failure of Materials 1 Brittle vs ductile + Griffiths

Question 1

What is the brittle and ductile behaviour seen on a Stress-Strain graph?

Answer 1

Brittle:
* Low % elongation to failure
* Often higher yield stress point
* Little plastic deformation (<5% elongation, we call a material brittle)

Ductile:
* High % elongation to failure
* Often lower yield stress point

Rember on a stress-strain graph we approximate work done to failure, by looking at the area under the curve. Higher work done means more ductile.

Question 2

Simply describe the appearance of a brittle and ductile fracture.

Answer 2

Brittle:
* Shows little to no sign of necking
* Brittle cleavage across the specimen

Ductile:
* Necks down, sometimes to a point
* More often gives a cup-cone appearance.

Question 3

Why do ductile materials often have a cup-cone fracture formation?

Answer 3

Cup-cone formation:
* Initial necking stress is concentrated in the neck region
* Small voids form around hard secondary particles (e.g. carbides in steel)
* Small voids coalesce to give an internal crack
* Remaining ligaments start to shear as internal crack grows by further void coalescence
* Final failure

Question 4

Describe the two types of brittle fractures that can form.

Answer 4

Intergranular cleavage:
* Crack propagates along the grain boundaries
* A much more 3D surface

Transgranular cleavage:
* Fracture cracks pass through the grains on particular cleavage planes.

Question 5

In three words or less, state these characteristics: brittle vs ductile:

• Fracture surface
• Deformation
• Crack propagation
• Type of failure

Answer 5

Question 6

Describe stress concentrations and how its measured.

Answer 6

• Somewhere in the material where stress is being amplified, such as voids or sudden changes in geometry in the material.
• Stress lines can’t go through voids, so stress deflects and we get peak stress regions, shown on the graph. This amplifies the stress at the edges of flaws.
• ‘a’ refers to the length of the flaw, ‘a’ is the length of an external flaw, so 2a is the length of an internal flaw.

Question 7

Describe how the parameters in this equation effects stress intensificaiton.

Answer 7

• The radius of the crack tip affects stress amplification, sharper means more likely to fail
• Longer bigger cracks will also make the flaw fail more.
• Usually assume we have a sharp crack.

Question 8

Simply describe the Griffith Approach

No need for the equations, or those factors

Answer 8

• By loading something up, elastically, we load energy into the material. We build elastic strain energy into the material.
• The reason a crack isn’t forming, we need to form a new surface to propagate a crack. As the middle has a stable and low-energy set-up.
• So Griffith realised the strain energy would propagate the crack when the energy is high enough to form a new surface, with higher energy.

Question 9

Try to state the Stored strain energy and Surface energy, and total energy equation.

Answer 9

• Stored strain energy equation (a is flaw size)
• Surface energy equation (2 is from the two surfaces when the surface splits, surface energy is based on surface size and area).
• Stored strain energy will drive the crack growth and surface energy will resist.

Question 10

When and where does crack growth occur, using the Griffith approach?

Answer 10

• Total energy is at a maximum at length (a)critical.
• Once (a) critical is reached, the crack growth will be sudden. This is because elastic energy is greater than or equal to surface energy.

Question 11

What is the equation for critical stress at fracture, using Griffith approach? Describe its relationship.

Answer 11

Note: This is really only for brittle materials, as ductile materials have much more stores and it still retains some elastic energy when stretching.