Rate-dependent Cohesive Zone Model Research Articles

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

This study presents a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

Influence of rate effects on delamination: From Crack Leap Shear tests to low-velocity impacts

This paper is devoted to the study of different aspects of rate effects in the case of delamination. Two rate dependent cohesive zone models are compared for which the shear rate dependency is identified using Crack Leap Shear experiments. For both models, the key factor appears to be the evolution of the critical energy release rate as function of the crack opening. Moreover, if for very low velocity (1 m/s) rate effects can be neglected, it is not the case for quite low velocity (10 m/s). In the case of a 16 plies quasi-isotropic plate for the size and the shape of the delamination are significantly influenced by the rate effects.

A rate-dependent cohesive zone model for dynamic crack growth in carbon nanotube reinforced polymers

Carbon nanotubes (CNTs) enhance the fracture toughness of polymer-based matrix composites by dissipating the fracture energy through the pull-out deformation damage mechanism. The rate-dependent behavior of the matrix phase and the CNT/matrix interface affects the contribution of CNTs in enhancing the fracture toughness under dynamic loading and rapid crack growth. A continuum-based finite element (FE) model is utilized in this research to analyze the CNT pull-out damage mechanism. The influence of CNTs on the dynamic fracture behavior of polymer-based composites is studied taking into account the crack opening speed and loading rate effects. The matrix phase is treated as a viscoelastic-viscoplastic material and a new rate-dependent cohesive zone model (CZM) is proposed for modeling the behavior of interface between the CNTs and matrix. The rate-dependent traction-separation laws for the cohesive zone elements are established at different pull-out or crack opening speeds. The proposed rate-dependent FE model of pull-out mechanism facilitates the investigation of the effective factors of CNTs, including length, orientation, and waviness, on fracture energy dissipation at different pull-out speeds. Developed model is very suitable for very long CNTs where atomistic-based molecular dynamics and molecular mechanics methods are associated with difficulties and are more costly and time-consuming.

Characterization of the Structural Response of Adhesively Bonded Ultra-High Strength Steel Tubes Under a Range of Loading Conditions and Assessment of a Rate Dependent Cohesive Zone Model

Characterization of the Structural Response of Adhesively Bonded Ultra-High Strength Steel Tubes Under a Range of Loading Conditions and Assessment of a Rate Dependent Cohesive Zone Model

Rate dependent cohesive zone model for fatigue crack growth

Experimental observations indicate that the frequency of cyclic loads can influence fatigue crack growth. To address this phenomenon in simulation modelling, this study introduces a rate-dependent cohesive zone model designed for analysing fatigue crack growth under arbitrary cyclic loading conditions. The model operates in the time domain, where both critical traction and fracture toughness are modelled as functions of the separation rate, thereby considering the rate dependency of material damage and cracking. Unlike conventional models, this approach does not rely directly on loading frequency, suggesting its capability to address fatigue crack growth under non-periodic loading or repeated impacts effectively. An algorithm for modelling fatigue crack evolution and growth was developed based on this model, employing a time-incremental strategy in conjunction with a linear cumulative damage method. This algorithm was implemented in ABAQUS using a user element subroutine (UEL). The effectiveness of the proposed model and algorithm is validated through examples of fatigue crack growth in a plate under cyclic loading with varying frequencies. The results demonstrate agreement with experimental and computational findings reported in the literature. Additionally, the model was applied to scenarios involving frequency-variable cyclic loadings, yielding reasonable outcomes. Analysis of these examples confirms the model's utility in predicting fatigue crack growth under diverse alternating load conditions.

A rate-dependent cohesive zone model for simulating fast crack evolution and growth

This paper proposes a rate-dependent cohesive zone model for simulating the evolution and growth of cracks under dynamic loading. This model takes into consideration the effects of cohesive separation rate and crack growth speed on the cohesive traction-separation relationship to reflect the rate-dependent characteristics of both material viscosity and energy dissipation of micro-crack branches. The evolution algorithm of the cohesive law is presented, wherein separation rate and crack growth speed are evaluated using the backward difference method explicitly in incremental computation, leading to the determination of rate-dependent critical traction and fracture toughness. The proposed model was implemented in ABAQUS software via UEL subroutine and utilized in an example of interfacial crack growth simulation, with satisfactory agreement found among the present results, experimental data, and numerical results from the literature. The effectiveness of the rate-dependent model and numerical algorithm in simulating high speed crack growth is validated through further numerical tests.

