribution must be used. However, because of the large number of samples involved, this technique was not used and will not be discussed further here. TESTS PERTAINING TO DIFFERENCES IN MEANS AND VARIANCE Once the fatigue data have been established, it is important to find out if the differences that appear are real or could happen simply by chance. In our case it is important to know if the means established at a given stress level for two different surface treatments represent a real difference or simply a difference that would probably occur because of the variability in the data that exist. In some cases of statistical data, once the data have been plotted it is quite apparent to the eye that a real difference in properties exists. However, thi is not always the situation and in some cases false conclusions may be drawn unless appropriate statistical tests are applied, 20

The University of Michigan * Engineering Research Institute Tests Pertainin to Differences in Variance.-Before one can test for differences in the means, it is important to know something about the variability of variance of the data. In particular, is the variance of the data the same within a given set of data, i.e., is the variance at one stress the same as that at a different stress within the same set of dataj and, secondly, is the variance of the data established for one particular surface treatment the same as that established for a different surface treatment? Standard tests are available to determine these two items. These tests are to be described below, but for a more detailed and complete explanation of these tests reference should be made to standard texts on statistical methods 1011l'"F" Test for Difference in Variance S a F - 2 where - N-i S2 22 N = C N-2 N = 5 o Therefore, F = (i2/^2 The critical value for this test is 9.60 for the case of a sample size of five. Thus, if the value of the ratio of the variances (F) is 9.60 or less, we will be wrong only 5 percent of the time in saying there is no difference in variance. This test will indicate a difference in variance at the same stress between two different surface conditions. These tests are shown below: As-Polished vs Electrolytic Cyanide Surface Treatments 150,000 psi F 564 4.44.005796.24884 130,000 psi F 24888 1.23 115,000 psi F =. - = 1.14.05025 21

The University of Michigan * Engineering Research Institute Since the F values are less than the critical value, we can assume no difference in variance. AsiPolished vs Acid-Pickled Surface Treatments 150,000 F =..22 = 2.21.00285.02072 130,000 F = o077 2.67.00777 115,000 F = 05025 1.52.03309 Again no difference in variance is indicated. To determine if the variances of two sets of data are completely homogeneous, i.e., that there is no difference within a given set and between two different sets of data, the Fisher Test11 should be used. The calculations of this test follow: As-Polished vs Electrolytic Cyanide Surface Treatments P (Probability Stress F of Occurrence) -in P 150,000 4.44 0.10 2.505 130,000 1.23 ro0.45 0.799 115,000 1.14 J0.48 0.734 3.836 x2 7.672 The probability of this value (7.672) occurring is between 20 and 30 percent of the time. This probability is high and thus it can be concluded that no difference in variance exists. As-Polished vs Acid-Pickled Surface Treatments P (Probability Stress F of Occurrence) -1n P 150,000 2.21 rJ 0.50 1.204 130,000 2.67 r 0.20 1.609 115,000 1.52 O. 40o 0.916 3.729 x2 22 7.458

The University of Michigan * Engineering Research Institute The same conclusion applies here as above. From the previous tests it is valid to assume in either of the two cases that cr, = c2. Hence, the following test pertaining to differences in means can be made. Test Pertaining to Differences in Means. —The standard "t" test is applied for small sample size. The hypothesis of this test is that the means are the same and the critical value for the test is + 2.506 for a sample size of five. Therefore, if the value of the test falls within + 2.306, the hypothesis cannot be rejected, and if outside of these limits, the hypothesis is rejected. ti - ^z i-;n —;2A t = where s N1r l + N2 C2 + N2 V N1 + N2 -2 N = 5. As-Polished vs Electrolytic Cyanide Surface Treatments 150,000 psi 4.18046 - 3.84190 t y s5(.005796) + 5(o025637) 41/5 + 1/ 5+ 5-2 - t = 3.82 130,000 psi 4.66802 P 4.1330 t j(.o02229).+ (o.024885) 4J/5 +1/5 t = 2.40 115,000 psi 4.90322 - 4.90107_ t = 5(.050258) + 5(.057562) 1/ + 1/ 5.-+5-2 t = 0.013 25

The University of Michigan * Engineering Research Institute It is apparent that at the 150,000- and 130,000-psi stress levels the differences in x are real differences,,but at 115,000 psi the difference does not seem to be significant. As-Polished vs Acid-Pickled Surface Treatments 150,000 psi 4.18046 - 3.98802 t = 5797.)0 5(i} + Jo/15 + 1/5 t 4.15 130,000 psi 4.66802 - 4,42597 t = 15(.020229); 5(.007768) 1/5- +/5 \J 5+5-2 t 2,9 115,000 psi 4.90107 - 4.71506 t 15(.0,50258) + 5(.o33091) 4/ + 1/'NI'~ ~ +5 - 2 t 1.1 At 150,000-psi and 130,000-psi stress levels the differences in. are real differences, but at 115,000 psi the difference does not seem to be significant'. 24

The University of Michigan * Engineering Research Institute REFERENCES 1. Siebert, C. A., and Jones, R. L., Literature Survey on the Effect of Surface Treatment on the Fatigue Strength of Steel distributed to Associated Spring Corporation, October, 1955. 2. Swanger, W. H., and France, R. D,, Proc. ASTM, 52, 430 (1932). 3. Kehl, Go L., and Offenhauer, Co Mo, Trans. ASM, 28, 238 (1940). 4. Frey, J. H., Jr., and Kehl, F. L., Trans. ASM, 26, 192 (1938). 5. Sopwith, D. G., and Gough, H. J., J. Iron and Steel Inst., 155, 315 (1937). 6.' Forsam, 0.,, and Lunden, E., ASM, Proceedings of the First World Metallurgical Congress, 1951 pp. 606-612. 7. American Society for Testing Materials, Symposium on the Statistical Nature of Fatigue, 1952, 64 pp. 8. Sinclair, G. M., and Dolan, T. J., Trans. ASME, 75, 867 (1953). 9. Ransom, J. T., and Mehl, R. F., Trans. AIME, 185, 364 (1949). 10. Duncan, A. J., Quality Control and Industrial Statistics, Irwin, 1953. 11. Fisher, R. A., Statistical Methods for Research Workers, Oliver and Boyd, Ltd., 1944. 25