[email protected] ENGR-45_Lec-20_Failure-2.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical

[email protected] • ENGR-45_Lec-20_Failure-2.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 45

MaterialMaterialFailure Failure

(2)(2)



Learning Goals.1 – FailureLearning Goals.1 – Failure

How Flaws In A Material Initiate Failure How Fracture Resistance is Quantified

• How Different Material Classes Compare

How to Estimate The Stress To Fracture

Factors that Change the Failure Stress• Loading Rate

• Loading History

• Temperature



Learning Goals.2 – FailureLearning Goals.2 – Failure

FATIGUE Failure• Fatigue Limit

• Fatigue Strength

• Fatigue Life

CREEP at Elevated Temperatures• Incremental Yielding at <y Over a Long

Time Period at High Temperatures



Fatigue DefinedFatigue Defined

ASTM E206-72 Definition

The Process of PROGRESSIVE LOCALIZED PERMANENT Structural

Change Occurring in a Material Subjected to Conditions Which Produce FLUCTUATING Stresses and Strains at

Some Point or Points Which May Culminate in CRACKS or Complete

FRACTURE After a Sufficient Number of Fluctuations



Fatigue FailureFatigue Failure Caused by Load-

Cycling at <y

Brittle-Like Fracture with Little Warning by Plastic Deformation• May take Millions of

Cycles to Failure

Fatigue Failure Time-Stages

1. Crack Initiation Site(s)

2. “Beach Marks” Indicate of Crack Growth

3. Distinct Final Fracture Region



Fatigue ParametersFatigue Parameters Recall Fatigue Testing (RR Moore Tester)

Stress Varies with Time; Key Parameters m Mean Stress (MPa)

• S Stress Amplitude (MPa)

tension on bottom

compression on top

countermotor

flex coupling

bearing bearing

specimen

max

min

time

mS

Failure Even thoughmax < c

Cause of ~90% of Mech Failures

2

2

minmax

minmax

Sm



More Fatigue ParametersMore Fatigue Parameters

σmax = maximum stress in the cycle

σmin = minimum stress in the cycle

σm = mean stress in the cycle = (σmax + σmin)/2

σa = stress amplitude = (σmax - σmin)/2

Δσ = stress range = σmax - σmin = 2σa

R = stress ratio = σmax/σmin



Fatigue Design ParameterFatigue Design Parameter Fatigue (Endurance)

Limit, Sfat in MPa

• Unlimited Cycles if S < Sfat

Some Materials will NOT permit Limitless Cycling• i.e.; Sfat = ZERO

Sfat

case for steel (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe




Factigue Crack Growth Factigue Crack Growth Fatigue Cracks Grow INCREMENTALLY

during the TENSION part of the Cycle Math Model for Incremental Crack Extension

Example: Austenitic Stainless Steel

typ. 1 to 6

dadN

K m

increase in crack length per loading cycle

253121065.

./ mMPaKcycmdN

da

Opening-Mode (Mode-I) Stress Intensity Factor

aK I ~



Improving Fatigue PerformanceImproving Fatigue Performance1. Impose a

Compressive Surface Stress (to Suppress Surface cracks from growing)

2. Remove Stress-Concentrating sharp corners

N = Cycles to failure

moderate tensile,

m

larger tensile, m


near zero or compressive, m

• Method 1: shot peening • Method 2: carburizing (interstitial)

C-rich gasput

surface into

compression

shot

bad

bad

better

better



Creep DeformationCreep Deformation

Creep Defined

HIGH TEMPERATURE PROGRESSIVE DEFORMATION of a material at

constant stress. High temperature is a relative term that is dependent on the

material(s) being evaluated. For Metals, Creep Becomes important

at Temperatures of About 40% of the Absolute Melting Temperature (0.4Tm)



Creep: Creep: εε vs t Behavior vs t Behavior In a creep test a

constant load is applied to a tensile specimen maintained at a constant temp. Strain is then measured over a period of time• Typical Metallic

Dynamic Strain at Upper-Right

Stage-1 → Primary • a period of primarily

transient creep. During this period deformation takes place, and StrainHardening Occurs



Creep: Creep: εε vs t Behavior cont.1vs t Behavior cont.1 Stage-II → Steady

State Creep• a.k.a. Secondary

Creep

• Creep Rate, dε/dt is approximately Constant

• Strain-Hardening and RECOVERY Roughly Balance

Stage-III → Tertiary Creep

• a reduction in cross sectional area due to necking, or effective reduction in area due to internal void formation

• Creep Fracture is often called “Rupture”



Secondary Creep Secondary Creep Most of Material Life Occurs in this Stage Strain-Rate is about Constant for Given T & σ

• Work-Hardening Balanced by Recovery

The Math Model

• Where– K2 A Material-

Dependent Constant

– σ The Applied Stress

– n A Material Dependent Constant

RT

QK

dt

d cns

s

exp2

– Qc The Activation Energy for Creep

– R The Gas Constant

– T The Absolute Temperature



Creep FailureCreep Failure Occurs Along Grain

Boundaries

Estimate Rupture Time• S590 Iron, T = 800 °C,

σ = 20 Ksi

The Time-to-Rupture Power-Law Model

appliedstress

g.b. cavities

time to failure (rupture)

function ofapplied stress

temperature

T(20 logtr ) L

L(103K-log hr)

Str

ess

, ks

i

100

10

112 20 24 2816

data for S-590 Iron

20

T(20 logtr ) L

1073K

Ans: tr = 233hr

24x103 K-log hr



WhiteBoard WorkWhiteBoard Work

Problem 8.17• Ø 0.60” 2014-T6 Al Round bar• Cyclic Axial Loading in

Tension-Compression• Design Life, N = 108 Cycles

• σmean = 5 ksi• S-N per Fig 8.34

Find Loads: Pmax, Pmin

• See NEXT Slide

P

P

Al2014-T6

0.60”

σm =5 ksi



S-N Data for 2014-T6 AlS-N Data for 2014-T6 Al

19.5 ksi







Creep

Test In

strum

ent

Creep

Test In

strum

ent

Documents

[email protected] ENGR-45_Lec-20_Failure-2.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical