S17-3 PAT318, Section 17, March 2005 STRAIN-LIFE (EN) THEORY
S17-4 PAT318, Section 17, March 2005 STRAIN-LIFE (EN) THEORY n Strain-life method is one of the most common life prediction methods used in the automotive industry. n It is also called the local strain approach, the crack initiation method, and the strain-life approach.
S17-5 PAT318, Section 17, March 2005 STRAIN-LIFE (EN) THEORY n Practically, crack initiation means that a crack of around 1-2 mm has developed. This is often a high proportion of the component life. n Many automotive components are designed to survive some significant plastic strains in use (especially on the test track!). The E-N method will handle these better than the S-N method which basically ignores plasticity. n The E-N method is not very suitable for structural joints such as welds, spot welds etc.
S17-6 PAT318, Section 17, March 2005 CRACK INITIATION (STRAIN - LIFE) METHOD - SIMILITUDE The crack initiation life here..... is the same as it is here..... if both experience the same local strains e
S17-7 PAT318, Section 17, March 2005 STRAIN - LIFE METHOD
S17-8 PAT318, Section 17, March 2005 STRAIN LIFE TESTING n Normally, polished cylindrical specimens of around 6- 8 mm diameter are tested according to the appropriate standards, though flat coupons may also be used. n The tests are carried out in strain control; the test machine uses the output from the strain gauge (clip gauge) to provide feedback to the servo-controlled test machine.
S17-9 PAT318, Section 17, March 2005 STRAIN CONTROLLED TESTING n Test carried out to ASTM E606 or equivalent n High quality test specimen n Polished surface n Precision machined for minimum surface residual stress n Strain monitoring using high quality clip gauge n Alignment very important
S17-10 PAT318, Section 17, March 2005 Input is time history of STRAIN Also known as Low Cycle Fatigue or Local Strain Approach Local strains can be elastic or plastic hence its suitability for Low Cycle fatigue E-N ANALYSIS
S17-11 PAT318, Section 17, March 2005 MATERIALS CHARACTERIZATION
S17-12 PAT318, Section 17, March 2005 STRAIN CONTROL VS. STRESS CONTROL n Strain Control actually uses an extensometer in the servo loop. n Stress Control is actually load control. n Strain Control controls plastic strain, the parameter which directly controls fatigue damage. n Stress Control controls the wrong parameter. n Local Stress and Strain are only equivalent, i.e. linearly related, under purely elastic conditions i.e. when there shouldnt be any fatigue damage.
S17-13 PAT318, Section 17, March 2005 CONTROL PARAMETER RESPONSE PARAMETER CYCLIC SOFTENING Note: Hysteresis loops normally stabilize after some number of cycles
S17-14 PAT318, Section 17, March 2005 CONTROL PARAMETER RESPONSE PARAMETER Note: Hysteresis loops normally stabilize after some number of cycles CYCLIC HARDENING
S17-15 PAT318, Section 17, March 2005 Companion Samples Method Companion samples are tested at various strain levels and cycled until the hysteresis loops become stabilized. Stable hysteresis loops are superimposed and the tips connected to form the cyclic stress-strain curve. This method is time consuming and requires many samples. CYCLIC STRESS-STRAIN CURVE DETERMINATION
S17-16 PAT318, Section 17, March 2005 Ramberg-Osgood Relationships = EK 1 n Monotonic Cyclic = EK' a a 1 n' STRESS-STRAIN RELATIONSHIPS
S17-17 PAT318, Section 17, March 2005 CYCLIC STRESS STRAIN BEHAVIOUR n Masings hypothesis: The hysteresis curve is the same shape as the cyclic stress-strain curve, but doubled up in both directions.
S17-20 PAT318, Section 17, March 2005 STRAIN LIFE RESULTS FROM A SERIES OF LCF TESTS n Basquin showed that for high cycle fatigue, fatigue life has a power law relationship with elastic strain. n Coffin and Manson did the same for low cycle fatigue and plastic strain. n Add the two together and you have a relationship between total strain and fatigue life covering low and high cycle fatigue.
