Rate-dependent Cohesive Model Research Articles

Numerical Study on the Dynamic Fracture Energy of Concrete Based on a Rate-Dependent Cohesive Model.

As an important parameter for concrete, fracture energy is difficult to accurately measure in high loading rate tests due to the limitations of experimental devices and methods. Therefore, the utilization of numerical methods to study the dynamic fracture energy of concrete is a simple and promising choice. This paper presents a numerical investigation on the influence of loading rate on concrete fracture energy and cracking behaviors. A novel rate-dependent cohesive model, which was programmed as a user subroutine in the commercial explicit finite element solver LS-DYNA, is first proposed. After conducting mesh sensitivity analysis, the proposed model is calibrated against representative experimental data. Then, the underlying mechanisms of the increase in fracture energy due to a high strain rate are determined. The results illustrate that the higher fracture energy during dynamic tension loading is caused by the wider region of the damage zone and the increase in real fracture energy. As the loading rate increases, the wider region of the damage zone plays a leading role in increasing fracture energy. In addition, as the strain rate increases, the number of microcracks whose fracture mode is mixed mode increases, which has an obvious effect on the change in real fracture energy.

A rate dependent cohesive model for the analysis of concrete-FRP bonded interfaces under dynamic loadings

Reinforced concrete structures, strengthened with fibre-reinforced polymers materials (FRP), are frequently subjected to dynamic loadings, due to, e.g., earthquake, blast, or impact events. The definition of proper cohesive laws to model the bond between the fibre-reinforced polymer sheet and concrete, under high deformation rates, is a crucial issue because the typical failure mode of these joints is debonding of the composite from the concrete substrate. Although numerous studies have already investigated the quasi-static interface response, experimental and numerical investigations, concerning the effect of deformation rate on the bond behaviour between a fibre-reinforced polymer sheet and concrete, are still few. This paper presents a cohesive law for the modelling of interfaces under mixed-mode dynamic loadings, considering the effect of deformation rate. The formulation is based on the decomposition of the discontinuity displacement vector across the interface into elastic and viscoplastic components, with the evolution of the latter being governed by a viscoplastic law formulated according to the overstress approach. Experimental results available in literature, related to double- and single-lap shear tests, performed on FRP reinforced concrete specimens, are exploited to validate the proposed model and to show its capacity to simulate closely the experimental behaviour.

Rate-Dependent Cohesive Models for Dynamic Mode I Interfacial Propagation and Failure of Unidirectional Composite Laminates

With the increasing application of composite materials in anti-impact structure, the development of reliable rate-dependent interlaminar constitutive model becomes necessary. This study aims to assess and evaluate the applicability of three types of rate-dependent cohesive models (logarithmic, exponential and power) in numerical delamination simulation, through comparison with dynamic test results of double cantilever beam (DCB) specimens made from T700/MTM28-1 composite laminate. Crack propagation length history profiles are extracted to calibrate the numerical models. Crack propagation contours and fracture toughness data are predicted, extracted and compared to investigate the difference of the three different rate-dependent cohesive models. The variation of cohesive zone length and force profiles with the implemented models is also investigated. The results suggest that the crack propagation length can be better predicted by logarithmic and power models. Although crack propagation length profiles are well predicted, the numerical calculated dynamic fracture toughness tends to be higher than that of experimental measured results. The three models also show differences in the prediction of maximum loading forces. The results of this work provide useful guidance for the development of more efficient cohesive models and more reliable interface failure simulation of impact problems.

Analysis of self-similar rate-dependent interfacial crack propagation in mode II

The present study analyzes the fundamental properties of a rate-dependent cohesive model applied to the description of dynamic mode-II crack propagation. To make a semi-analytical treatment possible, the idealised problem of a crack along the interface between a semi-infinite elastic layer and a rigid substrate is considered. Solutions corresponding to the propagation of the crack tip at a constant speed are constructed. Using asymptotic properties of the solution far from the crack tip allows obtaining the complete solution of the boundary value problem by direct integration without iterations, using a specific form of the shooting method. By conversion of the problem to dimensionless variables, the behavior of the system for all possible crack velocities and arbitrary combinations of material and geometric parameters can be characterized. The dependence of fracture energy and other important characteristics on model parameters and the crack speed can then be analyzed. Even if the approach is applied to a specific form of damage rate dependence and motivated by the analysis of delamination propagation, the same technique could be used for other classes of interfacial cohesive rate-dependent models.

Calibration of a Cohesive Model for Fracture in Low Cross-Linked Epoxy Resins.

