1.2 Griffith Energy Balance and Equations

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Last updated 10:02 PM on 4/22/26
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21 Terms

1
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Concept of Griffith energy balance

  • crack from when total energy decreases or remain constant

  • Surface energy: energy input to create new crack surface→ if this is dominating, fracture is delayed, as energy is used to create new cracks

  • Elastic strain energy: energy released when bond breaks/crack grows→ if this is dominating, shows that crack propagates

<ul><li><p>crack from when total energy decreases or remain constant</p></li><li><p>Surface energy: energy input to create new crack surface→ if this is dominating, fracture is delayed, as energy is used to create new cracks</p></li><li><p>Elastic strain energy: energy released when bond breaks/crack grows→ if this is dominating, shows that crack propagates</p></li></ul><p></p>
2
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Equation for internal surface and elastic strain energy

<p></p>
3
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Derivation of critical crack stress and length

Steps

  1. find total energy

  2. find dU/da=0

  • γ found experimentally for brittle materials

critical crack strength for material that exhibit plasticity

*after finding a value, internal crack length would be 2a

<p>Steps</p><ol><li><p>find total energy</p></li><li><p>find dU/da=0</p></li></ol><ul><li><p>γ found experimentally for brittle materials</p></li></ul><p>critical crack strength for material that exhibit plasticity</p><p>*after finding a value, internal crack length would be 2a</p><p></p>
4
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Material limitations of Griffith energy balance

only used for brittle material

metals cannot be used as…

  • has plasticity

  • energy used for plastic deformation (γp) and not purely for surface energy(γs)

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Reason for fracture

  • energy instability NOT stress

6
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Definition of stress concentration factor

ratio of maximum local stress and applied stress

<p>ratio of maximum local stress and applied stress</p>
7
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Formula for maximum local stress for brittle materials

σ_m refers to local stress tip=/= fracture strength

<p>σ_m refers to local stress tip=/= fracture strength</p>
8
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Equation for strain energy release rate G + fracture strength in terms of critical G_c

  • G_c can be back calculated after finding fracture stress

<ul><li><p>G_c can be back calculated after finding fracture stress</p></li></ul><p></p>
9
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Relationship of G_c with crack propagation

  • when critical rate occur, crack grows spontaneously (G>G_c)

  • higher Gc → higher ability for material to resist cracks

10
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Definition and equation of stress intensity factor

correlates to fracture toughness

<p>correlates to fracture toughness</p>
11
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Relationship of K_I and G

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Type of modes for fracture toughness

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Reason Mode I is the critical

  • produce max. crack opening

  • give highest energy release rate G

  • material weakest in tension

<ul><li><p>produce max. crack opening</p></li><li><p>give highest energy release rate G</p></li><li><p>material weakest in tension</p></li></ul><p></p>
14
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How twinning affect toughness and type of failure?

Dominant twinning:

  • similar deformation of planes

  • more limited plasticity

  • higher risk of brittle fracture

<p>Dominant twinning:</p><ul><li><p>similar deformation of planes</p></li></ul><ul><li><p>more limited plasticity</p></li><li><p>higher risk of brittle fracture</p></li></ul><p></p>
15
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How slip affect toughness and type of failure?

  • variation of deformation

  • more plasticity

  • higher fracture toughness

<p></p><ul><li><p>variation of deformation</p></li></ul><ul><li><p>more plasticity</p></li><li><p>higher fracture toughness</p></li></ul><p></p>
16
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Types of strengthening mechanism

  1. grain size reduction

  2. strain hardening, cold working

  3. solid solution strengthening

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Mechanism of grain size reduction

  • more grain boundaries block movement→less plane for deformation

  • strength increases

<ul><li><p>more grain boundaries block movement→less plane for deformation</p></li><li><p>strength increases</p></li></ul><p></p>
18
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Mechanism of dislocation

Distortion in crystal lattice

movement of dislocation produces plastic deformation (slip) where dislocation travels along a plane

19
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Mechanism or strain hardening(normal condition) or cold working (cold condition)

  • stress acts on material that can plastically deform

  • exisiting dislocation moves and new dislocation forms within lattice

  • increased number of dislocation causes them to interact and become pinned/tangled

  • lower mobility of dislocation which strengthen material and reduce ductility

<ul><li><p>stress acts on material that can plastically deform</p></li><li><p>exisiting dislocation moves and new dislocation forms within lattice</p></li><li><p>increased number of dislocation causes them to interact and become pinned/tangled</p></li><li><p>lower mobility of dislocation which strengthen material and reduce ductility</p></li></ul><p></p>
20
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Mechanism of solid solution strengthening

  • impurities atoms of different size creates dislocation

  • higher stress to deform

<ul><li><p>impurities atoms of different size creates dislocation</p></li><li><p>higher stress to deform</p></li></ul><p></p>
21
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Difference between strength and toughness

strength: resistance to plastic deformation

governed by yield stress and UTS

  • control yielding

  • dislocation

  • uniform properties

toughness: resistance to crack growth

governed by stress intentisty factor and energy release rate

  • control fracture

  • crack-tip processes

  • crack-size dependent