Micromechanics of the internal bond in wood plastic composites: integrating measurement and modeling
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In this study, an integrated approach combining experimental measurements and numerical modeling was used for characterization of load transfer in the wood/matrix interface in wood plastic composites (WPCs). The experimental methodology was based on optical measurement of surface displacements and strains in model WPC specimens subjected to tensile loads. The model specimens consisted of thin HDPE films with single embedded wood particles. The optical measurement of surface strains was based on the digital image correlation principle. The material point method was used for morphology-based numerical modeling of the loaded specimens. The exact location and morphology of the embedded particle determined by X-ray computed tomography were used as input for the numerical model. Imperfect interface characteristics, reflecting the efficiency of the load transfer through the interface in the numerical model of the composite, were determined using inverse problem methods. Good agreement was obtained between the simulated and measured strain maps determined on a number of specimens including particles with various orientations to the loading direction using the same values of interface parameters.
Wood plastic composites (WPCs) are heterogeneous materials comprised of irregular wood particles dispersed in thermoplastic polymer matrices. The matrix is typically high-density polyethylene (HDPE), polypropylene (PP), or poly (vinyl chloride) (PVC). The mechanical properties of such composites are determined by the micromechanics of the internal bonds between wood particles and the matrix. The ability to model and predict this interaction is crucial for designing improved, more efficient composites. This ability relies on a thorough knowledge and ability to predict the effect and efficiency of phase interaction on the bulk properties of the composite. Existing theories and models for short fiber composites allow prediction of composite properties based on the morphology of the composite, mechanical properties of the components, and the properties of the internal bond (Nairn and Shir Mohammadi 2015). However, these theories idealize the internal bond and particle morphology, typically considered to be continuous isotropic solids that are smooth and impermeable. Wood flour particles used in WPCs are generated in hammer mills and attrition mills by physically crushing and tearing larger pieces until the desired size is achieved. Their mechanical properties cannot be automatically assumed to match sound bulk wood tissue, but need to be experimentally characterized. It is unclear whether such idealization can be extended to WPCs where wood particles are anisotropic, porous, permeable, and irregular. In addition, there are many reasons that may negatively affect wood particle/matrix interactions (e.g., chemical incompatibility, compounding method, polymer penetration) and the resulting stress transfer between phases (Simonsen et al. 1997).
While bulk mechanical properties of particulate composites like WPCs can be determined by means of standard test methods, lack of reliable quantitative measurement techniques that would allow analysis of the load transfer between matrix and wood particles in composites at a scale relevant to the size of individual wood particles posed a serious challenge for empirical verification of theoretical predictions and numerical models.
Recently, Schwarzkopf and Muszyński (2015a) proposed an experimental methodology based on optical measurement of surface displacements and strains in thin HDPE film model WPCs subjected to tensile loads. The optical measurement technique based on the digital image correlation (DIC) principle returned full-field surface displacement and strain maps of the specimens without physical contact with the surface. One limitation of the method was that the surface measurements alone could not fully resolve the strain patterns in the 3D matrix neighborhood affected by the wood particle interaction, or the zone of influence (ZOI), beneath the surface. Essentially, the surface measurements reflected the magnitude and trajectories of strains at an arbitrary section of the ZOI determined by the position and depth of the particle beneath the surface, somewhat away from the matrix–particle interface through which the loads are transferred.
A parallel study on micromechanics of adhesive bonds in wood by Kamke et al. (2014) proved that a successful characterization of load transfer is possible by combination of direct measurements of the surface strains with morphology-based numerical simulations of deformation in the volume beneath the surface. In that study, material point method (MPM) modeling was coupled with micro-X-ray computed tomography (XCT) and optical measurements based on DIC. XCT data were used as direct morphologic and material input to a micromechanical MPM model of the scanned wood–adhesive interphase. The model was then validated by comparing simulated surface strains with those measured optically on the XCT scanned specimens in the course of non-destructive lap-shear tests. Selected model parameters (local mechanical characteristics of the wood and adhesive, and the wood–adhesive interface) were adjusted until a satisfactory agreement was achieved between the surface strains predicted with model simulations and the strains actually measured on the lap-shear specimens. This approach, based on inverse problem methodology, can be used for many applications in a variety of fields, particularly when there is a level of fundamental compatibility between the full-field optical measurement output and the input to the numerical model of the empirical scene (Muszyński and Launey 2010). While the theory of this approach is pretty intuitive, the practical application requires a close collaboration between the experimentalist and the modeler from the early stage of the project, and an efficient integration of these aspects is challenging.
