Structural Performance

Question 1

What are stress concentrations?

Answer 1

• Stress concentration factors describe the stress vs position along a flaw / notch position. Often stress is inversly proportional to 1/sqrt(r).
• These stress concentrations assume elastic behaviour (flaw / notch will extend out elastically where stress and strain are linear).
• Failure starts here but it only will carry on when the local stress is higher than the yield stress.
• In reality, the local stress will become higher than yeild stress and will deform plastically, not elastically, redistributing the stress that would otherwise be in the elastic assumption, till it follows the curve again. We must consider this plastic zone.

Question 2

What is the Griffith approach and strain energy release rate equation?

Answer 2

Griffith approach:
* Takes a global energy balance approach.
* Considers energy required to create (2) new surfaces, which is the energy that opposes crack growth. This is the (γe and γp) surface energy per unit area, for both brittle and plastic materials and processes.
* ductile materials have both elastic and brittle work to do so they are tougher
* This energy is supplied by the release of the stored strain energy around the crack (this is the crack driving force).

Stain energy release rate equation:

Question 3

What is the stress intensity factor, K?

What are the equations?

Answer 3

• Describes the Local stress field at the crack-tip, using linear elastic theory. I.e. describes the stress concentration curve for a specific crack and describes the stresses and strains.
• It can be linked to the energy balance approach and Griffiths approach.
• Can be calculated for specimen dimensions and external loading conditions.
• Kc describes the critical stress intensity factor where the specimen will fracture.
• K1c describes the critical stress intesnity factor (fracture toughness) under mode 1 loading (opening mode), where most brittle failures are controlled by maximum opening load and will fracture this way.

Equations below:

Question 4

What assumptions must be made for stress intensity factor, K, to be valid?

Answer 4

• K is based on linear elastic fracture mechanics
• Assumes stress and strain are directly proportional
• As long as the K-dominated stress field is the main factor controlling failure events in the crack tip region, then its still mainly valid.
• Rule of thumb: plastic zone approx 1/50 th of crack length, uncracked ligaments, thickness in the sample, then its valid.

Question 5

What are the assumptions about Kcrit?

Answer 5

Kcrit is only constant when the material meets the thickness criterion (i.e. is sufficienctly thick to reach plane strain).

Thickness criterion:
* If material is thin, then Kcrit will not be constant. The material will be under plane stress (where strain is zero, as essentially the materials will have little to no strain before just failing). It will fail under shear stress at 45 degrees to the tensile loading.
* If the material is sufficiently thick, it will be under plane strain (essentially majority of the material is blocked by the material surrouding and can’t change lengths, so strain is zero, except the very edges where it will be plane stress). So you will have triaxial stresses and a flat failure in the centre.

Question 6

What are the five types of loading modes?

Answer 6

• Mode 1 - opening
• Mode 2 - Shearing
• Mode 3 - twisting (torsion)
• Mode 4 - Bending => unidirectional or reverse
• Mode 5 - Bending (off-axis rotation)

Question 7

Under torsion (mode 2 or 3) what are brittle and ductile failures?

Answer 7

Ductile Torsion Failures:
* We see necking
* Plane of failure is perpendicular to torsion

Brittle Torsion Failures:
* helical failure
* Little deformation
* Plane of failure is on the maximum opening stress plane (45 degrees)