S19-1 PAT318, Section 19, March 2005 SECTION 19 FATIGUE CRACK PROPAGATION

S19-2 PAT318, Section 19, March 2005

S19-3 PAT318, Section 19, March 2005 FATIGUE CRACK PROPAGATION (LEFM) METHOD n What remnant life is there after initiation? n What is the safe life or inspection schedule for a component that is or may be cracked? n The crack growth method is based on the principles of Linear Elastic Fracture Mechanics (LEFM) n It relates stress intensity factors to crack growth rates n It uses cycle-by-cycle calculations to predict lifetimes n It is frequently used in Aerospace, Offshore, and Power Generation industries

S19-4 PAT318, Section 19, March 2005 FRACTURE MECHANICS TRIANGLE Stress Intensity (K) Stress (s)Crack Size (a)

S19-5 PAT318, Section 19, March 2005 FRACTURE MECHANICS RECTANGLE Final Crack Size (a f ) Cycles to Failure (N f ) Initial Crack Size (a i )Stress Range (DS)

S19-6 PAT318, Section 19, March 2005 CRACK STRESS CONCENTRATION A crack is an extreme stress/strain concentrator Elastic Stress Concentration max = K t K t =3 K t =(1+2a/b) b = 0 --> K t =

S19-7 PAT318, Section 19, March 2005 MODES OF CRACK OPENING

S19-8 PAT318, Section 19, March 2005 MECHANICS OF CRACKS n Stress Intensity Factor K I n General form of K K = Y a where the geometry function Y = Y (a/w, B,... )

S19-9 PAT318, Section 19, March 2005 TYPICAL GEOMETRY FUNCTIONS n Through Crack in Infinite Plate u Y = 1 n Edge Crack in Semi-Infinite Plate u Y = 1.12 n Edge Crack in Finite Plate u Y = (a/w) (a/w) (a/w) (a/w) 4

S19-10 PAT318, Section 19, March 2005 LINEAR ELASTIC FRACTURE MECHANICS

S19-11 PAT318, Section 19, March 2005 LINEAR ELASTIC FRACTURE MECHANICS

S19-12 PAT318, Section 19, March 2005 K CONTROLLED FRACTURE n In small scale yielding K controls everything near the tip - plasticity - void growth - cracking n Fracture occurs when K = K IC (The Fracture Toughness) K Controls the stress around the tip Fracture Zone Plastic Zone

S19-13 PAT318, Section 19, March 2005 ASSUMPTIONS OF SMALL SCALE YIELDING n Plastic zone size: n For LEFM to be valid, the plastic zone size must be small compared to crack length a and component geometry:

S19-14 PAT318, Section 19, March 2005 STAGES OF FATIGUE CRACK GROWTH

S19-15 PAT318, Section 19, March 2005 FATIGUE CRACK GROWTH MECHANISMS n Reversed plasticity n Corrosion

S19-16 PAT318, Section 19, March 2005 CRACK PROPAGATION METHOD SIMILITUDE This crack grows at the same rate as this one if both experience the same stress intensity factors

S19-17 PAT318, Section 19, March 2005 CRACK GROWTH RATES ARE CONTROLLED BY K da --- dN K Threshold Effects Fast Fracture Effects Paris Law Region da --- = C K m dN K = Y a

S19-18 PAT318, Section 19, March 2005 PROPAGATION RATES

S19-19 PAT318, Section 19, March 2005 FACTORS AFFECTING CRACK GROWTH RATE n Crack tip plasticity (crack closure) n Mean stresses n Threshold region (for low loads or short cracks) n Variable amplitude loading (overloads) n Environment

S19-20 PAT318, Section 19, March 2005 CRACK TIP PLASTICITY

S19-21 PAT318, Section 19, March 2005 PLASTIC ZONE AND CRACK CLOSURE n As crack grows, small region of plasticity develops around crack tip n Plastically deformed regions are surrounded by material that remains elastic n As material is unloaded, plastic region causes crack surfaces to be pulled toward each other causing CRACK CLOSURE n Crack closure can be induced by: u overloads u corrosion effects u surface roughness

S19-22 PAT318, Section 19, March 2005 MEAN STRESSES (R-RATIO EFFECTS)

S19-23 PAT318, Section 19, March 2005 SHORT CRACKS n SHORT CRACKS: u they tend to be free of closure effects. u LEFM is not applicable to them, in general. u They typically have higher growth rates than long cracks. NOTE: long cracks do not grow if K is smaller than a threshold value K th.

