Double Cantilever Beam Model Research Articles

Optimal dual actuator loading configurations for extracting mixed-mode cohesive relations from interacting beams

Cohesive zone models are often used in analyses of interfacial fracture where the damage process zones are relatively large and can be described by proper traction-separation relations. Successful implementation of the cohesive zone modeling depends upon the veracity of the interfacial traction-separation relations used to represent the interactions across the interface. To extract the generally mixed-mode traction-separation relations experimentally, we compare various loading conditions for simultaneous extraction of the normal and shear interactions using laminated beam specimens subjected to asymmetric end loading. We develop a mixed-mode double cantilever beam model with linear normal and shear interactions between the contact surfaces of the beams. Four different loading conditions are considered by controlling the end forces, end displacements, end moments, or end rotations. The model is validated by finite element simulations. Rotation control is found to be the optimal loading configuration, based on a condition number that reflects desirable experimental characteristics for extracting the traction-separation relations. By applying uneven end rotations, the whole range of mode-mix with combined normal and shear interactions can be extracted, while ensuring stable crack growth.

On the calibration of the cohesive strength for cohesive zone models in finite element analyses

Cohesive zone models are commonly used to numerically model fracture phenomena on the microscale. Typical fracture processes are described experimentally via the Double Cantilever Beam (DCB) test and the End Notched Flexure (ENF) test on the macroscale. Analytical solutions, e.g. the LEFM-based beam theory, are used to evaluate these tests and to validate numerical models. However, some input parameters of cohesive zone models, i.e. cohesive stiffness and cohesive strength, are independent of the analytical solutions. In particular, the cohesive strength has a significant effect on the accuracy of the numerical model compared to the analytical solution and thus needs to be calibrated. This work extends the available literature by fitting the numerical to the analytical solution of the DCB and ENF models through calibration of their cohesive strength by using more suitable and generally applicable criteria. It considers the deformation, the applied load and the crack length of the models. The latter has been neglected so far in the existing literature. Via a parametric study, the derived criteria are minimised to find the best fit to the analytical solution. In addition, the effect of all input parameters and of the numerical element size on the calibrated cohesive strength is investigated. The obtained information can be used to qualify numerical models with coarse meshes to accurately compute the fracture of DCB and ENF models. Further, it provides a comprehensive understanding of the cohesive strength as a modelling parameter.

Cohesive zone modeling of fatigue crack propagation in slab track interface under cyclic temperature load

The ballasless track has been massively applied nowadays, while the interface damage evolution of ballastless tracks is still rarely investigated. This work aims to investigate the damage evolution property of ballastless track under low-cycle fatigue load condition. The application of cyclic cohesive model as a key approach to simulated the damage evolution of ballastless track interface. Therefore, a low-cycle fatigue cohesive model (LCFC) that follows a bilinear law is established by combining and modifying existed cohesive models. The LCFC model is then implemented by a secondary development in Abaqus through implicit user-defined material subroutine (UMAT), and the validity of the model is verified though a double cantilever beam (DCB) model. To obtain the key parameters of the LCFC model for analyzing the fatigue damage of CRTS III (Chinese Railway Track System type III) ballastless track, the split tension test of specimen that is composed of the self-compacting concrete and the slab concrete is conducted, and the damage evolution process is captured through digital image correlation (DIC) technique. Further, a simulation model that involves the LCFC model is created for simulating and analyzing the interface fatigue damage of CRTS III- ballastless track under cyclic temperature gradient for the first time. The results show that the established LCFC model is suitable for studying the interface fatigue damage of CRTS III ballastless track under extreme temperature gradient cycles. The interface near the slab edge will be completely damaged within only several cycles when the cyclic temperature gradient is ± 61℃/m. The failure mode of the interface element is a kind of mixed mode failure which gradually changes from normal-dominated failure mode to shear-dominated failure mode with the increase of temperature gradient loading cycles.

Experimental and Simulation Analysis of the Evolution of Residual Stress Due to Expansion via CMAS Infiltration in Thermal Barrier Coatings

The failure behavior of thermal barrier coatings (TBCs) involves multilayered systems infiltrated with calcium–magnesium–alumino-silicates (CMAS). The metastable tetragonal phase is mainly composed of 7YSZ (7 mol.% Y2O3-stabilized ZrO2), and it destabilizes into the Y-lean tetragonal phase, which may be induced by CMAS infiltration, and transforms into a monoclinic phase during cooling. The phase transformation leads to volume expansion around the CMAS-rich layer. Furthermore, it is shown that the spalling of the coating system emerges when the surface of the coating system is subjected to significant residual stress. In this study, a double-cantilever beam model is established to describe the macroscopic phenomenon of thermal buckling induced via CMAS. The result of the buckle height is used to demonstrate the consistency of the experiment and finite element simulation. The experimental parameters are imported into a multilayer cantilever beam model to analyze the interfacial stresses due to CMAS infiltration. The finite element results indicate that the phase transformation leads to damage in the coating system wherein the interfacial stresses due to phase transformation are 27% higher than those in the model without phase transformation.

