influence of surface finish on bending fatigue of forged steel including heating method, hardness,...

8/3/2019 Influence of Surface Finish on Bending Fatigue of Forged Steel Including Heating Method, Hardness, And Shot Clean

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A Thesis

entitled

Influence of Surface Finish on Bending Fatigue of Forged Steel Including Heating

Method, Hardness, and Shot Cleaning Effects

by

Sean A. McKelvey

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Masters of Science Degree in Mechanical Engineering

__________________________________________

Dr. Ali Fatemi, Committee Chair

__________________________________________

Dr. Phillip White, Committee Member

__________________________________________Dr. Lesley Berhan, Committee Member

__________________________________________Dr. Patricia R. Komuniecki, Dean

College of Graduate Studies

The University of Toledo

May 2011


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An Abstract of

Influence of Surface Finish on Bending Fatigue of Forged Steel Including HeatingMethod, Hardness, and Shot Cleaning Effects

by

Sean A. McKelvey

Submitted to the Graduate Faculty as partial fulfillment of the

requirements for the Masters of Science Degree in Mechanical Engineering

The University of ToledoMay 2011

The overall objective of this study was to conduct a systematic and

comprehensive experimental investigation to evaluate and quantify forged surface finish

effect at several hardness levels (19 HRC, 25 HRC, 35 HRC, and 45 HRC) on bending

fatigue specimens of a commonly used forged steel (10B40 steel). Specimens were

subjected to reverse cantilever bending and rotating bending fatigue. Two surface

conditions were evaluated, a smooth-polished surface finish to be used as the reference

surface, and a hot-forged surface finish. The heating methods used for forging were gas

furnace heating as well as induction heating, to allow comparison of the two heating

methods, as decarburization depth differs between the two methods. Since shot blasting is

commonly used as a forged surface cleaning process with the additional benefit of

inducing compressive residual stress, the hot-forged surface finish was evaluated with

and without shot blasting. Some testing was also conducted to investigate the effect of the

flash left by the forging process. In addition, the effect of grain flow resulting from the

forging process was evaluated by testing smooth specimens machined from the same

rolled bar used for forging. Fatigue test results in this investigation confirm that the old


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data commonly used for the as-forged surface condition are too conservative. New forged

surface finish factors and curves as a function of hardness or tensile strength and fatigue

life were developed based on experimental data. A fracture mechanics-based approach

was also used to predict fatigue life for the as-forged fatigue specimens.


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Acknowledgements

I would like to thank Dr. Ali Fatemi for his guidance over the last few

years. I would also like to thank the staff in the MIME machine shop, Mr. John

Jagley, Mr. Tim Grivanos and Mr. Randall Reihing. Funding for this project was

provided by the Forging Industry Educational and Research Foundation (FIERF)

and the American Iron and Steel Institute (AISI). Support and technical assistance

of Karen Lewis, George Mochenal, and Carola Sekreter of FIERF and David

Anderson of AISI are appreciated. Materials and its chemical analysis were

provided by Robert Cryderman of Gerdau-MacSteel. Induction heated forged

specimens were provided by Keystone Forging Company, courtesy of Joe

Cipriani. Specimen heat treatment and metallurgical analysis was provided by

Peter Bauerle of Chrysler Group LLC. Shot cleaning was done by Westside Sand

Blasting. Surface profiler located in the Gear Research Laboratory at OSU was

used for surface roughness measurements.


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Table of Contents

Abstract ..................................................................................................................... iii

Acknowledgements .................................................................................................. v

List of Tables ............................................................................................................ x

List of Figures ........................................................................................................... xiii

List of Abbreviations ............................................................................................... xxiii

List of Symbols ......................................................................................................... xxiv

1 Introduction ........................................................................................................ 1

2 Literature Review .............................................................................................. 4

2.1 Forging Process ........................................................................................... 4

2.1.1 Types of forging .............................................................................. 4

2.1.2 Effect of inclusions and grain flow in forged steel on fatigue

behavior........................................................................................... 6

2.2 Surface Finish ............................................................................................. 8

2.2.1 Decarburization ............................................................................... 9

2.2.2 Roughness measurements and parameters ...................................... 12

2.2.3 As-forged surface condition ............................................................ 14

2.2.4 Effect of surface roughness on fatigue behavior ............................. 16

2.2.5 Fatigue limit evaluation for surface finish effect ............................ 17

2.3 Sand Blasting and Shot Cleaning ................................................................ 25


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2.4 Heat Treatment and Hardness Effects ......................................................... 27

2.4.1 Heat treatment ................................................................................. 27

2.4.2 Hardness effects on fatigue behavior .............................................. 29

2.5 Crack Growth Behavior .............................................................................. 31

2.5.1 Fracture mechanics .......................................................................... 31

2.5.2 Fatigue crack growth........................................................................ 32

2.6 Summary ..................................................................................................... 35

3 Experimental Program, Results and Analysis................................................. 73

3.1 Material and Specimen Preparation ............................................................ 73

3.2 Testing Equipment ...................................................................................... 75

3.2.1 Monotonic tension and cantilever bending fatigue tests ................. 75

3.2.2 Rotating bending fatigue tests ......................................................... 77

3.3 Test Methods and Procedures ..................................................................... 77

3.3.1 Metallurgical analysis ..................................................................... 77

3.3.2 Surface roughness measurements ................................................... 78

3.3.3 Monotonic tension tests .................................................................. 78

3.3.4 Cantilever bending fatigue tests ...................................................... 79

3.3.5 Rotating bending fatigue tests ......................................................... 80

3.4 Experimental Results and Analysis ............................................................ 81

3.4.1 Metallurgical analysis ..................................................................... 81

3.4.2 Surface roughness characterization................................................. 82

3.4.3 Monotonic deformation behavior ................................................... 84

3.4.4 Cantilever bending fatigue behavior ............................................... 84


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3.4.5 Rotating bending fatigue behavior .................................................. 86

4 Comparative Analysis and Discussion ............................................................. 125

4.1 Cantilever Bending vs. Rotating Bending Fatigue ..................................... 125

4.2 Forging Flash Effect ................................................................................... 126

4.3 Effect of Hardness....................................................................................... 127

4.4 Effect of Forging Heating Method .............................................................. 129

4.5 Effect of Shot Cleaning ............................................................................... 130

4.6 Forging Grain Flow Effect .......................................................................... 131

4.7 Effect of Surface Condition ........................................................................ 132

5 Fracture Mechanics Analysis ............................................................................ 154

5.1 Crack Growth Rate Estimation ................................................................... 154

5.1.1 Crack growth behavior and rate ...................................................... 154

5.1.2 Crack growth rate versus stress intensity factor range.................... 157

5.2 Fatigue Life Prediction ............................................................................... 160

6 Prediction of Fatigue Limit and Mathematical Representation of Surface

Finish Effects ...................................................................................................... 175

6.1 Roughness-Based Prediction Models for Fatigue Limit ............................. 175

6.1.1 Murakami model ............................................................................. 175

6.1.2 Arola-Ramulu model ...................................................................... 177

6.2 Mathematical Representation of Experimental Data .................................. 179

6.2.1 Surface finish factor as a function of Brinell hardness ................... 179

6.2.2 Surface finish factor as a function of cycles to failure.................... 181


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6.2.3 Surface finish factor as a function of both Brinell hardness and

cycles to failure ............................................................................... 182

7 Summary and Conclusions ............................................................................... 204

References ................................................................................................................. 208


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List of Tables

2.1 Commonly used temperatures when heating selected ferrous alloys for hotforging [6] ...................................................................................................... 38

