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Multiscale Science and Engineering

, Volume 1, Issue 2, pp 108–118 | Cite as

Evaluation of the Moisture Effect on the Material Interface Using Multiscale Modeling

  • Renyuan Qin
  • Denvid LauEmail author
Review
  • 135 Downloads

Abstract

Layered material systems are widely seen in various engineering applications such as thin films circuit boards in electronic engineering, lipid bilayer in biological engineering, and adhesive bonding in aerospace and civil engineering applications. However, the durability of the material interface can be seriously affected due to the prolonged exposure to water. Although the experimental studies have shown the reduction in terms of ultimate bond strength and fracture toughness for material interface, the shift in failure mode found in experiment cannot be explained using conventional fracture theory, which is related to the interaction between the water and material interface. To understand the debonding mechanism from a fundamental and comprehensive aspect and bridge knowledge from the atomistic scale to continuum scale, multiscale modeling approach has been proposed to study the debonding behavior of material interface under moisture effect. A number of studies have been conducted using multiscale modeling approach to investigate the debonding of material interface, and it is necessary to summarize these studies to understand the role of water molecules in weakening and diffusing at the material interface using different atomistic models, force fields and upscaling techniques. This paper provides a comprehensive review on the multiscale modeling of interfacial and delamination behavior of layered material system under moisture attack with the focus on the molecular dynamics simulation and finite element modeling. The FRP bonded concrete system is used as a representative to demonstrate the approach of multiscale modeling. The future research direction is recommended, which involves the consideration of roughness of substrate and structural voids at interface for the better understanding of durability issue for interface in layered material system under different environmental conditions.

Keywords

Interface Multiscale modeling Molecular dynamics simulation Finite element modeling 

Introduction

Layered material system is widely seen in different engineering aspects such as the thin films circuit boards in electronic engineering, the lipid bilayer in biological engineering, and the adhesive bonding in aerospace and civil engineering applications. The integrity of layered material systems is governed by the interfacial property of bonded materials. The interfacial delamination is one of the most critical issues in the laminated material systems, such as the delamination of epoxy/copper interface in plastic integrated circuit (IC) packages, the detachment of enamel/polymer interface in dental medicine and debonding of fiber reinforced polymer (FRP) from concrete substrate in repairing or strengthening construction structures. The service condition has significant impact on the integrity of interface in such composite system including environmental temperature or moisture levels. The FRP bonded concrete system is a good example to demonstrate such interfacial degradation, since the FRP bonded concrete system is subject to the various environmental loads, e.g. moisture penetration, temperature change, chloride ion penetration, and alkalinity in its service life. Among these environmental effects, the moisture penetration is reported as one of the most critical factors which significantly reduces the load bearing capacity of the reinforced element from its designed value and causes unexpected failure of structures [1, 2, 3, 4, 5, 6, 7, 8, 9]. Under the moisture condition, deterioration of the mechanical property of composite system could be caused by the strength reduction of the FRP composites, plasticization of the polymer matrix or the degradation of interface between adhesion and substrate [10, 11, 12, 13, 14, 15].

As a representative, the FRP bonded system can be regarded as a layered composite system consisting three components, namely FRP, epoxy and concrete substrate. It has been reported that the concrete/epoxy interface is more critical than FRP/epoxy interface, when the composite system is subjected to moisture penetration [16, 17]. Moreover, it was found that although the crack propagation in the dry specimens could be predicted by the fracture theory according to the material properties, i.e. Young’s modulus and Poisson’s ratio, it failed to explain the strength reduction and the shift in failure mode for wet specimens, in which the interaction at the material level between water, epoxy and concrete could result in the variation of the material and interfacial properties [18]. To further understand the interfacial debonding mechanism under the presence of moisture, a more fundamental approach which can capture the molecular interaction and the change of interfacial property at small scales is needed. Recently, atomistic modeling approach employing molecular dynamics (MD) simulation is studied to address the above issues [19, 20, 21].

