Lab 6B -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, s = P/A).

• FRACTURE TOUGHNESS, K 1c , is the key material property !!

• Fracture toughness, K 1c , 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

propagation

is the resistance of a material to the 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?

What happens when you nick a brittle material??

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!

Ductile Fracture: A plastic zone forms at the crack tip where the stress would otherwise exceed the yield strength

σ

y .

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

Tests for Toughness: (a) The tear test. (b) The impact test. Both are used as acceptance tests and for quality control,

but neither measures a true material property (one that is independent of size and shape)

.

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 to the number of lines per unit length, increasing steeply as the crack tip is approached.

s

local

 s    1 

Y



c

2 

r

   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: s

local



Y

s 

c

2 

r

The Mechanics of Fracture

s

local



Y

s 

c

2 

r

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

c

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 K 1 .

K

1 

Y

s 

c

The Mechanics of Fracture

K

1 

Y

s 

c

Constant depending on geometry/loading Average stress (i.e. away from crack) = mode 1 stress intensity factor Crack size

Failure when K

1

= K

1c

where K

1c

is a material property called fracture toughness.

The Mechanics of Fracture

K

1 

Y

s 

c

Constant depending on geometry/loading Average stress (i.e. away from crack) = mode 1 stress intensity factor Crack size

Failure when K

1

= K

1c

where K

1c

is a material property called fracture toughness.

K

1  s 

c

Mode 1 Stress intensities K 1 In all cases, c << w.

associated with short cracks.

K

1  1 .

1 s 

c K

1 

p



c K

1 

FL

3

bw

2 

c K

1  0 .

7 s Internal penny shaped crack 

c

Again, Failure when:

K

1 

Y

s 

c



K

1

c

s

f



K

1

c



c

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

c crit



K

2 1

c

s 2

y

Transition fro failure due to fracture vs failure due to yield will occur at c crit . Cracks < c crit will yield Cracks > c crit will fracture Think!

Failure by yield Failure by fracture

c crit



K

2 1

c

s 2

y

Summary:

How to measure fracture toughness, K 1c Measuring fracture toughness,

K

1c . Two test configurations are shown here. Again, fracture toughness is a material property not to be confused with impact.

A chart of fracture toughness

K

lc and modulus

E

.

The contours show the toughness,

G

c .

A chart of fracture toughness

K

1c and yield strength

σ

y .

The contours show the transition crack size, c crit .

Damage-tolerant Design

FUNCTION AND CONSTRAINTS TIES (tensile member) Maximize flaw tolerance and strength, load-controlled design Maximize flaw tolerance and strength, displacement-control Maximize flaw tolerance and strength, energy-control SHAFTS (loaded in torsion) Maximize flaw tolerance and strength, load-controlled design Maximize flaw tolerance and strength, displacement-control Maximize flaw tolerance and strength, energy-control BEAMS (loaded in bending) Maximize flaw tolerance and strength, load-controlled design Maximize flaw tolerance and strength, displacement-control Maximize flaw tolerance and strength, energy-control PRESSURE VESSEL Yield-before-break Leak-before-break MAXIMISE K K K K K K K K K IC IC IC IC IC IC IC IC IC 2 2 2 and σ / E and σ / / E and σ and σ / E and σ E and σ and σ / K IC / σ f K IC 2 / σ f f f f [1] / E and σ f f f E and σ f f f 1.K

IC = fracture toughness; E = Young's modulus; σ f = 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).