Cohesive Law Research Articles

Determination of the Matrix-Fiber Cohesive Material Law of FRCM-Concrete Joints

Fiber-reinforced cementitious matrix (FRCM) composites have been increasingly used to strengthen existing concrete and masonry structures in the last decade. Two guidelines are available for the design and construction of FRCM strengthened members: ACI 549.4R (2013) and CNR-DT 215 (2018). Both these guidelines employ the effective strain, i.e. the strain at which the composite action is lost, as key parameter for the evaluation of the capacity of FRCM strengthened members. The American guideline ACI 549.4R (2013) employs the results of clevis-grip tensile tests on FRCM coupons to determine the composite effective strain. Such strain is determined by the Italian guideline CNR-DT 215 (2018) combining the results of direct shear tests on FRCM-substrate joints and of tensile test of bare fiber textile. The effective strain is strictly related to the matrix-fiber bond behavior, which can be expressed by the interface shear stress-slip relationship, i.e. the cohesive material law (CML). The effective strain is not sufficient for a full understanding of the structural response of strengthened members, since the knowledge of the CML is needed to predict important parameters such as the crack pattern or the location where debonding occurs in beams strengthened in flexure. This paper provides a simple procedure to obtain the CML from the load response obtained by direct shear tests of FRCM-substrate joints. The procedure is discussed and applied to the case of poliparaphenilene benzobisoxazole (PBO) FRCM-concrete joints previously tested by the authors.

Strain-rate dependent mode I cohesive traction laws for glass fiber-epoxy interphase using molecular dynamics simulations

Using molecular dynamics (MD) simulations, we develop strain-rate dependent Mode-I cohesive traction laws for the glass fiber-epoxy interphase as a function of interphase structure. Interphase models with mono-layer glycidoxypropyltrimethoxy silane are prepared varying silane number density from 0.0 nm−2 to 3.9 nm−2. Interphase is formed through epoxy-amine diffusion in the silane layer followed by curing reaction. Traction laws are developed over a full range of strain rates from quasi-static to super-high strain rate (∼1e16/s) where a theoretical plateau strength limit is predicted. A stress-relaxation methodology is introduced to construct quasi-static traction-separation responses from high strain rate loading. Simulation results reveal that the interphase traction-separation responses are strain rate and silane number density dependent. Variations of peak traction and energy with strain rates show a characteristic S-shape pattern in a semi-log plot with a gradual increase in properties up to 1e12/s where a steep transition occurs between 1e13/s to 1e14/s followed by a strain rate independent plateau. Interphase properties (especially peak traction) increase almost linearly with silane number density for all strain rates. Mathematical correlations for the MD predicted traction versus strain rate and energy versus strain rate data are established to bridge length scales providing input micromechanics models for the prediction of fiber-matrix debonding in composites.

A coupled plasticity-damage cohesive-frictional interface for low-cycle fatigue analysis

A novel thermodynamically consistent cohesive-frictional model for the analysis of interface degradation and failure under either monotonic quasi-static loading or cyclic loading in low-cycle fatigue problems is proposed.Starting from the definition of a suitable Helmholtz energy density function, a phenomenological interface model is developed in the framework of plasticity and damage mechanics. In particular, a coupled plasticity-damage activation function is defined and employed together the consistent evolution rules to capture the evolution of damage and plasticity under the action of the external loads. Due to the specific features of such threshold and flow rules, the initiation and accumulation of damage under monotonic increasing loads is captured and accompanied by negligible plastic evolution, allowing to approximate pure damage-based cohesive laws. On the other hand, coupling associative plasticity and damage evolution allows linking the interface degradation in low-cycle fatigue processes to plastic hysteresis, on the basis of the phenomenological assumption that no infinite plastic flows may happen without microstructural transformation leading to loss of load bearing capability. The model also embodies a smooth transition from an initially cohesive to a residual frictional interface behaviour, governed by a Coulomb frictional activation function.The developed formulation has been implemented and assessed for individual interfaces, highlighting consistent phenomenological behaviour. It has been then applied to the analysis of delamination and de-bonding in composite test cases, showing accuracy against experimental data and confirming its potential.

