# Debonding quantification via Digital Volume Correlation. Application to a mortar reinforcement pull-out

Sylvain Langlois, Amélie Fau, Benjamin Smaniotto, Farid Benboudjema, Maroua Maaroufi, Fikri Hafid, François Hild

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Sylvain Langlois, Amélie Fau, Benjamin Smaniotto, Farid Benboudjema, Maroua Maaroufi, et al. Debonding quantification via Digital Volume Correlation. Application to a mortar reinforcement pull-out. PhotoMechanics - iDICs 2024 Conference, Oct 2024, Clermont-Ferrand, France. hal-05231451

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Distributed under a Creative Commons Attribution 4.0 International License
PhotoMechanics - iDICs Conference

29-31 Oct 2024, Clermont-Ferrand, France

Debonding quantification via Digital Volume Correlation. Application to a mortar reinforcement pull-out

S. Langlois, A. Fau, B. Smaniotto, F. Benboudjema, M. Maaroufi, F. Hafid, F. Hild

Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Laboratoire de Mécanique Paris-Saclay, Gif-sur-Yvette, France

**Abstract** – In composite materials, the debonding phenomenon is challenging to quantify directly via standard tests. This study applies Finite Element-based Digital Volume Correlation (FE-DVC) to investigate debonding between a mortar matrix and a reinforcement during an in-situ pull-out test within an X-ray tomograph. A 3D mesh replicates the foundation and reinforcement geometry. By splitting the nodes at the interface, the reinforcement kinematics is better captured, and debonding is assessed with displacement jumps.

**Keywords** – DVC, Mechanical regularization, Pull-out, Decohesion, Mortar

**Introduction** Debonding is a frequent phenomenon in composite materials, like reinforced concrete, which occurs within the material bulk and cannot be quantified directly via macroscopic measurements [1]. One way to overcome this issue is to use Computed Tomography (CT) coupled with Digital Volume Correlation (DVC) to measure displacement fields in samples with scans acquired during in-situ tests. Measuring phenomena such as debonding remains a challenge with DVC, given the finesse of the kinematic field. Global DVC [2] coupled with finite element methodology allows one to measure displacement fields on fine meshes with sub-voxel resolution.

In the present study, FE-DVC with mechanical regularization was used to quantify debonding at the interface between a Glass-Fiber-Reinforced-Polymer (GFRP) and mortar during an in-situ pull-out test. A mesh was created to describe the geometry of both materials from computed tomography reconstructions. Employing twin nodes to characterize the interface significantly reduces the correlation residual in the reinforcement and allows to measure displacement jumps.

**Methods** The specimen consists of a GFRP reinforcement anchored in a small-scale mortar foundation. Pull-out is performed by prescribing a vertical (z-axis) displacement with a stroke speed of 3 µm/s. The foundation is loaded in steps to perform scans along the loading history. Global DVC is used to measure displacement fields of the sample during the in-situ test and consists in minimizing the global image residual $\Phi_c$ over the entire Region Of Interest (ROI) between a reference volume $f(\mathbf{x})$ and a deformed volume $g(\mathbf{x})$

$$ \Phi_c^2 = \sum_{ROI} [f(\mathbf{x}) - g(\mathbf{x} + \mathbf{u}(\mathbf{x}))]^2 \quad (1) $$

The displacement field $\mathbf{u}(\mathbf{x})$ is expressed in terms of finite element discretization using 4-noded tetrahedra (T4). Let $\mathbf{v}$ denote the vector gathering all degrees of freedom (DOFs). For the reported analyses, DVC was regularized by adding an elastic-based cost function $\Phi_m$ derived from the equilibrium gap

$$ \Phi_m^2 = \frac{1}{2} \nu^T [\mathbf{K}]^T [\mathbf{K}] \nu \quad (2) $$

Both cost functions are normalized through a unitary displacement field. DVC consists in minimizing the sum of these two cost functions, with a weight $w_m$ dependent on a regularization length $l_{reg}$

$$ \mathbf{u}(\mathbf{x}) = \operatorname{Argmin}(\tilde{\Phi}_c^2(\mathbf{v}) + w_m(L_{reg})\tilde{\Phi}_m^2(\mathbf{v})) \quad (3) $$
The considered mesh is shown in Fig. 1(a) which involves split nodes to allow displacement jumps between mortar and GFRP at their interface [3].

**Results** The DVC computation was performed between an unloaded state and a deformed one, where the specimen had experienced failure at the chimney but bore the pull-out force in the slabs. The uncertainty of $u_z$ in the GFRP reinforcement increases from 0.02 to 0.05 voxel compared to an interface with single nodes, with no significant influence observed in mortar. The root mean square level residual in the GFRP decreases from 10.0 to 9.6, indicating improved capture of the kinematics in the fiber when allowing displacement jump at the interface with the mortar. Debonding is quantified by the displacement jump at the interface:

$$du = u_{\text{interface}}^{\text{GFRP}} - u_{\text{interface}}^{\text{mortar}} \quad (4)$$

Fig. 1(b) displays the displacement jump $du_z$ along the loading axis, as a function of the vertical z-coordinate of the mortar foundation. Mortar underwent downward sliding at the foundation upper section, while no significant debonding is observed in the chimney area. Chimney cracking occurred at $z = 450$ voxels, coinciding with the highest debonding amplitude. Interestingly, this amplitude is negative, indicating a slight elevation of the mortar in the upper part of the crack, coupled with sliding in the lower part.

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 1 Mesh of the specimen (a). Vertical displacement jump as a function of height of the studied foundation (b)</figcaption></figure>

**Discussion and Conclusion** Node splitting at the interface of the studied composite enabled DVC to reduce the registration residual in the fiber. The displacement fields are calculated with better reliability, but at the cost of higher uncertainties. Debonding was quantified by the displacement jumps at the interface between GFRP and mortar. The mortar foundation cracked at the chimney, which induced large strains in the corresponding element. Additional split nodes may be introduced in the DVC analyses, or reduced regularization in these areas.

## References

[1] E.D. Reis, R.C. de Azevedo, A.L. Christoforo, F.S.J Poggiali, A.C.S. Bezerra. Bonding of steel bars in concrete: A systematic review of the literature. *Structures* 49:508–519, 2023

[2] S. Roux, F. Hild, P. Viot, D. Bernard. Three-dimensional image correlation from X-ray computed tomography of solid foam. *Composites Part A: Applied Science and Manufacturing* 39:1253–1265, 2008

[3] G. Jänicke, A. Vintache, B. Smaniotto, A. Fau, I. Farina, F. Fraternali, F. Hild. Debonding analysis via digital volume correlation during in-situ pull-out tests on fractal fibers. *Composites Part C: Open Access* 9:100302, 2022.