PSI - Issue 47

Robert Eriksson et al. / Procedia Structural Integrity 47 (2023) 227–237 R. Eriksson, A. Azeez / Structural Integrity Procedia 00 (2023) 000–000

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5. Conclusion

A modified fracture mechanics based strip-yield approach was used to develop a model that captures and predicts the e ff ect of warm prestressing on the fracture resistance in steels. The main conclusions from the study are: • The model predicts experimental results with acceptable accuracy. • Unlike simpler models, the suggested strip-yield model capture the temperature dependence of WPS. • The plastic zone size plays an important role in the WPS phenomenon. It appears that fracture occurs as the plastic zone at low temperature reaches the same size as the plastic zone created by WPS load. • Active plasticity seems necessary for cleavage. • The WPS e ff ect can be modeled without any fracture toughness data as long as a constitutive model of the material is available.

Acknowledgments

Linko¨ping University is acknowledged for financial support and Siemens Energy is acknowledged for technical support.

Appendix A. The one-dimensional linear isotropic / kinematic hardening model

Algorithm 1 Pseudocode of 1D linear isotropic / kinematic hardening constitutive model ∆ ϵ = 1 N K κ 4 µ √ ρπ

▷ applied strain

for n = 1 , 2 , . . . , N do ϵ n + 1 = ϵ n +∆ ϵ

▷ update total strain ▷ elastic predictor ▷ trial yield function

= E ϵ n + 1 − ϵ p n = | σ trial

σ trial n + 1 f trial n + 1

+ H K α n )

n + 1 − q n | − ( Y

if f trial

n + 1 ≤ 0 then σ n + 1 = σ trial n + 1

▷ elastic step

ϵ e

σ n + 1 E

=

n + 1

else

▷ plastic step

f trial n + 1 E + H K + H

∆ γ =

∆ γ sgn σ trial

n + 1 − q n

trial n + 1 − E

σ n + 1 = σ

ϵ e

σ n + 1 E

=

n + 1 p n + 1 p n +∆ γ sgn σ α n + 1 = α n +∆ γ q n + 1 = q n + H ∆ γ sgn σ ϵ = ϵ

trial n + 1 − q n

▷ update hardening parameter

trial n + 1 − q n

▷ update back stress

end if n ← n + 1

▷ update values for next iteration

end for

The constitutive model used in this work is a 1D linear isotropic / kinematic hardening model as described below. Dots denote rates.

= E ϵ − ϵ

p elastic stress–strain relation

e

σ = E ϵ

(A.1)