Damage characterization of dental nanocomposite adhesive in orthodontic treatment applications

In orthodontic treatments, mechanical characterization of orthodontic bracket bonded to the tooth is essential to determine the bond strength and mechanical behavior of the bracket-adhesive-tooth system. In this study, the linear-nonlinear mechanical behavior and damage characterization of Filtek Z350 XT (3M ESPE) nanocomposite as a dental adhesive material to bond orthodontic brackets to tooth enamel, are investigated using numerical and experimental methods. Full sets of tensile, shear, and mixed modes I/II and I/II/III debonding experiments are conducted to extract the mechanical properties of the nanocomposite adhesive as the bracket/tooth interface. The results of the experiments are used to obtain the cohesive law and the damage model parameters. Three-dimensional finite element models of the bracket debonding tests are developed, while the cohesive zone model (CZM) is used to define the constitutive behavior of the nanocomposite interface under the tensile, shear, and mixed-mode loading conditions. The FE results showed a good correlation with the measured data, indicated the validity of the constitutive model, damage properties, and simulation process. The bond strengths of the nanocomposite adhesive are obtained 8.35 and 4.12MPa in modes I and II loadings, respectively.

Experimental evaluation of cohesive laws components of mixed-mode I + II fracture characterization of cortical bone

Mixed-mode I + II fracture characterization of cortical bone tissue is addressed in this work. The mixed-mode bending test was used to impose different mode ratios. An equivalent crack length data reduction method was considered to obtain the strain energy release rate components. Crack opening and shear displacements were measured by means of digital image correlation. These quantities were then integrated to propose a direct evaluation of cohesive laws. The components of the cohesive laws for each mixed-mode loading were obtained by the uncoupled and Högberg’s methods. The later provided consistent evolution of strain energy release rate and peak stresses components in function of mode-ratio, revealing its appropriateness regarding the fracture characterization of cortical bone under mixed-mode I + II loading.

Modeling the behavior of externally bonded reinforcement using a rigid-trilinear cohesive material law

Externally bonded reinforcement (EBR) represents a valid solution for strengthening and retrofitting existing structures. Among possible reinforcements, fiber-reinforced composites gained large popularity in the construction industry mainly due to their high strength-to-weight ratio and durability. Due to their high strength, failure of externally bonded fiber-reinforced composites is usually due to debonding, which makes understanding the bond behavior of these materials of paramount importance for the effectiveness of the strengthening application. Within this framework, bond tests are generally employed to obtain information on the stress-transfer mechanism between the composite and the substrate. The results of these bond tests can be employed to derive the interface cohesive material law (CML), which describes the relationship between the shear stress and corresponding slip at the interface where debonding occurs.In this paper, a rigid-trilinear CML is proposed to describe the stress-transfer mechanism of externally bonded composites that show the presence of frictional stresses at the debonding interface. The analytical solution of the full range behavior of composite-substrate joints with long and short bonded lengths and with free and fixed far end is provided using the proposed CML. Then, the results of thirty-five single-lap direct shear tests of PBO fiber-reinforced cementitious matrix- (FRCM-) concrete joints are presented and employed to calibrate the CML. Good agreement is found between the analytical and corresponding experimental direct shear test load responses.

Post-cracking regimes in the flexural behaviour of fibre-reinforced concrete beams

The flexural behaviour of steel fibre-reinforced concrete beams is discussed in the framework of Fracture Mechanics. The Bridged Crack Model is updated by means of a cohesive softening constitutive law of the reinforcement layers, taking into account the fibre slippage within the cementitious matrix. In this way, the model is able to describe the global response of the composite, including the local instability phenomena characterizing the different post-cracking regimes. The structural response is found to be governed by two dimensionless numbers: the reinforcement brittleness number, NP, which defines the minimum reinforcement condition of the composite beam, and the pull-out brittleness number, Nw, which describes its plastic rotation capacity. The former, NP = (Vfσ¯sh1/2)/KIC, depends on the fibre volume fraction, Vf, on the fibre slippage strength, σ¯s, on the concrete fracture toughness, KIC, and on the beam depth, h. The latter, Nw = (wcE)/(KICh1/2), depends on the fibre embedment length, wc, on the concrete Young’s Modulus, E, on the concrete fracture toughness, KIC, and on the beam depth, h. These two parameters make it possible to identify a softening post-cracking response of the fibre-reinforced concrete element that is scale-dependent. Finally, the numerical analyses are compared to several experimental results reported in the scientific literature, proving the effectiveness of the described model.

