Simulation of Self Healing Capacity of Hybrid Fibre Material E. Schlangen1*, S. Qian1, H. Liu1 1

Delft University of Technology, CiTG, Microlab, P.O. Box 5048, 2600 GA, Delft, The Netherlands * phone: +31 152786535 , e-mail: [email protected]

1. Introduction Fibre cement based materials have been developed during the past decades for many applications and with many different properties. Fibres of different dimension and of different materials have been used, e.g. steel, PVA, PE, glass or several kind of natural fibres. The fibres are added to the cement composites to enhance material toughness, strength, fatigue life, impact resistance and/or cracking resistance. A special type of fibre reinforced cement based composites is the group of materials that have a very high strain capacity of sometimes more than 6%. An example of these materials is ECC (Engineered Cementitious Composites) as described in [1]. These materials show upon loading a distributed crack pattern with fine cracks and a high strain capacity which make them especially suitable for application where imposed deformation is the loading mechanism. The design of these composites is based on an analytical micromechanical approach [1]. The parameters that determine the strain capacity in fibre cement based composite can be summarized as follows: - Fibre parameters: fibre length, fibre diameter, fibre stiffness, fibre strength, fibre volume fraction and fibre shape. - Matrix parameters: matrix stiffness, matrix strength and matrix fracture energy. - Fibre-matrix interaction parameters: interfacial frictional bond strength, stiffness and fracture energy. All these parameters can be derived from measured data obtained in experiments, see [2]. Experiments, however, are time-consuming, especially while certain time has to be allowed for the hydration of the cement and development of the mechanical properties. Therefore it was decided to adapt the 3D numerical lattice model to be used to predict the strain capacity of fibre reinforced materials. Inputs in the model are all the different parameters for fibres, matrix and interface as discussed above. The model is described in section 2 of this paper. Self Healing of cement based materials is getting a hot issue [3,4]. Durability of concrete structures is important; both to save on the maintenance costs for structures and to drastically reduce the use of raw materials. Two self healing processes are being studied for self healing concrete, i.e. filling cracks to block the path to the steel reinforcement and repair the crack to regain mechanical properties. Ductile fibre cement based materials are an excellent candidate to serve as a self healing material. The material itself is such that it spreads strain out over many cracks and as such only relatively small cracks develop in the material, which are easier to heal. Furthermore, when the material is functioning in a structure, there are still unhydrated cement particles in the material, which hydrate further when water penetrates into the crack [3,5,6]. However, by this mechanism only the smaller cracks

(<20μm) will be closed [5]. Therefore it was decided to start developing a hybrid fibre material. This hybrid fibre material consist of a fibre cement based material, similar to ECC, with PVA or PE fibres and with some additional hollow (natural) fibres containing healing agent. The principle is that the additional hollow fibres are relatively weak and break upon stretching, i.e. when the cement matrix breaks. At that moment the healing agent will be released can either fill or repair the crack. The healing agent can just be water. In that case it could be used to heal micro-cracks in an early stage by ongoing hydration of the unhydrated cement with the water from the hollow fibres. Alternatively the healing agent could be glue or an (expansive) gel, in which case it could be used to heal bigger cracks. With the model described in the next section the hybrid material can be designed. It can be studied what the optimum amount and mix of fibres should be to obtain a ductile behaviour, with a desired strain capacity and crack width. The amount, size and distribution of hollow fibres and the amount of healing agent in the fibres needed to obtain proper healing can be determined with the model. 2. Model Description Simulation of fibre concrete with lattice models is applied by Bolander [7]. The application of their models is mainly reduction of shrinkage cracks. The model presented in this paper is based on the principle of embedding discrete fibres in a random lattice representing the matrix. In the model presented in this paper the (cement) matrix is represented by a random lattice [see also 8]. The fibres are discrete beam elements connected to the lattice elements by interface beams. The procedure to generate the network is as follows: - A cubical grid is chosen. In figure 1 a schematic representation is shown in 2D. The real mesh is 3D, but more difficult to clearly visualize. - In each cell of the square (cubical for 3D) lattice, a random location for a lattice node is generated. - Then always the 3 nodes (4 nodes for 3D) which are closest to each other are connected by beam elements. - Next step is to generate fibre elements. First the number of fibres is calculated that have to be placed in a certain volume based on the length, diameter and volume percentage of fibres. These fibres are then a mix of fibres to obtain the proper ductile behaviour of the material and hollow fibres for the healing. Then the location of the first node of the fibre is randomly chosen in the volume. Next the x, y and z direction of the fibre is chosen randomly which determines the location of the second node. If the second node falls outside the volume the fibre is cut off at the boundary. The fibrevolume of the cut off part of the fibre is subtracted from the already placed fibre-volume in order to ensure enough fibres at the end of the procedure. - Extra nodes inside the fibres are generated at each location where the fibre crosses the square (cubical for 3D) grid. - Then interface elements (bond beams) are generated between fibre nodes and the lattice node in the neighbouring cell. Also the end nodes of the fibres are connected with an interface element to the cell-node in which the end node is located. - All the elements in the network are beam elements (with normal force, shear forces, bending moments and torsion moment), which have a local brittle behaviour. The beam elements fail only in tension (except for the interface elements, which can also fail in

