1 / 51

Fatigue

Fatigue. Outline. Fatigue Initiation and growth mechanisms Stress-life fatigue analysis Strain-life fatigue analysis Component testing Fatigue crack growth Design and validation of medical device fatigue performance Statistics. Fatigue Concepts. Definition of Fatigue:

Download Presentation

Fatigue

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Fatigue

  2. Outline Fatigue • Initiation and growth mechanisms • Stress-life fatigue analysis • Strain-life fatigue analysis • Component testing • Fatigue crack growth • Design and validation of medical device fatigue performance • Statistics

  3. Fatigue Concepts Definition of Fatigue: • The process of progressive, localized permanent structural change that occurs in a material subjected to cyclic loading • Fatigue can and does occur at stresses well below a given material’s yield strength • The annual cost of fatigue of materials has been estimated to be about 3% of the US Gross National Product (from N.E. Dowling, Mechanical Behavior of Materials, Prentice-Hall, 1998, pg. 358.)

  4. Fatigue Concepts The mechanism of fatigue crack initiation: • Requires local plastic deformation, usually at a stress concentration location or a properly oriented grain • Slip along slip bands- plane of maximum shear • Formation of intrusions and extrusions • Cracks form along slip planes

  5. Fatigue Concepts Fatigue crack initiation: • Often occurs at local stress discontinuities: notches, voids, inclusions, etc. • Affected by surface preparation and roughness • In general, increased surface roughness decreases resistance to fatigue crack initiation • Affected by residual stresses • Affected by material strength, in general, the higher the tensile strength, the higher the resistance to fatigue

  6. Fatigue Concepts Fatigue crack growth: • Literature focuses on striation-formation mechanisms in metals. Note – striations are frequently NOT observed on metal fracture surfaces after real-world (non-laboratory) fatigue: • Striations most obvious in very ductile metals • Striations only occur within a certain crack growth-rate “window” • Fracture surface damage from crack closure (rubbing) can remove striations • Fracture surface damage from corrosion can remove striations • A single striation can, but does not necessarily represent one cyclic event

  7. Fatigue Concepts Striation formation model

  8. Fatigue Concepts Design for Fatigue Prevention: • Stress-life approach • Strain-life approach • Fatigue crack propagation approach (LEFM-based damage tolerant design) • Component testing

  9. Stress-Life Fatigue stress range, σr = σmax – σminstress amplitude, σa = (σmax – σmin)/2mean stress, σo = (σmax + σmin)/2Stress ratio, R = σmin/ σmax

  10. Stress-Life Fatigue

  11. Stress-Life Fatigue S-N behavior can also be expressed with a power-law equation (linear line on log-log plot): σa = true stress amplitude2Nf = reversals to failure (1cycle = 2 reversals)σ'f = fatigue strength coefficient (approximately equal to true fracture strength)b = fatigue strength exponent

  12. Stress-Life Fatigue • How do you design a part if your R ratio (mean stress/strain) is different than your S-N data? • Use Goodman, Gerber, or Soderberg relations • Note that this mean stress/strain technique is not applicable to superelastic nitinol (to be discussed later)

  13. Stress-Life Fatigue Line a = Soderberg relation: Sa = Scr(1-So/Sy)Line b = Modified Goodman relation: Sa = Scr(1-So/Su)Line c = Gerber relation: Sa = [Scr(1-So/Su)2]Line d = Goodman relation modified with σf

  14. Stress-Life Fatigue • Soderberg relation is the most conservative • Goodman is frequently used for brittle metals, and is conservative for ductile metals • Gerber relation is good for ductile metals • Improved agreement for Goodman and Gerber using true fracture strength instead of ultimate tensile strength

  15. Stress-Life Testing • Modification to Goodman relation suggested by Morrow, replace σu (ultimate tensile strength) with σ'f (fatigue strength coefficient) from the unnotched axial S-N curve for R=-1 • Results in improved agreement for ductile metals