Polymer-based composites are becoming widely used for structural applications, in particular in the aeronautic industry. The present investigation focuses on the mechanical integrity of an epoxy resin of which possible damage results in limitation or early stages of dramatic failure. Therefore, a coupled experimental and numerical investigation of failure in an epoxy resin thermoset is carried out that opens the route to an overall micromechanical analysis of thermoset-based composites. In the present case, failure is preceded by noticeable plasticity in the form of shear bands similar to observations in ductile glassy polymers. Thus, an elastic-visco-plastic constitutive law initially devoted to glassy polymer is adopted that captures the rate- dependent yield stress followed by softening and progressive hardening at continued deformation. A general rate-dependent cohesive model is used to describe the failure process. The parameters involved in the description are carefully identified and used in a finite element calculation to predict the material’s toughness for different configurations. Furthermore, the present work allows investigation of nucleation and crack growth in such resins. In particular, a minimum toughness can be derived from the model which is difficult to evaluate experimentally and allows accounting for the notch effect on the onset of failure. This is thought to help in designing polymer-based composites.

Frequency-Dependent Cohesive Zone Models for Fatigue

This paper is concerned with a new cohesive zone model (CZM) to better describe the effects of rate and cyclic loading. Rate is known to affect the manner in which cracks propagate in materials, yet there presently exists no rate-dependent cohesive model for fatigue simulation. The frequency of the applied cyclic load is recognised to influence crack growth rates with crack growth significantly different at lower frequencies due to microstructural effects or other damage mechanisms such as creep or corrosion. A rate-dependent trapezoidal cohesive model is presented that has the ability to capture this behaviour and shows slower rates of crack propagation with higher loading frequencies. This is achieved by allowing the cohesive fracture energy to increase with frequency up to a specified limit. On unloading the cohesive model retains material separation, which accumulates with the number of loading cycles, leading to final failure. An experimental fatigue investigation is currently underway to validate the new cohesive model, which has been coded in a UMAT subroutine and implemented in ABAQUS.

Rate-dependent elastic and elasto-plastic cohesive zone models for dynamic crack propagation

To overcome deficiencies with existing approaches a new cohesive zone model is introduced and trialled in this paper. The focus is on rate-dependent cohesive zone models which have appeared in the recent literature but can be shown to suffer unrealistic behaviour. Different combinations of material response are examined with rate effects appearing either in the bulk material or localised to the cohesive zone or in both. A benefit of using a cohesive-zone approach is the ability to capture plasticity and rate effects locally. Introduced is a categorisation of bulk-material responses and cohesive zone models with particular prominence to the role of rate and plasticity. The shape of the traction separation curve is shown to have an effect and captured in this paper with application of a trapezoidal cohesive zone model. Rate dependency for the cohesive zone model is introduced in terms of a rate-dependent dashpot models applied either in parallel and/or in series. Traditionally, two possible methods are adopted to incorporate rate dependency, which are either via a temporal critical stress or a temporal critical separation. Applied singularly, tests reveal unrealistic crack behaviour at high loading rates. The new rate-dependent cohesive model introduced here couples the temporal responses of critical stress and critical displacement and is shown to provide for a stable realistic solution to dynamic fracture. Dynamic trials are performed on a cracked specimen to demonstrate the capability of the new approach.

Mesoscopic simulation of the dynamic tensile behaviour of concrete based on a rate-dependent cohesive model

We present a two-dimensional meso-scale finite element model for simulating the dynamic tensile behaviour of concrete. Aggregate, mortar and interface transition zone (ITZ) are explicitly modelled at the meso-scale. Rate-dependent cohesive elements, which take into account the effects of the viscosity occurring in the fracture process, are dispersedly pre-inserted to simulate the nucleation, coalescence, and propagation of cracks. The proposed model is validated by comparing with the experimental data of spall tests. The evolution of microcracks of concrete under dynamic loading is presented. The influences of the fracture parameters and the mesostructure on the dynamic tensile strength are investigated. The results suggest that the property of ITZ plays an important role on the dynamic tensile behaviour of concrete. The tensile strength and dissipated fracture energy under dynamic loading are affected by the mesostructure of concrete as well.

Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets

This paper proposes a computational framework for dynamic crack propagation in rubber in which a nonlinear finite element analysis using cohesive zone modeling approach is used. A suddenly initiated crack at the center of biaxially stretched sheet problem is studied under plane stress conditions. A transient dynamic analysis using implicit time integration scheme is performed. In the constitutive modeling, the continuum is characterized by finite-viscoelasticity theory and coupled with the fracture processes using a cohesive zone model. This computational framework was introduced previously by the present authors (Elmukashfi and Kroon, 2012). In the current work, the use of a rate-dependent cohesive model is examined in addition to investigation of generalized biaxial loading cases. A Kelvin–Voigt element is used to describe the rate-dependent cohesive model wherein the spring is described by a bilinear law and dashpot with a constant viscosity is adopted. An explicit integration is used to incorporate the rate-dependent cohesive model in the finite element environment. A parametric study over the cohesive viscosity is performed and the steady crack propagation velocity is evaluated and compared with experimental data. It appears that the viscosity varies with the crack speed. Further, the total work of fracture is estimated using rate-independent cohesive law such that the strength of the cohesive zone is assumed to be constant and the separation work per unit area is determined form the experimental data. The results show that fracture-related processes, i.e. creation of new surfaces, cavitation and crystallization; contribute to the total work of fracture in a contradictory manner.

