Representative Volume Element for Modelling the In-Plane Mechanical Behaviour of Paperboard: Utilizing Microstructure from X-ray Tomography

Abstract

The aim of this project is to establish a workflow that transforms CT-scanned images of paperboard into a calibrated Representative Volume Element (RVE). A RVE is defined as the smallest volume that accurately captures the macroscopic behaviour of the material.

First, CT-scanned images are converted into a finite element model that rep- resents the microstructure of the paperboard. Secondly, a discrete field of fiber orientations are established by using Structure Tensor analysis. Thereafter, trans- verse isotropic material parameters of fibers are calibrated using the Hill yield criteria and Ramberg-Osgood relation to describe plastic deformation. This is done through iterative adjustments of material parameters until agreement with experimental data is reached. Finally, a sensitivity study is conducted to evaluate the effects of different RVE sizes and resolutions on the accuracy and efficiency of the model.

The findings of this study suggest that the proposed workflow serves as a base for calibrating anisotropic material properties at the micro-scale to match macro- scale data. The derived material properties of fibers indicate a longitudinal elastic modulus on the order of 50 GPa and a transversal elastic modulus of approximately 4 GPa. For the plastic characteristics of fibers the calibrated properties closely approximate ideal plasticity.

The sensitivity analysis reveals that a volume of at least 0.33x0.33x0.12 mm is required to be considered representative of the paperboard investigated in this study. However, due to material inhomogeneities, the model is influenced by the location of extraction. Moreover, the conducted studies show a clear dependence on tested voxel resolutions.

Popular Abstract

Understanding the relation between the microstructure and mechanical prop- erties of paper materials is crucial for optimizing their performance in practical applications. This study focuses on characterizing the microstructure of pa- perboard by analyzing the relation between the microscopic properties and its macro-mechanical response.
The aim of this project is to establish a workflow that transforms CT-scanned images of paperboard into a calibrated Representative Volume Element (RVE). A RVE is defined as the smallest volume that accurately captures the macro- scopic behavior of the material and is independent on size and location of ex- traction. The workflow can be divided into four main steps.
1. Mapping CT-Images to a Virtual FE-Model: X-ray tomography images of paperboard are stacked to create a 3D volume. A finite element mesh is then generated, where each voxel in the image corresponds to an element in the mesh. These elements are binarized based on intensity values to distinguish between fiber and void.
2. Calculate Fiber Orientations: Fiber Orientations are identified and mapped to the model using structure tensor analysis that is based on analyzing intensity gradients. The fiber orientation is identified as the direction corresponding to the least change in intensity.
3. Calibrating Material Model: An automatic method is established to cali- brate a transverse isotropic material model to the fiber elements. The fiber ma- terial parameters are iterative adjusted until the RVE’s simulated stress-strain response aligns with experimental stress-strain response of paperboard.
4. Sensitivity Study: A sensitivity study is conducted to evaluate the effects of RVE size, location of extraction, and resolutions on the accuracy and efficiency of the model.

The proposed workflow can convert X-ray images of paperboard into a vir- tual model that includes fiber orientations and calibrated material properties. However, the material calibration is complex, and the number of parameters to be calibrated with limited data makes it sensitive to the initially estimated parameters and the hardening model used.

The sensitivity study revealed that the RVE must be at least 0.33x0.33x0.12 mm to ensure size independence, although larger RVEs are required for achiev- ing homogeneous properties. One way to model larger RVE’s without increasing the computational time could be to use lower resolution images. However, a clear dependency on resolution was observed when voxels were binned together. Overall, further studies on the RVE’s dependence on size, location and resolution are needed to draw statistically significant conclusions.

• author: Starkenberg, Stina and Wennerholm, Saga
• supervisor: Matti Ristinmaa; Eric Borgqvist; Eskil Andreasson
• organization: Solid Mechanics; Department of Construction Sciences
• course: FHLM01 20241
• year: 2024
• type: H3 - Professional qualifications (4 Years - )
• subject: Technology and Engineering
• keywords: Representative Volume Element, RVE, Finite Element Modelling, FEM, X-ray tomography, Xray- computed tomography, XCT, fiber, paperboard, material calibration, Structure Tensor Analysis, STA, Abaqus, resolution, voxel size, cellulose material, microstructure
• publication/series: TFHF-5000
• report number: TFHF-5261
• language: English
• id: 9164120
• date added to LUP: 2024-06-18 08:34:30
• date last changed: 2024-06-18 08:34:30