Modeling of Ceramic Oxide Fiber Bundles Mechanical Properties

Project manager:Dr. Rolf Janßen
Project worker:João Gustavo Pereira da Silva, Eng.
Supported by:CAPES (Brazil) / Deutsche Forschungsgemeinschaft (DFG)
Collaboration:Federal University of Santa Catarina (UFSC),
Florianópolis/SC, Brazil
Prof. Hazim Ali Al-Qureshi, PhD;
Prof. Dr.-Ing. Dachamir Hotza
Start:July 2010
End:May 2011


It is well-known that for bundles of fibers, that the bundle strength is always less than the sum of the fiber strengths, sometimes as much as 50%. In Fig. 1 are shown typical Weibull plots for single fiber strength, the strength of a bundle of these fibers, and the strength of a composite made with the bundle. Note that going from the fiber to the bundle, the average strength is decreased, but, as the bundle is made into a composite, the strength goes up; also notice that the Weibull modulus (m) increases, meaning the variability decreases. There are clearly things happening in the bundle and composite that cannot be explained deterministically.

Fig. 1:
Weibull plots for fiber tensile strength, bundle strength, and composite bundle strength [1].

This behavior can be explained by load-sharing models. So even when the weakest fiber fails, the remaining fibers share the load, and thus increasing the effective stress in these fibers. This eventually leads to an overloading, and subsequent failure. The load sharing can be equal (ELS), meaning that all fibers remaining on the bundle share the load of a failed fiber, or local (LLS), where only the nearest fibers to the failed one share the load [2].

More desirable, however, is being able to predict the bundle strength distribution from knowledge of the fiber strength distribution, as well as being able to predict the strength of a large bundle of fibers; as n -> ∞ the calculation of strength analytically becomes extremely tedious.

Also, during processing (infiltration and subsequent handling), and in the composite, the fibers are allowed a lesser degree of load transfer. This leads to local-load sharing. Local load sharing are quite difficult to implement analytically, but with the help of computing software (as Matlab), these rules can be simulated and determined via comparison with the experimental behavior.

The main activities in this work are the following:

  • Relate single-fiber properties and bundle properties;
  • Simulate diverse load-sharing models for fiber bundles and determine the best suited for the studied ceramic fibers;
  • Relate the fiber defect distribution to survival probabilities of single-fiber and bundles;
  • Study the influence of processing (thermal treatments, slurry infiltration) on the defect distribution of the fibers, and therefore, the mechanical properties.

The fibers to be investigated are 3M Nextel® 610 (Alumina) and 720 (Mullite-Alumina), oxide ceramic fibers widely used on the manufacturing of ceramic composites.

First of all, the load sharing models and the mechanical testing will be simulated using Matlab or FEM software. This is due to the difficult nature to find analytical solutions to load sharing when the number of fibers in the bundle is high (>400 fibers per bundle), as in case of the studied Nextel® fibers.

To validate the simulations, single and fiber bundle testing will be carried, and the data will be analyzed, together with SEM images of the fracture surface, to determine the failure mode of fibers, and consequentially, the critical defect type.

Fig. 2: Specimen for Single-fiber Testing [3].

The surface of the fibers will be characterized with Atomic Force Microscopy imaging, in order to determine the defect distribution and relate this distribution to the scatter in strength in mechanical testing.

Fig. 3: AFM imaging of glass fibers, in order to determine the defect distribution [4].

This project is part of a cooperation between Brazil and Germany called BRAGECRIM (Brazilian German Collaborative Research Initiative in Manufacturing). The Brazilian partner of TUHH in this project is the Federal university of Santa Catarina (UFSC).


  1. Schulte and Fiedler, 2005: Structure and Properties of Composite Materials
  2. Harlow and Phoenix, 1978: The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I
  3. Stutz, 2006: Recycling von CFK: Einfluss von Pyrolysetemperatur und -atmosphäre auf die Bildung von Pyrolysekoks und die daraus resultierenden Eigenschaften der Recyclatfasern. Studentarbeit, TUHH.
  4. Foray, Descamps-Mandine, 2010: Glass Fiber Statistical Strength Distribution: Correlation Between Mechanical Parameters and Microstructural Observations. Proceedings of the 7th International Conference of High Temperature Ceramic Materials and Composites.