MMJ1133 FATIGUE AND FRACTURE MECHANICS A - INTRODUCTION INTRODUCTION

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1 A - INTRODUCTION INTRODUCTION M.N.Tamin, CSMLab, UTM

2 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 2

3 Failure Versus Fracture Failure Inability of a component to perform according to its intended function. Fracture Separation of a component into two or more parts. INTRODUCTION M.N.Tamin, CSMLab, UTM

4 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

5 REVIEW OF LOAD AND STRESS ANALYSIS 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. Load Equilibrium equation Complex stresses Stress transformation Mohr s circle Stress-strain relations Stress concentration INTRODUCTION M.N.Tamin, CSMLab, UTM 5

6 Types of Loading on Structures INTRODUCTION M.N.Tamin, CSMLab, UTM 6

7 Typical Engineering Structures Applications involving combined loading INTRODUCTION M.N.Tamin, CSMLab, UTM 7

8 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. F = M o 0 = 0 INTRODUCTION M.N.Tamin, CSMLab, UTM 8

9 Equilibrium of a deformable body Determine the internal load at cross section marked C of each structure. INTRODUCTION M.N.Tamin, CSMLab, UTM

10 Stress Under General Loading Conditions Stress intensity of a force acting at a material point INTRODUCTION M.N.Tamin, CSMLab, UTM 10

11 Simple Stresses τ = Tr J σ = P A INTRODUCTION M.N.Tamin, CSMLab, UTM 11

12 Complex Stresses A T P 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 A τ Shear stress σ Normal stress what is the maximum & minimum (principal) stresses and maximum shear stresses? What is the corresponding strain values? On which planes do these stresses act? INTRODUCTION M.N.Tamin, CSMLab, UTM 12

13 Stress Transformation Equations σx + σy σx σy σ x = + cos2θ + τxysin2θ 2 2 σx σy τx y = sin2θ + τxycos2θ 2 INTRODUCTION M.N.Tamin, CSMLab, UTM 13

14 Mohr s Circle Graphical visualization of the stress states at a given material point INTRODUCTION M.N.Tamin, CSMLab, UTM 14

15 Fracture Planes INTRODUCTION M.N.Tamin, CSMLab, UTM 15

16 Engineering Stress-strain Curve σ Necking B C Fractured Tensile failure in ductile material is associated with large plastic deformation. ε Total = ε el + ε pl ε INTRODUCTION M.N.Tamin, CSMLab, UTM 16

17 Engineering Stress-Strain Curve 800 SS316 steel 600 STRESS, σ (M MPa) 400 Non-linear /Power-law σ= K(ε p ) n Linear σ= Eε STRAIN, ε(%) STRESS, σ (MPa) σ= Eε STRAIN, ε(%) INTRODUCTION M.N.Tamin, CSMLab, UTM 17

18 Mechanical Properties of Some Materials INTRODUCTION M.N.Tamin, CSMLab, UTM 18

19 Stress Concentration INTRODUCTION M.N.Tamin, CSMLab, UTM 19

20 Stress Concentration Stress concentration factor K t σ = max σ avg INTRODUCTION M.N.Tamin, CSMLab, UTM 20

21 Stress Concentration INTRODUCTION M.N.Tamin, CSMLab, UTM 21

22 Stress Concentration Factors INTRODUCTION M.N.Tamin, CSMLab, UTM 22

23 FATIGUE Deterioration of a material by initiation and propagation of crack when subjected to repeated load. INTRODUCTION M.N.Tamin, CSMLab, UTM 23

24 FATIGUE Deterioration of a material by initiation and propagation of crack when subjected to repeated load. INTRODUCTION M.N.Tamin, CSMLab, UTM 24

25 Fatigue design flow diagram INTRODUCTION M.N.Tamin, CSMLab, UTM 25

26 Fatigue life models Nominal stress-life (S-N) model Local strain-life (ε-n) model Fatigue crack growth (da/dn- K) model 2-stage model, combining ε-n and da/dn- K to incorporate fatigue crack nucleation and growth [1870s] [1960s] [1960s] INTRODUCTION M.N.Tamin, CSMLab, UTM 26

27 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 INTRODUCTION M.N.Tamin, CSMLab, UTM 27

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