Relationship between Results of Tensile Test of FRCM Composites and the Fiber-Matrix Bond Properties

The mechanical properties of fiber-reinforced cementitious matrix (FRCM) composites are derived from tensile tests of composite coupons and shear tests of composite strips bonded to the substrate. Different test set-ups are used for tensile coupons, which lead to different tensile responses depending on the mechanical properties of the matrix and bond properties of the fiber-matrix interface. Direct shear tests are employed to study the stress-transfer between the composite and the substrate onto which the composite is bonded. These tests can be employed to obtain the cohesive material law (CML) that describes the bond behavior at various interfaces, such as the matrix-substrate, matrix-matrix, and fiber-matrix interface. In this paper, the cohesive material law associated with the fiber-matrix interface of a polyparaphenylene benzo-bisoxazole (PBO) FRCM composite is employed in an analytical model to reproduce the tensile response of the FRCM composite, when the fibers are gripped directly. The results of the model are compared with corresponding experimental results of tensile tests of the same FRCM composite employed to calibrate the CML. The experimental work includes digital image correlation (DIC) analysis of the cracking process. A comparison between the analytical and the experimental results is performed in terms of load response focusing on the coupon deformation and opening of the cracks.

Calibration of a Rigid-Trilinear Cohesive Material Law to Describe the Matrix-Fiber Bond Behavior in FRCM Composites

Fiber-reinforced cementitious matrix (FRCM) composites have been increasingly adopted as externally bonded reinforcement (EBR) of existing concrete and masonry members. Being debonding at the matrix-fiber interface one of the most frequent failure mechanisms of externally bonded FRCM, the matrix-fiber bond behavior represents a fundamental aspect for the effectiveness of the external reinforcement. A cohesive material law (CML) that describes the interface where debonding occurs can be used to model the bond behavior observed. In this paper, a rigid-trilinear CML is used to solve the differential equation that governs the bond problem at the matrix-fiber interface of an FRCM composite. The CML adopted has peculiar characteristics that entail for a finite length of the bond stress transfer zone (BSTZ). Furthermore, it allows for a simple and accurate analytical solution of the bond problem. The analytical solution obtained is compared with the results of an experimental campaign comprising single-lap direct shear tests of a polyparaphenylene benzobisoxazole (PBO) FRCM composite specifically designed for masonry substrates. Different calibrations of the rigid-trilinear CML are proposed, also considering the matrix-fiber free end slip.

Finite Difference Model for the Bond Behaviour of Polyparaphenylene Benzobisoxazole (PBO) Fibre-Reinforced Composite System for Retrofitting Masonry

This study addresses a numerical investigation of the bond behaviour exhibited by an FRCM system when subject to tensile and single direct shear tests. A reinforcement system, based on a polyparaphenylene benzobisoxazole (PBO) bi-directional fibre mesh and a mixed cement-pozzolanic mortar is selected. The system is characterized by the presence of coated glass-fibre yarns and dry polypropylene yarns alternated to the PBO yarns in the warp and weft directions, respectively. The mechanical characterization of composite constituent materials is carried out together with tensile and direct shear tests. Concerning mechanical interpretation of the tests, within a mode II fracture mechanics, and assuming a trilinear cohesive material law (CML), the stress transfer law between the fibre and the matrix is back calibrated from single direct shear test results. The CML obtained is employed into a finite-difference model developed for the purpose. Tensile tests are modelled providing adequate boundary conditions. Results satisfactorily agree with the tested behaviour of the FRCM system.

Mode I fracture R-curve and cohesive law of CFRP composite adhesive joints

This work presents the fracture R-curve behavior of composite adhesive joints with both brittle and ductile epoxy adhesives using double cantilever beam (DCB) specimens. Carbon fiber reinforced polymer (CFRP) laminates were bonded using a brittle adhesive (Araldite® AV138) and a ductile adhesive (Araldite®2015). The mode I fracture tests showed that the crack path for both adhesive joints was observed to be cohesive in the adhesive at crack initiation, while the crack path shifted to a mix of both cohesive and interfacial failure at the steady-state region. The fracture tests along with digital image correlation (DIC) of the crack tip images were used to extract a tri-linear traction-separation laws (TSL) for the ductile adhesive and a bi-linear TSL for the brittle adhesive joint. Finite element model of the DCB specimen developed using the TSLs reasonably predicted the experimentally measured load response of the joint. The stiffness degradation study of the cohesive elements showed that the extent of the damage ahead of the crack-tip is high for the ductile adhesive than for the brittle adhesive.

