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International Journal of Fracture

, Volume 146, Issue 3, pp 173–188 | Cite as

Experimental and numerical analysis of in-plane and out-of-plane crack tip constraint characterization by secondary fracture parameters

  • Jochen Hebel
  • Jörg Hohe
  • Valérie Friedmann
  • Dieter Siegele
Original Paper

Abstract

In this study, several two-parameter- concepts are analyzed experimentally and numerically with respect to their capability of characterizing in-plane and out-of-plane crack tip constraint effects. Different approaches utilizing the second term T stress of the linear-elastic crack tip stress field, a higher term A 2 of the power-law hardening crack tip stress field, a hydrostatic correction term Q for a reference stress field or the local triaxiality parameter h are compared. Experimental results for a pressure vessel steel 22NiMoCr3-7 are investigated by means of the different approaches regarding their capability of constraint characterization for enhanced transferability. Theoretical aspects are investigated in a modified boundary layer analysis and in three-dimensional nonlinear elastic-plastic finite element analyses of the specimens. It is found that, with respect to their capability of quantifying combined in-plane and out-of-plane constraint effects, the investigated concepts differ significantly.

Keywords

Elastic-plastic fracture mechanics Crack tip constraint effects Two-parameter- concepts Transferability 

Nomenclature

a

Crack depth

Ai

Intensities of the first three terms of the power-law hardening crack tip stress field

B

Specimen thickness or crack front length

E

Young’s modulus

\(f^{(k)}_{ij}\)

Circumferential stress distribution of the linear-elastic crack tip stress field

h

Stress triaxiality parameter

I

Constant of the HRR-singularity

J

J-integral

Jc

Fracture toughness

Jelastic

Elastic part of the global J-integral

J2

Second invariant of the Cauchy stress tensor

K

Stress intensity factor

KI

Mode-I stress intensity factor

KIc

Fracture toughness

KJ

Stress intensity factor determined from J-integral

\(\dot{K}\)

Loading rate

KJc

Fracture toughness

l

Reference length scale parameter

n

Hardening exponent in the Ramberg–Osgood constitutive equation

Q

Q-parameter, additional hydrostatic stress superimposed on a reference field

QBLA

Q-parameter determined from a FE small scale yielding reference field

QHRR

Q-parameter determined from the HRR-singularity as reference field

Qt

Q-parameter determined from the out-of-plane stress component

r

Radius of crack front polar reference system

si

Exponents in the power-series expansion of the power-law hardening crack tip stress field

T

Actual testing temperature

T0

Master curve reference temperature

Tstress

Intensity of the second term of the linear-elastic crack tip stress field

w

Specimen nominal width

xi

Cartesian coordinates

z

Thickness coordinate of crack front polar reference system

α

Parameter in the Ramberg–Osgood constitutive equation

δij

Components of the unit tensor

εij

Components of the linearized strain tensor

ε0

Strain parameter in the Ramberg–Osgood constitutive equation

η

Plastic correction factor

ν

Poisson’s ratio

φ

Angle of crack front polar reference system

σij

Components of the Cauchy stress tensor

σ′ij

Deviatoric components of the Cauchy stress tensor

\(\tilde{\sigma}^{(k)}_{ij}\)

Circumferential stress distribution of the power-law hardening crack tip stress field

\({\sigma^{\rm ref}_{ij}}\)

Reference crack front stress field

σe

v. Mises equivalent stress

σI

Maximum principal Cauchy stress

σ0

Yield stress

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Jochen Hebel
    • 1
  • Jörg Hohe
    • 2
  • Valérie Friedmann
    • 2
  • Dieter Siegele
    • 2
  1. 1.Fachgebiet StrukturmechanikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Fraunhofer Institut für WerkstoffmechanikFreiburg/Brsg.Germany

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