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

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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.

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Abbreviations

a :

Crack depth

A i :

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

J c :

Fracture toughness

J elastic :

Elastic part of the global J-integral

J 2 :

Second invariant of the Cauchy stress tensor

K :

Stress intensity factor

K I :

Mode-I stress intensity factor

K Ic :

Fracture toughness

K J :

Stress intensity factor determined from J-integral

\(\dot{K}\) :

Loading rate

K Jc :

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

Q BLA :

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

Q HRR :

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

Q t :

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

r :

Radius of crack front polar reference system

s i :

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

T :

Actual testing temperature

T 0 :

Master curve reference temperature

T stress :

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

w :

Specimen nominal width

x i :

Cartesian coordinates

z :

Thickness coordinate of crack front polar reference system

α :

Parameter in the Ramberg–Osgood constitutive equation

δ ij :

Components of the unit tensor

ε ij :

Components of the linearized strain tensor

ε 0 :

Strain parameter in the Ramberg–Osgood constitutive equation

η :

Plastic correction factor

ν :

Poisson’s ratio

φ :

Angle of crack front polar reference system

σ ij :

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

σ e :

v. Mises equivalent stress

σ I :

Maximum principal Cauchy stress

σ 0 :

Yield stress

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Authors and Affiliations

  1. Fachgebiet Strukturmechanik, Technische Universität Darmstadt, Hochschulstr. 1, 64289, Darmstadt, Germany

    Jochen Hebel

  2. Fraunhofer Institut für Werkstoffmechanik, Wöhlerstr. 11, 79108, Freiburg/Brsg., Germany

    Jörg Hohe, Valérie Friedmann & Dieter Siegele

Authors
  1. Jochen Hebel
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  2. Jörg Hohe
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  3. Valérie Friedmann
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  4. Dieter Siegele
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Correspondence to Jochen Hebel.

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Hebel, J., Hohe, J., Friedmann, V. et al. Experimental and numerical analysis of in-plane and out-of-plane crack tip constraint characterization by secondary fracture parameters. Int J Fract 146, 173–188 (2007). https://doi.org/10.1007/s10704-007-9160-8

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  • DOI: https://doi.org/10.1007/s10704-007-9160-8

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