1. Fracture, Fatigue, Corrosion and Failure Analysis of Medical Devices Health Canada, March 7, 2012 Brad James Ph.D., P.E. Exponent Failure Analysis

2. Outline Fracture Structure and bonding of materials Stress effects Fracture of cracked members Fracture mechanics applications for medical devices

3. Fracture – Structure and Bonding Crystal Structure Unit cell – the smallest grouping of atoms to form a repeatable lattice to form a particular, perfect crystal Seven types of unit cells: cubic, tetragonal, hexagonal, orthorhombic, monoclinic, triclinic

4. Fracture – Structure and Bonding Examples: different cubic unit cells Primitive cubicBody-centered cubicFace-centered cubic

5. Fracture – Structure and Bonding Crystal structure imperfections 1.Reduce strength in brittle materials 2.Allow “slip” (permanent deformation) in ductile metals Examples: Dislocations Grain boundaries Vacancies Inclusions

6. Fracture – Structure and Bonding Example: single crystal iron whiskers have relatively low numbers of imperfections Can observe tensile strengths up to E/20 (1,500 ksi)

7. Fracture – Structure and Bonding How do these imperfections affect strength? Brittle materials: imperfections allow for areas of weaker bonds (see force v. bond distance plot) Ductile materials: dislocations allow slip along planes (called slip planes), allow ductile flow of material under sufficient stress

8. Fracture – Structure and Bonding Dislocation slip: Occurs most easily on close-packed planes Forms slip bands – deformation concentrated by many dislocations along a slip plane

9. Fracture – Structure and Bonding

10. Slip bands:

11. Fracture – Stress Considerations Definitions: Tensile Stress σ1σ1 Shear Stress τ xy τ yx

12. Fracture – Stress Considerations General Rule Brittle fracture – governed by breaking bonds at imperfections, fracture plane is perpendicular to principal (maximum tensile) stress Ductile fracture – governed by dislocation motion, fracture plane is parallel to maximum shear stress

13. Fracture – Stress Considerations

15. Effect of notches –Brittle materials –Ductile materials

16. Fracture – Stress Considerations Brittle materials –“notch sensitive” Ductile materials –“Notch strengthening” –For a given cross section (equivalent d), addition of a notch increases the yield and ultimate strength Notch changes local stress state

17. Fracture – Stress Considerations Yield criteria – which allow the determination of yielding in complex stress states (such as von Mises or maximum shear stress criteria) explain why: τ y = (σ 1 - σ 3 )/2 (maximum shear stress criteria) As σ 3 increases, σ 1 needs to increase to cause yielding

18. Fracture – Stress Considerations Stress Concentration Consider semi- infinite plate with elliptical hole σ max = K t σ nominal K t = stress concentration

19. Fracture – Stress Considerations Inglis Solution K t =1+2(c/d) K t =1+2(c/ρ) 1/2  =radius  max =(1+2(c/ρ) 1/2 ) σ nominal Many different stress concentration factors for various geometries, excellent source for solutions is: Peterson’s Stress Concentration Factors, by Walter D. Pilkey, © 1997, John Wiley and Sons

20. Fracture – Stress Considerations Inglis Solution σ max = (1+2(c/ρ) 1/2 ) σ nominal What happens when notch becomes more crack like? ρ approaches zero, σ max approaches infinity Impossible! Therefore, for sharp cracks, stress concentration approach does not work!

21. Fracture – Stress Intensity Approach Stress intensity factor, K, characterizes the stress field ahead of a sharp crack Stress intensity approach is the basis for linear-elastic fracture mechanics (LEFM) Stress intensity, K, is used for members with cracks, not the same thing as stress concentration, K t !!

22. Fracture – Stress Intensity Approach General form for stress-intensity factor K = σ (πa) 1/2 f(a/w) where: σ=global stress a=crack length f(a/w)=geometric factor that depends upon remaining thickness and crack length Units: ksi(in) 1/2, MPa(m) 1/2

23. Fracture – Stress Intensity Approach Stress-intensity factor K, is dependent upon geometry, strain rate, temperature

24. Fracture – Stress Intensity Approach Plane strain = highly constrained condition, three- dimensional stress state Plane stress = less constrained condition, near surfaces and in thin, ductile sections, two- dimensional stress condition Plane StrainPlane Stress

25. Fracture – Stress Intensity Approach

26. Define critical stress intensity factor, K C, called “critical fracture toughness” K C is the critical value of K, below which, brittle fracture will not occur K C is independent of specimen size and geometry, therefore K C is a material property K C is the “worst case” (plane strain) fracture toughness

27. Fracture – Stress Intensity Approach

28. K C is often referred to as K IC – the critical fracture toughness in Mode I (crack opening) crack extension Three modes of crack extension:

29. Fracture – Stress Intensity Approach Flaw tolerant design: we can tolerate cracks or flaws in our structure as long as we do not allow them to develop stress intensity greater than the plane strain fracture toughness (K IC ) Need K IC fracture toughness values for design materials – determined by testing per ASTM E399 Need relationship for K as a function of crack length for pertinent geometries and stress: can be determined from various handbooks and software