Fracture mechanics - structure of Materials

2. CONTENTS
• Introduction
• Modes Of Crack Surface Displacement
• Types of Fracture
• Linear Elastic Fracture
• Nonlinear Elasticity & Plasticity
• Design Philosophies
• Influence Of Fracture in Aircraft Design
• Environmental Effects
• Reference

3. Introduction
• It is the field of mechanics concerned with the study of the
propagation of cracks in materials.
• It uses methods of analytical solid mechanics to calculate the
driving force on a crack and those of experimental solid
mechanics to characterize the material's resistance to
fracture.

4. Modes of Crack Surface Displacement
Opening mode - Tensile stress is applied normal to
the plane of the crack.
Sliding mode - shear stress acts parallel to the plane
of the crack and perpendicular to the crack front.
Tearing mode - shear stress acts parallel to the plane
of the crack and parallel to the crack front.

5. CLASSIFICATION
Fracture
Brittle
Ductile

6. BRITTLE FRACTURE
• Brittle Fracture is the sudden, very rapid cracking of material under
stress where the material exhibited little or no evidence of ductility
or plastic degradation before the fracture occurs.

7. DUCTILE FRACTURE
• Ductile fracture is a type of fracture characterized by extensive
deformation of plastic or "necking.

8. Plasticity
• Most engineering materials show some nonlinear elastic
and inelastic behavior under operating conditions that
involve large loads.
• The size and shape of the plastic zone may change as the
applied load is increased and also as the crack length
increases.

9. Linear Elastic Fracture - Griffith’s Criterion
• Assuming E = 62 GPa, γ = 1 J/m2
E - Young's modulus of the material
γ - Surface energy density of the material
• These values gave excellent agreement of Griffith's predicted
fracture stress with experimental results for glass.

10. Irwin’s Modification
• Griffith's theory - Brittle materials
• Irwin's strategy was to partition the energy into two parts
• The Stored elastic strain energy which is released as a crack
grows.
• The Dissipated energy which includes plastic dissipation and the
surface energy provides the thermodynamic resistance to
fracture.
γ - Surface energy
Gp - Plastic dissipation per unit area of crack growth.
• Total energy

11. Environmental Effects
Stress Corrosion Cracking
• The traditional measure of stress corrosion is based on
the time-to-failure of effect of environment on crack
initiation and the slow growth of subsequent cracks.

12. Simulation of a Crack by FEA
• The use of Fracture mechanics techniques in
performance assessment and structure reliability has
increased, So the prediction of crack propagation is
crucial.
• Finite element method is a numerical technique to solve
problems with acceptable accuracy.

13. Influence Of Fracture in Aircraft Design
In conventional aircraft structural design, the following terms are
employed frequently
• Limit load (stress) is the maximum load expected in
operational service specifications and represents that value for
which the probability of exceeding that load is very small
• Ultimate load (stress) is the limit load times the factor of
safety, specifications usually require that the structure be
capable of sustaining ultimate load, as defined structure
collapse just beyond ultimate is accepted
• Factor of safety is the multiplying factor to convert limit load
to ultimate load practice is to employ a factor of safety
(ultimate of 1.5).

14. Design philosophies
• Fatigue or structural damage can be expected
during the operational life of aircraft or
spacecraft structures.
• "Fail Safe" philosophy (damage tolerant concept)
• "Safe Life" concept

15. Methods of Material Fracture Comparison
• In materials trade-off studies, it would be helpful if a
comparison based on weight could be made. For example, a
trade-off between weight, yield strength, and fracture
toughness (plane strain).
• Effective Or Equivalent Crack Length
• Crack Geometries

16. Reference
• Fracture Mechanics Guidelines for Aircraft Structural
Applications - D. P. WILHEM, Northrop Corporation,
Hatvthorne, California.
• Physical Metallurgy – K.M. Harris, CBS Publishers and
Distributors, Edition – 2016.