Molecular dynamics simulation is a powerful tool to perform simulations at molecular level, which can be used to study the molecular behavior of different substances and the mechanics of interfaces from a fundamental perspective [22, 23]. Moreover, it can provide the information about the mechanical behavior of the interfacial region by monitoring the interaction and deformation of the materials, so that the integrity of the bonded materials can be evaluated comprehensively. However, because of the limitation of computational power, MD simulation is mainly feasible for nanoscale, and the deformation mechanisms at interface can be various from different length scales. This fact requires a robust method that can translate the knowledge obtained from MD simulation to macroscale models such as finite element model, so that a prediction of mechanical behavior of materials and structural behavior of composite system can be achieved using a bottom-up approach [24, 25].

Recently multiscale modeling methods have been proposed to bridge the knowledge from different length scales from MD simulation to finite element simulation [26, 27]. The results from MD simulation, such as surface energy and intrinsic strength, can be converted to continuum interfacial properties by using traction–separation law for cohesive zone elements, which is widely used for modeling the interfacial fracture behavior of layered composite material system. The macroscale simulation can be conducted through finite element method to predict the structural behavior using the interfacial behavior captured by MD simulation. This multiscale modeling method enables the researchers to bridge the continuum and atomistic scale modeling and understand the structural behavior under the environmental attack from a fundamental and comprehensive aspect [28, 29, 30, 31, 32, 33].

The primary objective of this article is to provide a comprehensive review on the multiscale modeling of interfacial and structural behavior of layered material system under moisture attack with the focus on the molecular dynamics simulation and finite element simulation, and the FRP bonded system is used as the representative to demonstrate the multiscale modeling approach. The experimental studies towards the evaluation of epoxy/concrete interface under moisture attack are firstly discussed, in which the conventional fracture theory fails to explain the shift in failure mode in experimental findings, and interaction between water and materials is needed to be considered for the understanding of debonding mechanism in a multiscale manner. The MD simulations in terms of investigating the effect of water molecule on epoxy/concrete interface are reviewed, and upscaling techniques are provided to transfer the knowledge from nanoscale to macroscale scale. Besides, the finite element modeling using the interfacial behavior captured by MD simulation is discussed with a case study on the prediction of structural behavior of FRP bonded concrete under both dry and wet condition. This review work would enrich the understanding of debonding mechanism of layered material system under moisture attack at different length scales, and it could benefit the interested researchers to further use the multiscale modeling method to investigate the durability issues of such material system under different environmental conditions.

Moisture Effect on the Material Interface: FRP Bonded Concrete System

Experimental Studies on the FRP Bonded Concrete Under Moisture Attack

The FRP bonded concrete is a good example to study the delamination of layered material, since it is a typical laminated composite system consisting FRP, epoxy and concrete, and such structures are commonly found under environmental moisture attack. As FRP materials are now widely consumed in civil infrastructure application for strengthening or retrofitting concrete structures, the debonding between FRP and concrete substrate has been a critical issue of interdisciplinary research because of its significant impact on the structural performance of reinforced members. To investigate and quantify the interfacial degradation between FRP and concrete, two approaches are commonly used, i.e. strength-based approach and fracture-based approach. Strength-based approach adopts the calculation of the bond stress distribution in FRP reinforced elements based on the elastic material properties to predict the debonding between FRP and concrete substrate by comparing the calculated maximum stress with the strength of the materials [34, 35, 36, 37, 38, 39, 40]. ACI Committee 440 recommends guidelines on the strain level developed in the FRP to prevent debonding failures [41, 42], which is given as follow:
$$\varepsilon_{\text{fe}} = \varepsilon_{\text{cu}} \left( {\frac{h - c}{c}} \right) - \varepsilon_{\text{bi}} \le {\text{K}}_{\text{m}} \varepsilon_{\text{fu}}$$
(1)
where \(\varepsilon_{\text{fe}}\) is the maximum allowed effective strain in FRP, \(\varepsilon_{\text{fu}}\) is the ultimate strain in the FRP, \(\varepsilon_{\text{cu}}\) is the ultimate strain of concrete, h and c are the beam height and neutral axis depth, respectively, \(\varepsilon_{\text{bi}}\) is the concrete strain when the FRP reinforcement installs, and the \({\text{K}}_{\text{m}}\) is the limiting strain coefficient related to the layers, thickness and the elastic modulus of the FRP reinforcement. From the Eq. (1), it is shown that in the current design code developed by strength-based approach, the geometric and elastic material properties are the main concerns, which is feasible to predict the short-term performance of the FRP bonded system. However, the failure process of crack initiation and propagation at local debonding regions are intrinsically neglected in the strength-based approach. The fracture-based approach makes use of the interfacial fracture toughness, Γ, to quantify the debonding between FRP and concrete based on the kink criterion, which is considered as a bond property of the multilayer material system [43, 44]. This approach is considered to be robust in determining the debonding mechanism of FRP bonded system since it is able to predict the crack initiation and propagation at a local region by assessing the bonding property between multilayers on bond lines, in which case the real scale structures can be represented by mesoscale interface fracture specimens.