The objective of this study was to adopt this approach for an efficient integration of optically measured deformations and strains, with predictive MPM numerical modeling tools to characterize the load transfer at the internal bond between the particles of wood flour and a polymer matrix in wood plastic composites.
Materials and methods
The general approach of this project followed the major steps of the methodology described by Muszyński et al. (2013) and Kamke et al. (2014). Specimen fabrication and testing followed methods described by Schwarzkopf and Muszyński (2015b). The outline of the procedure was as follows: (1) manufacture model WPC specimens; (2) use XCT scans for characterization of the internal morphology of the specimens; (3) perform mechanical tests on the specimens and optically measure the surface displacements and strains; (4) numerically simulate the mechanical test with a morphology-based MPM model; and (5) refine model parameters in an iterative process using inverse problem methods to deduce properties of wood particles and of the particle/matrix interface (Muszyński et al. 2013).
The authors were not aware of any viable method for planting individual wood particles in plastic films preserving even rudimentary elements of the compounding process, which is crucial for forming a realistic wood particle/matrix interphase, resembling that in WPCs. Therefore, the approach selected in this study was to compound sparsely filled composites and select specimens with isolated wood particles for testing.
In addition to the set of specimens with wood particles, a set of reference specimens were made in a similar fashion with small sections of embedded wire instead of wood particles. These reference specimens were intended to mimic the somewhat idealized particle morphology assumed in most existing particle/matrix theories (Tucker and Liang 1999). A more detailed description of the specimen manufacturing process is offered in Schwarzkopf and Muszyński (2015a).
Characterization of specimen morphology
Mechanical test and surface strain measurements
Specimens were tested in tension using an Instron ElectroPuls E1000 test machine. The specimen free length of 20 mm included portions of the tabs on both sides (Fig. 1). Specimens were loaded in displacement mode at a constant rate of 0.5 mm/min (strain equivalent to 0.02 mm/mm per minute) for 2 min. The force was measured using a ±2 kN load cell (Instron 2527 Series Dynacell). During the test, images of the specimen surface in the immediate neighborhood of the embedded particles (field of view: 7.18 mm × 6.00 mm) were recorded every 1 s for 2 min with the VIC-Micro 3D™ system (Correlated Solutions, Inc., Columbia, SC, USA). The working distance from the microscope lens to the specimens was 30 mm.
These images were used to determine surface coordinates, components of displacement vectors, and calculated surface strain tensor components by means of VIC-3D 2012 optical measurement software based on the DIC principle integrated with the optical system. To enhance the DIC analysis, which relies on measuring displacements of unique targets identified on the specimen surface, printer toner was used to apply a fine speckle pattern directly to the light-colored specimen surfaces (Fig. 2a), which provided sufficient contrast with the toner. The pattern was applied by means of air deposition apparatus and fixed on the surfaces by heating in an oven at 103 °C for 10 min. The technique is described in greater detail in Schwarzkopf and Muszyński (2015a).
The uncertainty of optical measurement is not only a function of the robustness of the DIC algorithm and the attached optical hardware (cameras, lenses, etc.), but is also affected by variables specific to the experimental scene like the quality of the speckle pattern, light, and calibration which at the scale used in this study are much harder to control and assess separately. Therefore, in this project, the accuracy and precision of the optical measurement is performed on the actual test scene of undeformed specimens just before loading. The displacement and strain components for all points on the undeformed specimen are expected to be zero. Thus, simple statistical analysis of nonzero residuals at all points within the area of interest provides us with convenient estimates of systematic bias (average) and random error (standard deviation). These snapshots of undeformed specimens just before the loading allow us, if need be, to analyze the effects of minute differences in speckle pattern distribution between the specimens. This simple routine provides us with an easy metric for the combined uncertainty involved in the optical measurement. This approach was used in the preliminary study to select optimal setup conditions, speckle pattern density, and DIC algorithm parameters: the facet size and the step size. Using a subset facet size of 49 pixels × 49 pixels and a step size of 5 pixels allowed a displacement resolution of 0.038 μm ± 0.020 μm and strain resolution of 50 μm/m ± 2.5 μm/m.
