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Application of fracture mechanics to welds with crack origin at the weld toe—a review. Part 2: welding residual stresses. Residual and total life assessment

  • U. ZerbstEmail author
Research Paper

Abstract

The two-part paper series provides an overview on the state-of-the-art in the application of engineering fracture mechanics to weldments limited to butt and fillet welds with crack initiation at weld toes. In the present second part, one focus is on welding residual stresses, their characteristics and stability under cyclic loading and their effect on structural integrity. Subsequently, features will be addressed which are essential for applying fracture mechanics to overall fatigue life and fatigue strength considerations of weldments. These comprise fatigue life relevant initial crack sizes and multiple crack initiation and propagation due to various stress peaks along the weld toe. A concept is briefly introduced which covers all these aspects.

Keywords

Fracture mechanics Welding residual stresses Multiple crack propagation Fatigue strength 

Nomenclature

a

Crack length (crack depth for surface cracks)

ai

Initial crack depth (for fracture mechanics analysis)

a0

Initial crack depth (fracture mechanics specimen)

a/c

Crack aspect ratio (changes during crack propagation and coalescence)

B

Specimen thickness (fracture mechanics specimen) or plate width (length of weld toe)

c

Half crack length at surface (semi-elliptical crack)

C

Fit parameter of the da/dN-ΔK curve in the Paris regime

da/dN

Fatigue crack propagation rate

E

Modulus of elasticity (Young’s modulus)

E

= E for plane stress and E/(1 – ν2) for plane strain conditions

f(Lr)

Plasticity correction function (monotonic loading)

f(ΔLr)

Plasticity correction function (cyclic loading)

h

Weld reinforcement

J

J-integral (monotonic loading)

k

Depth of a secondary notch, e.g. an undercut

k

Slope of finite life (high cycle) fatigue S-N curve in double logarithmic scale

K

Stress intensity factor (K-factor)

Kmat

Fracture resistance, monotonic loading (general term)

Kmax

Maximum K-factor in a loading cycle

Kmin

Minimum K-factor in a loading cycle

Kop

K-factor above which the crack is open (crack closure concept)

Kr

K-factor due to residual stresses

Kr

Ordinate of the FAD diagram (= K/Kmat)

Kt

Elastic stress concentration factor

\( \overline{K} \)

Mean value of the K-factor (in the loading cycle)

Kp

K-factor due to primary stresses

Ks

K-factor due to secondary stresses

Section width of weld toe (simulation of multiple crack propagation), Figs. 25 and 27

Lr

Ligament yielding parameter (monotonic loading)

M

Crack plane mismatch (Fig. 22)

N

Number of loading cycles

Nc

Number of loading cycles up to fracture

R

Loading ratio (= σminmax or Kmin/Kmax)

ReL

Lower yield strength (materials showing a Lüders’ plateau)

Rp0.2

0.2% proof strength (materials without Lüders’ plateau)

T

Plate thickness

t8/5

Time it takes for the weld to cool from 800 to 500 °C

U

Crack closure factor (=ΔKeff/ΔK)

ULC

Crack closure factor for long cracks, independent of crack depth a

USC

Crack closure factor for short cracks, as function of crack extension Δa

V

Plasticity correction factor for secondary stresses

W

Specimen width or half width (fracture mechanics specimen)

z

Coordinate in a weld (Fig. 5)

Z

Elastic follow-up factor

α

Weld flank angle

Δa

Amount of crack propagation

Δεref

Reference strain range, reference stress approach applied to cyclic loading

ΔJ

Cyclic J-integral (cyclic loading)

ΔK

K-factor range (KmaxKmin)

ΔKeff

Effective K-factor range (= KmaxKop)

ΔKp

(Formally) plasticity-corrected ΔK

ΔKth

Fatigue crack propagation threshold

ΔKth,eff

Intrinsic fatigue crack propagation threshold (no crack closure effect)

ΔKth,LC

Fatigue crack propagation threshold in the long crack regime

ΔKth,op

Crack closure component of the fatigue crack propagation threshold

ΔKth,SC

Fatigue crack propagation threshold in the (physically) short crack regime

ΔLr

Ligament plasticity factor (cyclic loading)

Δσ

Stress range (σmax–σmin)

Δσapp

Applied stress range (refers to cross-section without crack)

σa

Stress amplitude (= ½ Δσ)

σapp

Applied stress

Δσref

Reference stress range, reference stress approach applied to cyclic loading

εref

Reference strain (reference stress method)

μ

Expected value (statistical distribution), Fig. 27

ρ

Weld toe radius

ν

Poisson’s ratio

σ

Stress

σ

Standard deviation of statistical distributions, Fig. 27

σa

Stress amplitude (= ½ Δσ)

σapp

Applied (mechanical) stress, Eq. (1)

σe

Endurance limit (stress amplitude)

σN

Net section stress

σmax

Maximum stress in the fatigue cycle

σmin

Minimum stress in the fatigue cycle

σref

Reference stress (reference stress method)

σ0

Reference yield stress

σY

Yield strength, general (either ReL or Rp0.2)

σp

Primary stress

σr

Residual stress

\( {\sigma}_r^L \)

Longitudinal residual stress

\( {\sigma}_r^T \)

Transverse residual stress

σs

Secondary stress

Abbreviations

bcc

Body-centred cubic (crystal system)

BS

The British Standards Institution

COV

Coefficient of variation, statistical parameter = σ/μ

CTOD

Crack tip opening displacement

FAD

Failure assessment diagram

FAT

FAT class, stress range referring to 2 × 106 loading cycles

FCP

Fatigue crack propagation

fcc

Face-centred cubic (crystal system)

HAZ

Heat-affected zone

IBESS

Method for fracture mechanics-based determination of the fatigue strength and life, Section 3.5

IIW

International Institute of Welding

L

Longitudinal

LC

Long crack

MAG

Metal active gas (welding)

( )p

Plasticity corrected

( )p

Primary

PWHT

Post-weld heat treatment

R-curve

Crack resistance curve (monotonic and cyclic version)

( )s

Secondary

SC

Short crack

T

Transvers

TIG

Tungsten inert gas (welding)

TTT

Time-temperature-transformation (diagram)

Notes

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Copyright information

© International Institute of Welding 2019

Authors and Affiliations

  1. 1.Bundesanstalt für Materialforschung und -prüfung (BAM)BerlinGermany

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