Interfacial Degradation

Externally bonded FRP system usually involves three materials, i.e. FRP, epoxy and concrete, and two interfaces, i.e. FRP/epoxy and epoxy/concrete. The failure modes of the system can always be summarized into following categories, namely (a) FRP delamination; (b) FRP/epoxy separation; (c) epoxy decohesion; (d) epoxy/concrete separation; and (e) concrete substrate fracture. It is reported that the debonding at epoxy to concrete interface is the vulnerable and the most critical in FRP bonded concrete system under moisture condition, which are shown in Fig. 1.
Fig. 1

Idealization and definition of debonding scenarios, including FRP delamination, FRP/epoxy separation, epoxy decohesion, epoxy/concrete separation and concrete substrate fracture. Among this debonding scenarios, the debonding at epoxy to concrete interface in the most critical under moisture effect

To evaluate the debonding behavior of FRP bonded system under moisture condition, experimental tests have been carried out using peel and shear test to determine the interface fracture toughness [17, 18]. The interface fracture toughness was calculated by specialized fracture energy release rate, G. The interface fracture toughness values can be computed by following equations:
$$\varGamma_{\text{peel}} = \frac{{N_{{{\text{y}},{ \hbox{max} }}}^{2} }}{{B^{2} \bar{E}_{3} h^{3} }}\left( {\frac{{(l + a)^{2} - l^{2} }}{{2I_{1} }} + \frac{{6l^{2} }}{{\mathop \sum \nolimits_{13} }}} \right)$$
(2)
$$\varGamma_{\text{shear}} = \frac{{N_{{{\text{x}},{ \hbox{max} }}}^{2} }}{{2B^{2} \bar{E}_{3} }}\left( {\frac{1}{{A_{1} h}} + \frac{{\varPsi^{2} }}{{I_{1} h^{3} }}} \right)$$
(3)
where \(\varGamma_{\text{peel}}\) and \(\varGamma_{\text{shear}}\) are the interface fracture toughness for the peel fracture and shear fracture, respectively; \(N_{{{\text{y}},{ \hbox{max} }}}^{ }\) and \(N_{{{\text{x}},{ \hbox{max} }}}^{ }\) are the critical peel and shear load, respectively; B is the width of the bond; h is the thickness of FRP; l is the cantilever length; \(a\) is the pre-crack length; \(\bar{E}_{3}\) is the degraded plain strain elastic modulus of concrete; \(\mathop \sum \limits_{13}\) is the ratio of plain strain modulus of FRP to that of concrete; \(A_{1}\) is the dimensionless composite area; \(I_{1}\) is the dimensionless moment of inertia; \(\varPsi\) is the eccentricity function. For the details of the determination of these parameters, the reader is referred to the literature [17, 18].
The experimental results of peel and shear test for FRP bonded system under moisture condition are summarized in Fig. 2 from literature [17, 45]. It is found that in fracture tests, the different amount of reduction in terms of fracture toughness can be seen after the moisture duration. The fracture toughness was reduced to 37% of that in dry case after 8 weeks conditioning in peel test. For shear fracture scenario, the reduction of fracture toughness is less than that in peel fracture scenario, given that the friction between bilayers plays an important role during the fracture process with a treated rough bond surface. However, still 14% reduction of fracture toughness can be seen after 8 weeks moisture condition comparing with that in dry case for shear fracture scenario. It is noticed that the debonding mode of epoxy/concrete separation was consistently observed after 2 weeks moisture conditioning, while the concrete delamination was observed for all dry specimens. However, when the crack kink criterion theory was adopted, although it could predict the crack propagation observed in the dry cases, it failed to explain the reduction of strength and the shift in debonding mode for wet specimens. Such results indicate that this failure mode is due to an interfacial material toughening or an interface weakening mechanism caused by externally moisture penetration, which involves the complex interactions between the water molecules and materials close to the interface. According to these findings, a more fundamental approach should be used to study the debonding mechanism of the interface under moisture penetration, and molecular dynamics simulation is particularly suitable to be used for such study by providing fundamental information for the interaction between the materials at interface.
Fig. 2