Axial strain maps (in the direction of loading) were recorded at a nominal stress level of 5 MPa on specimens with particles oriented at an angle of 0°, 45°, and 90° to the direction of load. The maps were then cropped to uniform dimensions and used as reference data for the numerical analysis. The area of interest (AOI) was 3 mm × 3 mm for specimens with particles inclined at 0° and 45° and 3 mm × 2 mm for particles inclined at 90°.
The numerical simulations of the tensile tests were carried out using the MPM (Sulsky et al. 1994), which is a particle-based method analogous to finite element analysis (FEA). The particle nature of MPM makes it easier to discretize complex, realistic morphologies (Nairn 2006, 2007; Kamke et al. 2014; Aimene and Nairn 2015) and also, potentially, allows for improved calculations of interfacial contact and imperfect interfaces (Nairn 2013). Both these advantages were needed for this work.
A custom MPM code called OSParticulas (Nairn 2016) was used to build 3D morphologically accurate numerical models of the regions of interest of individual specimens, which allowed us to run virtual experiments of numerical representations of the specimens used in the physical experiments. In the MPM method, a numerical model can be generated directly from the XCT scans, by turning selected voxels into material points (Kamke et al. 2014). X-ray attenuation of the scanned material reflected by the grayscale intensity of the voxels was used to assign either particle or matrix properties to each material point. In this work, the XCT scans for wood particle and embedded wire specimens had a voxel size of 10 µm × 10 µm × 40 µm (the lower dimension was the axial direction of 0° particles). These scans were input to MPM calculations, which were run with a particle size of 40 µm × 40 µm × 40 µm. Each simulation was comprised of about 1.2 million material points and took about 18 h. Without higher-resolution XCT scans, it had to be assumed that the available resolution was sufficient for accurate numerical modeling. The use of much higher resolution would likely be impractical due to long simulations and the need for multiple simulations to solve inverse problems.
Mechanical properties used for HDPE matrix, wood particles, and copper wire in the MPM numerical modeling
E (or E L ) (MPa)
E R and E T (MPa)
G LR and G LT (MPa)
G RT (MPa)
ν (or νRT)
ν LR and ν LT
σ Y0 (or σ Y,LL) (MPa)
σ Y,RR and σ Y,TT (MPa)
τ Y,LR and τ Y,LT (MPa)
τ Y,RT (MPa)
The Hashin (1990, 1991) imperfect interface analysis is based on interfacial stiffness and meant to apply up to the point of debonding or failure. To model strength as well, the relations in Eq. (4) could be modified to have a maximum normal or shear strength. In other words, interfacial failure would have D n and D t as functions of displacement discontinuities (possibly being nonlinear) and drop to zero (i.e., convert to a debonded interface) after failure. These experimental and numerical results had no evidence of significant debonding. This work thus focused on interfacial stiffness and avoided introduction of additional interfacial strength parameters.
Finally, to solve the approximate inverse problems, MPM simulations were performed for the same nominal stress level at which the surface strain maps were measured and MPM simulations were done on specimen morphologies derived from XCT data. In principle, by comparing simulated results to experimental results as a function of all input parameters, one could determine those parameters. In practice, this can be done only for a limited number of input parameters. One way of reducing the amount of computation is to exclude parameters to which the model is less sensitive or focusing on least known parameters, for which good estimates are not available. In this study, to simplify the analysis, the unknowns were reduced to a single property or one interface parameter D = D n = D t, which was then determined by inverse methods of matching predictions to experiments.
These interface properties are difficult to verify independently. However, some degree of validation may be achieved by comparing the results obtained for the wire reference with theoretical results obtained using one of the short fiber theories and/or by comparing interface property values determined on different specimens with wood particles used in this study.
Results and discussion
The initial results presented here are proof of concept for an integrated procedure as a tool for characterizing load transfer between particles and matrix in WPCs expressed through the interphase integrity parameter D. First, the method was validated by using a model system with a copper wire embedded in HDPE instead of a wood particle. This model material was used because the properties of the component phases were determined with little uncertainty and because the phases were certain not to mix at the interface, which left the interfacial properties as the only unknown material parameter in the composite.
Composites with wire particles
The experimental results show low axial strain near the center of the copper wire. At either end of the embedded particle, high strain concentrations in the matrix are seen. This behavior is the expected behavior arising from mechanics of load transfer from compliant matrix to stiff wire. All observations are consistent with measured and theoretical descriptions of load transfer in short fiber composites (Cox 1952; Clyne 1989; Nairn 2004; Sretenovic et al. 2006; Schwarzkopf and Muszyński 2015a).
