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Sequence Effects in FatigueProfessor Darrell F. Socie University of Illinois at Urbana-Champaign © 2002 Darrell Socie, All Rights Reserved Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50 Outline 1. Mean Stress 2. Nonlinear Damage Models 3. Crack Growth Interactions 4. Crack Tip Plasticity Models 5. Crack Closure Models Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 50 Mean Stresses mean stress stress range s t r e s s 2 S S S min max mean + = S max S min max min S S R = Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 50 General Observations Tensile mean stresses reduce the fatigue life or decrease the allowable stress range Compressive mean stresses increase the fatigue life or increase the allowable stress range Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 4 of 50 Mechanism Fatigue damage is a shear process ∆S Tensile mean stresses open microcracks and make sliding easier 2 S mean Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 5 of 50 Goodman 1890 Mechanics Applied to Engineering John Goodman, 1890 “.. whether the assumptions of the theory are justifiable or not …. We adopt it simply because it is the easiest to use, and for all practical purposes, represents Wöhlers data. S ultimate = S min + 2 ∆S Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 6 of 50 Goodman Diagram Mean stress A l t e r n a t i n g s t r e s s S u 0 S e 10 7 cycles 10 5 cycles | | . | \ | − | . | \ | ∆ = ∆ − = ultimate mean 1 R S S 1 2 S 2 S R = -1 R = 1 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 7 of 50 Test Data ( 1941 ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.2 0.4 0.6 0.8 1.0 1.2 0 Mean Stress Ultimate Strength A l t e r n a t i n g S t r e s s F a t i g u e L i m i t J.O. Smith, The Effect of Range of Stress on the Fatigue Strength of Metals, Engineering Experiment Station Bulletin 334, University of Illinois, 1941 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 8 of 50 Compression S e S u 0 R = -1 R = 1 -S u R = -∞ no influence detrimental beneficial Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 9 of 50 Modified Goodman ( no yielding ) S e S u 0 R = -1 R = 1 -S u R = -∞ S ys S ys -S ys ys mean S S 2 S < + ∆ Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 10 of 50 Mean Stress Influence on Life 0.1 1 10 100 1000 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Mean Stress Ultimate Strength R e l a t i v e F a t i g u e L i f e Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 11 of 50 Stress Concentrations Plastic Zone ∆ε ∆ε The elastic material surrounding the plastic zone around a stress concentration forces the material to deform in strain control Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 12 of 50 Mean Stresses at Notches σ ε σ ε σ ε elastic plastic Nominal Notch Notch Nominal Nominal mean stress is less than notch mean stress Nominal mean stress is greater than notch mean stress Nominal Notch Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 13 of 50 Morrow Mean Stress Correction c f ' f b f mean ' f ) N 2 ( ) N 2 ( E 2 ε + σ − σ = ε ∆ 10 -5 10 -4 0.001 0.01 0.1 1 Reversals, 2N f S t r a i n A m p l i t u d e 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 E mean σ Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 14 of 50 Smith Watson Topper σ ε ∆ε σ max c b f ' f ' f b 2 f 2 ' f max ) N 2 ( ) N 2 ( E 2 + ε σ + σ = ε ∆ σ Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 15 of 50 Mean Stress Relaxation Stadnick and Morrow, “Techniques for Smooth Specimen Simulation of Fatigue Behavior of Notched Members” ASTM STP 515, 1972, 229-252 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 16 of 50 Loading Histories Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 17 of 50 Test Results Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 18 of 50 Sources of Mean/Residual Stress Loading History Fabrication Shot Peening Heat Treating Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 19 of 50 Loading History Tension overloads produce favorable compressive residual stress Compressive overloads produce unfavorable tensile residual stress σ ε σ ε Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 20 of 50 Fabrication Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 21 of 50 Cold Expansion 1965 Basic Cx process conceptualized (Boeing) The split sleeve is slipped onto the mandrel, which is attached to the hydraulic puller unit. The mandrel and sleeve are inserted into the hole with the nosecap held firmly against the workpiece. When the puller is activated, the mandrel is drawn through the sleeve radially expanding the hole. Courtesy of Fatigue Technology Inc. Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 22 of 50 Theory of Cold Expansion Courtesy of Fatigue Technology Inc. Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 23 of 50 Fatigue Life Improvement Courtesy of Fatigue Technology Inc. 100 200 300 0 10 8 10 7 10 6 10 5 10 4 10 3 N o m i n a l S t r e s s Fatigue Life Cold Expanded Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 24 of 50 Shot Peening -600 -400 -200 0 200 0 0.2 0.4 0.6 0.8 Depth (mm) R e s i d u a l S t r e s s ( M P a ) Residual stress in a shot peened leaf spring Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 25 of 50 Shot Peening Results www.metalimprovement.com 500 1000 1500 500 0 0 1000 1500 2000 2500 F a t i g u e s t r e n g t h a t 2 x 1 0 6 c y c l e s , M P a Ultimate Tensile Strength, MPa 2 S S u FL = Smooth Notched Shot Peened Smooth & Notched Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 26 of 50 Heat Treating 200 600 400 0 0 5 10 15 B r i n e l l H a r d n e s s Depth, mm 0 5 10 15 -1500 -1000 -500 0 500 1000 Depth, mm R e s i d u a l S t r e s s , M P a Radial Circumferential Axial 50 mm diameter induction hardened 1045 steel shaft Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 27 of 50 Outline 1. Mean Stress 2. Nonlinear Damage Models 3. Crack Growth Interactions 4. Crack Tip Plasticity Models 5. Crack Closure Models Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 28 of 50 Cumulative Damage …. …. …. …. High - Low Low - High n H n L n L n H ∆S L ∆S H Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 29 of 50 Linear Damage ∆S H ∆S L N f H N f L L f L H f H F N n N n N n Damage + = = ∑ Miners Rule: Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 30 of 50 Nonlinear Damage 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0 0 Cycle ratio, D a m a g e f r a c t i o n n N f 004 0. = ε ∆ 020 0. = ε ∆ ΣD = 0.7 ΣD = 1.3 ΣD ~ 1 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 31 of 50 Periodic Overload Results 10 100 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 -3 10 -4 0.01 0.1 S t r a i n A m p l i t u d e Fatigue Life …. …. The fatigue limit is reduced by a factor of 3 when a few large cycles are applied Bonnen and Topper, “The Effects of Periodic Overloads on Biaxial Fatigue of Normalized SAE 1045 Steel” ASTM STP 1387, 2000, 213-231 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 32 of 50 Relative Miner’s Rule 3 . 0 N n D f = = ∑ ∑ Set Miner’s damage sum to a number less than 1 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 33 of 50 Outline 1. Mean Stress 2. Nonlinear Damage Models 3. Crack Growth Interactions 4. Crack Tip Plasticity Models 5. Crack Closure Models Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 34 of 50 Crack Growth Physics σ σ Maximum load Minimum load σ ε Mean stresses in plastic zone are small Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 35 of 50 Mean Stress Effects From Dowling, Mechanical Behavior of Materials, 1999 ( ) γ − ∆ = R 1 K C dN da m 0 < γ < 0.5 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 36 of 50 Sequences time + - L o a d time + - L o a d time + - L o a d time + - L o a d a d b c Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 37 of 50 Crack Growth 10 20 30 40 50 60 70 Cycles x 10 3 25 30 35 40 45 50 C r a c k l e n g t h , m m d c b a No overload Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 38 of 50 Crack Growth Rate 10 -4 10 -3 10 -5 0 1 2 3 4 Distance from peak load, mm G r o w t h r a t e , m m / c y c l e Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 39 of 50 Outline 1. Mean Stress 2. Nonlinear Damage Models 3. Crack Growth Interactions 4. Crack Tip Plasticity Models 5. Crack Closure Models Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 40 of 50 Stress Fields After Overload monotonic plastic zone cyclic plastic zone overload compressive plastic zone overload monotonic plastic zone Before After Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 41 of 50 Crack Growth Retardation 10 -4 10 -3 10 -5 0 1 2 3 4 Distance from peak load, mm G r o w t h r a t e , m m / c y c l e Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 42 of 50 Wheeler Model CA i p yi dN da a a r dN da | . | \ | | | . | \ | − = γ a p a i r yi Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 43 of 50 Outline 1. Mean Stress 2. Nonlinear Damage Models 3. Crack Growth Interactions 4. Crack Tip Plasticity Models 5. Crack Closure Models Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 44 of 50 Compression Crack open Crack closed Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 45 of 50 Compressive Stresses Compressive stresses are not very damaging in crack growth S t r e s s Crack opening level Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 46 of 50 Crack Closure - Elber ( ) m eff K C dN da ∆ = ( ) K R 4 . 0 5 . 0 K eff ∆ + = ∆ Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 47 of 50 Maximum Stress Dependence Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 48 of 50 Newman Model 1 A A 2 A A A A 1 A S ) 071 . 0 415 . 0 ( A 2 S cos ) 05 . 0 34 . 0 825 . 0 ( A R A R A R A A S S K R 1 S S 1 K 1 0 3 3 1 0 2 0 max 1 1 0 max 2 0 3 3 2 2 1 0 max o max o eff − + = − − − = σ α − = ( ¸ ( ¸ | | . | \ | σ π α + α − = + + + = ∆ ( ( ( ( ( ¸ ( ¸ − | | . | \ | − = ∆ α Newman Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 49 of 50 Closure Observations a b d c c 1 st subcycle d 500 th subcycle σ ε a b 1026 steel ∆ε 1 /2 = 0.005 ∆ε 2 /2 = 0.001 Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 50 of 50 Spectrum Loading -1000 1000 S t r a i n ( µ ε ) Non Damaging Cycles Sequence Effects in Fatigue
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