Summarized of peeling and shear test results for FRP bonded concrete conditioning in wet environment for 4 and 8 weeks. It is noticed that the debonding model of epoxy/concrete separation was consistently observed after 2 weeks moisture conditioning, while the concrete delamination was observed for all dry specimens

Modeling of Separation at Interface Under Moisture Attack

Molecular Dynamics Simulations

MD simulations have been applied to study the molecular behavior of different substances as a powerful numerical modeling technique [46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61]. According to the previous experimental studies, the critical region of the FRP debonding from substrate under moisture attack locates at the interface between epoxy and substrate. This fact allows the using of MD simulation to model the composite system as a bilayer structure, which consists of epoxy and substrate, to understand the debonding mechanism [62, 63, 64, 65].

MD simulation is based on the modeling of behavior of atoms and molecules explicitly to capture the nature of the matter at atomistic level, which provides a fundamental description of material property and a dynamic evolution of equilibrium and non-equilibrium processes. The interaction between the fundamental units or atoms, i.e. attraction or repulsion, is governed by interatomic potential or force field (FF), which is determined by a function of distance between the atoms. This approach has been used in solving the small scale structural mechanics problems, such as localized fracture processes in materials [66, 67, 68, 69, 70, 71, 72, 73]. One of the challenges in using MD simulation is to build up the atomistic model that can accurately describe the structure and property of the system, and balance the computational amount in a reasonable range.

To capture the accurate interaction between the epoxy and concrete interface under moisture attack and simplify the system in MD simulation, the diglycidyl ether of bisphenol A (DGEBA) [74, 75, 76, 77, 78, 79, 80, 81] is commonly used to represent the molecular structure of epoxy, which is the key functional group in most of the construction-related epoxy possess. For concrete, it is more complex since it is a heterogeneous composite, which consists of hydrated cement and different size of aggregates. It is reported that silica accounts for more than 40% by weight of the solid ingredients of cement and aggregates in concrete, which can be adopted for construction atomistic model of concrete with well-defined chemical formula [19]. Recent studies have shown that crystalline silica (SiO2) can be used to represent both the cement and aggregate as well [82, 83]. After the construction of the atomistic model, the proper force field should be chosen to well describe the interaction between the atoms in the system. Several force fields have been developed in past decades to simulate the behavior of polymers including epoxy-based material, such as ClayFF, DREIDING, PCFF, CFF91 and CVFF [84, 85, 86, 87, 88, 89, 90]. Among these force fields, it is reported that CVFF is capable to describe the atoms behavior of inorganic materials as well, so it is appropriate to be used in the MD simulation to capture the atomic behavior at epoxy and silica interface.