S19-24 PAT318, Section 19, March 2005 VARIABLE AMPLITUDE LOADS High - low sequences change the crack closure

S19-25 PAT318, Section 19, March 2005 ENVIRONMENT Crack growth rates are higher in corrosive environments (e.g. salt water) than in air. They are the lowest in vacuum.

S19-26 PAT318, Section 19, March 2005 CALCULATING LIFETIMES n Need: u Initial crack size u Final crack size u Stress range u K calibration u Material growth law

S19-27 PAT318, Section 19, March 2005 CRACK GROWTH LAWS n There are many crack growth laws in the literature: u Paris (the most known) u Forman (MSC/Fatigue uses similar method for fast fracture correction) u Lucas-Klesnil u Elber u Walker u Wheeler u Willenborg (MSC/Fatigue uses extension of this model)

S19-28 PAT318, Section 19, March 2005 EFFECTIVE K APPROACH The key to MSC/Fatigue crack growth analysis is the correction of the apparent K (based on applied load) to an effective K (i.e. the crack driving force actually seen at the crack front) n Usual Method MSC.Fatigue Method

S19-29 PAT318, Section 19, March 2005 MSC/FATIGUE CRACK GROWTH ANALYSIS STEPS n Input next cycle Calculate apparent K from lookup table Correct to effective K for u closure/short crack u notch field influence u static fracture mode contribution u history effects u environmental effects da = C K eff m n a = a+da (if no fast fracture, go to next cycle)

S19-30 PAT318, Section 19, March 2005 IMPLEMENTATION IN MSC.FATIGUE Time Cycle Counter TCY MDB Materials Database Manager Geometry function Library KSN CRACK GROWTH ANALYSER CRG

S19-31 PAT318, Section 19, March 2005 CYCLE-BY-CYCLE CRACK GROWTH n Features: u Cycle-by-Cycle Modelling u Time-sequenced Rainflow Cycle Counting u Multi-environment Material Properties u Kitagawa Minimum Crack Sizing u Threshold Modelling u Crack Closure and Retardation u User Defined Life u Fracture Toughness Failure Criterion u Surface or Embedded Cracks u Modified Paris Law (modified Willenborg model)

S19-32 PAT318, Section 19, March 2005 SUMMARY OF APPROACH n Identify critical region and select node/element for nominal stress n Identify geometry from library of compliance functions n Identify initial crack size n MSC.Fatigue calculates change in crack length on a cycle-by-cycle basis until fast fracture occurs n Life estimates are normally within a factor of 2 if all the control parameters are modeled correctly

S19-33 PAT318, Section 19, March 2005 MSC/FATIGUE CRACK GROWTH ANALYSIS - APPLICATIONS n Design analysis n Pre-prediction of test programs n Inspection strategy n Failure investigation n Decision support

S19-34 PAT318, Section 19, March 2005 EXAMPLE PROBLEM: CRACK PROPAGATION ANALYSIS n Lug problem n Single load

S19-35 PAT318, Section 19, March 2005 LINEAR ELASTIC FRACTURE MECHANICS ANALYSIS (LEFM)

S19-36 PAT318, Section 19, March 2005 DEFINE A CRACK AND PLOT COMPLIANCE FUNCTION

S19-37 PAT318, Section 19, March 2005 LOADING INFO SETUP

S19-38 PAT318, Section 19, March 2005 MATERIAL INFO SETUP n Create a group far_field with node 223 in it only.

S19-39 PAT318, Section 19, March 2005 PERFORM LEFM ANALYSIS

S19-40 PAT318, Section 19, March 2005 EXERCISE n Perform Quick Start Guide Chapter 7 Exercise, Introduction to Crack Growth n Be sure to ask for help if theres anything you dont understand