PSI - Issue 57

Magnus Andersson et al. / Procedia Structural Integrity 57 (2024) 307–315 M. Andersson et al. / Structural Integrity Procedia 00 (2023) 000–000

315

9

the potential relaxation must also be investigated. An interesting method for cyclic plasticity that may be used for the relaxation phase is outlined by Ince et al. (2013), see also the master thesis work at Volvo CE by Johansson (2019).

Appendix A. The pre-calculated database

The database has been created using FEA (see Fig. A.13) and consists of output from two use cases (UC) where the (linearized) structural stress is either pure membrane (use case UCm) where the membrane stress, σ m = 1MPa and bending stress is σ b = 0 MPa or pure bending (UCb), where σ m = 0MPa and σ b = 1 MPa, in a path through the weld at an angle of v = 45°. The geometry factors, for mode I and II, in the stress intensity expression have been calculated (using the same FE model) from the two UC so that it relates to membrane and bending stress respectively: K I ( a , v ) = β I , UCm ( a , v ) · σ m ( v ) · √ π a + β I , UCb ( a , v ) · σ b ( v ) · √ π a = β I , UC ( a , v ) · σ m ( v ) σ b ( v ) · √ π a

Fig. A.13. (a) FE model; (b) crack; (c) linearized structural stress.

The intention with the method is to extract membrane and bending stress at the reference crack angle, v = v ref = 45 ◦ only. From the UC a [2x2] transformation matrix, A UC , ref ( v ), is created that transforms the structural stress from the reference angle to any angle (0 ≤ v ≤ 90 ◦ ) by: σ m ( v ) σ b ( v ) = A UC , ref ( v ) · σ m ( v ref ) σ b ( v ref )

References

ABAQUS, https: // www.3ds.com / products-services / simulia / products / abaqus / (2020). ADAMS, https: // hexagon.com / products / product-groups / computer-aided-engineering-software / adams (2022). Anderson, T. L., ”Fracture Mechanics - Fundamentals and Applications”. p 517, 2nd edition (1995). ANSYS, www.ansys.com (2022). ASTM E 1049-85 ”Standard practices for cycle counting in fatigue analysis”, ASTM International (2005). Hobbacher, A., IIW document XIII-2151-07 / XV-1254-07, ”Recommendations for Fatigue Design of Welded Joints and Components”, Interna tional Institute of Welding (2007). Ince, A., Glinka, G., ”A numerical method for elasto-plastic notch-root stress-strain analysis”, The Journal of Strain Analysis for Engineering Design, vol 48, pp 229-244 (2013-04), Johansson, N. ”Estimation of fatigue life by using a cyclic plasticity model and multiaxial notch correction”, Master thesis, LiTH, Sweden (2019) Madia, M., Zerbst, U., Beier, H. Th., Schork, B., ”The IBESS model – Elements, realisation and validation”. Eng. Frac. Mech. (2017). Susmel, L., ”A simple and e ffi cient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems”. Interna tional Journal of Fatigue, (2010).