##  [Griffith Fracture Criterion](/griffith-fracture-criterion-0) 

 Definition

An energy‑balance fracture criterion stating that a crack will propagate when the elastic energy released per unit new crack surface area (the energy release rate G) equals or exceeds the material’s critical energy release rate Gc; in linear elastic brittle solids Gc is often approximated by twice the surface energy, but Gc more generally includes all dissipation in the process zone.

 

 

 

 

 

 





## Principle

Principle

Crack extension is controlled by a comparison of available elastic strain energy release (G) with the energetic cost of creating fracture process zone and surfaces (Gc); propagation occurs whenever G ≥ Gc under the applicable mechanical assumptions.

 

 

 

 

 





## Demonstration

Demonstration

Illustrative scenario → A pre‑cracked brittle plate under increasing tensile remote stress: compute G from applied stress and crack length (or via stress intensity factor K where G ∝ K^2/E) → When the computed G reaches the independently measured Gc the crack runs unstably and extends across the plate, demonstrating energy balance control of propagation in the linear elastic regime.

 

 

 

 

## Misapplication

Misapplication

Applying the Griffith criterion without accounting for inelastic dissipation (plasticity, frictional sliding, phase transformation) and thereby equating Gc with simple surface energy in ductile or tough materials; the semantic error is treating the original brittle energy balance as a universal stress threshold rather than a criterion whose resistance term must include all relevant dissipation mechanisms.

 

 

 

 

 





## Consequence

Consequence

In appropriate brittle, linear‑elastic contexts the criterion provides a physically grounded threshold for crack growth and justifies fracture‑toughness testing (Gc or Kc); misapplication (ignoring inelastic dissipation or scale effects) leads to under‑ or overestimation of load‑carrying capacity and unsafe or overly conservative designs.

 

 

 

 

## Reversal

Reversal

When fracture involves significant inelasticity in a process zone (large‑scale yielding) or when time‑dependent dissipation occurs, the simple Griffith form must be replaced or augmented by fracture parameters that include plastic work (e.g., J‑integral, R‑curves) or by cohesive/process‑zone models that incorporate nonelastic energy absorption.

 

 

 

 

 





## Boundary

Boundary

Clearly within: brittle, linear‑elastic solids with small process zones relative to crack dimensions and where surface creation dominates dissipation. Boundary case: materials exhibiting modest process‑zone plasticity where Gc includes both surface energy and plastic work. Clearly outside: ductile fracture regimes dominated by extensive plasticity, rate‑dependent or environmental crack growth where additional physics control propagation.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Energy‑based fracture criterion (Griffith/G) ↔ stress‑intensity or local stress‑based views (K‑field, local microstructural failure criteria); both perspectives are linked but emphasize different measurable resistances and scales.

 

 

 

 

 





## Synthesis

Synthesis

Griffith’s insight converts crack stability into an energy accounting problem: it gives a principled threshold for brittle crack growth and establishes the conceptual foundation of fracture mechanics, while practical application requires extending the resistance term to include all process‑zone dissipation when materials are not ideally brittle.