The steered molecular dynamics (SMD) have been performed on the silica-epoxy system for computational peel and shear tests by fixing the silica substrate and applying the pulling force with the velocity ranging from 2 to 1000 m/s [91]. The pulling force was applied to the end carbon atom in the epoxy by a virtual spring with the normal and parallel direction to the interface to simulate the peeling and shear loading. The moisture attack was simulated by the incorporation of water molecule in the simulation box. The simulation results show that for the dry case, the adhesive energy, Eb, was 9.10 kcal/mol and 7.06 kcal/mol for peeling and shear case, respectively. For the wet case, the corresponding adhesive energy was 7.74 kcal/mol and 5.99 kcal/mol for peeling and shear case, which indicated that the adhesive strength between silica and epoxy reduced at 14.9% and 15.2% for peeling and shear case with the presence of water. Moreover, the phenomena that some water molecules can seep into the gap between silica and epoxy under wet condition was captured by molecular dynamics simulation, which is shown in the Fig. 3.
Fig. 3

The snapshots captured by MD simulation at different time for a better understanding on the interaction among epoxy, silica and water: a time = 0 ps; b time = 200 ps; c time = 450 ps in dry condition and d time = 0 ps; e time = 200 ps; and f time = 450 ps in wet condition. The presence of water molecules hinders the attraction between epoxy and concrete (represented by silica), which results in a weaker bond

The failure mode of silica–epoxy system in molecular dynamics simulations is consistent with the results from experimental studies of FRP bonded concrete specimens under prolonged moisture. Results from MD simulations provides an atomistic-based understanding on the reduction of adhesive strength of the interface, which is due to interaction between epoxy and water. However, the simulation results from this study can only describe the considered system correctly on limited length and time scales, which lead to the needs that can expend the knowledge to a larger length scale [92, 93, 94, 95].

The MD simulation has also been applied to study the transport of moisture at silica-epoxy interface [96, 97]. The condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) force field was applied to the epoxy and silica system with a ratio of 3:7 in this study, and water molecules were directly arranged manually at interface in the system [98, 99]. After an equilibration step, the MD simulations were performed at several temperatures for 2 ns to study the diffusion coefficients. The results show reasonable agreement between experimental and simulation results, and diffusion of water moisture at interface between silica and epoxy is faster than that in the epoxy bulk. Such results further indicate that the interface between silica and epoxy is the critical region under moisture attack [100].

Upscaling

The multiscale approach used for modeling the interface of bilayer system usually involves a systematic determination of interfacial parameters for upscaling. In the nanoscale modeling, the atomistic model can provide the nano-mechanical properties of bonded system using a free energy approach [101, 102]. The surface energy can be characterized by a free energy surface (FES) from an attached stage referring to the lowest free energy state to a detached stage when the separation between two materials is larger than the cutoff distance of the pair potential. The difference in the free energy between the attached and detached stages can be normalized by the corresponding molecular contacting area between two materials, which results an estimate of the upper bound of the surface between two materials. Such procedure can be achieved using the metadynamics methods [103, 104, 105].

After the calculation of surface energy from MD simulation, the interfacial behavior can be then determined for continuum modeling. One method to convert the results from MD simulation to determine the debonding mechanism is using worm-like-chain (WLC) based fracture model [106]. The WLC fracture model is based on the rubber elasticity concept and can be used to describe the interfacial debonding at molecular level as a molecular peeling process from a single polymer chain. A combination of WLC model and fracture approach enable us to obtain the energy release rate (G), which is equal to the surface energy between two material in the bilayer system at the stage just before the onset of rupture, and the intrinsic strength of interface can be then expressed as follow [91]:
$$F_{\text{break}} = \frac{{k_{B} T}}{{4\xi_{\text{p}} }}[(1 - \alpha_{\text{cr}} )^{ - 2} + 4\alpha_{\text{cr}} - 1]$$
(4)
where \(k_{B}\) is equilibrium bond length, \(\xi_{\text{p}}\) is the persistence length, \(\alpha_{\text{cr}}\) is the ratio between chain length and contour length when debonding occurs, and T is the temperature set in the simulation. The surface energy and instrinstic strength of interface can be then used to quantify the interfacial behavior of bilayer system, which provides a bridge between the discrete atomistic model and finite element model.
Another upscaling approach is directly modeling the epoxy into bulk material through cross-linking the single epoxy polymer chains [107, 108]. The single epoxy polymer chain is formed from polymerization among the associated monomers and such polymer chain can then cross-link with each other, which leads to a bulk cross-linked structure. An effective dynamic cross-linking algorithm has been studied for epoxy modeling in MD simulation under three force fields, i.e. CVFF, Dreiding and PCFF [109, 110, 111]. The calculated mechanical properties, including Young’s modulus, bulk modulus, shear modulus and Poisson’s ratio, are in good accordance with experimental observables. Such cross-linking process in MD simulation enables us to model the system as two bulk materials. The atoms in MD simulation are normally modeled as point masses, and the potential energy of the system provides the forces on each atom, which can be adopted to determine the acceleration, velocity and positions of each atom. The stress σ for atom i in the region V can be calculated by the relation [112, 113]:
$$\sigma = \frac{1}{V}\mathop \sum \limits_{i \in V} \frac{{\partial \varPhi_{\text{i}} }}{\partial \varepsilon }$$
(5)
where \(\varepsilon\) and V are the strain and volume over the region which the stress is calculated, and \(\varPhi_{\text{i}}\) is the potential energy. To capture the interfacial behavior in MD simulation using such approach, a tensile or shear strain can be applied to the model in each simulation step and the displacement should be maintained before the further displacement is applied. By repeating this procedure in MD simulation until the complete separation of the bilayer is achieved, the tensile or shear stress at interface can be calculated from simulation. With the recorded displacement, the stress–displacement relation can be obtained from MD simulation [113, 114, 115].