S17-21 PAT318, Section 17, March 2005 COFFIN-MANSON-BASQUIN EQUATION el f E ' plf ' f a f b E (2N f )(2N f ) c ' ' Basquin Coffin Manson (2N f ) c (2N f ) b
S17-22 PAT318, Section 17, March 2005 Cross Plot of Data : 10 Strain(uE) Stress(MPa) Total strain range Plastic strain range SEPARATION OF ELASTIC & PLASTIC STRAIN FROM THE STABLE HYSTERESIS LOOP
S17-23 PAT318, Section 17, March 2005 STRAIN LIFE RESULTS FROM A SERIES OF LCF TESTS
S17-24 PAT318, Section 17, March 2005 STRAIN LIFE CURVE The Transition Life, 2N f, represents the life at which the elastic and plastic curves intersect.
S17-25 PAT318, Section 17, March 2005 STRAIN LIFE CURVE At shorter lives more plastic strain is present and the loop is wider. At longer lives the loop is narrower, representing less plastic strain
S17-26 PAT318, Section 17, March 2005 THE S-N AND E-N LIFE CURVES /S N 1000 Cycles Low Cycle Region (EN Method) High Cycle Region (SN or EN Method) 'Infinite Life' 10 7 Cycles S-N Life Curve E-N Life Curve S-N & E-N curves coincide in high cycle region because nominal stresses will be linear elastic E-N can also be used in low cycle region. S-N cannot, because linear stress-strain relationship is invalid
S17-28 PAT318, Section 17, March 2005 RAINFLOW CYCLE COUNTING
S17-29 PAT318, Section 17, March 2005 RAINFLOW CYCLE COUNTING n The story goes Matsuishi and Endo got the idea for the method while watching rain water cascading down a pagoda roof. n Basic rules: rain flows down from each turning point and continues until either: u it is interrupted by flow from above, or u it reaches a turning point which is larger that the one it started from and in the same sense n Good way of representing cycles is Rainflow Cycle Count Matrix
S17-31 PAT318, Section 17, March 2005 RAINFLOW COUNTING AND STRESS/STRAIN SPACE
S17-32 PAT318, Section 17, March 2005 RAINFLOW COUNTING AND STRESS/STRAIN SPACE n Materials under cyclic loading exhibit material memory effect (they remember the largest previously reached stress-strain state) n What is stress-strain curve in monotonic loading is hysteresis loop in cyclic loading n Rainflow counting identifies closed hysteresis loops as cycles u Some cycles stand within the largest hysteresis loop and some hang; this depends on cycle sequence
S17-33 PAT318, Section 17, March 2005 MEAN STRESS CORRECTIONS
S17-34 PAT318, Section 17, March 2005 MEAN STRESS CORRECTIONS n Two main methods for correcting for mean stress in the local strain (E-N) approach: u Morrow Moves the elastic life line up and down according to the mean stress of each cycle u Smith-WatsonTopper (SWT or STW) Uses a damage parameter which includes the maximum stress of each cycle
S17-35 PAT318, Section 17, March 2005 MORROW CORRECTION
S17-36 PAT318, Section 17, March 2005 SMITH WATSON TOPPER CORRECTION
S17-37 PAT318, Section 17, March 2005 SWT VS MORROW n SWT makes bigger corrections than Morrow n SWT tends to be conservative (tension). n SWT tends to be non-conservative (compression)
S17-38 PAT318, Section 17, March 2005 ELASTIC-PLASTIC CORRECTION AND LOCAL GEOMETRY
S17-39 PAT318, Section 17, March 2005 The Local Strain Method requires the notch root local stresses and strains to model the plasticity that leads to fatigue damage. These can be derived by: Neuber worked in statics, not fatigue, but noticed that the ratios of plastic strain and plastic stress were different. STRAIN LIFE MODELLING n Measurement from a strain gauge precisely located at the critical location. n Elastic-plastic finite element analysis with a very refined mesh. n Using an empirical rule, usually NEUBERS RULE (but not always) to estimate elastic-plastic strain from nominal strain or Linear FE results.
