Chapter 7: Mechanical Properties (Part 2)

What is fracture toughness?

the ability of a material containing a flaw/crack to resist sudden failure or fracture under applied load

Fracture mechanics

discipline concerned with the behaviour of materials containing cracks and other flaws

ex. microcracks, pores, inclusions

Fracture toughness

measure of the ability of a material with flaws to withstand applied loads

Stress concentration

Introduced by flaws that act as a local stress riser

What effect does a small, rounded flaw have on stress concentration?

• causes some stress concentration

• stress is spread over a smoother curved surface

• local stress increase is relatively limited

What effect does a larger flaw have?

• removes more load-bearing area and disturbs the stress field more

• local stress near the flaw becomes higher

What effect does a sharp flaw or crack have?

• most dangerous because the crack tip has a very small radius of curvature

• sharper tip → more stress is concentrated at that point

How does stress concentration increase?

• when the flaw becomes larger and sharper

• sharper cracks create very high local stresses at the crack tip

• rounded defects are less severe

How do you determine fracture toughness?

apply a tensile stress to a specimen prepared with a flaw of known size and geometry

Applied stress is intensified at…

the flaw

Stress intensity factor (K)

• measures how severe stress field is near crack tip

K = f*stress*sqrt(PI *a)

When is a material property, Kc, reached?

when a material with flaw breaks into 2 pieces

Plain strain

• occurs in thick plates/specimens

• through-thickness strain is approximately zero

• thickness deformation is restricted

• high crack tip constraint → less plastic deformation

• provides a lower, more conservative fracture toughness (K_IC)

Plane stress

• occurs in thin sheets/plates

• through thickness stress is approximately 0

• material can deform freely through the thickness

• lower crack tip constraint → more plastic deformation

• usually gives higher apparent fracture toughness

What is K_IC?

• plane strain fracture toughness

• used for safe fracture design

• represents the most constrained condition

What happens to measured fracture toughness (K_c) as specimen thickness increases?

It decreases until reaching the constant plane strain value (K_IC)

What is the thickness-independent fracture toughness value?

The plane strain fracture toughness K_IC

Which stress state occurs in thin sheets?

Plane stress

Which stress state occurs in thick sheets?

Plane strain

In plane stress, what is the out-of-plane stress?

σ_z = 0

In plane strain, what is the out-of-plane strain?

ε_z = 0

Why do thin specimens show higher apparent toughness?

They can deform out-of-plane, reducing crack-tip constraint

Why do thick specimens show lower toughness?

Out-of-plane deformation is restricted, increasing crack-tip constraint

What does the plateau in the toughness vs thickness curve represent?

The plane strain fracture toughness K_IC

Which condition produces the most constrained crack-tip?

Plane strain

Which condition produces the least constrained crack-tip?

Plane stress

In plane stress, is out-of-plane strain zero?

No, ε_z ≠ 0

In plane strain, is out-of-plane stress zero?

No, σ_z becomes tensile

What causes the transition region between plane strain and plane stress?

Intermediate thickness whether neither condition fully dominates

Why is K_IC reported for materials rather than the higher K_c (thin materials)?

Because we want the safest and most conservative fracture toughness value

What is the fracture criterion involving K and K_c?

If K > K_c, the crack can grow

What is the formula for the stress intensity factor, K?

K=f*σ*sqrt(πa)

Why does thickness affect the measured fracture toughness?

It changes the crack-tip stress state from plane stress to plane strain

The ability of a material to resist the growth of a crack is dependent on what factors?

1. Flaw size → smaller flaw is better, larger flaws reduce permitted stress

2. Ductility → can deform to blunt crack-tip providing higher fracture toughness

3. Grain size → fracture toughness improves with reducing grain size

4. Thickness → thinner sections provide higher fracture toughness values

5. Applied strain rate → higher rates (impact conditions) reduce fracture toughness

6. Temperature → higher T = higher fracture toughness

7. Compressive internal stresses → increase required stress for crack propagation

What does increasing the strength of a metal do to its ductility and fracture toughness?

It decreases the ductility and fracture toughness of the metal

What is the overall relationship between K_c and strength?

increased K_c = increased strength

Which material decreases in K_c when strength increases?

Metals because they have a wide range (processing, microstructure)

How do ceramics appear on the K_c vs strength graph?

high strength but low toughness

When does fracture occur?

K >= K_c

What is the goal of Leak-Before-Break?

Ensure a crack leaks through a wall before exploding

What is the formula for hoop stress in a pressurized pipe?

σ_hoop=Pd/2t

What causes a surface flaw in a pressured vessel to grow?

Hoop stress pulling the crack open

What is the critical crack size, a_c?

The critical crack length at which fracture becomes unstable and catastrophic

Why do we want a_c >=t ?

It creates a leak that reduces pressure and prevents unstable crack growth

What fracture toughness condition ensures LBB?

K_IC ≥ 1.1 σ sqrt(πt)

What does the factor 1.1 represent in the LBB toughness requirement?

A safety margin to prevent unstable fracture.

Why must pressure‑vessel materials have high K_IC?

To prevent cracks from reaching ac while still inside the wall.

What type of crack growth is desired in LBB?

Stable crack growth through thickness leading to a leak.

What type of crack growth must be avoided in LBB?

Unstable crack growth once K > K_IC.

What happens to internal pressure when a crack leaks?

It decreases, reducing hoop stress.

Why does unstable crack growth cause instant failure?

The crack propagates through the remaining thickness without resistance.

What is the relationship between stress and crack growth in LBB?

Higher stress increases crack opening; reduced stress from leaking slows crack growth.

If a_c is reached, what happens to the final propagation?

instantaneous (implosion)

Fractography

What are the two ways to classify fracture in metals?

1. Ductile fracture (slow)

2. Brittle fracture (fast)

What is ductile fracture?

• slow process with plastic deformation

• material absorbs more energy

• crack growth is slow and controlled

• fracture surface is rough and fibrous

What is brittle fracture?

• fast with little to no plastic deformation

• crack propagation is fast

• low absorbed energy

• fracture surface is typically flat and shiny

How is ductile fracture caused?

• overloading (large stress) of metals with good ductility and toughness

• occurs via transgranular (through the grain) failure

Internal flaws

• weak points

• higher local stress value

What is the progression of ductile fracture?

1. necking

2. microvoids

3. void growth

4. fibrous shear

After microvoids combine, they show up as _____________

dimples

Equiaxed

• stretched in all directions the same amount

• round

• usually form near the center of the fracture surface

• dominated mainly by tensile opening

• voids grow fairly uniformly in all direction

Columnar

• one axis is extremely larger than the other

• usually form near the shear lip

• experiences significant shear deformation/slip during final fracture

• voids are pulled and stretched as material shears

A chain used to hoist heavy loads fails. Examination of the failed link indicates considerable deformation and necking prior to failure. What are the possible reasons for the accident?

• overloading of the chain (stress > yield strength)

• impact/shock/dynamic loading

• wrong material/wrong heat treatment

• local damage or notch (localizes stress concentration)

How can you tell the loading direction from a brittle fracture surface?

Chevron patterns (V-shaped markings) point to failure point

What is the worst type of fracture?

Intergranular Fracture

• requires low force and happens fast

• indicates the metal broke at the GBs

• GBs were weak because of unwanted impurities, incorrect heat treatment, corrosion attack

Creep

slow deformation under constant load and high temperature

What are the causes of creep?

• diffusion

• dislocation glide or climb

• grain boundary sliding

Explain diffusion

At high temp, atoms have enough thermal energy to move through crystal lattice

Atomic motion allows for change of shape

Explain grain boundary sliding

boundaries between grains move easier at higher temp

Discuss the process of voids created during creep

creep cavities form along GBs → reduction of effective load bearing area → creep becomes self-accelerating

What happens if there are more voids during creep?

more voids = smaller effective area = higher local stress = faster creep = cracking = final rupture

As the voids form, is creep easier?

Yes

Stress rupture

final fracturing of a material due to creep

True or False: creep facture is the same as final fracture

False

True or False: A material can be considered ‘failed’ by creep even before final fracturing

True

How do you perform creep test on ductile materials?

Use a uniaxial tension test

How do you perform a creep test on brittle materials and why?

Use a uniaxial compression because you don’t want it to break easily

What are the main takeaways from this graph?

• stress is constant but strain increases over time at the elevated temperature

• strain = deformation

• accel/decel rate = slope (creep rate)

Primary creep

• strain increases quickly at first

• creep rate gradually decreases

• material becomes harder to deform due to strain hardening (dislocation-dislocation interaction and multiplication)

  • creep deformation vs strain hardening → strain hardening winning

Secondary creep

• strain increases at an almost constant rate

• called steady-state creep

• most important stage for design because it often occupies most of creep life

• balance between strain hardening and high temp recovery mechanisms

  • strain hardening vs recovery mechanisms → neither is winning

  • strain hardening slow deformation → dislocation entanglement → greater resistance to motion → lower creep rate

  • recover through climb makes deformation easier → fewer effective obstacles → easier continued deformation

Tertiary creep

• creep rate increases rapidly

• internal damage accumulates: voids, cracks, necking

• effective load-bearing area decreases

• ends with final fracture, called stress rupture

• easier creep deformation (lower load bearing area = more stress)

For dislocation climb, the location of dislocation moves ___________________________________

perpendicular to the slip plane

What is the main mechanism in normal plastic deformation?

Dislocation glide, in the direction of the slip plane with enough shear force

What is creep deformation controlled by?

dislocation glide + dislocation climb + diffusion

Why are high temperatures needed for climb?

At low temperatures, diffusion is too slow for climb, so obstacles strongly restrict motion.

At high temperatures, vacancy diffusion makes climb possible.

Higher stress =

higher creep rate & shorter rupture time

lower temperature =

lower creep rate = longer rupture time

What would you use the secondary creep rate formula for?

• chemical rxns

• atomic diffusion

• vacancy formation

• dislocation climb

Stress-Rupture Time

predicts the time to rupture/how long a material survives before final creep fracture

Larsen-Miller Parameter

simplifies creep rupture data

Why do material with high melting temperatures resist creep? (ex. superalloys, ceramics)

creep strongly depends on diffusion

T_homogolous = T_service / T_m

T_m increases → T_homo decreases

T_homo = slower diffusion = dislocation climb more difficult = GB sliding more difficult = slower steady creep rate

Stress corrosion

phenomenon in which materials react with corrosive chemicals in the environment

• leads to formation of cracks and failure

• can occur below yield strength

• stress + environment is synergistic: affect is greater than expected from either alone

Stress corrosion cracking

• formation and growth of cracks by the combination of tensile stress, susceptible materials and corrosive environment

• crack propagation is usually slow until cross section is reduced sufficiently for fast fracture

How do you identify stress corrosion cracking in metals an alloys?

• deep, fine cracks are formed without any evidence of overall general corrosion

• cracks are extensively branched along grain boundaries

Intergranular cracks

the crack travels mainly along GBs

Transgranular cracks

the crack travels through the grains

Fatigue

failure of a material due to repetitive/cyclic stress which may be larger or smaller than yield strength

What does cyclic stress do?

Lowers the strength of a material below its normal yield strength

What must be true for fatigue to occur?

A portion of the stress must be tensile. Loading cannot be purely compressive because tensile force is necessary for cracking