Effects of grain boundary heterogeneities on creep fracture studied by rate-dependent cohesive model

To simulate creep fracture of ceramics at high temperatures, we have developed a user-defined element (UEL) subroutine and a user-defined material properties (UMAT) subroutine to analyze the rate-dependent cohesive behavior of the grain boundary and the creep deformation of the grain, respectively, and implemented them in ABAQUS. The model presented here accounts for grain boundary sliding, nucleation of grain boundary cavities, their growth by diffusion and creep, and link up of microcracks to form macrocracks. Numerical examples demonstrate that the rate-dependent cohesive element has a better numerical stability than the existing work and the entire cavity growth process can be simulated. Also, in the presence of grain boundary heterogeneities, stress distribution becomes localized which, in turn, induces localized grain boundary cavitation and promotes creep fracture.

The interfacial fracture behavior of foam core composite sandwich structures by a viscoelastic cohesive model

A sandwich beam model consisting of two face sheets and a foam core bonded by a viscoelastic adhesive layer is considered in order to investigate interfacial fracture behavior. Firstly, a cohesive zone model in conjunction with a Maxwell element in parallel, or with a Kelvin element in series, respectively, is employed to describe the characteristics of viscoelasticity for the adhesive layer. The models can be implemented into the implicit finite element code. Next, the parametric study shows that the influences of loading rates on the cohesive zone energy and strength are quite different for different models. Finally, a sandwich double cantilever beam model is adopted to simulate the interface crack growth between the face sheet and core. Numerical examples are presented for various loading rates to demonstrate the efficacy of the rate-dependent cohesive models.

Cohesive zone model for direct silicon wafer bonding

Direct silicon wafer bonding and decohesion are simulated using a spectral scheme in conjunction with a rate-dependent cohesive model. The cohesive model is derived assuming the presence of a thin continuum liquid layer at the interface. Cohesive tractions due to the presence of a liquid meniscus always tend to reduce the separation distance between the wafers, thereby opposing debonding, while assisting the bonding process. In the absence of the rate-dependence effects the energy needed to bond a pair of wafers is equal to that needed to separate them. When rate-dependence is considered in the cohesive law, the experimentally observed asymmetry in the energetics can be explained. The derived cohesive model has the potential to form a bridge between experiments and a multiscale-modelling approach to understand the mechanics of wafer bonding.

A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials

Numerical investigations are conducted to simulate high-speed crack propagation in pre-strained PMMA plates. In the simulations, the dynamic material separation is explicitly modeled by cohesive elements incorporating an initially rigid, linear-decaying cohesive law. Initial attempts using a rate-independent cohesive law failed to reproduce available experimental results as numerical crack velocities consistently overestimate experimental observations. As proof of concept, a phenomenological rate-dependent cohesive law, which bases itself on the physics of microcracking, is introduced to modulate the cohesive law with the macroscopic crack velocity. We then generalize this phenomenological approach by establishing a rate-dependent cohesive law, which relates the traction to the effective displacement and rate of change of effective displacement. It is shown that this new model produces numerical results in good agreement with experimental data. The analysis demonstrates that the simulation of high-speed crack propagation in brittle structures necessitates the use of rate-dependent cohesive models, which account for the complicated rate-process of dynamic fracture at the propagating crack tip.

Analysis of a rate-dependent cohesive model for dynamic crack propagation

The effect of including rate-dependence in the cohesive zone modeling of steady-state and transient dynamic crack propagation is analyzed. Spontaneous crack propagation simulations are performed using a spectral form of the elastodynamic boundary integral equations, while the solution to the steady-state problem is obtained by solving the governing Cauchy singular equation on the crack plane. The steady-state analysis shows that the existing techniques for solving the Cauchy singular integral equation are not suitable. A solution technique for the underlying Riemann–Hilbert problem for the chosen rate and damage-dependent cohesive law is presented. Under spontaneous propagation conditions, quasi-steady-state speeds slower than the theoretically predicted shear wave speed are possible. Results also show that, due to the dissipation of energy inside the cohesive zone, the energy required for crack propagation increases with the crack speed.