an introduction of fatigue and fracture

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

A - INTRODUCTION

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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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

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.

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Failure Versus Fracture

FailureInability of a component to perform according to its intended function.

FractureSeparation of a component into two or more parts.

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Some modes of failure• Gross yielding• Ductile failure• Brittle fracture• Creep Rupture and relaxation• Buckling• Stress corrosion cracking• Wear • Fatigue fracture

• Fatigue crack nucleation and growth• Uniaxial and multiaxial fatigue• Creep-fatigue• Corrosion fatigue• Constant and variable amplitude loading

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Load

Equilibrium equation

Complex stresses

Stress transformation

Mohr’s circle

Stress-strain relations

Stress concentration

Mechanics of Materials

A branch of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces acting within the body.

REVIEW OF LOAD AND STRESS ANALYSIS

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Types of Loading on Structures

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Applications involving combined loading

Typical Engineering Structures

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Equilibrium of a Deformable Body

A body is said to be in equilibrium when the resultant of all forces and moments acting on the body is zero.

0

0

oM

F

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

Equilibrium of a deformable body

Determine the internal load at cross section marked C of each structure.

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Under General Loading Conditions

Stress – intensity of a force acting at a material point

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Simple Stresses

J

Tr

A

P

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Complex Stresses

T

P•A

What is the magnitude of stress and strain on specific plane at A?

Does the stress and strain represent critical / maximum values at A?

If not…

what is the maximum & minimum (principal) stresses and maximum shear stresses?

What is the corresponding strain values?

On which planes do these stresses act?

A

Shear stress

Normal stress

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Transformation Equations

2sin2cos22 xy

yxyxx

2cos2sin2 xy

yxyx

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Mohr’s Circle

Graphical visualization of the stress states at a given material point

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Fracture Planes

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Engineering Stress-strain Curve

Necking

Fractured

Tensile failure in ductile material is associated with large plastic deformation.

Total = el + pl

B

C

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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STRAIN,

0.0 0.1 0.2 0.3 0.4 0.5 0.6

ST

RE

SS

, (

MP

a)

0

200

400

600

800

STRAIN,

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

ST

RE

SS

, (

MP

a)

0

50

100

150

200

= E

Linear

Non-linear /Power-law

= E

= K(p)n

SS316 steel

Engineering Stress-Strain Curve

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Mechanical Properties of Some Materials

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Concentration

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Concentration

Stress concentration factor

avgtK

max

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Concentration

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Stress Concentration Factors

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Deterioration of a material by initiation and propagation of crack when subjected to repeated load.

FATIGUE

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Deterioration of a material by initiation and propagation of crack when subjected to repeated load.

FATIGUE

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Fatigue design flow diagram

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Fatigue life models

• Nominal stress-life (S-N) model [1870s]

• Local strain-life (-N) model [1960s]

• Fatigue crack growth (da/dN-K) model[1960s]

• 2-stage model, combining -N and da/dN-K to incorporate fatigue crack nucleation and growth

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Fatigue life models

• Nominal stress-life (S-N) model [1870s]

• Local strain-life (-N) model [1960s]

• Fatigue crack growth (da/dN-K) model[1960s]

• 2-stage model, combining -N and da/dN-K to incorporate fatigue crack nucleation and growth

INTRODUCTION M.N.Tamin, CSMLab, UTM

MMJ1133 – FATIGUE AND FRACTURE MECHANICS

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Fatigue design criteria

• Infinite-life design Unlimited safety criterion where local stresses and strains are essentially elastic, and below fatigue limit.

• Safe-life design Designing for finite life with consideration on margin for scatter in fatigue data.

• Fail-safe design Structures are arranged so that cracks will not lead to failure before they are detected and repaired. Requires that if one part fails, the system does not fail.

• Damage-tolerant design Leak-before-burst design. Fracture mechanics analysis and tests are used to ensure that existing cracks will not propagate before they are detected by periodic inspection