High-fidelity computational modeling of scratch damage in automotive coatings with machine learning-driven identification of fracture parameters

As one of the key components of a vehicle, automotive coating systems are typical micro-size multilayer composites, which normally suffer from intricate scratch damage. Currently, it is a challenging task to reproduce the complex physical phenomena of automotive coatings with micron thickness using numerical simulations. The purpose of this work is to develop a computational framework for an accurate evaluation of such scratch damage. To achieve this end, a high-fidelity finite element (FE) model is proposed, where a rate-dependent cohesive zone model is developed to account for coating crack behaviors. A reverse identification approach based on the machine learning (ML) method is suggested to determine the rate-dependent cohesive parameters that are difficult to be measured via direct experiments. In the course of recognition, this work develops a two-step regional data augmentation strategy based on the existing single-shot recognition method. The developed strategy is capable of reducing the number of training data samples, while improving identification accuracy and robustness. With the identified cohesive parameters, the proposed finite element model is applied to simulate speed-dependent coating scratch behaviors. The good agreement between numerical and experimental results demonstrates the capacity of our developed computational framework for coating scratch problems.

Rate-dependent properties of resistance-welded carbon fiber-reinforced polyetheretherketone joints: Simulations and experiments

The rate-dependent characteristics of the resistance-welded joints of thermoplastic composites are investigated via simulations and experiments. A rate-dependent cohesive zone model based on the Kohlrausch–William–Watts formulation is proposed to capture the mechanical response of the joints at different loading rates, which is validated by the experimental results in terms of stiffness, strength, and failure. The proposed model is equivalent to the generalized Maxwell model with only eight input parameters to describe the welding interface's time- and history-dependent mechanical response. The stress distribution, crack emergence, and damage evolution of welded joints at different loading rates are revealed through numerical calculations. Additionally, the experimental results indicate that the strength of the joint is enhanced with the increase in the loading speed, as the strengthening effect caused by the high strain rate and the shorter loading time results in a tightly bonded stainless-steel/matrix interface and a rougher fracture surface.

A rate-dependent cohesive zone model for adhesive damage considering fibrillation

The pressure-sensitive adhesive (PSA) has been widely utilized in engineering and biomedicine fields. It is known the fibrillation process of PSA can considerably increase the adhesive energy, which significantly affects its adhesive behavior. Since the classical bilinear cohesive zone model (CZM) did not account for the fibril evolution, this paper aims to propose a rate-dependent CZM based on the physical mechanism of fibrillation to describe the cohesive failure of PSA. The multilinear traction-separation law (TSL) was established accordingly, including homogeneous deformation, cavity nucleation and dilatation, and fibril evolution. After being implemented into the FE software using a user-subroutine UMAT, the proposed CZM was validated by experimental data from probe-tack tests and then was utilized to investigate the effect of loading rate on PSA's adhesive performance of the peeling test. By examining the fibril's strain rate distribution using the proposed CZM, it is possible to correlate the PSA's adhesive performance under 90° peeling tests and the probe-tack test, thereby compensating for the theoretical prediction's inaccuracy due to the assumption of constant strain rate. It demonstrates the proposed CZM is a promising approach to investigating the rate-dependent cohesive failure of PSA considering fibrillation.

On the applicability of rate-dependent cohesive zone models in low-velocity impact simulation

This paper studied the applicability of logarithmic, exponential and power cohesive zone models by carrying out experiments and simulations of low-velocity impact on composite laminates. The results show that the dynamic mechanical response and delamination damage under low-velocity impact simulated by the logarithmic rate-dependent CZM have the best agreement with experimental ones than other two models. The delamination damage simulated by exponential model are significantly higher than experimental results, which indicates that the delamination initiation strength and fracture toughness are less estimated under impacting load. The simulation by power model also generally has a good agreement with experimental result but the predicted dynamic mechanical response is a little bit worse than logarithmic model. This study suggests that logarithmic rate-dependent CZM is optimal during low-velocity impact simulation, followed by power model and exponential model.

A strain rate-dependent cohesive zone model for shear failure of hat-shaped specimens under impact

The shear behaviors of U71Mn rail steel are investigated during different impact pressures using hat-shaped specimens, where the dynamic shear stress-strain responses of the specimens can be obtained by utilizing a split Hopkinson pressure bar apparatus. The maximum shear tractions are determined through the shear stress-strain curves of the experiments, and cohesive energies are obtained by trial and error method, i.e., the strain waves of the simulations are compared with those of the experiments. It is found that the maximum shear tractions and shear cohesive energies of U71Mn steel are sensitive to strain rates. Further, a strain rate-dependent cohesive zone model is developed to describe the dynamic fracture behaviors. Finally, the crack velocities are acquired under different impact pressures, and the dynamic stress intensity factors and dynamic energy release rates vary with the crack velocity.

