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Multiscale Methods for Fracture

Final Report Summary - MULTIFRAC (Multiscale Methods for Fracture)

The objective of this project was to setup and strengthen international collaborations in the field of ’multiscale modelling for fracture’. The scientific goal is to get a better understanding of how materials fail and to develop better predictive tools for Engineering applications. This requires the combination of knowledge from different areas, i.e. Computational Mechanics, Computational Material Science and Experimental Testing. The focus of the work was on developing a framework for predicting and optimizing macroscopic material properties – in particular properties related to fracture such as strength of materials or fracture toughness – for composite materials. For validation, carbon (such as Carbon Nanotubes (CNT) reinforced) based composites were considered; the matrix material was polymeric.

In order to reach the overall objective, the consortium developed computational methods for transferring fracture related material properties over several length scales. These methods can be classified into three categories:
1. hierarchical multiscale methods where information is passed from the fine-scale to the coarse-scale only,
2. semi-concurrent multiscale methods where information is passed between the fine-scale and coarse-scale and vice versa but the fine-scale geometry is not embedded into the coarse scale. Such an approach is suitable for modeling efficiently non-linear material behavior but not fracture and
3. concurrent multiscale methods where the fine-scale is embedded and adaptively adjusted in the coarse scale when fracture propagates.
Finaly a hybrid multiscale framework has been implemented. Due to the high complexity of coupling disparate models (atomistic and continuum models), information has been passed hierarchical at the ‘smallest’ length scales. At the ‘larger’, i.e. ‘Engineering’, length scales, the hybrid approach exploited all three coupling methods. Fine-scale mesoscopic (or microscopic) domains around the macroscopic fractures were embedded by a concurrent coupling technique while the rest of the domain was considered as homogenized material. The material properties in those domains far away from macropscopic fracture was upscaled by either a hierarchical or semi-concurrent approach. In the first part of the project, the theoretical background for the coupling has been developed, implemented and verified by simple examples.

In the second phase of the project, the methodology was extended to ‘realistic’ materials, i.e. composites. Therefore, models at different length scale for a particular composite, i.e. CNT-reinforced polymeric nanocomposites, were developed. Simulations at the nanoscale were carried out in order to predict for instance the interface/interphase behavior between the polymer and the CNT. This interface behavior was upscaled to the next higher (micro-scale) level. At the macroscopic level, finally the fine-scale structure of this particular composite has been inserted as pointed out above. The approach was subsequently refined to account more complicated fracture patterns at the fine-scale and to upscale those complex fracture patterns into simple fracture patterns at the macro-scale. Experiments were carried out in order to validate the approach. For the validation, the consortium also carried out an extensive literature study to find suitable benchmark problems for our computational framework.

All methods have been implemented in our own academic software. Therefore, several exchanges were carried out in order to ensure that all members of the consortium were able to work with our software. This software could be the basis for further developments with the final goal of industrial use for the computational design of new materials. In particulate, the design of composite materials have seen a tremendous growth in recent years, with significant uptake in the aerospace, transport and energy sectors. Major new aircraft programmes now almost inevitably have a large composite content (also CNT based polymeric nanocomposites studied in our project). For several reasons, current design methodologies for composites do not yet make extensive use of numerical modeling and instead rely on largely empirically based methods. One main reason is the lack of robust design tools which accurately and reliably capture detailed structural behaviour with an acceptable level of conservatism. Another reason is the lack of sufficiently trained and experienced personal in the area of numerical modeling of composite failure. For example, light-weight structural materials are of prime interest for the future of civil aviation: reduction of fuel consumption and emissions are imperative. Composite materials are good candidates, but their damage tolerance is not sufficiently understood to take all the benefit of the theoretical capabilities of e.g. carbon fiber-epoxy composites. The ability to accurately model the fracture of these materials would allow significant airframe weight savings. Any saving on airframe weight allows to also reduce the weight of engines and systems because less power will be required to accelerate and control the aircraft, the snow ball effect. Furthermore, it is expected that an improved understanding of failure made possible by use of the software will allow substantial improvements in the design of the material itself as well.

All results have been published in international journals. Furthermore,