PSI - Issue 68

Josef Arthur Schönherr et al. / Procedia Structural Integrity 68 (2025) 425–431 J. A. Scho¨nherr et al. / Structural Integrity Procedia 00 (2024) 000–000

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2.3. Dissipated creep stress power method

Analogous to the interpretation of the J integral as an energy release rate, C ∗ may be interpreted as the di ff erence in dissipated creep stress power regarding a virtual crack extension ∂ a over a width B , C ∗ = − 1 B ∂ U ∗ ∂ a . (4) The dissipated creep stress power U ∗ = − ˙ v cr 0 F d˙ v (5) follows by integrating the applied force F with the steady-state load line creep displacement rate ˙ v cr . To calculate the C ∗ -integral numerically, the above formulae were translated into an approximate solution, taking into account the results obtained for two distinct crack lengths a and a +∆ a with corresponding dissipated creep powers of U ∗ a and U ∗ a +∆ a , as C ∗ ≈− 1 B U ∗ a +∆ a − U ∗ a ∆ a = − 1 B ∆ U ∗ ∆ a . (6) In general, ˙ v cr is not a readily available result in a finite element simulation. In the finite element software Abaqus Standard, the dissipated through viscoelasticity or creep W cr can be requested as an output variable. Following Kon termann (2018), the load line creep displacement v cr can be calculated from W cr as v cr = W cr 0 1 F d W , (7) providing ˙ v cr as its time derivative in steady state. The di ff erence in dissipated creep power ∆ U ∗ can be determined approximately by a series of finite element simulations with applied forces in the interval of [0 , F ] to obtain a su ffi ciently fine resolved force vs. load line creep displacement rate curve, Fig. 1. The creep power approach for evaluating C ∗ is not dependent on assumptions such as the material model used (as long as there is a distinct steady state creep stage) and is therefore feasible to be used in multi material setups such as specimens made from welded joints and thus used and labeled as the reference method in this paper.

Fig. 1. Force vs. load line creep displacement rate curve for two di ff erent crack lengths. ∆ U ∗ follows as the orange filled area in between the two curves for crack lengths a +∆ a and a , schematic.