S17-40 PAT318, Section 17, March e Cyclic Stress- Strain Curve Neuber Equation Solution point Elastic FE Strain e e ELASTIC-PLASTIC CORRECTION
S17-41 PAT318, Section 17, March 2005 USE OF K f IN STRAIN LIFE MODELLING The strain concentration factor, K = / e is > K t and the stress concentration factor, K = / s is < K t after plastic yielding. Neither are known but Neuber found that their geometric average was equal to K t. Hence Neubers Rule is simply: K. K = ( K t ) 2 Re-arrangement of this Rule gives a useful equation: ( K t ) 2 s.e =
S17-42 PAT318, Section 17, March 2005 Another re-arrangement gives: ( K t e ) 2 E = in which the LHS is known. This can be solved with the cyclic stress strain curve equation simultaneously to derive and Topper simply replaced K t by K f to make Neubers Rule applicable in fatigue analysis for local stress strain tracking. USE OF K f IN STRAIN LIFE MODELLING (Contd.)
S17-43 PAT318, Section 17, March KfKfKfKf e s CSSC Neuber Equation Solution point E-P CORRECTION INCLUDING K f
S17-44 PAT318, Section 17, March 2005 REFINEMENTS TO THE NEUBER METHOD n The Neuber Method is an approximation, suitable for stress and strain estimation where plasticity is limited, e.g. at notches. n At locations where there is no well defined notch, it may underestimate the strains. n The Seeger-Beste and Mertens-Dittmann methods use a shape factor or plastic strain concentration factor to modify the amount of the estimated stress redistribution
S17-45 PAT318, Section 17, March 2005 These methods take into account plasticity which is more extensive by moving the origin of the Neuber hyperbola to a point calculated using plastic strain concentration factors : Mertens-Dittmann Equation : e e Seeger-Beste Equation : where : p p y L L and = e p / e p / e e SEEGER-BESTE METHOD AND MERTENS- DITTMAN METHOD
S17-46 PAT318, Section 17, March 2005 e e new originat ( Graphical representation of Mertens-Dittmann Method e p / = e p /, ) MERTENS-DITTMAN METHOD
S17-47 PAT318, Section 17, March 2005 SEEGER-BESTE METHOD e e Graphical representation of Seeger-Beste Method e p / new origin at (, )
S17-48 PAT318, Section 17, March 2005 SHAPE FACTORS (PLASTIC STRAIN CONCENTRATION FACTORS) Assuming elastic-perfectly plastic loading, the yield moment for a rectangular cross section bar in bending is: B A y y The plastic limit moment is : So the shape factor p = M p /M y = 1.5
S17-49 PAT318, Section 17, March 2005 SURFACE FACTORS n Extra factors are required for: u surface finish (ground, machined, hot rolled, cast, forged, corroded); u surface treatment (nitrided, shot peened, cold rolled): u loading mode (axial, bending, torsion) u anything else (environment etc.). As in the S-N method, surface factors can be used to modify the strain life curves to account for surface finish etc. These factors are applied to the elastic strain-life curve at the endurance limit. Polished, untreated, stress free, is considered as the starting point with Surface Factor = 1 (as in LCF test specimens).