  16. Stress-Life Fatigue Generation of an S-N curve at non-zero mean stress: σar = fully reversed (R=-1) alternating stressσa = alternating stress at some mean stressσm = mean stressσ'f = fatigue strength coefficientb = fatigue strength exponent Nf = number of cycles to failure Allows the generation of S-N curves for different values of mean stress based on fully reversed S-N behavior

  17. Stress-Life Fatigue Constant-life diagram for solution-treated and aged Ti-6Al-4V

  18. Stress-Life Fatigue Variable amplitude loading: Palmgren-Miner Rule: ΣNj/Nfj = 1

  19. Stress-Life Fatigue Variable amplitude loading: effect of periodic overstress into plastic region: Fatigue strength, no overstress Stress Amplitude Periodic overstress Nf = Cycles to Failure

  20. Strain-Life Fatigue • More than just substituting strain for stress in lifetime testing • Uses cyclic stress-strain curve to obtain strain versus life • Elastic and plastic strain considered separately, then summed • Considers plastic deformation that may occur in localized regions (instead of nominal stresses and stress concentration factors as in stress-life)

  21. Strain-Life Fatigue Most metals display metastable cyclic stress strain behavior when subjected to cyclic loading • Cyclic strain hardening • Cyclic strain softening

  22. Strain-Life Fatigue Cyclic Strain Hardening:

  23. Strain-Life Fatigue Cyclic Strain Softening

  24. Strain-Life Fatigue

  25. Strain-Life Fatigue

  26. Strain-Life Fatigue Find Elastic Portion of equation: σa = true stress amplitude2Nf = reversals to failure (1cycle = 2 reversals)σ'f = fatigue strength coefficientb = fatigue-strength exponent

  27. Strain-Life Fatigue Elastic portion of equation: Δεe = elastic component of cyclic strainE = elastic modulusσa = true stress amplitude2Nf = reversals to failureσ'f = fatigue-strength coefficientb = fatigue-strength exponent

  28. Strain-Life Fatigue Determine plastic side of equation: Power law plastic strain-life relation established by Coffin and Manson independently in the 1950s: Δεp = plastic component of cyclic strainε'f = fatigue ductility coefficient 2Nf = reversals to failure c = fatigue-ductility exponent

  29. Strain-Life Fatigue Coffin-Manson relation for strain-life fatigue

  30. Strain-Life Fatigue

  31. Strain-Life Fatigue Mean Stress/Strain Effects: Similar approach as with stress-life fatigue Allows generation of εa versus Nf at varying mean stress

  32. Component Testing • Component fatigue testing is S-N or ε-N fatigue testing of many exemplar components to failure in order to determine/validate fatigue properties • For implantable medical devices, commonly use component fatigue testing to validate design • Advantage of component testing for medical devices is use of actual geometry, surface conditions, residual stresses • Component fatigue testing relies on principles of S-N and ε-N fatigue analysis • Medical device component fatigue validation also relies on finite element analysis to determine stresses and strains

  33. Component Testing Examples of component fatigue testing: • ASTM F 382, Annex A2 – Standard Test Method for Determining the Bending Fatigue Properties of Metallic Bone Plates • Used as a means to characterize different bone plates • Cardiovascular implant testing – S-N • Cardiovascular implant durability testing – 400 to 600 million cycles, pass/fail • Note: pass/fail testing to 400 or 600 million cycles (10 years of life) does not characterize fatigue performance, safety factor or margin

  34. Component Testing Example of Component Testing Process: Vascular Implant • Conduct deflection-life testing of device (includes finished surface conditions, sterilization, expansion, etc.) • Generate deflection-life curve • Use finite element (FE) analysis to convert deflections (or loads) to stress and strain • Generate S-N or ε-N curve • Conduct statistical analysis of data, typically generate 1st percentile, 95% confidence line • If mean stress/strain variation is a concern, generate Goodman-type relation • Conduct FE analysis of stresses or strains on device for conservative in-vivo condition, compare with fatigue performance to validate design

  35. Component Testing

  36. Fatigue Crack Growth • Damage tolerant design method • Analysis of growing cracks based on linear elastic fracture mechanics • Assume a structural component contains cracks, all smaller than the minimum detectable length (ad) • Ensure insufficient stress to cause minimum detectable crack to grow (fatigue threshold, ΔKth approach), or insufficient cycles to grow crack to critical length for fracture (ac) over lifetime • Aircraft, nuclear industries use approach where inspection intervals are much shorter than time required to grow from ad to ac.

