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Fracture, Toughness and Strength

Fracture, Toughness and Strength. by Gordon Williams. Introduction. Strength is not a material property For ductile materials we have flow and necking For brittle materials we have failure from flaws Surface polishing, a transition from brittle to ductile Griffith ideas. Griffith(1922).

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Fracture, Toughness and Strength

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  1. Fracture, Toughness and Strength by Gordon Williams

  2. Introduction • Strength is not a material property • For ductile materials we have flow and necking • For brittle materials we have failure from flaws • Surface polishing, a transition from brittle to ductile • Griffith ideas

  3. Griffith(1922) • All bodies contain flaws • Fracture is from these flaws • Used “Energy Release Rate” (see later) • Defined as “G” • G>Gc, energy per unit of created surface area (J/m^2) • Gc is a basic material property

  4. s 2a H W b Fig 1

  5. Griffith • at fracture • In general, • Y2 is a geometric factor, Y2= p for an infinite plate • To find Gc vary a, measure s, calculate Y2 hence EGc • From E find Gc

  6. Griffith • From E find Gc • If only stresses needed use Kc • Gc preferred , better physics • The strength problem • “a” exists, flaws, hence s is determined

  7. F F d F+dF F C(a+da) a da C d b o d d+dd Compliance Method (Composites)

  8. Compliance Method (Composites) Initial Energy: Work done on a a+da, Final Energy: Change in energy=U1+U2-U3 (Shaded area) ie

  9. Compliance Method (Composites) Compliance: Hence Energy release rate

  10. Compliance Method (Composites) • Energy form:

  11. F b d h h a Used in impact For DCB

  12. Experimental Method • Measure C(a) • Measure F at fracture Gc • True for any form

  13. Compliance Method From Griffith Solution in General

  14. rr sx r a Plasticity and Size Effects • Basic method is elastic (LEFM) • All cracks have a local plastic/damage zone • Let sc be the zone stress

  15. Plasticity and Size Effects • Local stresses, (singular) • (const., 2p can change) • rr makes response non-linear, • Must be within limits, e.g F5% , Fmax

  16. Plasticity and Size Effects • Gc & Kc are dependent on Constraint • Lowest values are for Plane strain,ez=0 in the plastic zone, i.e. lateral constraint. • Highest values are for Plane stress, sz=0

  17. Plane stress Kc z b Plane strain rb bc Plasticity and Size Effects

  18. Plasticity and Size Effects • Forb >> rr, ez=0, plane strain • For b≈ rr, sz=0, plane stress Transition: b<bc high value

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