S17-50 PAT318, Section 17, March 2005 Polished Forged USE OF K f FOR SURFACE FINISH
S17-51 PAT318, Section 17, March 2005 STRESS STRAIN TRACKING, NEUBER ANALYSIS, MATERIAL MEMORY AND DAMAGE CALCULATION
S17-52 PAT318, Section 17, March 2005 e(t) P P Nominal stress, strain - s,e Local stress, strain - s,e CSSCSWT-Life STRESS-STRAIN TRACKING & DAMAGE CALCULATION
S17-53 PAT318, Section 17, March 2005 A E e(t) B C D known K f A B = e 1, B C = De 2 C D = De 3, D E = De 4 STRESS-STRAIN TRACKING
S17-54 PAT318, Section 17, March 2005 A e(t) B e1e1 s 1 = E. e 1 CSSC = E k) 1/n A e1e1 s1s1 K f.e 1 K f.s 1 K f.e 1. K f.s 1 = NP = NP 1 plotting position is 1, 1 s B STRESS-STRAIN TRACKING - 1ST EXCURSION
S17-55 PAT318, Section 17, March 2005 STRESS-STRAIN TRACKING Basic Rule: Reset the origin and set off in the right direction!
S17-56 PAT318, Section 17, March 2005 e(t) C B A B ( 1, 1 ) 2 x CSSC = E k) 1/n 2 2 = NP 2 plotting position is 2 =( ), 2 =( ) K f. e 2. K f. s 2 = NP 2 e 2 s 2 2nd Excursion C ( 2, 2 )
S17-57 PAT318, Section 17, March 2005 e(t) C D 3rd Excursion A (0,0) C ( 2, 2 ) B ( 1, 1 ) 3 3 = NP 3 plotting position is 3 =( ), 3 =( ) D ( 3, 3 )
S17-58 PAT318, Section 17, March 2005 e(t) D E 4th Excursion - Material Memory D plotting position is NOT 4 =( ), 4 =( ) BUT 4 =( ), 4 =( ) B C E A Not E C B
S17-59 PAT318, Section 17, March 2005 Extracted Cycle max SWT = max. /2
S17-60 PAT318, Section 17, March 2005 SWT = max. /2 d = 1 / N f 2 N f Partial Damage for the Extracted Cycle
S17-61 PAT318, Section 17, March 2005 d i = 1 / N fi Damage Summation for All the Extracted Cycles D = d i Damage for each cycle: Damage sum for the repeat: Life to crack initiation in repeats: N i = 1 / D
S17-62 PAT318, Section 17, March 2005 IMPLEMENTATION IN MSC.FATIGUE n For each node or element: u True stress-strain tracking too time-consuming u Rainflow cycle count elastic strain time history u Correct each cycle for plasticity using Neuber (or similar) u Calculate mean stress for each cycle for both hanging and standing within largest cycle u Calculate damage for hanging and standing and record mean damage for each cycle u Sum damage for all cycles to give total life
S17-63 PAT318, Section 17, March 2005 CRACK INITIATION IN MSC.FATIGUE n Features: u Based on Local Strain Concepts u Mean Stress Correction u Elastic-Plastic Conversion u Statistical Confidence Parameters u Palmgren-Miner Linear Damage u User Defined Life u Cyclic Stress-Strain Modeling u Surface Conditions u Factor of Safety Analysis u Biaxiality Indicators s 1/2cycle 1cycle 1/2cycle 1cycle 1/2cycle e Strain e Time
S17-64 PAT318, Section 17, March 2005 EXAMPLE PROBLEM: E-N ANALYSIS OF A SPIDER Perform simple crack initiation analysis of a spider. Single input load. Create new database and read in the results.
S17-65 PAT318, Section 17, March 2005 REVIEW STRESS CONTOURS
S17-66 PAT318, Section 17, March 2005 FATIGUE ANALYSIS n Reference single load (sine01) n Create new group for analysis n Submit Job
S17-67 PAT318, Section 17, March 2005 PLOT LIFE CONTOURS
S17-68 PAT318, Section 17, March 2005 EXERCISE n Perform Quick Start Guide Chapter 5 Exercise, A Simple E-N Analysis n Perform Quick Start Guide Chapter 6 Exercise, Residual Stress n Be sure to ask for help if theres anything you dont understand