Macroscale Model Using Finite Element Method

To predict the structural behaviour of FRP bonded in a macroscale manner, the interfacial parameters generated by MD simulation can be converted into finite element simulation using cohesive zone model (CZM), which is widely used in simulating the fracture process in polymers, metals and composites [116, 117, 118]. CZM was first introduced as a technique to study the fracture in quasi-brittle materials such as ceramic and concrete. The mechanical property of CZM is governed by a given traction–separation relationship, which is defined by initial stiffness, damage initiation threshold, and damage evolution properties. In aforementioned WLC fracture model, these parameters can be determined by maximum debonding stress, σth, which can be predicted as Fbreak/s2, where s is the grid length in MD simulation; the fracture energy, Γs, which is predicted by σ th 2 H/2G, where H and G are the thickness and shear modulus of epoxy; and Young’s Modulus, E, which is predicted by kL/A0, where k is the interfacial stiffness, L is distance between epoxy chain and substrate and A0 is the contact area [60].

In applying tensile or shear strain in bulk material in MD simulation, the stress–displacement curve can be directly calculated from simulation results, and this relationship describes the relationship of interfacial traction force and interfacial bonding opening displacement during delamination of the bilayer system, which is exactly the cohesive constitutive relation of the interface. Apart from quantifying the traction–separation relation for modeling the interface from empirical approaches, the interface property converted from MD simulation provides the scientific support in explaining the interaction between two materials at the interfacial region from the physics and/or chemistry point of view, which is a more efficient and fundamental approach to evaluate the structural behavior under moisture or other environmental attack [15, 21, 119, 120, 121].

Case Study of Delamination of FRP Bonded Concrete

To evaluate the structural performance of FRP bonded concrete under moisture attack, we reproduce the finite element model in literature considering the traction–separation law captured from MD simulation with the presence of water molecular [80, 91]. A two-dimensional finite element model has been built, whose dimensions are shown in Fig. 4.
Fig. 4

The schematic diagram of a the dimensions of FRP bonded concrete system simulated in finite element simulation and b the material properties of FRP, epoxy and concrete are determined from experiment, and the interface between epoxy and concrete is modeled based on the results from MD simulation

The properties of bulk materials including concrete, FRP and epoxy are determined from experimental studies using solid elements. Since the study focus on the interfacial debonding, the concrete is modeled as elastic material with the elastic modulus of 26.2 ± 2.2 GPa. The elastic modulus and tensile strength of CFRP laminates are defined as 148 GPa and 2.7 GPa, respectively, according to the experimental measurement in the literature [17, 18]. The elastic and tensile strength of epoxy adhesive are set as 1.5 ± 0.1 MPa and 23.0 ± 2.2 MPa, respectively. The details of the material properties can be found in the literature.

