Fracture Toughness and Fracture Toughness-limited Design

Big bang for the buck!

What is Fracture Toughness??• Toughness is the resistance of a material to the

propagation of crack.• Assumes that a sample of material contains a

small sharp crack (i.e. so small it doesn’t really reduce the cross sectional area, = P/A).

• FRACTURE TOUGHNESS, K1c, is the key material property!!

• Fracture toughness, K1c, is measured in the lab using compact fracture specimens – see samples.

Fracture Toughness versus Strength:

• Strength is resistance to plastic flow and thus is related to the stress required to move dislocations through the solid. The initial strength is called the yield strength. Strength generally increases with plastic strain because of work hardening, reaching a maximum at the tensile strength. The tensile strength is related to the strength of atomic bonds.

• Toughness is the resistance of a material to the propagation of a crack. A material with low fracture toughness, if it contains a crack, may fail before it yields. A tough material will yield, work harden even when cracked – the crack makes no significant difference.

What happens to a material with a small crack?

Yields then work hardens, absorb energy and redistribute stress. In other words, crack makes no significant difference!

Get high stress around crack, crack propogates and get sudden failure. Stress around crack is high due to Kt , but nominal stress is much lower than material yield strength!

What happens when you nick a brittle material??

A plastic zone forms at the crack tip where the stress would otherwise exceed the yield strength σy.

Ductile Fracture:

Stages of ductile fracture:

b. Plastic def’m when stress exceeds yield.

c. Weaken and fail locally due to inclusions which act as stress concentrations – this creates tiny voids.

Voids continue to grow and coalesce to form larger voids.

d. Remaining area gets smaller increasing stress until tensile strength is exceeded then fracture.

Motivation for Fracture Mechanics• Very hard (if not impossible) to build a structure that is

defect free (completely without cracks).– Cracks already in material (inclusions or voids).– Cracks caused by shrinkage in castings and welding.– Cracks caused by machining.– Cracks caused by cyclic loading (fatigue).– Cracks caused by corrosion.

• Are we all doomed to mega disasters???• KEY – DAMAGE TOLERANT DESIGN – THE

MATERIAL MUST HAVE SUFFICIENT FRACTURE TOUGHNESS SO A NOTICEABLE CRACK CAN BE DETECTED BEFORE FAILURE. THIS IS THE BASES OF DAMAGE TOLERANT DESIGN – EXTREMELY IMPORTANT FOR AERSOPACE INDUSTRY.

Brittle Behavior Causes:

• Boilers to burst• Bridges to collapse• Aircraft to crash• Pipes to split• CATASTROPHIC FAILURES

(a) The tear test. (b) The impact test. Both are used as acceptance tests and forquality control, but neither measures a true material property (one that is

independent of size and shape).

Tests for Toughness:

To get at the real, underlying material properties we need the ideas of stress intensity and fracture toughness!!

The Mechanics of Fracture

Lines of force in a cracked body under load; the local stress is proportional tothe number of lines per unit length, increasing steeply as the crack tip is

approached.

Far from the crack where r >> c, the local stress falls to the value of s.

Near the crack r << c, the local stress rises sharply as:

The Mechanics of Fracture

So, for a given value of r, the local stress scales as

Which there fore is a measure of the intensity of the local stress.

This quantity is called the mode 1 stress intensity factor (the ‘mode 1’ means tensile fracture and is given the symbol K1.

Again, Failure when:

Failure stress at which fracture will occur. For small cracks, failure will be yield not fracture – check both!!!!

Transition fro failure due to fracture vs failure due to yield will occur at ccrit. Cracks < ccrit will yield

Cracks > ccrit will fracture

Think!

Failure by fracture

Failure by yield

Summary:

Measuring fracture toughness, K1c. Two test configurationsare shown here. Again, fracture toughness is a material property not to be confused with impact.

How to measure fracture toughness, K1c

A chart of fracture toughness Klc and modulus E.The contours show the toughness, Gc.

A chart of fracture toughness K1c and yield strength σy.The contours show the transition crack size, ccrit.

Damage-tolerant Design

FUNCTION AND CONSTRAINTS MAXIMISE [1]

TIES (tensile member)

Maximize flaw tolerance and strength, load-controlled design KIC and σf

Maximize flaw tolerance and strength, displacement-control KIC / E and σf

Maximize flaw tolerance and strength, energy-control KIC2 / E and σf

SHAFTS (loaded in torsion)

Maximize flaw tolerance and strength, load-controlled design KIC and σf

Maximize flaw tolerance and strength, displacement-control KIC / E and σf

Maximize flaw tolerance and strength, energy-control KIC2 / E and σf

BEAMS (loaded in bending)

Maximize flaw tolerance and strength, load-controlled design KIC and σf

Maximize flaw tolerance and strength, displacement-control KIC / E and σf

Maximize flaw tolerance and strength, energy-control KIC2 / E and σf

PRESSURE VESSEL

Yield-before-break KIC / σf

Leak-before-break KIC2 / σf

1.KIC = fracture toughness; E = Young's modulus; σf = failure strength (the yield strength for metals and ductile polymers, the tensile strength for ceramics,

glasses and brittle polymers loaded in tension; the flexural strength or modulus of rupture for materials loaded in bending).