Fundamentals of Fracture Mechanics

Failure of Engineering Materials

• Improper material selection 
• Material processing (impurities, defects)
• Inadequate design of components
• Misuse 

Failure (or fracture) in materials is of 2 types:

1. Ductile Fracture  ⇔  accompanied by significant plastic deformation, showing necking behavior.
2. Brittle Fracture  ⇔  little (or no) plastic deformation, catastrophic (or instantaneous) failure.

Classification of Failure

Failure is further divided into following types depending on percentage elongation (%EL).

1. Very Ductile  ⇔  if  %EL > 20%, which can be converted into wires (like gold, etc.)
2. Moderately Ductile  ⇔  if  20% < %EL < 5%, almost all metals.
3. Brittle  ⇔  if  %EL < 5%, flat deformation.

Failure is further divided into following depending on crack propagation.

1. Trans-Granular Fracture  ⇔  If crack propagates within the grains. If plane is weak, crack propagates through grains.
2. Intra-Granular Fracture  ⇔  If crack propagates through the boundary of grains, since boundary is amorphous (weak).

Engineering Fracture Design

Stress concentration increases with the increase in sharpness of edges (so avoid cornering in design), means your corner should have larger fillet radius.

• If difference between width 'W' and height 'h' is higher  ↠  convergence of stress line is greater, so higher stress concentration.
• Cracks having sharp tips propagate easier than cracks having blunt tips.
• If you see crack  ↠  stop it by punching it to decrease convergence, stress concentration decreases.
• Elastic Strain Energy  ↠  energy stored in material as it is elastically deformed.

Critical Energy

Crack propagates if crack tip stresses (σm) exceeds a critical stress (σc).

•  For ductile material  ↠  replace (γS) with (γs + γp), where γp = plastic deformation energy.

Fracture Toughness

It is defined as, "ability of a material to resist fracture".

• Stress Intensity Factor, K  ↠  defines the beginning of thin crack in a material grows.
• If K is greater (like of metals) ↠ toughness is greater ↠ greater resistance to crack propagation.
• With the increase in carbon content, toughness increases and impact energy decreases.
• FCC, HCP metals  ↠  survive at larger impact energy.
• With the increase in temperature, ductility increases. At low temperature, material behaves in a brittle way.

Fatigue and It's Behavior 

It is defined as, "failure under applied cyclic stress".

• Can cause part failure  ↠  when σmax < σy. 
• responsible for 90% machine failure.   
• Stress varies with time, amplitude (S), σm and cyclic frequency.
• No fatigue if S < Sfat (Fatigue limit)
• For steel (ferrous metals), fatigue limits are 35-60% of tensile strength.
• Most non-ferrous metals (like Al, Cu, Mg) has no fatigue limit.

Improving Fatigue Life

1. Impose compressive surface stress (to suppress surface cracks from growing).
2. Shot peening  ↠  plastically deform the surface.
3. Carburizing  ↠  diffusion of carbon-rich gas into a surface and get in interstices.
4. Remove stress concentrators  ↠  by making corners fillet.

Creep 

It is a tendency of a material to fail or deform permanently under the presence of mechanical stresses.

• Strain rate increases with increasing temperature, stress.

Creep Rupture Life

• It predicts the life of material and how much a material survive at particular temperature.
• Very effective like When to change turbine blades?
• With the decrease in temperature, life increases.
• 2nd or Indentation method  ↠  used to find properties of material without any experiment but have errors.

Note: Turbine blade creep for understanding creep phenomena.

References:

• Material from Class Lectures + Book named Materials Science and Engineering: An Introduction by Callister and Rethwick + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube.