Chapter 8 mechanical failure

MSE-211-Engineering Materials 1

Mechanical Failure

Chapter reading 8 ISSUES TO ADDRESS...

1

• How do cracks that lead to failure form?

• How is fracture resistance quantified? How do the fracture

resistances of the different material classes compare?

• How do we estimate the stress to fracture?

• How do loading rate, loading history, and temperature

affect the failure behavior of materials?

Ship-cyclic loading

from waves.

Computer chip-cyclic

thermal loading.

Hip implant-cyclic

loading from walking.


Mechanical Failure

Why study failure?

Design of a component or structure: Minimize failure possibility

It can be accomplished by understanding the mechanics of failure

modes and applying appropriate design principles.

Failure cost

1. Human life 2. Economic loss 3.Unavailability of service

Failure causes:

1. Improper material selection 2. Inadequate design 3. Processing

Regular inspection, repair and replacement critical to safe design


Fracture

Fracture is the separation of a body into two or more

pieces in response to an imposed stress

Steps in Fracture:

Crack formation

Crack propagation


Fracture Modes

Depending on the ability of material to undergo plastic deformation

before the fracture two fracture modes can be defined - ductile or

brittle.

Ductile fracture - most metals (not too cold):

Extensive plastic deformation ahead of crack

Crack is “stable”: resists further extension

unless applied stress is increased

Brittle fracture - ceramics, ice, cold metals:

Relatively little plastic deformation

Crack is “unstable”: propagates rapidly without

increase in applied stress

Ductile fracture is preferred in most applications


Ductile Vs Brittle Fracture

Very

Ductile

Moderately

Ductile Brittle

Fracture

behavior:

Large Moderate %AR or %EL Small


Ductile Fracture

• Evolution to failure:

(a) (b) (c) (d) (e)

(a) Necking

(b) Formation of microvoids

(c) Coalescence of microvoids to form a crack

(d) Crack propagation by shear deformation

(e) Fracture

Cup and cone

fracture


(Cup-and-cone fracture in Al)

Ductile Vs Brittle Fracture

brittle fracture ductile fracture

Brittle fracture in a mild steel

MSE-211-Engineering Materials

Ductile Fracture

(a) SEM image showing spherical dimples resulting from a

uniaxial tensile load representing microvoids. (b) SEM image of

parabolic dimples from shear loading.

8


Brittle Fracture

Arrows indicate point at failure origination

Distinctive pattern on the fracture surface: V-shaped “chevron”

markings point to the failure origin.


Brittle Fracture

Lines or ridges that radiate from the origin of

the crack in a fanlike pattern


Transgranular fracture

Fracture cracks pass through grains.


Intergranular fracture: Fracture crack propagation is

along grain boundaries (grain boundaries are weakened

or embrittled by impurities segregation etc.)

MSE-211-Engineering Materials 13 13 13

• Ductile failure:

-- one piece

-- large deformation

Example: Pipe Failures

• Brittle failure:

-- many pieces

-- small deformations


Studies the relationships between:

material properties

stress level

crack producing flaws

crack propagation mechanisms

Fracture Mechanics


Stress Concentration

Measured fracture strength is much lower than predicted by calculations

based on atomic bond energies. This discrepancy is explained by the

presence of flaws or cracks in the materials.

The flaws act as stress concentrators or stress raisers,

amplifying the stress at a given point.

The magnitude of amplification depends on crack

geometry and orientation.



If the crack is similar to an elliptical

hole through plate, and is oriented

perpendicular to applied stress, the

maximum stress, at crack tip

where t = radius of curvature

so = applied stress

sm = stress at crack tip

a = length of surface crack or ½

length of internal crack

2/1

2

t

om

a

ss



2/1

2

t

om

a

ss

The stress concentration factor is

A measure of the degree to which an external

stress is amplified at the tip of a crack.

(1)

Rearranging equation 1

sm 2so

a

t

1/2

Ktso

MSE-211-Engineering Materials 19 19

Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.0 1.0

1.5

2.0

2.5

Stress Conc. Factor, K t =

• Avoid sharp corners! s

Adapted from Fig.

8.2W(c), Callister 6e.

(Fig. 8.2W(c) is from G.H.

Neugebauer, Prod. Eng.

(NY), Vol. 14, pp. 82-87

1943.)

r , fillet

radius

w

h

smax

smax

s0



Crack propagation

Cracks with sharp tips propagate easier than cracks having blunt tips

2/1

2

t

om

a

ss

In ductile materials, plastic deformation at a crack tip “blunts” the crack.


Crack propagation


Critical stress for crack propagation

γs = specific surface energy

When the tensile stress at the tip of crack exceeds the critical stress value

the crack propagates and results in fracture.


EXAMPLE PROBLEM 8.1 Page 244

A relatively large plate of a glass is subjected to a tensile stress of 40

MPa. If the specific surface energy and modulus of elasticity for this

glass are 0.3 J/m2 and 69 GPa, respectively, determine the maximum

length of a surface flaw that is possible without fracture.

𝑎 =2𝐸𝛾𝑠

𝜋𝜎2

𝐸 = 69 𝐺𝑃𝑎

𝛾𝑠 =0.3 J/m2

𝜎 = 40 𝑀𝑃𝑎

Rearranging the equation

𝑎 = 8.2 * 10-6 m


Home Work Problems

Exercise Problems 8.1-8.4


Fracture Toughness

• Fracture toughness measures a material’s resistance to

fracture when a crack is present.

• It is an indication of the amount of stress required to propagate a preexisting flaw.

𝐾𝑐 = 𝜎𝑐 𝜋𝑎

𝐾𝑐= Fracture toughness


Fracture Toughness

𝑲𝒄is a material property depends on temperature, strain rate

and microstructure.

The magnitude of Kc diminishes with increasing strain rate

and decreasing temperature.

Improvement in yield strength wrought by alloying and

strain hardening generally produces corresponding decrease

in Kc .

Kc normally increases with reduction in grain size as

composition and other microstructural variables are

maintained constant.


Impact Fracture Testing

Testing fracture characteristics under high strain rates

Two standard tests, the Charpy and Izod, measure the impact

energy (the energy required to fracture a test piece under an

impact load), also called the notch toughness


(Charpy)

Impact Fracture Testing

Izod

final height initial height


Ductile-to- brittle transition

As temperature decreases a ductile material can become

brittle - ductile-to-brittle transition.

The ductile-to-brittle transition can be measured by impact testing:

the impact energy needed for fracture drops suddenly over a

relatively narrow temperature range – temperature of the ductile-to-

brittle transition.

The ductile to-brittle transition is related to the temperature

dependence of the measured impact energy absorption

MSE-211-Engineering Materials 29 29

Adapted from Fig. 8.15,

Callister & Rethwisch 8e.

• Ductile-to-Brittle Transition Temperature (DBTT)...

Low strength steels(BCC)

Imp

act E

ne

rgy

Temperature

High strength materials

polymers

More Ductile Brittle

Ductile-to-brittle transition temperature

Low strength (FCC and HCP) metals (e.g., Cu, Ni)


• Pre-WWII: The Titanic • WWII: Liberty ships

• Problem: Steels were used having DBTT’s just below

room temperature.

Design Strategy:

Stay Above The DBTT!


Fatigue

Failure under fluctuating / cyclic stresses

e.g., bridges, aircraft, machine components, automobiles,etc..

Fatigue

• Stress varies with time.

s max

s min

s

time

s m S


Fatigue failure can occur at loads considerably lower

than tensile or yield strengths of material under a static

load.

Fatigue

Estimated to causes 90% of all failures of metallic structures

Fatigue failure is brittle-like (relatively little plastic

deformation) - even in normally ductile materials. Thus

sudden and catastrophic!

Fatigue failure proceeds in three distinct stages: crack

initiation in the areas of stress concentration (near stress

raisers), incremental crack propagation, final catastrophic

failure.


Fatigue

CYCLIC STRESSES

1.Reversed stress cycle

Periodic and symmetrical

about zero stress

2.Rpeated stress cycle

Periodic and asymmetrical

about zero stress


Fatigue

CYCLIC STRESSES

3.Random stress cycle Random stress fluctuations


Fatigue

CYCLIC STRESSES

Mean stress (𝜎𝑚)


Fatigue

S — N curves

(stress — number of cycles to failure)

Fatigue properties of a material (S-N curves) are tested in

rotating-bending tests in fatigue testing apparatus

Result is commonly plotted as S (stress) vs. N (number of

cycles to failure)


S — N curves

Fatigue limit (endurance limit) occurs for some materials

(e.g. some Fe and Ti alloys). In this case, the S—N curve

becomes horizontal at large N, limiting stress level. The fatigue

limit is a maximum stress amplitude below which the material

never fails, no matter how large the number of cycles is.

For many steels,

fatigue limits

range between

35% and 60%

of the tensile

strength.


S — N curves

In most non ferrous alloys(e.g., Aluminum, Copper,

Magnesium) S decreases continuously with N. In this

cases the fatigue properties are described by

Fatigue strength: stress at which

fracture occurs after a

specified number of cycles (e.g.

107)

Fatigue life: Number of cycles to

fail at a specified stress

level


Fatigue

Fracture surface characteristics

Beach marks and striations


Creep is a time-dependent and permanent deformation

of materials when subjected to a constant load or stress.

For metals it becomes important at a high temperature

(> 0.4 Tm). Examples: turbine blades, steam

generators, high pressure steam lines.

Creep

Polymers are specially sensitive to creep.

For details read the book pages 265-267


Stages of Creep


1. Instantaneous deformation, mainly elastic.

2. Primary/transient creep. Slope of strain vs. time

decreases with time: strain-hardening

3. Secondary/steady-state creep. Rate of straining is

Constant

4. Tertiary. Rapidly accelerating strain rate up to

failure:

formation of internal cracks, voids, grain boundary

separation, necking, etc.

Stages of Creep


Parameters of creep behavior

The stage of secondary/steady-state creep is of longest

duration and the steady-state creep rate 𝜺.𝒔 =

∆𝜺

∆𝒕.is the

most important parameter of the creep behavior in long-life

applications e.g. nuclear power plant component.

Another parameter, especially important in short-life

creep situations, is time to rupture, or the rupture

lifetime, tr.. e.g., turbine blades in military aircraft and

rocket motor nozzles, etc….


Creep: stress and temperature effects

Chapter 8 mechanical failure

Technology

Transcript of Chapter 8 mechanical failure