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Creep of Metallic Materials in Bending

  • Mesoscale Materials Science: Experiments and Modeling
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Abstract

The creep behavior of metallic materials in bending has received limited attention because of the complexity of the stress state and the nontrivial correlation with an equivalent uniaxially deformed state. Furthermore, conventional creep testing methods, i.e., under uniaxial tension and compression, which have a constant stress state during creep and well-established data interpretation protocols, are adequate for studying the creep properties of most materials. Hence, the creep properties of metallic systems have rarely been evaluated in bending. Currently, there is an increase in the demand for testing in-service components and materials having microstructures on small length scales (e.g., a few tens to hundreds of micrometers). In this situation, the material for testing is often in short supply and the dimensions of the relevant samples are very small, thus limiting the feasibility of uniaxial tests. This warrants development of alternate testing techniques, such as indentation and bending, that are ideally suited for testing small-volume samples. In particular, cantilever bending is quite attractive given the possibility of obtaining multiple data points covering a range of stresses from a single sample and the ease of sample fabrication, alignment, and gripping while testing at a small length scale. In addition, the mechanics of power-law creep in bending is well understood and developed. We present herein a review of seminal literature on power-law creep in bending, a topic which has been investigated for almost 90 years now, and an outlook on adopting bending of cantilevers as a mainstream methodology for characterizing the creep behavior of metallic systems.

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Notes

  1. Creep is a time-dependent deformation process that becomes relevant at temperatures higher than 0.35 times the melting temperature for metals.

  2. The definition of a small sample depends on the testing method as well. A compression sample of < 1.5 mm to 3 mm in diameter and a tensile sample having a gauge length of < 5 mm to 12 mm are usually considered small. Hyde and Sun46 discuss the small sample size in more detail.

  3. Note that many of the datum points in Fig. 3b cannot be plotted in Fig. 3c because they were not recorded at the same time interval.

  4. Sato et al. 47 defined the constants C1, C2, and C3 more elaborately.

  5. A comprehensive report on the possible errors in measuring creep data in bending is provided by Boyle and Spence24, while those related to experimentation of cantilever beam under creep condition are described by Zhuang et al.26.

  6. Beams with L/h < 5 develop significant shear stresses, which becomes negligible for beams with L/h > 10. L/h of 5 to 10 represents the transition region, which is sometimes chosen to avoid the large deflections observed in beams with L/h > 10.

Abbreviations

\( \varepsilon \) :

Total strain (elastic and creep)

\( \dot{\varepsilon }_{\text{ss}} \) :

Steady-state strain rate

y :

Distance from neutral axis of beam

z :

Distance from loading end of beam

L :

Span length of four-point beam or length of cantilever

\( \delta_{\text{tip}} \) :

Steady-state deflection at loading end of beam

\( \dot{\delta }_{\text{tip}} \) :

Steady-state deflection rate at loading end of beam

\( \dot{k} \) :

Rate of curvature of beam

\( \sigma_{\text{s}} \) :

Saturated stress state in beam during creep

\( \sigma_{\hbox{max} } \) :

Saturated stress state in beam during creep at the outer fiber

\( \varepsilon_{\hbox{max} } \) :

Creep strain in beam at the outer fiber

\( \dot{\varepsilon }_{\hbox{max} } \) :

Creep strain rate in beam at the outer fiber

\( \varepsilon_{{\hbox{max} - {\text{ss}}}} \) :

Steady-state creep strain in beam at the outer fiber

\( \dot{\varepsilon }_{{\hbox{max} - {\text{ss}}}} \) :

Steady-state creep strain rate in beam at the outer fiber

\( \varepsilon_{\text{elastic}} \) :

Elastic strain

\( \varepsilon_{\text{pri}} \) :

Primary strain

\( \varepsilon_{\text{ss}} \) :

Steady-state strain

\( \varepsilon_{\text{creep}} \) :

Creep strain = \( \varepsilon_{\text{pri}} + \varepsilon_{\text{ss}} \)

n :

Stress exponent

d :

Measured deflection

M :

Applied moment (M, is generically used throughout the paper. M is constant for four-point bending, equal to PL/4 at the loading end for three-point bending, and equal to Pz for cantilever)

P :

Applied load

k :

Curvature of beam

h :

Full beam height

b :

Width of beam

t :

Time

I :

Second moment of inertia

Q :

Activation energy for creep

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Acknowledgements

The authors would like to thank the Aeronautical Research and Development Board, India (ARDB 0242), India and Ministries of Human Resource Development and Power, Government of India (IMPRINT 0009) for financially supporting this work. Authors would also like to thank Drs. Abhijit Ghosh and Jyotirmay Kar, and Mr. Dinesh Singh, Ms. Priya Goel, Mr. Faizan Hijazi and Mr. Shreehard Sahoo for meaningful discussions.

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  1. Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012, India

    Syed Idrees Afzal Jalali, Praveen Kumar & Vikram Jayaram

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Jalali, S.I.A., Kumar, P. & Jayaram, V. Creep of Metallic Materials in Bending. JOM 71, 3565–3583 (2019). https://doi.org/10.1007/s11837-019-03707-1

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