2.2 Hardness variation between surface and subsurface for four types offorged steels used in fatigue tests in [3] ......................................................... 38

2.3 Fatigue test results for four types of commonly used forged steels with the

as-forged and machined and polished surface conditions used in [3] ........... 39

2.4 Fatigue test results for a high strength forged steel from two manufacturerswith the as-forged and machined and polished surface conditions used in

[4] ................................................................................................................... 40

2.5 Relationship between surface carbon content, depth of decarburization,and fatigue limit for a 605 M36 through-hardened steel [14] ........................ 40

2.6 Summary of endurance limits and tensile strengths for ground, machined,hot-rolled, and as-forged surface conditions used to calculate surface

finish factors from [2] .................................................................................... 41

2.7 Values of Rarea parameter used in Murakami equation to predict fatigue

limit for specimens which have surface roughness defects [23].................... 41

2.8 Results of experimental and predicted fatigue limits using the Murakamiequation for JIS S45C steel specimens having surface roughness defects

[23] ................................................................................................................. 42

2.9 Surface finish modification factors at 104 and 106 cycles for hardenedmachined surfaces calculated using the Goodman, Morrow, and SWT

models [5] ...................................................................................................... 43

2.10 Constants for use in Eqn. 2.22 for determining surface finish factors forground, machined, hot-rolled, and as-forged surfaces [27] ........................... 43

2.11 Fatigue test results on as-forged, as-forged/shot blasted, forged/heattreated, and forged/ heat treated/ shot blasted specimens of EN15R steel

[1] ................................................................................................................... 43


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2.12 List of typical heat treatment procedures for steels [40]................................ 44

2.13 Material conditions, test parameters and fatigue lives for notched 4340low alloy steel specimens with and without decarburization [46] ................. 45

2.14 Roughness measurements for various types of surface preparations in type304 stainless steel [47] ................................................................................... 45

3.1 Material composition of 10B40 steel (Courtesy of Robert Cryderman ofGerdau-MacSteel) .......................................................................................... 88

3.2 Summary of surface roughness measurements (m) of as-forged, as-forged and heat treated, and as-forged and heat treated and shot cleanedfor 10B40 steel ............................................................................................... 88

3.3 Summary of monotonic tension test results ................................................... 89

3.4 Summary of fatigue test results with different heating methods and surfacefinish conditions for 45 HRC specimens ....................................................... 90




3.8 S-N line equation constants and fatigue strengths ......................................... 94

4.1 Summary of calculated surface finish factors for as-forged gas furnaceheated, as-forged induction heated, as-forged and shot cleaned gas furnaceheated, and as-forged and shot cleaned induction heated specimens, as

well as historical surface finish factors .......................................................... 137

5.1 Summary of threshold stress intensity factor range and transition crackdepth calculations for as-forged specimens forged at different hardness

levels .............................................................................................................. 163

6.1 Summary of calculations of square root area parameters and fatigue limit predictions using Murakami model for as-forged specimens ........................ 187


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6.2 Summary of calculations of stress concentration factors, fatigue notchfactors, and fatigue limit predictions using Arola-Ramulu and Neuber

models for as-forged specimens ..................................................................... 188

6.3 Summary of R2 values used in three dimensional fits to the surface finish

factor data as a function of hardness and cycles to failure for the differentsurface conditions tested ................................................................................ 189

6.4 Summary of constants for use in Eqn. 6.17 for the three dimensionalsurface finish data fits shown in Figures 6.9 through 6.12 ............................ 189


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List of Figures

2-1 Illustration of (a) closed-die [7] and (b) open-die [8] showing howmaterial protrudes between upper and lower die ........................................... 46

2-2 The relative shape change of treated and untreated inclusions compared to

shape change of the steel billet for strains of 0.2 and 1.0 at 1000 C [11] .... 47

2-3 Illustration of a cross section of a forged steel part showing grain flow[12] .............................................................................................................47

2-4 Projection of a defect on to a plane perpendicular to maximum tensilestress which is used to calculate the square root area parameter [22] ........... 48

2-5 Endurance limit versus tensile strength for as-forged surface finish and polished surface finish specimens [36] .......................................................... 48

2-6 Brinell hardness versus distance from surface for as-forged specimenswith average core hardness of (a) 185 HB, (b) 200 HB, (c) 260 HB, and

(d) 360 HB [2] ................................................................................................ 50

2-7 Magnified images (150 x magnification) of a cross section of as-forgedspecimens showing surface decarburization with average core hardness of

(a) 185 HB and decarburization ranging from 0.64 mm to 0.76 mm, (b)200 HB and decarburization ranging from 0.25 mm to 0.30 mm, (c) 260

HB and decarburization ranging from 0.76 mm to 0.89 mm, and (d) 360

HB and decarburization ranging from 0.30 mm to 0.38 mm [2] ................... 51

2-8 Endurance limit versus tensile strength showing upper and lower limits foras-forged surface specimens [13]................................................................... 52

2-9 Definition of (a)Ra, (b)Rz, (c)RtandRy, and (d) Sm to characterize surfaceroughness [18] ................................................................................................ 53

2-10 Maximum working stress (at 107

cycles) versus mean working stress (at10

7cycles) for the ground, machined, hot-rolled and as-forged surface

conditions of steel (302 HB-321 HB) [2] ...................................................... 54

2-11 Relationship between Brinell hardness and tensile strength for steels [2]..... 54


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2-12 Plot of endurance limit (defined at 107 cycles) versus tensile strength forsteels having ground, machined, hot-rolled and as-forged surface

conditions of steels [2] ................................................................................... 55

2-13 Surface roughness versus median fatigue life for SAE 1035 and SAE 3130steels [20] ....................................................................................................... 55

2-14 Scatter of fatigue test results for SAE 1035 and SAE 3130 steels having arange of surface roughness [20] ..................................................................... 56

2-15 Configuration and dimensions (mm) of JIS S45C steel fatigue specimensused in [23] .................................................................................................... 57

2-16 Magnified image of artificially induced surface roughness for annealed(A) and quenched and tempered (QT) JIS S45C steel with roughness pitch

at 100, 150 and 200 in [23] ............................................................................ 57

2-17 Composite plot of stress versus fatigue life for different types of roughnessin JIS S45C steel specimens [23] ................................................................... 58

2-18 Relationship between Rarea /2b and a/2b for annealed (A) and

quenched and tempered (QT) JIS S45C steel fatigue specimens [23] ........... 58

2-19 Relationship between predicted and experimental fatigue limits forannealed and quenched and tempered JIS S45C steel [23] ............................ 59

2-20 Specimen geometry and test set up for the hardened SAE 4140 steel shaftsubjected to bending fatigue in [5]................................................................. 59

2-21 Surface finish modification factors for fatigue life ranging from 104

to 106

cycles for hardened machined surfaces calculated using the Goodman,

Morrow, and SWT models for hardened machined steel surfaces [5] ........... 60

2-22 Roughness profile showing definition of the parameter (average radius

of the dominant profile valleys) used in Arola-Ramulu Model [25] ............. 60

2-23 Fatigue stress concentration factor calculated using Arola-Ramulu and

Neuber models, and experimental fatigue stress concentration factorversus average surface roughness for a high strength low alloy steel [25] .... 61

2-24 Surface finish modification factor for steels versus tensile strength orBrinell hardness for ground and polished, machined, hot-rolled, and as-

forged surface conditions [26] ....................................................................... 61


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2-25 Stress versus cycles to failure for two type of as-forged surface finishspecimens made from SAE 1035 steel (233 HB-280 HB) and SAE 4063

steel (388 HB-444 HB) [13] .......................................................................... 62

