1: Brittle Fracture Mechanics

Introduction to Brittle Fracture Mechanics

• Previous modules covered metals and polymers, emphasizing ductility (plastic deformation prior to failure).
• Brittle materials (glasses, ceramics) do not exhibit plastic deformation; they deform elastically before fracturing.

Stress-Strain Behavior of Brittle Materials

• Brittle materials have a straight line elastic stress-strain curve until fracture occurs.
• Once failure starts, crack propagation is rapid and catastrophic, contrasting with ductile materials (e.g., metals) that show slow crack growth and plastic deformation prior to fracture.

Ductile vs. Brittle Fracture

Ductile Fracture

• Characterized by plastic deformation before failure.
• Involves void nucleation and coalescence (small voids in the material grow and link, leading to fracture).
• Energy absorption during plastic deformation reduces the energy required to fracture.

Brittle Fracture

• No significant plastic deformation occurs before fracture.
• Crack propagation can lead to sudden failure without warning.

Factors Influencing Brittle Fracture in Metals

• Metals can exhibit brittle behavior depending on several factors:
  • Material Structure: Body-centered cubic (BCC) and hexagonal close-packed (HCP) structures are more prone to brittle fractures compared to face-centered cubic (FCC) metals.
  • Temperature: Lower temperatures can lead to brittle fractures (ductile to brittle transition temperature, or DBTT). BCC metals are particularly susceptible to DBTT.
  • Strain Rate: Higher strain rates increase the likelihood of brittle fractures.
  • Stress Conditions: Triaxial stress states (three non-zero principal stresses) can lead to brittle failure. Notch and crack tips often exhibit these stress states.

Griffith Brittle Fracture Theory

• Involves energy balance between stored elastic strain energy and energy required to create new crack surfaces.
  • Crack growth occurs when released energy exceeds the energy needed to create new surfaces.
  • Condition for fast fracture: \Delta U{elastic} \geq \Delta U{crack} (energy released must equal or exceed energy consumed).

Center Crack in Thin Plate Model

• Configuration: Griffith's analysis involves a center crack in a thin plate.
• Energy for New Surfaces: Given by g_c t \Delta a where:
  • \Delta a is the change in crack length (original length 2a ).
  • t is the plate thickness.
  • g_c is the energy required to create new crack surfaces.

Energy Considerations

• In brittle fractures:
  • Energy required to create new surfaces is equal to two times the material's surface energy ( 2 \Delta s ).
• In ductile fractures:
  • Energy is influenced by plastic dissipation ( g_p ) and is typically larger than surface energy component.

Strain Energy Release Rate

• Strain Energy Release Rate ( g_c ) measures material's resistance to fracture:
  • gc = \frac{\sigmac^2}{E} \cdot \frac{1}{\pi a}
  • \sigma_c is the critical stress at which material fractures (not a true material property).
• Distinct Terms: gc is not the same as fracture toughness ( K{1c} ).

Critical Stress and Modes of Deformation

• Critical stress in a plane stress condition is indicated, while a plane strain condition modifies the equation by including Poisson's ratio.
• Understanding these conditions is vital for analyzing fracture toughness, setting the stage for further study.

Conclusion

• The introduction to brittle fracture mechanics underlines critical distinctions between ductile and brittle behaviors, necessary theoretical foundations for assessing material fracture properties and their practical implications in engineering.
• Next discussions will expand on the relationship between strain energy release rate and fracture toughness metrics.