Fatigue and fracture of rubber: Accelerated and experimentally validated phase-field damage models

Rubbers behave very particularly. Anyone who has stretched a rubber band knows that large elastic deformations over 400% can be attained with a minimal force.
In order to utilize the full potential of the material and to improve the performance of a product, it is imperative to accurately model the material's failure. This thesis focuses on the development, experimental validation and application of a fatigue damage model for rubber.

Cohesive zone models or nodal enrichment strategies, which treat cracks as sharp discontinuities, require a priori knowledge of the crack path or are limited in their ability to handle complex crack phenomena like branching and coalescence. On the other hand, the results of standard continuum damage models are affected by the mesh size. Phase-field damage models avoid sharp discontinuities by adding a smooth damage process zone to the crack. The width of this zone is controlled by a length scale parameter. Because of this pure continuum description, the mentioned complex phenomena are simulated without additional effort. Furthermore, the introduction of the length scale ensures mesh-independence during strain softening.

Despite these advantages, phase-field models to describe the failure of rubber parts are still limited. Firstly, most published works focus only on monotonic loading. Fatigue damage of rubber has never been considered in a phase-field model. Secondly, the computational burden is too large so that only examples with limited practical relevance can be simulated. Thirdly, there is insufficient experimental validation in the literature and the process of parameter identification is not adequately addressed. For instance, the selection of the length scale parameter is often arbitrary. This thesis collects three works that have been presented to the scientific community in an effort to overcome the mentioned problems.

Because the fracture resistance of rubbers is a function of the loading rate, the first work presents a rate-dependent phase-field damage model for rubber and finite strains. Rate-dependency is considered in the constitutive description of the bulk as well as in the damage driving force. All the material parameters are identified from experiments. Particular attention is paid to the length scale parameter, which is calibrated by means of local strain measurements close to the crack tip obtained via digital image correlation.

The second work extends the phase-field damage model so that fatigue failure can be predicted. For this purpose, an additional fatigue damage source depending on an accumulated load history variable is introduced. The thermodynamical consistency is demonstrated by measuring the energy storage and dissipation of the various model components. Dedicated fatigue experiments are conducted in order to identify additional (fatigue) parameters. The extended model reproduces Woehler curves and Paris theory for fatigue crack growth.

Using explicit and implicit cycle jump schemes, the third work focuses on the reduction of the computation time. A finite number of load cycles is simulated and the results for the next cycles are extrapolated. By alternating simulations and jumps until the component failure is reached, the total number of simulated cycles is significantly reduced, with respect to the full simulations. As the size of the cycle jump governs the acceleration of the simulations, but also the numerical stability, an adaptive cycle jump scheme for the implicit acceleration framework is proposed. Consequently, no manual adjustment of the step size is necessary. Additional experiments validate both the numerical model and the identified material parameters.

Finally, the fatigue phase-field damage model is used in two industry-relevant examples demonstrating how this technology creates immediate benefits in product development.