2-26 S-N curves for steel specimens having machined and polished surface and

as-forged surface conditions .......................................................................... 62

2-27 Atomic structure of iron showing (a) body centered cubic, and (b) facecentered cubic [43] ......................................................................................... 63

2-28 Phase diagram for plain carbon steels [43] .................................................... 63

2-29 Hardness versus carbon concentration in plain carbon steels [43] ................ 64

2-30 Tensile strength, yield strength, and reduction in area versus temperingtemperature for 4340 oil quenched steel with martensitic microstructure

[43] ................................................................................................................. 65

2-31 Monotonic and cyclic stress-strain curves for (a) SAE 1045 steel at 595HB, 500 HB, 450 HB, and 390 HB, as well as (b) SAE 4142 steel at 670

HB, 560 HB, 475 HB, 450 HB, and 380 HB [44] ......................................... 66

2-32 Stress amplitude versus plastic strain amplitude for SAE 1045 steel at 595HB, 500 HB, 450 HB, and 390 HB, and for SAE 4142 steel at 670 HB,560 HB, 475 HB, 450 HB, and 380 HB [44] ................................................. 67

2-33 Total strain amplitude versus cycles to failure for strain-controlledcompletely-reversed fatigue testing of (a) SAE 1045 steel at 700 HB, 600HB, and 450 HB, as well as (b) SAE 4142 steel at 670 HB, 560 HB, and

450 HB [44] ................................................................................................... 67

2-34 Total strain amplitude versus hardness for different cycles to failure forstrain-controlled completely-reversed fatigue testing of (a) SAE 1045

steel, and (b) SAE 4142 steel [44] ................................................................. 68

2-35 Plot of growth rate (da/dN) versus stress intensity factor range (K) formartensitic steels having various yield and tensile strengths [45] ................. 69

2-36 Specimen configuration and dimensions for a 4340 low alloy steel notchedspecimen used to determine the effect of decarburization on fatigue

behavior in [46] .............................................................................................. 69

2-37 Magnified image of surface roughness for type 304 stainless steel having(a) ground and polished surface, and surface roughened with (b) 600 grit,

(c) 240 grit, and (d) 50 grit sand paper [47] ................................................... 70


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2-38 Crack length versus number of cycles for type 304 stainless steelspecimens at four levels of surface roughness [47] ....................................... 71

2-39 Crack initiation life versus surface roughness for type 304 stainless steelspecimens [47] ............................................................................................... 71

2-40 Notch geometry of three-point bending steel specimen with hardnessbetween 180 HB and 230 HB used for crack growth study in [48] ............... 72

2-41 Number of cycles versus average roughness for three-point bending steelspecimens with hardness between 180 HB and 230 HB [48] ........................ 72

3-1 Photograph of (a) gas furnace heated specimen, (b) induction heatedspecimen, and (c) machined and polished specimen ..................................... 95

3-2 Specimen configuration and nominal dimensions (mm) for as-forged

surface finish specimens subjected to (a) cantilever bending fatigue, and(b) rotating bending fatigue ........................................................................... 96

3-3 Flow charts showing (a) specimen preparation, and various testingconditions for (b) specimens machined form rolled bar, (c) gas furnaceheated forged specimens, and (d) induction heated forged specimens .......... 99

3-4 Test setup used for reversed cantilever bending fatigue testing of as-forged, shot-cleaned, and machined and polished specimens........................ 100

3-5 Plot of calculated strain versus measured strain used to verify cantilever bending test setup ........................................................................................... 101

3-6 Four-point rotating bending fatigue testing machine ..................................... 102

3-7 Cross section of specimen gage section area prior to heat treatmentshowing a mixture of ferrite and pearlite (Courtesy of Peter Bauerle of

Chrysler) for (a) induction heated specimens, and (b) gas furnace heatedspecimens ....................................................................................................... 103

3-8 Magnification of gage section area showing decarburization for gasfurnace heated specimens with martensitic microstructure (Courtesy ofPeter Bauerle of Chrysler) at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and

(d) 19 HRC ..................................................................................................... 104

3-9 Magnification of gage section area showing decarburization for inductionheated specimens at 45 HRC with martensitic microstructure (Courtesy of

Peter Bauerle of Chrysler) ............................................................................. 104


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3-10 Grain flow resulting from forging process for induction heated specimens(Courtesy of Peter Bauerle of Chrysler) ........................................................ 105

3-11 Magnified image showing surface irregularities for induction heatedspecimens prior to heat treatment (Courtesy of Peter Bauerle of Chrysler) .. 105

3-12 Brinell hardness versus depth below the surface for induction heatedforged and gas furnace heated forged specimens .......................................... 106

3-13 Roughness profiles for induction heated specimens (a) prior to heattreatment, (b) as-forged at 45 HRC, and (c) as-forged and shot cleaned at

45 HRC .......................................................................................................... 107

3-14 Roughness profiles for gas furnace heated specimens (a) prior to heattreatment, (b) as-forged at 45 HRC, and (c) as-forged and shot cleaned at

45 HRC .......................................................................................................... 108

3-15 Roughness versus hardness for shot cleaned and as-forged surfaces for (a)roughness parameter Ra, (b) roughness parameter Rt, (c) roughness

parameterRy, and (d) roughness parameterRz............................................... 109

3-16 Monotonic stress-strain curves at different hardness levels for 10B40 steel . 110

3-17 Tensile strength versus Brinell hardness for 10B40 steel .............................. 110

3-18 Typical fracture surface of as-forged specimens subjected to fully-reversedcantilever bending fatigue at (a) stress amplitude of 927 MPa at 45 HRC,

(b) stress amplitude of 301 MPa at 45 HRC, (c) stress amplitude of 610MPa at 35 HRC, (d) stress amplitude of 251 MPa at 35 HRC, (e) stress

amplitude of 609 MPa at 25 HRC, (f) stress amplitude of 260 MPa at 25

HRC, (h) stress amplitude of 500 MPa at 19 HRC, and (i) stress amplitudeof 249 MPa at 19 HRC................................................................................... 111

3-19 Displacement amplitude versus normalized cycles in cantilever bendingfatigue tests for 45 HRC specimens (a) as-forged with induction heat, (b)

as-forged with gas furnace heat, (c) as-forged with induction heat and

shot-cleaned, and (d) as-forged with gas furnace heat and shot cleaned ....... 112






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as-forged with gas furnace heat, (c) as-forged with induction heat andshot-cleaned, and (d) as-forged with gas furnace heat and shot cleaned ....... 115

3-23 Displacement amplitude versus normalized cycles in cantilever bendingfatigue tests for machined and polished specimens at (a) 45 HRC, (b) 35HRC, (c) 25 HRC, and (d) 19 HRC ............................................................... 116

3-24 Stress-life curves under cantilever bending fatigue for as-forged inductionheated specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d) 19HRC ............................................................................................................... 117

3-25 Stress-life curves under cantilever bending fatigue for as-forged and shotcleaned induction heated specimens at (a) 45 HRC, (b) 35 HRC, (c) 25HRC, and (d) 19 HRC .................................................................................... 118

3-26 Stress-life curves under cantilever bending fatigue for as-forged gasfurnace heated specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d)

19 HRC .......................................................................................................... 119

3-27 Stress-life curves under cantilever bending fatigue for as-forged and shotcleaned gas furnace heated specimens at (a) 45 HRC, (b) 35 HRC, (c) 25

HRC, and (d) 19 HRC .................................................................................... 120

3-28 Stress-life curves under cantilever bending fatigue for machined andpolished specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d) 19

