Cracks in Metal Components

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Mechanical design – Static design

Tópicos/Outline

Introduction to Fracture Mechanics 5.12

- Concept (idea)

- Crack propagation modes

- Stress intensity factor (SIF) – K

- Fracture Toughness

- SIF applied to design

- Validity of the project concerning LEFM

Failure theories (Tresca; von Mises; MNS, Coulomb-Mohr) vs

Linear elastic fracture mechanics 5.13

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Concept of Fracture Mechanics

It is based on the assumption that all materials contain defects or these

ones are introduced during the manufacturing process or appear in

service by a process of fatigue or corrosion

Mechanical design – Static design

Idea is that cracks exist in parts even before service begin and

those cracks can grow during service

The focus of this philosophy is on crack growth until it

becomes critical, and the part is removed from service

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Fracture Mechanics

Linear elastic

fracture mechanics

(LEFM)

Elasto-Plastic fracture

mechanics (EPFM)

Defect ?

Pore/void

crack

Inclusion/flaw

Unfavorable shape of the grain (rolling)

Mechanical design – Static design

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Fracture Mechanics

Stress concentration factors are limited to structures for which all

dimensions are precisely known no longer valid for FM k

t

Mechanical design – Static design

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Stress Intensity Factor (SIF) - K

Controls the crack propagation conditions

a – dimension´s defect (m)

KI – Stress Intensity Factor (MPa.m^0.5)

- Stress Intensity modification Factor

- nominal stress (MPa)

Is function of: geometry of component (plate; shell; tube),

geometry of crack (elliptic; circular; corner) and crack

propagation modes (mode I, II or III)

Mechanical design – Static design

KI=a

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For the analytical model consisting

of an infinite plate uniformly

tensioned

= Y = 1

Mechanical design – Static design

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Crack propagation modes

Mechanical design – Static design

Opening crack propagation

mode – the most common in

practice – most dangerous

Sliding mode

In plane shear Tearing mode

Out of plane shear

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Mix mode opening crack

Slant cracks

Consider mix mode opening crack:

?

Mechanical design – Static design

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Opening crack propagation mode I- KI

Mode I – the most

dangerous!!!

Survey of SIF:

-Rooke and Cartwright, “Compendium

of stress intensity factors”

-Y. Murakami, “Stress intensity factors

Handbook”, Pergamon Press

Mechanical design – Static design

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Mechanical design – Static design

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Mechanical design – Static design

Fig. 5-26

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Mechanical design – Static design

Beams of

rectangular cross

section having an

edge crack

-Pure bending

- 3PB

Fig. 5-27

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Mechanical design – Static design

Fig. 5-28: Plate in tension containing a circular hole with 2 cracks

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Fig. 5-29: Cylinder loading in axial tension having a radial

crack of a depth a around the circumference

Mechanical design – Static design

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Internal pressure p

& radial crack

Mechanical design – Static design

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Fracture Toughness – KIC ?

Mechanical design – Static design

Is a material property that dependes on the material, crack

mode, processing of the material, temperature, loading rate,

and the state of stress at the crack tip site.

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Apllying SIF to design

Known KIC and the solution KI=a for a specific case,

we can compute:

1. The critical fracture stress of the component

a

kICcr

2

1

IC

cr

ka

ICI kak

2. The critical crack length

3. The fracture toughness which should be specified for a

material

ICI kak

Mechanical design – Static design

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Design concerning

fracture: n = KIC / KI

yieldIC

cra

k

Fracture design vs Yielding design

Yielding controls

the design!!!!

Mechanical design – Static design

Apllying SIF to design

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Yield stress, Sy corresponds to yield design (von Mises)

As fracture toughness, KIC, corresponds to Linear Elastic Fracture

design (LEFM)

Mechanical design – Static design

Apllying SIF to design

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The zone of plastic deformation in the front of the crack is

small or large?

- There is very little plasticity max. brittleness

Specimen fracture in a state of plane strain (SPS)

tri axial stress state

Condition to check: Tick.min. ≥ 2.5 (KIC / C)^2

Mechanical design – Static design

Validity of the project concerning LEFM

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In the case of cracks in reservoirs of pressure two

possibilities of ruin exist:

- Leakage before fracture:

- Unexpected and brittle fracture,

without leakage aC

?

Mechanical design – Static design

Fracture design vs Yielding design

crack reaches a length

superior to the thickness, leading to leakage

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PROJECTO MECANICO

EXERCISES FROM BOOK

Static Loading exercises: 5-19;5-36; 5-63; 5-76

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Mechanical design – Static design

Fig. 5-26