compression) when the stress of the element exceeds its strength. For the fracture criteria only the normal force is taken into account to determine the stress in the beams. The fracture modelling in the lattice model is only a sequence of linear elastic steps, which makes it fast and without numerical difficulties. For the set of equations and model properties the reader is referred to [8]. square grid lattice node lattice beam extra node fibre beam fibre node bond beam

Fig. 1. Schematic 2D representation of generation of fiber-lattice.

3. Model Results With the model tensile tests and four point bending tests are simulated with different amount of fibres. In figure 2 the final crack pattern for tensile tests with a low (1%) and high (4%) amount of mechanical fibres are shown as well as for a bending test with 4 % fibres. In case of 1% fibres a single crack develops and a brittle response. In case of 4% fibres a ductile response is obtained with multiple cracking. In the mixes also healing fibres are placed, with an amount equal to the 1% mechanical fibres. In Figure 2 also the healing fibres that are broken in each of the specimens are shown. It can be seen that in the case of the ductile material much more fibres are broken, however the cracks that should be healed are also much smaller. If it is assumed that the specimen in both cases is stretched to the same strain, then in the present simulations, (with the present specimen length) it means that the crack width in the 1% fibre material is about 10 times larger. Also the amount of healing fibres that is broken is 10 times less. From this it can be concluded that 10 times more healing agent would be needed in the 1% fibre material and that most of the healing agent will not be used. In case of a ductile hybrid material (in this case with the 4% mechanical fibres) the healing agent is used everywhere and the healing agent is not placed at locations where it is not used. It is optimized for perfect healing ability and use of material. As explained above the healing mechanism can be ongoing hydration (water in the healing fibres) or crack filling with glue or even an expanding epoxy. 4. Conclusions In this paper a model is presented to study the self healing of hybrid fibre reinforced cement based materials. The model can be used to design a proper mix with the right amount, size and distribution of fibres. Furthermore the desired ductility in relation with the moment and amount of healing can be studied by varying the mixture of mechanical (PVA or PE) and healing (hollow, natural) fibres.

a)

b)

c)

d)

e) Fig. 2. Cracked specimens with 1% (a) and 4% (c) mechanical fibres loaded in tension and 4% fibres in bending (e) and healing fibres broken in simulation with 1% (b) and 4% (d) mechanical fibres.

5. Acknowledgement The authors would like to thank Senter Novem for financial support of this project (IOP-Healing Built-in Building Materials).

6. References 1. V.C. Li, On Engineered Cementitious Composites (ECC) – A Review of the Material and its Applications. J. Advanced Concrete Technology, 2003. 1(3): p. 215-230. 2. E. Schlangen, Z. Qian, M.G. Sierra-Beltran & J. Zhou, Simulation of fracture in fibre cement based materials with a micro-mechanical lattice model. In proceedings ICF12, 12th International Conference on Fracture, July 12-17, 2009, Ottawa, Canada. 3. Li, V. C. and E. Yang, 2007, Self Healing in Concrete Materials, Self Healing Materials – an Alternative Approach to 20 Centuries of Materials Science, Edited by S. van der Zwaag, Springer Series in Materials Science 100, 2007, pp.161-193. 4. E. Schlangen and C. Joseph, 2008, Self-healing Processes in Concrete, in Self-healing Materials: Fundamentals, Design Strategies, and Applications, edited by S.K. Ghosh, Wiley-VCH, 2008, pp. 141182. 5. S. Qian , J. Zhou, M. R. de Rooij, E. Schlangen, G. Ye and K. van Breugel. 2009, Self-Healing Behavior of Strain Hardening Cementitious Composites (SHCC). Accepted for publication in Cement and Concrete Composites. 6. S. Qian, J. Zhou, H. Liu, M. R. de Rooij, E. Schlangen, W. Gard, J. W. van de Kuilen. 2009, SelfHealing Cementitious Composites under Bending Loads. This conference. 7. J.E. Bolander, Numerical modeling of fiber reinforced cement composites: linking material scales, in Proc. Rilem Symposium BEFIB 2004, September 2004, Varenna Italy, pp. 45-60. 8. E. Schlangen and Z. Qian. 2009, 3D Modelling of Fracture in Cement Based Materials. Journal of Multiscale Modelling, Vol. 1, No. 2, 2009.