  37. ac Crack length, a da/dN ad Cycles, N Fatigue Crack Growth Fatigue crack growth under constant amplitude loading:

  38. Fatigue Crack Growth Apply linear-elastic fracture mechanics to crack growth (Paul Paris – 1960s, from Boeing) General form: Apply to fatigue use stress range, Δσ: Units are ksi(in)1/2 or Mpa(m)1/2

  39. Fatigue Crack Growth

  40. Fatigue Crack Growth • Fatigue Crack Growth Regions: • Fatigue threshold region: ΔKth is the fatigue threshold, the asymptotic value of ΔK at which da/dN approaches zero • Power law region: da/dN = C(ΔK)m, where c=constant, m=slope • Near- ΔKIC region: static fracture mechanisms become intermixed with fatigue crack growth, growth rate departs from linear, power-law behavior

  41. R= -1/2 R=0 R=1/2 da/dN R= -1 ΔK Fatigue Crack Growth Effect of mean stress on fatigue crack growth (typically described as the R ratio, σmin/σmax): Note: compressive stress does not contribute to crack growth except in very ductile materials –crack closure effects

  42. 10 example ΔKth 1 0 1 Fatigue Crack Growth Effects of stress ratio (R) on ΔKth: ΔKth is highest near R=O, typical ΔKth values range from 1 to 15 ksi(in)1/2 R

  43. Fatigue Crack Growth Limitations of da/dN technique for medical devices: • Plasticity: if plastic zone ahead of crack is very large compared to specimen or component thickness, linear-elastic fracture mechanics may not apply. Given small sizes of many devices, needs to be examined. • Minimum detectable crack/flaw size for ΔKth may be impractical/too costly to detect • Small crack behavior: if a crack is sufficiently small, it can interact with the microstructure and grow faster than predicted by da/dN versus ΔK

  44. Fatigue Crack Growth Small v. Short cracks: • Small cracks have dimensions on the microstructural scale – e.g. grain size • Short cracks have one dimension that is large compared to the microstructure

  45. Fatigue Crack Growth Small crack da/dN v. ΔK behavior:

  46. Statistics in Fatigue “There are three kinds of lies: lies, damned lies and statistics.”- Mark Twain • Statistics are important! • Durability testing statistics are easy, testing involving cycles-to-failure requires more sophistication • Fatigue testing (to failure) is well known for significant data scatter • Statistics should be used to ensure results are significant with confidence

  47. Statistical Analysis of Test Data • Characterization of strain-life or stress-life relationship • Choice of parametric regression model • Evaluation of goodness-of-fit • Estimates and confidence bounds • Robustness of conclusions • Run-outs (specimens surviving to end of test) • Treat as censored failure times using maximum likelihood methods • Do not ignore or count as failures

  48. Statistical Regression Models • Common choices • Lognormal • Weibull • Gumbel (smallest extreme value) • Example—lognormal model: log(cycles) = a + b*log(strain) + error (a = intercept, b = slope)

  49. Checking Adequacy of Chosen Model • Residual=Difference between observed value and value predicted from model • Graphical methods • Probability plots of residuals • Goodness-of-fit statistics • Summary measures calculated from residuals

  50. Estimates and Confidence Bounds • Quantities of interest at design strain/stress • Median life • Percentile life (e.g., 5th) • Mean life • Confidence bounds express uncertainty associated with estimated fatigue life

More Related