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Comprehensive creep-pore diffusional growth calculations vs. previous approximations

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Abstract

Brittle rupture—via nucleation/growth/interconnection of grain-boundary (g.b.) creep pores—is a major cause of failure for materials not-resisting creep (e.g., through precipitation); and, the prediction of the relevant rupture-time with its dependency on stress/temperature/etc. represents a major challenge. Due to mathematical complexity, previous pore-growth calculations contain simplifications with indeterminable errors. Some calculations utilize 1-D (g.b.-vacancy) diffusional models having multi-sized/multi-spaced (‘infinitely’) long-parallel cylinders/pores instead of real-world spheroids (i.e., allowing for diffusion only between closest-neighbors). Other calculations utilize realistic 2-D g.b.-diffusional models but of equi-sized/equi-spaced spheroidal pores (hence ignoring ripening/coalescence); or, of just a couple of configurations of non-uniform/randomly spaced/spheroidal pores (thus not allowing for reliable statistics). Herein, the use of an innovative simulation-technique permits the examination of hundreds of complicated configurations with exceptionally low (w.r.t. the literature) computer-resource-expenditure, leading to proper adjustment/correction of all previous relevant 1-D/2-D works, making their results ‘real-world’ (on major issues, i.e., creep-rupture-time estimations and dependencies on stress/temperature/etc.).

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Abbreviations

\({A}_{cav}\) :

Grain boundary cavitation percentage or damage fraction

\({d}_{G}\) :

Grain size

\({D}_{b}\) :

Grain boundary diffusion coefficient

L:

Characteristic length of diffusional unit cell

R:

‘Grain boundary plane’ cavity radius

\({R}_{\text{curv}}\) :

Cavity radius of curvature (\({R}_{\text{curv}}=R/sin\theta \))

T:

Temperature

\({t}_{r}\) :

Rupture time

\(\beta \) :

Atom plating rate (atoms per unit grain boundary area & per unit time)

\({\gamma }_{b}\) :

Grain boundary tension

\({\gamma }_{s}\) :

Surface tension

\({\delta }_{b}\) :

Grain boundary ‘width’

\(\dot{\varepsilon }\) :

Strain rate

\(\theta \) :

Dihedral angle (\({\gamma }_{b}=2{\gamma }_{s}cos\theta \))

\(\mu \) :

Vacancy chemical potential (\(\mu ={\sigma }_{n}\Omega \) )

\(\sigma \) :

Applied remote stress

\({\sigma }_{n}\) :

Normal local stress at grain boundary

\(\Omega \) :

Atomic volume

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  1. Ministry of Transport, Civil Aviation Authority, Amphanae Str. No. 17, 38500, Saint Stephen, Greece

    Kostas Davanas

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Davanas, K. Comprehensive creep-pore diffusional growth calculations vs. previous approximations. Journal of Materials Research 38, 4225–4234 (2023). https://doi.org/10.1557/s43578-023-01134-2

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