Interfaces in composites: pulling a rebar out of a matrix

Key to composite response are interfaces. For instance, reinforced concrete works only because the matrix cracks and the steel slips against it. Here a single rebar is pulled out of a concrete cylinder on a 3D lattice, with a plasticity bond in which slip generates a normal plastic strain that splits the matrix.

Interfaces make composites interesting. The macroscopic response is set by how the matrix and the inclusion interact. Reinforced concrete is the classic case. It works only through two coupled mechanisms. The matrix cracks, and the steel slips against the matrix at their interface.

In this example, the coupling is analysed with a single rebar that is pulled out of a concrete cylinder. Matrix, steel and bond are all modelled with discrete lattice elements.

What the model shows

The pullout test is displacement controlled. First the pullout force increases. It reaches the peak and then reduces with increasing pull out displacement. Splitting cracks initiate at the bar matrix interface and propagate radially outward through the concrete cover.

The mechanism

The bond between matrix and rebar is modelled with a plasticity interface model (Grassl & Davies, 2011). Axial slip along the bar generates a radial component of plastic strain. The rebar is modelled in 3D, so that radial plastic strain pushes against the surrounding matrix. The matrix resists the radial plastic strain by hoop tensile stresses. These tensile stresses induce the splitting cracks. Without the dilatancy in the flow rule, slip would generate shear only.

Setup

The example consists of a concrete cylinder, 100 mm long, 100 mm diameter; a centric steel bar with a 16 mm diameter is placed in the centre of the cylinder. For the steel concrete interface, a thin (0.1 mm) shell of latticecontact3d bond-contact elements carrying the plasticity bond law is placed. At the face where the bar is pulled out, a 20 mm bond-free length is introduced. This is often the case in pull-out tests so that the measured bond strength is not affected by the confinement generated by the friction between concrete and the loading plate which restrains the specimen. Here, it does not matter because the matrix face at the side where the steel is pulled out is only supported in the pullout direction and can therefore expand freely in the lateral direction without generating any confinement. The concrete response is modelled with a damage-plasticity model. This works better than isotropic damage models in cases in which radial compression generates tensile cracking.

Toward more accurate modelling

The setup is modelled with a coarse mesh so that generating the results does not take too long. Steps to obtain more accurate results would be to refine the lattice and add heterogeneity to the matrix. The heterogeneity can be added by mapping a random field of strength on the lattice as in the 2D random tensile example, or an explicit aggregate arrangement, as in the aggregate placement example.

Reproduce

git clone https://github.com/githubgrasp/oofem-examples.git
cd oofem-examples/lattice-pullout
docker run --rm -v "$PWD":/work ghcr.io/githubgrasp/oofem-public:lattice-pullout bash run.sh

The image tag :lattice-pullout is the exact one used for the results above and is immutable. Use :latest for the current OOFEM build; results may drift as the code evolves.