HRC ............................................................................................................... 121

3-29 Midlife load versus displacement curves for highest load amplitude tests at45 HRC, 35 HRC, 25 HRC, and 19 HRC for (a) induction heated forgedspecimens, and (b) machined and polished specimens .................................. 122

3-30 Typical fracture surface of as-forged specimens subjected to rotatingbending fatigue at (a) stress amplitude of 551 MPa at 35 HRC, (b) stressamplitude of 229 MPa at 35 HRC, (c) stress amplitude of 502 MPa at 19

HRC, and (d) stress amplitude of 227 MPa at 19 HRC ................................. 123

3-31 Stress-life curves under rotating bending fatigue for (a) gas furnace heatedas-forged surface at 35 HRC, (b) machined and polished surface at 35

HRC, (c) gas furnace heated as-forged surface at 19 HRC, and (d)

machined and polished surface at 19 HRC .................................................... 124


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4-1 Cantilever bending versus rotating bending for as-forged and polishedsurface conditions at (a) 35 HRC, and (b) 19 HRC ....................................... 138

4-2 Forging flash effect on fatigue behavior of as-forged specimens with gasfurnace heating in cantilever bending tests for (a) 45 HRC, and (b) 25

HRC ............................................................................................................... 139

4-3 Effect of hardness on fatigue behavior of machined and polishedspecimens in cantilever bending .................................................................... 140

4-4 Effect of hardness on cantilever bending fatigue behavior for as-forgedspecimens with (a) induction heating, and (b) gas furnace heating ............... 141

4-5 Effect of hardness on cantilever bending fatigue behavior for shot cleanedforged specimens with (a) induction heating, and (b) gas furnace heating ... 142

4-6 Effect of heating method on cantilever bending fatigue for as-forgedsurface specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d) 19HRC ............................................................................................................... 143

4-7 Effect of heating method on cantilever bending fatigue for shot cleanedforged surface specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d)

19 HRC .......................................................................................................... 144

4-8 Effect of shot cleaning on cantilever bending fatigue for induction heatedforged specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d) 19

HRC ............................................................................................................... 145

4-9 Effect of shot cleaning on cantilever bending fatigue for gas furnaceheated forged specimens at (a) 45 HRC, (b) 35 HRC, (c) 25 HRC, and (d)

19 HRC .......................................................................................................... 146

4-10 Comparison of cantilever bending fatigue behavior between forgedspecimens with forged surface removed (circular symbols) and machinedspecimens from rolled bars (triangular symbols) at 45 HRC and 25 HRC

hardness levels ............................................................................................... 147

4-11 Surface finish effect on cantilever bending fatigue behavior at 45 HRChardness level with induction and gas furnace heating for (a) as-forged,

and (b) as-forged and shot cleaned conditions ............................................... 148




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4-14 Surface finish effect on cantilever bending fatigue behavior at 19 HRC

hardness level with induction and gas furnace heating for (a) as-forged,and (b) as-forged and shot cleaned conditions ............................................... 151

4-15 Composite plot of surface finish factor at 106 cycles versus tensile strengthor hardness showing differences between induction and gas furnaceheating forging and old and current data with (a) as-forged surface, and (b)

as-forged and shot cleaned surface ................................................................ 152

4-16 Predicted fatigue life based on historical data (cycles) versus experimentalfatigue life (cycles) for as-forged, and as-forged and shot cleaned

specimens at 45 HRC, 35 HRC, 25 HRC, and 19 HRC hardness levels ....... 153

5-1 Plots of (a) measured crack length and (b) calculated crack depth versuschange in displacement amplitude for as-forged cantilever bending

specimens at 45 HRC, 35 HRC, 25 HRC and 19 HRC ................................. 164

5-2 Measured crack depth versus measured crack length at fracture for 45HRC, 35 HRC, 25 HRC and 19 HRC specimens having an as-forged

surface from cantilever bending fatigue tests ................................................ 165

5-3 Schematic illustrations for as-forged surface specimens plotted in Figure5.2 of (a) crack depth, a, and crack length, b, and (b) crack shape................ 165

5-4 Change in displacement amplitude versus normalized cycles in cantilever bending fatigue tests of as-forged surface specimens at (a) 45 HRC

hardness level, (b) 35 HRC hardness level, (c) 25 HRC hardness level, and(d) 19 HRC hardness level ............................................................................. 166

5-5 Calculated crack depth (using Eqn. 5.3) versus normalized cycles incantilever bending fatigue tests of as-forged surface specimens at (a) 45

HRC hardness level, (b) 35 HRC hardness level, (c) 25 HRC hardness

level, and (d) 19 HRC hardness level ............................................................ 167

5-6 Schematic plot of crack growth rate versus stress intensity factor range[26] ................................................................................................................. 168

5-7 Crack growth rate (da/dN) versus stress intensity factor range (K) forforged specimens subjected to cantilever bending fatigue at (a) 45 HRC,

(b) 35 HRC, (c) 25 HRC, and (d) 19 HRC .................................................... 169


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5-8 Composite plot of crack growth rate (da/dN) versus stress intensity factorrange (K) for 45 HRC, 35 HRC, 25 HRC, and 19 HRC forged specimens

subjected to cantilever bending fatigue .......................................................... 170

5-9 Schematic plot of a Kitagawa-Takahashi diagram giving the relationship

between stress range and crack length [26] ................................................... 171

5-10 Schematic plot of crack growth rate (da/dN) versus stress intensity factorrange (K) showing effect of short cracks and extrapolation of Paris

equation line [26] ........................................................................................... 171

5-11 Estimated cycles to failure versus experimental cycles to failure for as-forged at 45 HRC, 35 HRC, 25 HRC and 19 HRC specimens using

averageA and n values from [46] in Paris equation ...................................... 172

5-12 Estimated cycles to failure versus experimental cycles to failure for as-

forged specimens using experimentalA and n values at (a) 45 HRC and 35HRC, and (b) 25 HRC and 19 HRC ............................................................... 173

5-13 Plot of estimated cycles to failure versus experimental cycles to failurefor 45 HRC forged specimens showing effect of assumed Kc value in life predictions ...................................................................................................... 174

6-1 Predicted fatigue limit versus experimental fatigue limit using Murakamimodel for as-forged specimens at 45 HRC, 35 HRC, 25 HRC, and 19 HRC 190

6-2 Predicted fatigue limit versus experimental fatigue limit for as-forgedspecimens at 45 HRC, 35 HRC, 25 HRC, and 19 HRC using (a) Arola-Ramulu model, and (b) Neuber model ........................................................... 191

6-3 Surface finish factor (ks) versus hardness at different fatigue lives for as-forged specimens with (a) induction heating, and (b) gas furnace heating ... 192

6-4 Surface finish factor (ks) versus hardness at different fatigue lives for shotcleaned specimens with (a) induction heating, and (b) gas furnace heating .. 193

6-5 Surface finish factor versus Brinell hardness for as-forged and as-forgedand shot cleaned specimens with gas furnace and induction heating at 10

6,

3x105, 10

5, and 3x10

4cycles to failure .......................................................... 194

6-6 Surface finish factor (ks) versus cycles to failure at different hardnesslevels for as-forged specimens with (a) induction heating, and (b) gasfurnace heating ............................................................................................... 195


