Domain

Explanation

Material failure

• Failure to reach or maintain ultimate performance, load / stress
• Types:

1. Yielding: permanent deformation
2. Creep: elongation(t)
3. Rupture
4. Aging (polymers)
5. Corrosion (material loss)
6. Fatigue: cyclic load/unload
7. Fracture: crack initiation, propagation, growth & failure

• S

Fracture

• Started: 60’s due to Timoshenko, Griffith’s & George Irwin
• Assumption: Cracks always present due to imperfections in geometry, material & stress concentrations (residual stress)
• Approach atomic level physics-engineering: atomic bond breaking – theoretical strength with analytical & experiment
• Major guiding concepts:

1. Griffith’s Energy Release Concept (’50s)
2. George Irwin’s stress intensity factor, energy release rate

• Modes: I-perpendicular (easiest crack growth), II-shear, III-torsion
• A typical course & Tutorial

Griffith criterion

• For cracks to grow, set criterion with energy concept
• COE: energy input = absorbed strain energy + crack growth energy
• Find the critical load & displacement (constant or varying) that meets the Energy Balance criterion
• s = K_I / + O(1) = (singular) + (non-singular) components, where x is the displacement from the crack tip – thus at x® 0, s ® ¥ (wrong, since s _max<=s _ult in plasticity)
• Issues:

1. K-dominance: s.t. non-singular component can be neglected

• d

George Irwin

• Max. stress criterion with s _max
• Fracture toughness: low if brittle
• Issues:

1. Crack growth direction, especially in mixed-mode fracture
2. Crack propagation: straight-curved, tunneling effect
3. Strain energy density: explanation to cracking only at MIN strain energy density

• sd

Calculation of energy release rate, G

• From the uncracked to cracked state
• 3 methods:

1. Griffith’s energy concept: G=K_I²/E (plane stress) & =K_I²(1-n ²)/E (plane strain)
2. J-integral: Jim Rice – Gauss theorem
3. Using FEM to model

• Sd

Plane problem

• Simplification into plane problems because of singularity
• Approximation:

1. At crack tip: use plane strain
2. Away from crack tip: use plane stress

• Plastic zones around crack tip: different for plane problems
• Issues:

1. Elastic confinement of plastic zones: increase strength, lower crack growth
2. Crack linkage: between large & small cracks – when small crack meets large crack, the larger plastic zone of big crack lower resistance to small crack – higher small crack growth
3. Boundary layer: close to free edge, s drops to zero – needs model

• General strain equation: e = s _zz / [n .(s _xx + s _yy)]

1. e =1: plane strain
2. e =0: plane stress s _zz=0

Sun’s comments

• Jokes lighten, refresh & enlighten
• Humility & praise softens & awakens
• Small country merging into big one ~ small crack propagating into the plastic zones of large ones: crack linkage where the small is the criteria to growth propagation