Fracture, Toughness and Strength

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Fracture, Toughness and Strength

• by
• Gordon Williams

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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

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Griffith(1922)

• All bodies contain flaws
• Fracture is from these flaws
• Used Energy Release Rate (see later)
• Defined as G
• GgtGc, energy per unit of created surface area
  (J/m2)
• Gc is a basic material property

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Fig 1
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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

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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

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Compliance Method (Composites)
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Compliance Method (Composites)

• Initial Energy
• Work done on a ada,
• Final Energy
• Change in energyU1U2-U3 (Shaded area)
• ie

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Compliance Method (Composites)

• Compliance
• Hence

Energy release rate
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Compliance Method (Composites)

• Energy form

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Used in impact

• For DCB

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Experimental Method

• Measure C(a)
• Measure F at fracture Gc
• True for any form

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Compliance Method

• From Griffith Solution
• in General

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Plasticity and Size Effects

• Basic method is elastic (LEFM)
• All cracks have a local plastic/damage zone
• Let sc be the zone stress

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Plasticity and Size Effects

• Local stresses, (singular)
• (const., 2p
  can change)

• rr makes response non-linear,
• Must be within limits, e.g F5 , Fmax

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Plasticity and Size Effects

• Gc Kc are dependent on Constraint
• Lowest values are for Plane strain, ez0
• in the plastic zone, i.e. lateral constraint.
• Highest values are for Plane stress, sz0

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Plasticity and Size Effects
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Plasticity and Size Effects

• For b gtgt rr, ez0, plane strain
• For b rr, sz0, plane stress
• Transition

bltbc high value