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List of Abbreviations

EPFM elastic-plastic fracture mechanics

HB Brinell hardness number

HCF high cycle fatigue

HRB, HRC Rockwell B-scale, C-scale number

HV Vickers hardness number

LCF low cycle fatigue

LEFM linear elastic fracture mechanics

RMS root mean square


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xxiv

List of Symbols

geometry factor used in calculation of stress intensity factor

a material constant used to determine the notch sensitivity

displacement amplitude

a change in displacement amplitude

true strain range

K stress intensity factor range

Kth threshold stress intensity factor

e true elastic strain

f fatigue ductility coefficient

p true plastic strain

ratio between spacing and height of surface irregularities

notch radius

average notch radius determined from the dominate roughness profile

valleys

true stress

a stress amplitude

f fatigue strength coefficient

w fatigue limit predicted in area parameter model

w, wo fatigue limit, fatigue strength

a crack length or depth

a0 initial crack length

ad length of decarburized layer

acr critical crack length


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A fatigue strength coefficient or constant in Paris equation for intercept of line

B fatigue strength exponent

d diameter

de effective diameter used for nonrotating bending size factor

e engineering strain

E modulus of elasticity

K monotonic strength coefficient

ka, ks surface finish modification factor

kb size factor

kc loading factor

fK effective fatigue notch factor in Arola-Ramulu equation

tK effective stress concentration factor in Arola-Ramulu equation

Ma alternating moment

n strain hardening exponent, slope in Paris equation, or loading factor in

Arola-Ramulu equation

N number of cycles

Nb cycles to grow crack to critical length

Nd cycles to grow crack through decarburized layer

Nf, Nt cycles to failure

q notch sensitivity

R stress ratio

Ra arithmetic average height roughness parameter

Rp maximum peak height roughness parameter

Rq root mean square roughness parameter

Rt maximum height of profile roughness parameter

Rv maximum depth of valley roughness parameterRy largest peak to valley height roughness parameter

Rz the ten-point height roughness parameter

S engineering stress

Sa alternating stress

Se, Sf fatigue limit


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Sm mean stress or mean spacing between profile peaks at the mean line

Su ultimate tensile strength

Sy yield strength


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1

Chapter 1

Introduction

Fatigue fractures are the most common type of mechanical failures of components

and structures. Fatigue failures typically initiate at the surface where micro-cracks form.

A majority of life consists of crack initiation in the case of a smooth and polished surface.

Depending on the surface finish, micro-cracks may already be present, resulting in a

significant reduction of fatigue life.

Forgings are typically accompanied by surface roughness and decarburization. It

has been shown by many investigators that as surface roughness increases there is a

significant decrease in fatigue life in the high cycle fatigue (HCF) region. Surface

roughness has less of an effect in the low cycle fatigue (LCF) region due to a high degree

of plastic deformation. Decarburization reduces the hardness in the decarburized area.

The reduction in hardness results in a reduction of strength, but an increase in ductility.

Decarburization normally results in reduced fatigue life in the HCF region. However, the

reduction is dependent upon the depth of the decarburization.

The correction factors typically used in fatigue design and implemented in many

mechanical design textbooks to correct for the as-forged surface condition are typically

based on data published in the 1940s. It has been found by several investigators that the


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2

existing data for as-forged surface condition is too conservative. Such conservative

values often result in over-engineered designs of many forged parts, leading not only to

increased cost, but also inefficiencies associated with increased weight, such as increased

fuel consumption in the automotive industry. In addition, this can reduce forging

competitiveness as a manufacturing process in terms of cost and performance prediction

in the early design stage, compared to alternative manufacturing processes. Although

many forgings are machined in critical areas to remove the forged surface, some forgings

are not machined in all critical areas subsequent to forging, such as the shank areas in

forged connecting rods. Therefore, the overall objective of this project was to conduct a

systematic and comprehensive study to evaluate and quantify forged surface finish effect,

with and without residual stresses, at several hardness levels (19 HRC, 25 HRC, 35 HRC,

and 45 HRC), on bending fatigue specimens of a commonly used forged steel.

Specimens were subjected to reverse cantilever bending and rotating bending

fatigue. Two surface conditions were evaluated; a smooth-polished surface finish to be

used as the reference surface, and a hot-forged surface finish, as hot forging is the most

common type of forging. The heating methods used for forging were gas furnace heating

as well as induction heating, both common heating methods, to allow comparison of the

two, as surface roughness and decarburization depths differ between the two methods.

Shot blasting is commonly used as a surface cleaning process of forgings with the

additional benefit of inducing surface compressive residual stress. Since residual stresses

play a critical synergistic role with surface finish, the hot-forged surface finish is

evaluated with and without residual compressive stresses from shot cleaning. Some

testing was also conducted to investigate the effect of the flash left by the forging


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process. This was done by placing the flash at the location of maximum stress under

cantilever bending conditions. However, in the majority of the tests, the flash line was

located at the neutral axis. In addition, the effect of grain flow resulting from the forging

process was evaluated by testing smooth specimens machined from the same rolled bars

used for forging of the specimens.

Chapter 2 presents a literature review on surface finish effects on forgings. This

includes the effect of decarburization, hardness, and surface roughness on fatigue

behavior of steels. Chapter 3 describes the experimental procedure used and results

obtained. Specimen preparation, metallurgical analysis, roughness measurements, testing

equipment and procedures are all discussed. Chapter 4 covers a comparative analysis and

discussion of results. Comparisons of loading method and heating method used are made.

The effects of forging flash line, grain flow, hardness and surface finish are also

discussed. In addition, the surface finish factors calculated in the current investigation are

compared to the surface finish factors based on old data currently available for design.

Chapter 5 describes a fracture mechanics analysis of the fatigue data obtained in this

study. In this analysis, crack growth rates and fatigue lives of the as-forged surface

specimens are predicted. Chapter 6 discusses data fits and mathematical representation of

the data. Chapter 6 also contains fatigue limits calculated from exiting prediction models

discussed in the literature review and compares the calculations to fatigue data. Finally,

Chapter 7 summarizes the findings from this investigation.


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Chapter 2

Literature Review

Forging is a commonly used manufacturing method. Vehicles are made of up to

25% forged components [1]. The existing information for the as-forged surface condition

effect on fatigue behavior is too conservative. Although significant improvements to the

steel making and forging processes have been made, the correction factors used in fatigue

design for the as-forged surface condition are still based on data published in the 1930s

and 1940s [2-4]. This results in an over-engineered design of many mechanical parts,

which is accompanied by an increase in production cost [5]. This chapter reviews

previous studies on the effects of surface condition, most importantly the as-forged

surface condition, on the fatigue behavior of steels.

2.1 Forging Process

2.1.1 Types of forging

Forging is a manufacturing process where compressive stresses are used to form

or shape material. There are three types of forging; cold forging, warm forging, and hot

forging [6]. Cold, warm, and hot refer to the temperatures at which the process takes

place. Cold forging typically takes place around room temperature. Hot forging is done at


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a temperature which allows recrystallization of the material being forged, typically

around 1200C for steels. Forging above the recrystallization temperature requires less

power due to increased ductility. Most forgings are hot forged due to the fact that it

allows for a more complex geometry than cold or warm forging. In addition, cold forging

can limit the size of the part being forged. Examples of parts hot forged include crank

shafts, connecting rods, gears, and tools. When hot forging, the material can be heated up

by use of gas furnace or induction heating. Typically induction heating is thought to

produce a higher quality forging than gas furnace heating. The specimens used in the

current investigation were hot forged by use of both induction heat and gas furnace heat.

Induction heating is where electrical currents are used to heat up the material, and

only the material, unlike gas furnace heating [7]. When heating by gas furnace, the whole

atmosphere inside the furnace needs to be brought to temperature in order to heat the

material. Gas furnace heating is a long process when compared to induction heating,

which heats the material more rapidly and uniformly. In addition, the gas furnace can

produce a poorer quality of surface finish than induction heating; more scale formation,

oxidation, decarburization and grain coarsening [7]. The decarburization and scale

formation is significantly decreased for induction heating. The gas furnace also takes up

more room and produces more negative byproducts than an induction heater. Therefore,

induction heating is generally a more consistent and efficient process than gas furnace

heating.

