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Modelling and experimental study of the tertiary creep stage of Grade 91 steel

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An Erratum to this article was published on 29 March 2011

An Erratum to this article was published on 29 March 2011

Abstract

This article addresses experimental studies and analytical simulations of the tertiary creep stage of Grade 91 steel tested at various stresses and temperatures between 500°C (up to 160 × 103 h) and 600°C (up to 94 × 103 h). The strain rate increases after its minimum mainly because of the softening of the material which microstructure evolves strongly during creep deformation. An interrupted creep test shows that necking significantly affects the acceleration of the reduction in cross-section only during the last 10% of the creep lifetime. The Hoff model based on homogeneous reduction of cross-section correctly predicts lifetimes only for high applied stress. The Hart necking model using the Norton power-law allows fair predictions of lifetimes up to 60 × 103 h at 500°C. The necking model using a modified Norton power-law combined with a material softening term allows predictions of lifetimes for all creep tests, differing from the experimental results by less than 50%, which is consistent with the experimental scatter. The evolution of the cross-section predicted by this model is in agreement with measurements carried out during the interrupted creep test. Two prediction rules for the lifetime prediction are deduced from the necking model that takes into account the material softening. For a large number of tempered martensitic steels, these two criteria bound the experimental lifetimes up to 200 × 103 h at 500–700°C.

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Abbreviations

A :

Constant of the power function given by Eq. 2, (h−α)

C :

Coefficient of the Norton power-law (MPa−N h−1)

D :

Diameter of the creep specimen (mm)

k :

Slope of creep softening

N :

Exponent of the Norton power-law

r c :

Necking section at fracture divided by the initial cross-section = s(rupture)/S init

r inf :

Inferior limit of the fraction of the necking section

r sup :

Superior limit of the fraction of the necking section

S :

Cross-section of the homogeneous part of the creep specimen (mm2)

S min :

Cross-section of the homogeneous part of the creep specimen when the strain rate reaches the minimum (mm2)

S init :

Cross-section of the creep specimen at the initial state (mm2)

s :

Necking cross-section of the creep specimen (mm2)

s min :

Necking cross-section of the creep specimen when the strain rate reaches the minimum (mm2)

t :

Time (h)

t min :

Time when the strain rate reaches the minimum (h)

t R :

Time to rupture (h)

t Rinf :

Lifetime predicted by the lower bound law (h)

t Rsup :

Lifetime predicted by the upper bound law (h)

T :

Temperature (°C)

α :

Exponent of the power function given by Eq. 2

δ D :

Variation in diameter caused by the roughness of specimen surface (μm)

δ D necking :

Difference in diameter between the homogeneous cross-section and the necking cross-section at the onset of necking (μm)

δ D r :

Variation in diameter relative to the average diameter of the specimen = δ D/D

δ S :

Difference in area between the homogeneous cross-section and the necking cross-section (mm2)

ε :

True or logarithm strain

ε eng :

Engineering strain or relative elongation

ε min :

True strain at which the true strain rate reaches the minimum

\({\varepsilon_{min}^{eng}}\) :

Engineering strain corresponding to ε min (h−1)

\({\dot{\varepsilon}_{min}}\) :

Minimum true strain rate (h−1)

\({\dot{\varepsilon}_{min}^{eng}}\) :

Minimum engineering strain rate (h−1)

\({\dot{\varepsilon}_{min}^{Norton}}\) :

Minimum true strain rate predicted by the Norton power-law (h−1)

σ :

True stress (MPa)

σ eng :

Engineering stress (MPa)

σ hom :

True stress in the cross-sections of the homogeneous parts (MPa)

σ necking :

True stress in the necking cross-section (MPa)

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Authors and Affiliations

  1. DEN/DMN/SRMA, CEA Saclay, 91191, Gif-sur-Yvette, France

    Rattanak Lim, Maxime Sauzay, France Dalle & Ivan Tournie

  2. DEN/DMN/SRMP, CEA Saclay, 91191, Gif-sur-Yvette, France

    Patrick Bonnaillie

  3. Centre des Matériaux UMR CNRS 7633, MINES ParisTech, BP 87, 91003, Evry, France

    Rattanak Lim & Anne-Françoise Gourgues-Lorenzon

Authors
  1. Rattanak Lim
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  2. Maxime Sauzay
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  3. France Dalle
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  4. Ivan Tournie
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  5. Patrick Bonnaillie
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  6. Anne-Françoise Gourgues-Lorenzon
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Correspondence to Rattanak Lim.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10704-011-9594-x

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Lim, R., Sauzay, M., Dalle, F. et al. Modelling and experimental study of the tertiary creep stage of Grade 91 steel. Int J Fract 169, 213–228 (2011). https://doi.org/10.1007/s10704-011-9585-y

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