Evolution of the stress distribution during the lifetime under sinusoidal load oscillations applied on the top boundary in y-direction.
Source: BAM, Division Experimental and Model Based Mechanical Behaviour of Materials
Lifetime aspects including fatigue failure are traditionally of major importance for the safety of components and structures. Because the overall lifetime spans over millions of loading cycles, most approaches used for fatigue problems are of an empirical nature. They approximate the lifetime as a function of the loading amplitude. Nevertheless, these techniques do not reflect a realistic degradation of the material in each loading cycle. Consequently, stress redistribution, permanent deformations and interaction of a variety of phenomena (creep, oxidation, damage from thermal loading etc.) are not taken into account. Therefore, reliable numerical models to predict the performance of such components over the lifetime are required, which accurately capture the steady damage accumulations and full three-dimensional stress states.
A key challenge of those models is to address issues related to fatigue on the structural level. This is due to the enormous computational costs arising from solving each load cycle by conventional temporal incremental integration. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of the temporal scale separation incorporated into an extrapolation procedure. The response fields are approximated by a Fourier series whose basis functions reproduce the oscillatory fast-time scale, whereas the Fourier coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of permanent deformation and material damage. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases. A further idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the equations describing evolution of damage and inelastic flow. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration and results thus in an additional speedup.
The performance of the FTTI technique is demonstrated for a finite element simulation of viscoplastic solids under repeated loading-unloading cycles. The obtained solutions perfectly reproduce creep deterioration and stress redistribution while significantly reducing the computational costs.
A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration
Jörg Unger, Vitaliy Kindrachuk
International Journal of Fatigue, Volume 100, Part 1, July 2017, Pages 215-228
BAM Department Materials Engineering, Division Experimental and Model Based Mechanical Behaviour of Materials; Department Safety of Structures