MMJ1133 – FATIGUE AND FRACTURE MECHANICS

C – FATIGUE: STRESS-LIFE APPROACH

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Course Content:

A - INTRODUCTION

Mechanical failure modes; Review of load and stress analysis –

equilibrium equations, complex stresses, stress transformation,

Mohr’s circle, stress-strain relations, stress concentration; Fatigue

design methods; Design strategies; Design criteria.

B – MATERIALS ASPECTS OF FATIGUE AND FRACTURE

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 2

Static fracture process; Fatigue fracture surfaces; Macroscopic features; Fracture mechanisms; Microscopic features.

C – FATIGUE: STRESS-LIFE APPROACH

Fatigue loading; Fatigue testing; S-N curve; Fatigue limit; Mean

stress effects; Factors affecting S-N behavior – microstructure, size

effect, surface finish, frequency.

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Fatigue Loading

Flight load spectrum

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 3

Jack-up structure

Flight load spectrum

SAE test

spectra

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Stress-time Relations

Fluctuating

stress, R<1

Non-

sinusoidal

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 4

Repeated

stress, R=0

Completely

reversed stress,

R = -1

sinusoidal

fluctuating

stresses

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Objective:

To establish the stress-life (S-N) diagram and determine fatigue

strengths of a material.

Fatigue Testing

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 5

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Rotating Bending Fatigue Test

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 6

R.R. Moore rotating-bending

fatigue-testing machine

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

(MPa)

800

1000

Cr-Mo steel, normalized

SUT = 800 MPa

Se = 338 MPa

Stress-Life (S-N) Curve

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 7

Fatigue strength, Sf(M

Pa)

300

400

500

600

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

Fatigue limit /

Endurance limit

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Stress-Life (S-N) Curve

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 8

Wrought steel

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit, Se , for Some Materials

MATERIAL SUT (MPa) Se (MPa) SD (MPa) SD (%)

SAE 4130730 276 7.6 2.7

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 9

SAE 4130

(Cr, Mo)730 276 7.6 2.7

SAE 4340

(Ni, Cr, Mo)1310 586 46.2 7.8

7076 Al

alloy 524 186 11.0 6.0

Ti-Alloy1000 579 37.2 6.4

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Fatigue limit – tensile strength relationship

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 10

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Fatigue limit – tensile strength relationship

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 11

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Mean stress effects on S-N behavior

Cyclic creep or ratchetting under

constant amplitude testing, Sm>0,

may result in excessive deformation

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 12

Tensile mean stress is detrimental

but compressive mean stress is

beneficial to fatigue life

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Tensile mean stress effects on alternating fatigue strength

1=+u

m

f

a

S

S

S

S

1

2

=

+ ma SS

Modified

Goodman

Gerber

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 13

Al alloy at ~107 cycles

Sf – fully reversed, R = -1.

1=

+u

m

f

a

S

S

S

S

1=+f

m

f

a S

S

S

σ

Gerber

Morrow

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Compressive and tensile mean stress effects

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 14

• Al alloyso Steels 1=+

u

m

f

a

S

S

S

S1=+

f

m

f

a S

S

S

σ

Modified

GoodmanMorrow

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Modified Goodman Diagram

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MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Modified Goodman Diagram

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MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

efedcbae SkkkkkkS ′=

a

k

k - Surface factor

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 17

e

f

e

d

c

b

S

k

k

k

k

k

′

- Size factor

- Reliability factor

- Temperature factor

- Factor for stress concentration

- Miscellaneous-effects factor (eg. cyclic frequency, corrosion)

- Endurance limit for rotating-beam specimen

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

ak -Surface factor

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 18

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

bk -Size factor

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 19

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

)2508(

189.1 097.0

mmdmm

dkb

≤<

= −

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

ck -Reliability factor

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 20

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

rc zk 08.01−=

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

dk -Temperature factor

≤=

CT o3501

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 21

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

≤<

≤=

CT

CTk

od5003505.0

3501

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Endurance Limit Modifying Factors

ek -Stress concentration effect

1=

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM 22

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

( )11

1

−+=

t

eKq

k

Kt – Theoretical stress

concentration factor

q – Notch sensitivity

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Example

An unnotched circular rod with a diameter of 10 mm is

subjected to constant amplitude bending at room

temperature, with Sm = 200 MPa. The material is 4340 Q&T

alloy steel with Su = 1240 MPa, Sy = 1170 MPa and S’y =

1000 MPa. If the rod is commercially polished, estimate the

value of Sa ,Smax ,Smin and R for a median fatigue life of

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM

value of Sa ,Smax ,Smin and R for a median fatigue life of

50000 cycles and no yielding.

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Sample test question:

A simply supported shaft is loaded as illustrated in Figure Q2. The shaft rotates with fixed

loading resulting in a fluctuating load with positive mean stress at R = 0.25. The shaft is

made of BS826 M40 HT steel with tensile and yield strength of 1300 and 850 MPa,

respectively. The fatigue limit of the material, defined for 106 cycles for smoothed

specimen can be estimated as, Sf’ = 0.5Sut. The surface of the shaft is ground while the

groove at B is machined. Based on the critical section at point B;

(i) Sketch the fatigue stress cycles experienced by the material point at B. Indicate the

stress amplitude and the mean stress level.

(ii) Draw the modified Goodman line and gross yielding line on Sa versus Sm plot. Indicate

the operating stress point on the diagram.

FATIGUE: STRESS-LIFE APPROACH M.N.Tamin, CSMLab, UTM

the operating stress point on the diagram.

(iii) Calculate the allowable maximum stress corresponding to fatigue life, Nf = 106 cycles,

using the modified Goodman equation.

Figure Q2