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See detailAccelerating fatigue simulations of a phase-field damage model for rubber
Loew, Pascal Juergen UL; Poh, Leong Hien; Peters, Bernhard UL et al

in Computer Methods in Applied Mechanics and Engineering (2020), 370(113247),

Phase-field damage models are able to describe crack nucleation as well as crack propagation and coalescence without additional technicalities, because cracks are treated in a continuous, spatially finite ... [more ▼]

Phase-field damage models are able to describe crack nucleation as well as crack propagation and coalescence without additional technicalities, because cracks are treated in a continuous, spatially finite manner. Previously, we have developed a phase-field model to capture the rate-dependent failure of rubber, and we have further enhanced it to describe failure due to cyclic loading. Although the model accurately describes fatigue failure, the associated cyclic simulations are slow. Therefore, this contribution presents an acceleration scheme for cyclic simulations of our previously introduced phase-field damage model so that the simulation speed is increased to facilitate large-scale simulations of industrially relevant problems. We formulate an explicit and an implicit cycle jump method, which, depending on the selected jump size, reduce the calculation time up to 99.5%. To circumvent the manual tuning of the jump size, we also present an adaptive jump size selection procedure. Thanks to the implicit adaptive scheme, all material parameters are identified from experiments, which include fatigue crack nucleation and crack growth. Finally, the model and its parameters are validated with additional measurements of the fatigue crack growth rate. [less ▲]

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See detailFatigue and fracture of rubber: Accelerated and experimentally validated phase-field damage models
Loew, Pascal Juergen UL

Doctoral thesis (2020)

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 ... [more ▼]

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. [less ▲]

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See detailFatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation
Loew, Pascal Juergen UL; Peters, Bernhard UL; Beex, Lars UL

in Mechanics of Materials (2020), 142

By regularizing sharp cracks within a pure continuum setting, phase-damage models offer the ability to capture crack nucleation as well as crack propagation. Crack branching and coalescence can ... [more ▼]

By regularizing sharp cracks within a pure continuum setting, phase-damage models offer the ability to capture crack nucleation as well as crack propagation. Crack branching and coalescence can furthermore be described without any additional efforts, as geometrical descriptions of the cracks are not required. In this contribution, we extend our previous phase-field model for rate-dependent fracture of rubbers in a finite strain setting (Loew et al., 2019) to describe damage under cyclic loading. The model is derived from the balance of mechanical energy and introduces a fatigue damage source as a function of the accumulated viscous dissipation under cyclic loading. We use uniaxial cyclic tension to present the influence of the fatigue material parameters and to confirm the model’s energy balance. The parameters are subsequently identified using monotonic and cyclic experiments of a plane stress nature. Finally, the model is validated by separate experiments, which demonstrate that the model accurately predicts (fatigue) crack nucleation as well as propagation. [less ▲]

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See detailPhase field fracture model for viscoplastic materials in large deformations
Kabore, Brice Wendlassida UL; Loew, Pascal Juergen UL; Peters, Bernhard UL

Scientific Conference (2019, June 13)

Phase-field modeling approach to material fracture and damage has received a growing interest among researchers. It has proven to be an effective way to address crack related discontinuities in continuum ... [more ▼]

Phase-field modeling approach to material fracture and damage has received a growing interest among researchers. It has proven to be an effective way to address crack related discontinuities in continuum mechanics. Also, it solves the problem related to tracking the fracture surface by simply representing the fracture phase with a continuous field variable. Recently, phase-field fracture models have been extended to finite deformations, crack nucleation and applied to complex material behaviors such as plasticity and viscoplasticity. In this contribution we describe a viscoplastic model coupled with a phase-field dynamic fracture model in a large strain formulation. The model include damage, history, rate and temperature dependent behavior. A finite element implementation is presented in a staggered time integration. Moreover, we address the crack closure and crack surfaces interpenetration taking into account tension-compression strength asymmetry. Performance of the model on dynamic crack propagation are presented. [less ▲]

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See detailRate-dependent phase-field damage modeling of rubber and its experimental parameter identification
Loew, Pascal Juergen UL; Peters, Bernhard UL; Beex, Lars UL

in Journal of the Mechanics and Physics of Solids (2019)

Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe and ... [more ▼]

Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe and Schänzel (2014) introduced a rate-independent phase-field damage model for finite strains in which a viscous damage regularization was proposed. We extend the model to depend on the loading rate and time by incorporating rubber’s strain-rate dependency in the constitutive description of the bulk, as well as in the damage driving force. The parameters of the model are identified using experiments at different strain rates. Local strain fields near the crack tip, obtained with digital image correlation (DIC), are used to help identify the length scale parameter. Three different degradation functions are assessed for their accuracy to model the rubber’s rate-dependent fracture. An adaptive time-stepping approach with a corrector scheme is furthermore employed to increase the computational efficiency with a factor of six, whereas an active set method guarantees the irreversibility of damage. Results detailing the energy storage and dissipation of the different model constituents are included, as well as validation results that show promising capabilities of rate-dependent phase-field modeling. [less ▲]

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