The traction–separation law for cohesive zone elements is defined according to the results from MD simulation for both dry and wet conditions using aforementioned approach, which is arranged at interface between epoxy and concrete. The predicted material properties at epoxy–silica interface at both dry and wet condition is determined from results of MD simulation available in the literature, which is shown in Table 1. It should be noticed that the FES captured at single molecule level can only reflect the interfacial behavior between epoxy and silica system at certain extent, given that there are various defects with unknown sizes along the interface. For the continuum epoxy–silica bilayer system, it can be visualized as a series of cross-linked polymer chains connected to the silica surface through the adhesion at the chain tail, and the free volume in the cross-linked structure near the interfacial region can be regarded as the local heterogeneity or defects at this region. After carefully reviewing the upscaling approaches and techniques, the results from molecular dynamics simulations using a grid system to illustrate the adhesion behavior between cross-link network of epoxy and silica were used [91]. According to the reported results from MD simulations, when the 2 nm grid size is adopted in the molecular model, a good agreement can be achieved between molecular dynamics simulations and experimental results in terms of material and interfacial property [80, 91]. Moreover, 2 nm is also a reasonable distance between adjacent cross-links for a fully cured epoxy, which can reflect the material morphology.
Table 1

Prediction of the material properties at epoxy–silica interface

 

E (GPa)

σth (MPa)

Γs (J/m2)

Dry

4.54

33.50

292.00

Wet

4.37

15.20

146.00

The finite element simulation is performed exactly according to the experimental setup for the peeling test of FRP bonded concrete system and the comparisons between experimental and simulation results are shown in Fig. 5.
Fig. 5

Comparison of experimental and simulation results. a The load–displacement curve of FRP bonded system in dry and wet condition determined in experiment and simulation; and b the comparison of ultimate load for experiment and simulation results, indicates that the traction–separation relation conducted by MD simulation is capable to be used in finite element simulation to predict the structural behavior of FRP bonded concrete system in both dry and wet condition

The simulation results show good agreement with the experimental results in terms of ultimate bond strength as well as the structural behavior. The ultimate bond strength from simulation is determined as 132.9 N and 58.9 N for peeling test in dry and wet condition respectively, whose deviation with the experimental results are 10.75% and 17.80% for samples conditioning in dry and wet environment. Such results indicate that the traction–separation law obtained from MD simulation is capable to predict the structural behavior of FRP bonded concrete system under moisture attack. Moreover, it explains the debonding mechanism from atomistic scale fundamentally with the reason why the interface is degraded when water molecule is presented.

Summary and Future Challenges

This paper has provided a review on the multiscale modeling of layered material interface under moisture attack in terms of MD simulations, upscaling techniques and finite element simulations with a specific focus on the interface separation between epoxy and concrete. The multiscale modeling provides a bottom-up approach to predict and understand the interfacial debonding mechanism. However, there is still extensible space for such multiscale approach in modeling the material interface. In most of the MD simulations, the substrate is modeled as crystalline structures, which assumes a perfectly flat interfaces. In fact, the interface of materials will not be intact and smooth, which accelerates the water diffusion into materials interface. Recently, efforts have been made to construct the coarse-grain models parameterized from molecular models at targeted length scale [122, 123, 124, 125]. It will be advantageous to take such coarse-grained models in the multiscale modeling scheme, which can better understand the interfacial behavior of materials with consideration of interfacial roughness and the heterogeneity of the materials. Moreover, the microscopic structural voids generally existing in the epoxy cross-linked networks, which has a detrimental influence on the epoxy mechanical properties [126, 127]. Such structural voids should be considered at different length scale in the multiscale modeling to better understand the interface of porous materials under moisture attack. By considering a more realistic modeling of material interface, it is envisioned that such multiscale modeling scheme can be further developed and adopted in the design and applications of composite structures in different engineering aspects.

Notes

Acknowledgements

The authors are grateful to the support from the Research Grants Council (RGC) in Hong Kong through the General Research Fund (GRF) with the Grant no. 11255616.

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Copyright information

© Korean Multi-Scale Mechanics (KMSM) 2019

Authors and Affiliations

  1. 1.Department of Architecture and Civil EngineeringCity University of Hong KongKowloonHong Kong
  2. 2.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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