A customized shear traction separation law for cohesive zone modelling of creep loaded ENF adhesive joints

Considering the creep behavior of bonded joints is of paramount importance since a constant service load can significantly change the properties of adhesives. Several models have been proposed to analyze the creep response of adhesive joints. However, none of them considers the cohesive zone modelling (CZM) as a robust damage analysis approach. The aim of the current work is to present a customized CZM based approach to predict the creep behavior of adhesives subjected to pure shear loading conditions using end notched flexure (ENF) samples. To achieve this a triangular shape cohesive law was used and the variation in cohesive properties of the adhesive was addressed through the proposition of two developed equations, one for the mode II fracture energy and the other for the shear traction. A family of numerical curves can be obtained for each creep condition, thus, the best numerical curve was achieved through a statistical analysis. The effects of the model on the cohesive parameters were also evaluated. The model was validated by an additional creep test. The numerical results were compared to the experimental data obtained in previous work and a good agreement was observed.

A general solution to the maximum detachment force in thin film peeling

While it is well known that the steady-state detachment force during 90° peeling of an elastic film on a rigid substrate provides a simple and powerful method to determine the interfacial work of adhesion, the situation is less clear for the maximum detachment force associated with the peeling process. Here, we propose a general solution to this maximum detachment force during 90° peeling, which is shown to depend on the interfacial work of adhesion, interfacial strength, bending modulus of the film, as well as an interfacial cohesive law shape factor. Combining this solution with Kendall’s classical model provides a method that allows the interfacial work of adhesion and interfacial strength of a film-substrate system to be simultaneously determined via peeling test.

Mode III testing of structural adhesive joints at elevated loading rates

The Out-of-plane loaded Double Cantilever Beam (ODCB) test has proven to be a well-suited test method for determining both energy release rate and cohesive law of adhesive layers in mode III under quasi-static conditions. As the rate-dependency of the fracture behaviour of adhesive layers in shear is still a topic of ongoing research, we aim to investigate, whether the ODCB test can be modified to be applicable at elevated loading rates. For this purpose, the experimental setup of the ODCB test was modified to allow testing at elevated loading rates. Tests were performed on an epoxy adhesive at outer loading rates over several orders of magnitude, ranging from quasi-static conditions up to the maximum possible test speed of the used servo-hydraulic test machine. The results of these experiments are discussed thoroughly to gain insight into the applicability of the ODCB test at moderate loading rates. Furthermore, the experimental challenges associated with an increase in loading rate are highlighted to identify limitations of the experimental setup that need to be addressed when transitioning to impact testing.

Adaptive affine homogenization method for Visco-hyperelastic composites with imperfect interface

Despite intense research on homogenization methods, it is a still challenging task to predict the nonlinear mechanical responses of visco-hyperelastic particle-reinforced composites. In this work, we propose an adaptive affine method, a novel mean-field homogenization method designed to ensure the consistency of the accumulated strain state and the concentration tensor, and apply the method to predict the mechanical responses of the composites in the large strain regime under uniaxial, cyclic, and biaxial loading conditions. Our method is also extended to predict the mechanical response in the presence of interfacial imperfections described by linear cohesive traction-separation laws. The analytic predictions are validated against finite element analyses of representative volume elements. We believe that our adaptive affine method can be extended to model various nonlinear responses of load-bearing composites including the effects of (visco)plasticity and finite deformation.

Study on test set-ups for determining the failure characterisation in masonry components

This paper presents experimental studies and detailed micro-modelling on test set-ups to determine the strength and failure mechanism of brick masonry components. Experimental studies include compressive strength tests of masonry units, red clay brick masonry triplet tests and Z-shaped flexural bond tests. Failure mechanisms for masonry relates not only to mortar and brick material properties, but also to the bond strength between the brick and mortar. A contact law based on the cohesive zone model and Coulomb's law was used to describe the fracture behaviour of mortar joints. Numerical studies are based on the interface cohesive model for mixed modes I and II. Tests were evaluated numerically using the Benzeggagh–Kenane mixed mode criterion. The results obtained from finite-element (FE) simulation showed the reliability of computational modelling approaches for masonry bed joint behaviour. Finally, a parametric study on masonry triplet under various compression stresses was carried out by using the FE simulation. The results indicate that an increase in normal compression stress leads to an increase in shear bond strength of masonry.

