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The small punch creep test: some results from a numerical model

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Abstract

Obtaining accurate estimates of remanent creep life is of great importance to the power generating industry. The small punch creep test promises to be a useful way forward in this respect. However, a major concern with the test revolves around the ability to convert small punch test data into the required uniaxial equivalents. Experimental results within the literature have given contradictory results partly due to the large experimental scatter inherent within the test and so this article reports some results from a recently developed stochastic finite element model of the small creep punch test that provides guidance on this matter. The uniqueness of the model is based on its realistic creep deformations laws, including strain hardening, thermal softening and damage accumulation that enables it to produce life predictions for virgin material as well as for material with pre existing damage. It is shown that the model produces excellent life predictions for virgin 0.5Cr–0.5Mo–0.25V steel and for damaged 1.25Cr–1Mo steel over a wide range of test conditions. The model also predicts that the dependency of the time to failure on minimum displacement rates is such that small punch test data can be converted into uniaxial data using relatively simple analytical expressions.

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Abbreviations

\(\dot {\xi}_{ij}\) :

Strain rate tensor

ɛt :

Total creep strain at time t (%/100)

ɛf :

Elongation at failure (%/100)

ɛmin :

Minimum creep rate (s−1) from uniaxial tests

ɛd,min :

Minimum displacement rate (mm(s−1)) from small punch test

θj :

Theta parameter used to describe a creep curve (j = 1, 4)

Θi :

Natural log of θj

\(\bar{\Uptheta}_j\) :

Mean value for Θj

\(\hat{\Uptheta}_{i,j}\) :

Randomly generated value for Θj

\(\hat{\theta}_j\) :

Randomly generated value for θj

\(\bar{\tau}\) :

Local Von Mises flow stress

\(\tau_{ij}\) :

Cauchy stress tensor

\({\tau}_{ij}^{\prime}\) :

Deviatoric stress

τm :

Mean stress

γj :

Variance of θj

ρj :

Mean variance of Θj

σ*:

Normalised stress

σ:

Stress (MPa)

a j,0, b j,0, c j,0, d j,0 :

Parameters of the theta interpolation/extrapolation function in the deterministic model

a j,k, b j,k, c j,k, d j,k :

Parameters of the theta interpolation/extrapolation function for the kth run of the stochastic model

a, b, c, d :

Parameters of the failure strain interpolation/extrapolation function in the deterministic model

d :

Punch head displacement (mm)

m k, f k :

Parameters of the critical damage interpolation/extrapolation function for the kth run of the punch test model

r, z :

Disc point coordinates

T :

Temperature (K)

t f :

Time at failure

U :

A randomly drawn number between 0 and 1

Φ(U)−1 :

A standard normal variate

u i :

Velocity field

V :

Velocity

W crit :

Continuum damage at failure (dimensionless)

x 1 :

Punch hole diameter (mm)

x 2 :

Disc diameter (mm)

x 3 :

Disc thickness (mm)

x 4 :

Punch head radius (mm)

x 5 :

Friction coefficient (0 ≤ x 5 ≤ 1)

x 6 :

Preexisting damage (dimensionless)

x 7 :

Load (N)

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Authors and Affiliations

  1. Materials Research Centre, School of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    M. Evans

  2. Interdisciplinary Research Centre, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    D. Wang

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  1. M. Evans
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  2. D. Wang
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Correspondence to M. Evans.

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Evans, M., Wang, D. The small punch creep test: some results from a numerical model. J Mater Sci 43, 1825–1835 (2008). https://doi.org/10.1007/s10853-007-2388-x

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  • DOI: https://doi.org/10.1007/s10853-007-2388-x

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