Hot forging begins with a billet or a bar. As the material is heated up its yield

strength is decreased and ductility is increased, making it easier to form. Table 2.1 lists

typical forging temperatures for some steels [7]. Flow stress is an important factor in


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determining how a material can be formed [8]. Flow stress, or yield stress, is a function

of temperature, strain, strain rate, and microstructure of the billet or bar. Since hot forging

is done at temperatures above the recrystallization temperature the flow stress is mostly

affected by temperature and strain rate, and not by strain, thus reducing strain hardening.

Closed-die forging is done by placing a heated billet in between an upper and

lower die and then bringing the upper and lower dies together. The heated material then

fills the cavity in the die. In many cases excess material is allowed to protrude from a

narrow gap between the upper and lower dies creating the flash (see Figure 2-1(a)). It is

possible to produce closed-die forgings without flash; however this is a much more

controlled, therefore more costly process and may not be necessary for most applications.

Open-die forging is a similar process involving upper and lower dies. However, the dies

are typically flat or have a simple contour. In addition, material expansion is not

restricted in the plane perpendicular to the loading direction (see Figure 2-1(b)) [9].

Open-die forgings also require larger tolerances compared to closed-die forgings and

require more machining for close tolerances [10]. It should be noted that the specimens in

the current study were forged using a closed-die forging process.

2.1.2 Effect of inclusions and grain flow in forged steel on fatigue behavior

In a study by Collins and Michal [11] tension-tension fatigue tests (R = 0.1) were

performed on forged specimens made of AISI 4140 steel in order to determine the effects

of changes in shape and distribution of MnS inclusions. Three types of AISI 4140 steel

were used, IGS/HS, IGS, and IGS/SC, each with a different composition. The specimens

were machined from a forged block of material in both longitudinal and transverse


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directions. The specimens were then quenched and tempered to a hardness of 38 HRC

with a tempered martensite microstructure. Finally, they were polished to a 0.25 m

surface finish. It should be noted that the specimens had compressive residual stresses at

the surface around 357 MPa resulting from machining [11]. During the forging process, it

is possible for the inclusions to be reoriented following flow lines. It is also possible for

the inclusions to deform more than the material surrounding it during forging. They

describe a method of controlling the shape of an inclusion, which has been shown to

improve the fatigue life. Different chemicals and thermal treatments can be used. Adding

calcium can harden the inclusions to prevent deformation during working. Figure 2-2

shows the shape change of MnS inclusions and Ca treated MnS inclusions. It can be seen

that the treated inclusions experienced little change in shape. The results from fatigue

testing showed that forging improved the fatigue behavior of the base material. The Ca

treatment was shown to improve fatigue behavior by preventing the MnS inclusions from

fracturing during forging. In addition, the grain flow and inclusion redistribution resulting

from forging enhanced the mechanical properties of the base material

Chastel et al [12] performed an analysis of the impact of forging on fatigue of

steels. Their study involved a finite element model for analyzing the forging process.

This model considers grain flow and anisotropy. Figure 2-3 shows the grain flow of a

steel part. This grain flow can also lead to grain fragmentation and deformation of

inclusions. Ductile inclusions can stretch. Hard inclusions are realigned. This results in

anisotropic fatigue properties. Once the anisotropic mechanical properties are determined

the authors suggest using the Murakami model, which predicts fatigue limit for

specimens with defects and inclusions. The Murakami equation treats defects and


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inclusions as cracks. The following equation is for determining the stress intensity factor

at the tip of a surface defect or inclusion:

areaK 65.0 (2.1)

The area parameter is defined as the defect area projected onto the plane perpendicular

to the applied stress (see Figure 2-4). The following equation relates the threshold stress

intensity factor range,thK , to the defect size:

4)10(HV226.0

3/13

25.0))(120HV()10(3

R

areaKth (2.2)

In this equationR is the stress ratio and HV is the Vickers hardness. When Eqns. 2.1 and

2.2 are combined, the result is:

4)10(HV226.0

6/1 25.0

120HV43.1

R

areaw (2.3)

where w is the fatigue limit. It should be noted that Eqn. 2.3 is for surface defects. For

internal defects the constant in Eqn. 2.3 of 1.43 is changed to 1.56. The projected area of

the inclusion perpendicular to the normal stress is used to characterize the anisotropic

effects of the deformed inclusion.

2.2 Surface Finish

It is widely recognized that surface finish has a significant effect on fatigue

behavior. Forging is usually accompanied by considerable surface roughness, surface

decarburization and scale defects. In general, fatigue life decreases as surface roughness

increases, particularly in the high cycle fatigue (HCF) region. Surface roughness has less

of an effect in the low cycle fatigue (LCF) region. Decarburization results from forging


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were subjected to rotating bending fatigue. The fatigue specimens had the same

dimensions as in their previous study [3]. The high tensile strength as-forged specimen

had a very low endurance limit when compared to the machined and polished condition

(see Table 2.4 and Figure 2-5). Normally the endurance limit of a polished specimen is

around half of the ultimate tensile strength. However, in Table 2.4, it can be seen that the

endurance limit of the polished specimens is only around 40% of the tensile strength. As

a result, the author decided to subject the machined specimens to a better polishing

procedure, which resulted in a significant improvement in endurance limit (683 MPa

increased to 896 MPa). The authors suggest that the surface irregularities may have more

of an effect on fatigue strength than the surface decarburization for high tensile strength

forgings.

In a paper by Noll and Lipson [2], as-forged specimens of different hardness

levels were investigated. It was found that the surface hardness was much lower than the

hardness of the inner material for the forged specimens due to the decarburization, similar

to results from Hankins et al. Figure 2-6 shows plots of the Brinell hardness versus

distance form the surface for specimens of four hardness levels. Figure 2-7 shows

magnified photographs of the specimens cross-section showing the decarburized layer. It

should be noted that the pictures in Figure 2-7 correspond to the plots in Figure 2-6. The

lighter colored area shown in the pictures represents the decarburized section. It can be

seen in Figure 2-6 that the surface hardness was significantly lower than the interior

hardness. This difference in hardness is one explanation for decreased life in the HCF

region for forged specimens, since higher hardness (higher strength) is a desired property

for long fatigue life. As previously mentioned, controlled forging can result in less


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decarburization and increased endurance limit, as seen in Figure 2-8, which shows a plot

of endurance limit versus tensile strength for as-forged specimens. There are two curves

in this figure, with the upper curve representing a controlled forging process and the

lower curve representing a less controlled (standard large scale manufacturing) forging

process [13]. The controlled forging process results in decarburization depths less than

0.13 mm, compared to depths as deep as 0.89 mm for the less controlled process [13]. In

addition, the controlled forging process results in less surface irregularities than the

standard large scale forging process.

Gildersleeve [14] investigated the relationship between decarburization and

fatigue strength of a low alloy steel (605 M36). Rotating bending tests were used to

determine the fatigue behavior. The specimens had decarburized layers up to 1 mm in

depth. The results showed that the fatigue limit was mostly independent of the depth of

decarburization (see Table 2.5). The author also examined surface carbon concentration

and found the fatigue limit to be linearly dependent upon the carbon concentration at the

surface.

Adamaszek and Broz [15] investigated the effects of decarburization on hardness

changes in carbon steels caused by high temperature surface oxidation. The

decarburization they studied resulted from annealing. They state that the decarburization

causes the grains near the surface to grow. In addition to grain growth, there is formation

of surface scales, which are solid, firm and porous. The authors explain that during the

decarburization process oxygen penetrates the surface through cavities, pores and cracks.