A CDM-like constitutive law for predicting degradation of strength and ductility of steel subjected to cyclic loading

This paper presents a continuum-damage-model-like constitutive law embedding cohesive cracks with plasticity-induced damage to represent the degradation of strength and ductility of steel under cyclic loading. The proposed constitutive law accommodates an arbitrary hyperelasticity-based plastic model with the use of the deformation gradient multiplicatively decomposed into separation-induced, elastic and plastic parts, and incorporated with an additional isotropic hardening rule endowed with a memory surface. While the elastic–plastic deformation along with isotropic and kinematic hardening is represented by a Hencky-type model, the separation-induced deformation gradient due to material separation is employed to embed an arbitrary cohesive traction separation law (CTSL) into the hyperelasticity-based plastic model. Also, a plasticity-induced damage variable is added to the selected CTSL to degrade the critical energy release rate. In addition, a new material constant is introduced to adjust the ratio between the critical values of cohesive traction and material separation width in the CTSL. On the other hand, the additional hardening rule depending on memory surface is appended in conjunction with the conventional isotropic and kinematic hardening rules to reflect the difference in plastic deformation with various ranges of cyclic loading. Several experiments are conducted to identify the material parameters and verify the validity of the proposed model. By reference to the experimental results, the capability of our proposed constitutive law is demonstrated in predicting the degradation of tensile strength and breaking elongation of a steel after cyclic loading.

Bridging length scales from micro to mesoscale through rate-dependent traction-separation law predictions

Mesoscale models are useful for modeling dynamic impact on fiber reinforced polymer composites . Mesoscale damage can be modeled using cohesive zones , but determining the governing traction-separation laws is a challenge. We developed finite element models with a stochastic fiber-matrix microstructure embedded within a larger mesoscale continuum to study transverse tension and shear loading of unidirectional S-glass/epoxy composite. We included rate-dependent matrix constitutive behavior and failure and rate-dependent fiber-matrix interface debonding, which are important microscale damage mechanisms that comprise mesoscale fracture. With these multiscale models , we simulated mode I and II crack initiation and propagation. We determined mesoscale, mode I and II, rate-dependent cohesive laws from the models using a domain J-integral approach to calculate the fracture energy as a function of crack opening displacement. We explored the effects of loading rate, matrix failure strain, and fiber-matrix interface debonding properties on the traction laws and crack morphologies. Finally, consistent bridging between length scales is demonstrated by comparing energy dissipation of microstructurally-resolved fracture to mesoscale continuum cohesive zone fracture. This work provides a methodology for determining rate-dependent traction-separation laws, derived from accurate micro-mechanics and experimental input, for bridging lengths scales and use in mesoscale models to evaluate ballistic performance of composites.

Employing phase‐field descriptions of cohesive zone placements in cohesive fracture simulations

AbstractCohesive zone models suffer from the fundamental problem that potential crack paths must be determined beforehand. Phase‐field models for (brittle) fracture, that have recently become immensely popular, are able to naturally handle essentially arbitrary crack patterns. However, due to their energetic nature, phase‐field approaches have difficulties to predict, for example, crack nucleation in consequence of their lack of strength criteria which are naturally incorporated in the cohesive zone model. In this contribution, an alternative approach is presented that allows the embedding of established (cyclic) cohesive laws into phase‐field modeling. Our work is conceptually in line with the ideas proposed by Verhoosel and de Borst in 2013. Since this novel approach to cohesive fracture is still in its infancy, many open challenges remain, of which the following are addressed in this article: (i) A strict separation between the description of the cohesive zone and the cohesive law itself is realized, (ii) the interplay between the different physical length‐scales inherent to the formulation is carefully investigated in order to quantify the parameters introduced in the phase‐field description, and (iii) an alternative finite element treatment is proposed, implemented, and tested that avoids spurious solutions for unstructured meshes. In this context, fatigue crack growth is simulated as a quantitative benchmark problem relevant to engineering applications.

An experimental and numerical study on the age depended bond-slip behavior between nano-silica modified carbon fibers and cementitious matrices

Electrophoretic deposition of nano-silica on the surfaces of carbon fibers (CF) is a novel approach for modifying the interfacial bond properties between the fibers and cementitious matrices. To understand its pullout behavior with increasing age, single fiber pullout tests and scanning electron microscopy were performed at various curing times for pristine and modified fibers. In this article, a new approach for calculating the debonding energy is introduced and two theoretical models – a stress-controlled and an energy-controlled – were employed to obtain the critical interface failure criterion. The results showed that interfacial adhesion at fiber-matrix interface was increasingly improved with age compared to the untreated fiber, due to the formation of C–S–H gel in the vicinity of the fiber surface. Meanwhile, the untreated fibers exhibited only a slightly increasing trend of interfacial bonding with longer curing time. A finite element model was applied to simulate the fiber pullout failure, which incorporated a discrete cohesive concept into the smeared phase-field method in a Representative Crack Element (RCE) framework. Using a phenomenologically defined cohesive traction-separation law, the numerical simulations successfully captured the characteristics of the experimental pullout curves. According to proper parametric calibrations, good agreement was obtained between the numerical results and the respective experimental evaluations.