A novel rate-dependent cohesive zone model for simulation of mode I dynamic delamination in laminated composites

The previous experimental studies have demonstrated that fiber-reinforced laminated composites exhibit lower interlaminar fracture resistance at high loading rates. This global behavior has been physically attributed to the rate dependency of the fiber bridging extent. The first aim of the present paper is to assess the influence of the local separation rate on the stress distribution within the fracture process zone near the crack tip. The practical traction-separation laws for the double-cantilever beam specimens under various imposed loading rates are characterized by using the J-integral approach. The derived bridging laws show that the maximum bridging traction decreases by increasing the separation rate. Subsequently, the tetralinear cohesive zone model is modified to include the rate dependency of the bridging energy and the bridging traction in the numerical simulation of mode I dynamic delamination. The proposed model has been implemented in the commercial finite element ABAQUS software via a user-defined subroutine. Good agreement between the finite element and experimental results verifies the reliability and accuracy of the model to account for the rate effects in presence of the large-scale fiber bridging.

Review of Strain Rate Effects of Fiber-Reinforced Polymer Composites.

The application of fiber-reinforced polymer (FRP) composites is gaining increasing popularity in impact-resistant devices, automotives, biomedical devices and aircraft structures due to their high strength-to-weight ratios and their potential for impact energy absorption. Impact-induced high loading rates can result in significant changes of mechanical properties (e.g., elastic modulus and strength) before strain softening occurs and failure characteristics inside the strain localization zone (e.g., failure mechanisms and fracture energy) for fiber-reinforced polymer composites. In general, these phenomena are called the strain rate effects. The underlying mechanisms of the observed rate-dependent deformation and failure of composites take place among multiple length and time scales. The contributing mechanisms can be roughly classified as: the viscosity of composite constituents (polymer, fiber and interfaces), the rate-dependency of the fracture mechanisms, the inertia effects, the thermomechanical dissipation and the characteristic fracture time. Numerical models, including the viscosity type of constitutive models, rate-dependent cohesive zone models, enriched equation of motion and thermomechanical numerical models, are useful for a better understanding of these contributing factors of strain rate effects of FRP composites.

A rate-dependent cohesive zone model with the effects of interfacial viscoelasticity and progressive damage

A generalized rate-dependent cohesive zone model for describing the interfacial viscoelasticity and progressive damage of mode I fracture is presented. The proposed model has efficiently extended the traditional bi-linear cohesive traction-separation law to remove the assumptions that some of the rate-dependent parameters such as elastic stiffness, initial separation and strength, critical separation are constant at different loading speeds. Furthermore, the rate-dependency of the damage evolution, which is observed in experiments but largely neglected in the previous models, is established to describe the rate-dependent fracture process linked with the generalized traction-separation law, and an equivalent generalized Maxwell model (GMM), based on the Kohlrausch-William-Watts function with significant fewer material parameters required as input, is proposed to describe the time and history dependent stress–strain relationship of the viscoelastic interface material. The proposed model is validated by the simulations of the DCB tests with both the SBR/NR rubber interface and Polyurethane interface.

A multiscale cohesive zone model for rate-dependent fracture of interfaces

Rate-dependent fracture has been observed for a silicon/epoxy interface as well as other polymer interfaces, where both the interfacial strength and toughness increase with the separation rate. Motivated by this observation, we propose a multiscale approach to modeling a polymer interface, from atomic bonds to the macroscopic specimen, considering the energetics of bond stretching, the entropic effect of long molecular chains, the kinetics of thermally activated chain scission, and statistical distributions of the chain lengths. These multiscale features are seamlessly assembled to formulate a rate-dependent cohesive zone model, which is then implemented within a standard finite element package for numerical simulations. This model relates the macroscopically measurable interfacial properties (toughness, strength, and traction-separation relations) to molecular structures of the interface, and the rate dependence results naturally from the kinetics of damage evolution as a thermally activated process. The finite element simulations with the cohesive zone model are directly compared to double cantilever beam experiments for the rate-dependent fracture of a silicon/epoxy interface, yielding reasonable agreement with just a few parameters for the molecular structures of the interface. Such a multiscale, mechanism-based cohesive zone model offers a promising approach for modeling and understanding the rate-dependent fracture of polymer interfaces.

Rate-Dependent Cohesive Zone Model for Fracture Simulation of Soda-Lime Glass Plate

In this paper, rate-dependent cohesive zone model was established to numerical simulate the fracture process of soda-lime glass under impact loading. Soda-lime glass is widely used in architecture and automobile industry due to its transparency. To improve the accuracy of fracture simulation of soda-lime glass under impact loading, strain rate effect was taken into consideration and a rate-dependent cohesive zone model was established. Tensile-shear mixed mode fracture was also taken account. The rate-dependent cohesive zone model was implemented in the commercial finite element code ABAQUS/Explicit with the user subroutine VUMAT. The fracture behavior of a monolithic glass plate impacted by a hemispherical impactor was simulated. The simulation results demonstrated that the rate-dependent cohesive zone model is more suitable to describe the impact failure characteristics of a monolithic glass plate, compared to cohesive zone model without consideration of strain rate. Moreover, the effect of the strain rate sensitivity coefficient C, the mesh size of glass plate and the impact velocity on the fracture characteristics were studied.

Rate-dependent traction-separation relations for a silicon/epoxy interface informed by experiments and bond rupture kinetics

In this work, double cantilever beam specimens were used to investigate the rate-dependent fracture of a silicon/epoxy interface. Fracture experiments were conducted at 5 different separation rates, ranging from 0.042 to 8.5 mm/s. For each separation rate, the interfacial properties were extracted by a beam on elastic foundation model and an iterative method, assuming a bilinear traction-separation relation. Rate dependence is observed for the silicon/epoxy interface as both the interfacial toughness and strength increased with the separation rates, which is opposite to the rate dependent fracture behavior of the bulk epoxy in its glassy state. Motivated by this observation, a rate-dependent cohesive zone model is proposed based on a thermally activated bond rupture mechanism. This model relates the interfacial fracture to the breakage of molecular bonds at the interface, and the rate effect develops naturally from the kinetics of damage evolution via the statistical concept of bond survival probability. The double cantilever beam problem with the interfacial bond rupture kinetics was then solved numerically, and the model parameters were extracted by fitting the numerical results to the experimental data. Ideally, this model should be able to explain and predict the rate-dependent fracture of a specific interface (e.g., silicon/epoxy interface) with four parameters, including the bond energy, the critical stress, the initial stiffness and a time scale. However, in order to fit the experimental data, the critical stress had to be adjusted in the present study. Nevertheless, this mechanism-based cohesive zone model offers a promising approach for modeling the rate-dependent fracture, which may also incorporate other mechanisms in future studies.

Explicit dynamic fracture simulation of two-phase materials using a novel meso-structure modelling approach

In order to reduce the experimental cost and enable the numerical modelling better approaches the actual meso-structures of two-phase materials, a novel meso-scale modelling approach, combining the image-based and the parameterized modelling approaches, has been presented. In this approach, only limited samples of the studied two-phase material need to be provided for establishing an aggregate library, through which finite element models with different spatial distributions and volume fractions of aggregate can be arbitrarily generated for the use of virtual test. In the present virtual test, fracture failures were simulated in the framework of explicit dynamics. A rate-dependent cohesive zone model (CZM) was implemented through the user subroutines in ABAQUS to characterize the dynamic damage and fracture of the meso-structures. At the same time, an algorithm of embedding cohesive elements automatically into the potential damage zones was put forward. Finally, two typical numerical examples were given to verify these proposed methods and models, meanwhile the influences of spatial distribution and volume fraction of aggregate on the mechanical performance of the meso-structure were investigated. It can be validated that the present developed methods and models can effectively and efficiently characterize the dynamic fracture behavior of two-phase materials.

On the rate dependent behaviour of epoxy adhesive joints: Experimental characterisation and modelling of mode I failure

The increasing use of adhesive joints in dynamic applications require reliable measurements of the rate-dependent stress-displacement behaviour. The direct measurement of the stress-displacement curve is necessary when using cohesive models in discretised solutions of boundary value problems in solid mechanics. This paper aims to investigate the rate-dependent tensile failure of adhesive joints by using a new experimental methodology – it relies upon the combination of the stress wave propagation theory and digital image correlation methods on high speed footage to quantify the tensile stress and the dissipated energy respectively. For this purpose, the Split Hopkinson Bar methodology was employed – the experimental configuration was optimised using numerical modelling. To prove the sensitivity of our framework, two different adhesives are characterised at different loading rates: the adhesive failure strength was found to increase considerably with the strain rate, while the plastic deformation of these adhesives was reduced. The film adhesive showed superior performance over the particle toughened one. In the final part, a rate-dependent cohesive zone model is proposed, one which captures the measured behaviour and which has the potential to be used in industrial applications.

Thermodynamic Derivation and Damage Evolution for a Fractional Cohesive Zone Model

AbstractA thermodynamic derivation is presented for a fractional rate-dependent cohesive zone model recently proposed by the authors to combine damage and linear viscoelasticity. In this setting, t...