This oxygen reacts with the different chemicals (elements) in the metal causing the

decarburization. The decarburization is worse for metals with higher Fe concentration.


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The authors also state that there are hardness changes due to the decarburized layers

resulting in lower fatigue resistance.

2.2.2 Roughness measurements and parameters

Before determining how surface roughness affects fatigue life, it is necessary to

measure and define surface roughness. The most common method of measuring surface

roughness is the mechanical profiler. It works by dragging a stylus (probe) across the

surface [16, 17]. As the stylus is drawn slowly across the surface, it moves up and down

with the contours of the surface. This motion is then recorded. However, this instrument

is limited by the radius of the stylus tip. If the radius is too large it may not be able to

penetrate the finer cracks or scratches, resulting in an incorrect surface roughness

measurement. It is also a possibility that the surface could be damaged by the stylus. A

non-destructive method of measuring surface roughness is the laser speckle contrast

method [16]. In this method a helium-neon light is pointed at the surface at various

angles. As this light hits the surface it is reflected creating a speckle. It was found [16]

that there is a linear relationship between the surface roughness and the speckle contrast

of an illuminated surface up to a certain roughness (0.1 mRa).

Once the surface topography is recorded it is necessary to define it. Gadelmawla

et al [18] describe 59 different parameters for describing surface roughness. The authors

state that the arithmetic average height parameter (Ra), also known as the center line

average (CLA), is the most widely used parameter. This parameter is the average

deviation from the mean line over a sampling length (see Figure 2-9(a)). This is shown

mathematically below:


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l

a dxxyl

R0

)(1

(2.4)

WhileRa is easy to define, it does not describe wavelength and is not sensitive to small

changes in roughness profile. It should be noted that when reporting the value ofRa it is

necessary to also report the cutoff length, which is the length that the roughness is

averaged over. Rq orRMS is the root mean square roughness, which is the standard

deviation of the distribution of surface heights, and is another common parameter. Rq is

more sensitive to a large deviation from the mean line than Ra. This parameter is

expressed mathematically as:

l

q dxxyl

R0

2)}({1

(2.5)

The parameterRz, known as the ten-point height, is defined as the average

summation of the five highest peaks and the five lowest valleys (see Figure 2-9(b)). It

should be noted that Ra is not as sensitive to occasional peaks and valleys as Rz. Rz is

defined mathematically by:

n

i

n

i

iiDINz vpn

R1 1

)(

1(2.6)

The maximum height of profile parameter,Rt, is most sensitive to large peaks and

valleys. It is defined as the distance measured between the highest peak, Rp, and the

lowest valley,Rv, (see Figure 2-9(c)). It is defined mathematically by:

vpt RRR (2.7)

In Figure 2-9(c),Rv is equal toRv4 andRp is equal to Rp3. Therefore,Rt is equal toRp3 +

Rv4. In Figure 2-9(c), Ry, not to be confused with Rt, is the largest peak to valley height

(i.e.Rp3 +Rv3).


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Mean spacing between peaks, Sm, is another parameter used to characterize

surface roughness. It is defined as the mean spacing between profile peaks at the mean

line (see Figure 2-9(d)) and is defined mathematically as:

n

i

im SN

S1

1(2.8)

There are many more parameters used to quantify surface roughness. Each parameter is

designed to be more sensitive to different variations in roughness such as height and

depth of roughness, frequency of roughness, and distance between peaks.

Novovic et al [19] performed a literature review on the effect of machined surface

topography and integrity on fatigue life and examined different roughness parameters.

They examined surface roughness parameters and concluded that Ra is the most

commonly used parameter in describing fatigue behavior. However, they found that there

is typically a 20% scatter in fatigue results for specimens of the same Ra value. The

authors suggest that Rt and Rz are better to use in determining fatigue performance than

Ra, because these parameters represent the worst defects in the surface.

2.2.3 As-forged surface condition

As stated earlier, most of the available data for the effect of as-forged surface

condition on fatigue are old and very conservative. The paper entitled Allowable

Working Stresses by Noll and Lipson [2] is one of the main sources of data used to

develop the endurance limit modification factors for the as-forged surface condition,

which are still used in fatigue design and analysis. The authors investigated the

relationship between endurance limit (defined at 107

cycles to failure) and surface

condition (ground, machined, hot-rolled, and forged). The forged surface condition is


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described as having large surface irregularities, including oxide, scale defects, as well as

total surface decarburization and is regarded as the worse of the above mentioned surface

conditions. They grouped fatigue data on steels with hardness ranging from 160 HB to

555 HB from previous studies by other authors into the above categories. Some of the

data for the as-forged surface condition are from data published by Hankins et al [3, 4].

However, most of the data for the as-forged surface condition were obtained from

fabricated parts tested at the Chrysler Laboratories. The actual test data and experimental

details performed at Chrysler Laboratories, from which the data were derived, are not

included in [2]. From this data, Noll and Lipson developed several figures of allowable

stress versus mean stress for each type of specimen (see Figure 2-10 for an example).

Data from the 1945 version of the SAE Handbook were used by Noll and Lipson to

define the relationship between tensile strength and hardness (see Figure 2-11), which is a

mostly linear relationship. Noll and Lipson used the most conservative values from

Figure 2-11 in their analysis. In addition, they developed a figure plotting endurance limit

versus tensile strength (see Figure 2-12) for the four surface conditions investigated. The

data used to develop Figure 2-12 are listed in Table 2.6. It can be seen in Figure 2-12 that

the as-forged surface condition results in the lowest endurance limit for a given tensile

strength of the four surface conditions described in [2]. It should be noted that controlled

forging conditions can produce surface finish quality similar to hot-rolled surfaces [13].

In a discussion of the paper Allowable Working Stresses, Lessells compares

endurance limit data on as-forged and ground and polished surface conditions from Noll

and Lipson to data from Hankins et al [3, 4]. Lessells found the data from Noll and

Lipson to be much more conservative than the data from Hankins et al. Noll and Lipson


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in their reply state that the discrepancies are due to modification of data for size effect,

reducing Hankins endurance limit data by 15%. Noll and Lipson explain that there is

more of a difference between data for forged surface than for the ground and polished

surface due to the broad definition of the forged surface condition.

2.2.4 Effect of surface roughness on fatigue behavior

Fluck [20] studied the influence of surface roughness on fatigue life and scatter of

test results of two steels. The steels used for the cantilever rotating bending tests were a

quenched and tempered SAE 3130 steel (30 HRC) and an annealed SAE 1035 steel (69

HRB). The specimens, which were machined from 12.7 mm rolled bars, were grouped

into six categories of surface roughness, lathe-formed, partly hand-polished, hand-

polished, ground, ground and polished, and superfinished. The surface roughness

measurements were made with a Brush surface analyzer. This instrument indicated the

root mean square of the surface roughness. Figure 2-13 shows a plot of the RMS (Rq)

surface roughness versus median fatigue life. The results show that the ground and

polished specimens, which represent the smoothest surface, always experienced the

longest life and the lathe-formed specimens, which represent the roughest surface,

experienced the shortest life.

Figure 2-14 shows the scatter of these results. It can be seen in Figure 2-14 that

there is generally more scatter for a given polishing condition at longer life for both of the

materials used. The author concluded that fatigue life can be significantly increased by

reducing the size of circumferential scratches. Specimens polished to roughness below

six microinches experienced a large increase in fatigue life. In a discussion of this paper,


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Lessells points out that the author did not consider surface residual stresses and surface

hardening through cold work and martensite formation that could have been introduced

by the polishing procedures. As a result, according to Lessells, surface roughness is not

the only cause for the differences in fatigue life data reported by Fluck.