The MPM results in the middle show numerical predictions with D = ∞ (representing a perfect interface) and then for decreasing values of D = 10,000, 5000, and 1000 MPa/mm representing increasing level of imperfection of the internal bond. The perfect interface simulation (D = ∞) shows lower strain in the fiber and higher stress concentration in the matrix. Both of these differences indicate better stress transfer in the simulation than in the experiments (Nairn 2004). With the decreasing value of the interface parameter reflecting less perfect stress transfer between the wire and the matrix, the simulated surface strains gradually became closer to those measured experimentally.
To visualize the difference between simulation and experiments, plots mapping the magnitude of the net difference were added in the right column. A perfect agreement would be seen as a 0.000 difference across the entire area in the right column. For D = 1000, regions of disagreement were lowest with the maximum difference being about 0.002 strain (20,000 μm/m). This is well within the DIC measurement resolution of 50 μm/m ± 2.5 μm/m.
Composites with wood particles
The next comparison is focused on the strain maps obtained from simulations and experimental measurements for specimens with embedded wood particles oriented at 0° to the loading direction. Figure 2 shows the specimen, and Fig. 2c shows MPM discretization of the particle derived from XCT experiments. The MPM model shows only the wood particle material points, while the material points for the matrix have been removed for clarity. The particle had a much rougher surface than the copper wire, but, by using XCT data, the simulations can model the roughness and can match roughness of simulated particles to the roughness of the experimental specimen.
Another difficulty in interpreting experiments with embedded wood particles compared to experiments with embedded copper was that the mechanical properties of hammer milled wood particles were estimated with greater uncertainty due to lack of reliable data. The wood properties used for numerical simulations (Table 1) were set at the low end of values quoted for clear southern yellow pine and for simplicity used E R = E T and G LR = G LT (they are similar). The material properties are still, however, orthotropic because of low G RT. Although it is possible the properties of particles would be reduced compared to clear wood due to hammer milling used to extract them, the authors did not have properties specific for particles. The choice for wood properties might have affected the results for D, which was assumed to be the only needed variable in the numerical analysis. The authors tried scaling down wood properties by various factors and did not find significant differences in the overall conclusions. All simulations shown here thus used the full properties in Table 1. A better approach would be to deduce both the mechanical properties of wood and the imperfect interface factor by inverse problem methods. This more advanced approach would require coupled analysis of greater number of experimental specimens, which is beyond the scope of this proof-of-concept study.
An integrated method was presented for coupling experimental measurements of strain fields on the surface of wood particle composites with 3D numerical simulations of the strain fields in the specimen volume to assess particle/matrix load transfer and interfacial properties of the composite. The analysis was performed at a spatial scale that is relevant to the wood particle/matrix interactions. The numerical model was based on morphological input data from XCT scans. These scans were needed to properly reflect the particle position within the specimens and to capture effects of surface roughness of wood particles.
Inverse problem methods were used to determine one input parameter—an imperfect interface value D (MPa/mm)—used in the model to characterize the efficiency of load transfer between the particle and the matrix. The value of this parameter was varied until good agreement was obtained between the simulated and measured strain maps determined on a number of specimens including particles with various orientations to the loading direction using the same values of interface parameters. The other uncertain parameters were assumed as known.
A relatively low value of this parameter (D = 1000 MPa/mm) was determined for reference copper wire/HDPE composites meant to simulate the idealized short fiber/matrix interface. By contrast, an effectively perfect interface parameter (D = ∞) was found to provide simulations closest to the actual measurements for wood/HDPE composite samples. This high load transfer efficiency in wood/HDPE composite samples might be due to mechanical interlocking in the porous wood/polymer interphase observed in other studies.
In future work, the analysis may be fine-tuned by increasing the number of unknown parameters to be determined in the inverse problem method (e.g., the mechanical properties of wood particles). This work, however, will require a greater number of input experiments, different loading modes, multiple particle interactions, and greater computing power.
The authors gratefully acknowledge: Urszula Iwaniec and the micro-XCT laboratory at OSU for conducting the XCT scans, the USDA National Research Initiative Grant Program Award No. 2008-35504-19227, the National Science Foundation grant CMMI 1161305, and the European Commission for financial support through the project InnoRenew CoE, Grant Agreement #664331 under the Horizon2020 Widespread-2015 program.
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