Sibel and Gaier [21] investigated the influence of surface roughness on fatigue

strength of steels and non-ferrous alloys [21]. Axial and reverse bending fatigue tests

were performed on several types of steels (medium carbon, Cr-Mo, spring steel, and

stainless) as well as brass and some aluminum alloys. Roughness was applied to the

specimen surface by polishing, grinding and turning. The specimens had an hour glass

shape with 8.4 mm and 7.5 mm minimum diameters for the axial and bending specimens,

respectively. The roughness parameter used was Rv, the maximum depth of groove, with

values ranging from 1 to 50 microns. There was a similar decrease in fatigue strength, for

both axial and reverse bending fatigue tests, as surface roughness increased.

2.2.5 Fatigue limit evaluation for surface finish effect

Murakami and Endo [22] performed an extensive literature review on the effects

of defects, inclusions and inhomogenities on fatigue strength and the existing models.

The authors classify the different approaches into three categories: empirical models,

models based on fatigue notch factor approach, and fracture mechanics models. Many of

them can be used to determine behavior of specimens with scratches, cracks or notches.

As presented earlier, Murakami et al developed an equation (Eqn. 2.3) for

prediction of the fatigue limit for specimens with small defects and inclusions [22].

Although this equation was developed for specimens with small defects and inclusions,


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they have shown it to be applicable to surface roughness conditions by performing

rotating bending fatigue testing on a medium carbon JIS S45C steel [23, 24]. The

specimens were machined after heat treatment or annealing (see Figure 2-15 for specimen

configuration and dimensions). After machining, artificial roughness in the form of

notches of various depth and pitch was applied to the specimens by use of a lathe. The

depth of the artificial roughness was considered random because of build up on the

cutting tool, but the pitch between notches was considered constant (see Figure 2-16 for

magnified views of the different types of artificial surface roughness applied). There were

also some electro-polished specimens. Some of the electro-polished specimens had a

single notch applied to them after polishing. Roughness was measured by use of a

mechanical profiler. Figure 2-17 shows a plot of the stress-life data. All fatigue failures

occurred at the root of an artificially induced notch. The fatigue strength decreased as the

depth of the notch increased. It was shown that the specimens with a single notch

experienced fatigue strength that was about 30% lower than that of specimens with

multiple notches. This is because interference between notches reduces the fatigue notch

effect. As a result the authors determined that the pitch between notches must be

considered, which is not considered in the area parameter.

In order for Eqn. 2.3 to be used to evaluate surface roughness, Murakami et al

developed an equivalent defect size for surface roughness Rarea to replace area ,

which accounted for both depth and pitch. They assumed that periodic roughness notches

are equivalent to periodic cracks. It should be noted that this problem was evaluated as a

crack problem and not a notch problem. They derived the following equations:


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32)2/(47.9)2/(51.3)2/(97.2

2bababa

b

areaR For 195.02/ ba (2.9)

38.0

2

b

areaRFor 195.02/3 ba (2.10)

where a is the crack depth and 2b is the distance between the two cracks. Figure 2-18

shows a plot of Rarea /2b versus a/2b. This figure includes superimposed data points

calculated from experimental data. When considering value of depth, a, the authors chose

to use the maximum height parameterRy. The following equation was used to calculate

the fatigue limit for the electro-polished specimens (without notch) and the artificially

roughened specimens, respectively:

HV6.1w )400HV( For polished surface condition (2.11)

6

1

)(

]2/)1)[(120HV(43.1

R

w

area

R

For rough surface condition (2.12)

Table 2.7 displays the Rarea values for each type of artificial surface roughness. Table

2.8 shows the experimental and calculated values of fatigue limit along with the hardness

values and the Rarea parameter. Materials 100A and 150QT listed in Tables 2.7 and

2.8 have similar crack depth, but different pitch (100 m, 150 m and 200 m). The

numbers in the specimen ID listed in Tables 2.7 and 2.8 refer to the pitch. It can be seen

that the decreased pitch distance results in a lower value of Rarea . This lower value of

Rarea would result in a larger value of w , which is in agreement with experimental

data. Figure 2-19 shows a plot of the experimental life versus the predicted life using

Eqns. 2.11 and 2.12, showing an error less than 10% in predicting fatigue limit for most

specimens.


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Shareef and Hasselbusch [5] investigated endurance limit modifying factors for

hardened machined surfaces. They state that existing surface finish modification factors,

derived from Allowable Working Stresses, are limited to hardness up to 33 HRC, and

when this factor is extrapolated to higher hardnesses it produces overly conservative

values. The authors performed fatigue tests on specimens made from SAE 4140 steel

with a machined surface and hardness ranging between 50 and 55 HRC. The average

hardness of the specimens tested was 53.4 HRC. The roughness was defined by the Ra

parameter. The specimens had an average roughness of 3.51 m. The specimens also had

surface compressive residual stresses with an average value of -331 MPa. Figure 2-20

shows the specimen geometry as well as the test set up used. The shafts were subjected to

three-point bending while strain was monitored using gages. They used three different

stress equivalency methods to calculate the surface finish correction factor, ka:

polishede

aa

machinede

a

Sk

S

(2.13)

cff

b

f

fa

NNE

k

222

0

(2.14)

cb

fffa

b

f

faNkN

E

k

22

2

2

2

max

(2.15)

They solved forka and found that the SWT relationship (Eqn. 2.15) resulted in the best

predictions. Table 2.9 shows the correction factors calculated using Eqns. 2.13-2.15 for

104

and 106

cycles to failure. It should be noted that in Eqns. 2.14 and 2.15, ka was

applied to only the elastic portion of the curve. Figure 2-21 shows that Eqns. 2.14 and

2.15 result in a decreased effect of surface roughness with a decrease in fatigue life, but

Eqn. 2.13 shows no difference between LCF and HCF. Existing data, derived from


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Allowable Working Stresses, gives an endurance limit modification factor ofka = 0.44

for machined specimens at 53.4 HRC. Shareef and Hasselbusch state that the use of their

most conservative modification factorka = 0.75, derived from Eqn. 2.13, would result in

cost and weight savings up to 50%. This is an example of how conservative the data

published by Noll and Lipson are.

Arola and Williams [25] investigated the effects of surface texture on a high

strength low alloy steel. In their investigation, surface roughness parameters were used to

calculate an effective stress concentration factor, which was then used to determine an

effective fatigue notch factor. The effective stress concentration factor based on

roughness parameters was defined as:

z

ya

tR

RRnK

1 (2.16)

where Ra is the average roughness, Ry is the peak to valley height, Rz is the 10-point

roughness, and is the average radius determined from the dominant profile valleys (see

Figure 2-22 for definition of). The value ofn in Eqn. 2.16 is equal to two for tension

loads and equal to one for shear loads. Equation 2.16 can then be substituted into Eqn.

2.17 below to calculate an effective fatigue notch factor, as:

)1(1 tf KqK (2.17)

In Eqn. 2.17, q is defined as the notch sensitivity and is given by:

1

1q (2.18)

where for steels is define by:


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8.1

2070025.0

u

MPa

(2.19)

In Eqn. 2.19, u is the ultimate tensile strength in MPa and is in units of mm. Figure

2-23 shows a plot of fatigue stress concentration factor versus average surface roughness.

This plot superimposes calculated values along with experimental values. It can be seen

influence of surface finish on bending fatigue of forged steel including heating method, hardness,...

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