An Investigation of Interface Bonding Strength of Bimetal Plate Based on the Optimization of Asymmetric Double Cantilever Beam Model

An Investigation of Interface Bonding Strength of Bimetal Plate Based on the Optimization of Asymmetric Double Cantilever Beam Model

Mode-I fracture analysis of micro-scale high-temperature superconductors via the double cantilever beam model and gradient elasticity theory

In this paper, fracture behavior of a micro-scale double cantilever beam (DCB) made of superconducting materials is investigated based on the strain gradient theory. Both zero-field cooling (ZFC) and field cooling (FC) magnetization processes are considered. The closed-form solutions of the energy release rates and stress intensity factors are obtained. For ZFC process, superconducting materials are easy to damage during the process of reducing magnetic field rather than increasing magnetic field. For FC process, applied magnetic field will impede superconductors to damage. Moreover, the normalized energy release rate predicted by classical beam theory is larger than that predicted by strain gradient theory. As the characteristic length increases, the normalized energy release rate decreases. The present model may be useful for designing experiments to test the fracture toughness of micro-scale high-temperature superconductors.

A double cantilever beam incorporating cohesive crack modeling for superconductors

In this paper, a double cantilever beam (DCB) specimen incorporating cohesive crack is developed for superconductors which have potential applications in high temperature superconducting cables in space solar power station. The cohesive interface is introduced along the crack front of the DCB model under electromagnetic force. The load-separation relation (i.e. the crack opening displacement) is used as the fracture mechanics parameter and the corresponding curves during fracture process are obtained and verified by the finite element numerical method. Results show that the presence of tensile electromagnetic force makes crack propagate easily. Superconductors with small cracks have good adaptability to the oscillation of magnetic fields while that with large cracks are easier to fracture during the descent of the magnetic field. In addition, the ductility ratio of the cohesive interface can significantly increase the fracture strength. The length of fracture zone decreases as the crack length increases.

Modeling of delamination in fiber-reinforced composite using high-dimensional model representation-based cohesive zone model

Prediction of delamination failure is challenging when the researchers try to achieve the task without overburdening the available computational resources. One of the most powerful computational models to predict the crack initiation and propagation is cohesive zone model (CZM), which has become prominent in the crack propagation studies. This paper proposes a novel CZM using high-dimensional model representation (HDMR) to capture the steady-state energy release rate (ERR) of a double-cantilever beam (DCB) under mode I loading. The finite element models are created using HDMR-based load and crack length response functions. Initially, the model is developed for 51-mm crack size DCB specimens, and the developed HDMR-based CZM is then used to predict the ERR variations of 76.2-mm crack size DCB model. Comparisons have been made between the available unidirectional composite (IM7/977-3) experimental data and the numerical results obtained from the 51-mm and 76.2-mm initial crack size DCB specimens. In order to demonstrate the efficiency of the proposed model, the results of the second-order nonlinear regression model using RSM are used for the comparison study. The results show that the proposed method is computationally efficient in capturing the delamination strength.

Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches

Virtual crack closure technique (VCCT), cohesive zone modeling (CZM) and extended finite element method (XFEM) are three well-known numerical methods frequently used for crack propagation modeling. It is often questioned by new researchers and engineers: which method is more appropriate for modeling of delamination propagation in composites? In this study, advantages, limitations, and challenges of each method are discussed with the goal of finding a suitable and cost-effective solution for modeling of delamination propagation in laminated composites. To this end, a composite double cantilever beam (DCB) specimen as a benchmark example is modeled in ABAQUS and delamination propagation is simulated using three above methods and the combination of XFEM with VCCT and CZM. Two-dimensional plain strain and three-dimensional DCB models are both considered. Finite element results are compared with experimental results available in the literature for unidirectional DCB specimens. Finally, the accuracy, convergence speed, run-time and mesh dependency of each method are discussed. The XFEM-CZM was found as a suitable method for simulation of delamination growth.

A double cantilever beam model for fracture toughness analysis of superconductors

Due to their high current-carrying property, high-temperature superconductors such as multilayered superconducting cables have great potential applications in space solar power stations. The force induced by flux pinning may be very high and cause damage of superconductors. In this paper, the double cantilever beam (DCB) specimen for high-temperature superconductors is investigated and the energy release rate, mode I and mode II stress intensity factors are obtained in closed-form. For mode I crack, the energy release rate and stress intensity factor under magnetic field are found to be larger than those without magnetic field. However, mode II stress intensity factor is independent of applied magnetic field. In addition, mode I stress intensity factors with root effect are dependent of the ratio of length to thickness. This is contrary to the results without root part, which is independent of the ratio of length to thickness. The results are useful for determining fracture toughness of superconductor materials.

A study on fatigue fracture at double and tapered cantilever beam specimens bonded with aluminum foams

Abstract In this study, the models of simple double cantilever beam (DCB) and tapered double cantilever beam (TDCB) were designed to analyze the fracture behavior of the aluminum foam. The fracture behaviors of composite materials exhibit similar trends. The energy release rate increases as the crack length increases and the specimen height decreases. The bonding force influences the adhesive joints of structure. The DCB and TDCB model can be applied generally to the structure with complex configuration. An aluminum foam model has been constructed by using the configuration of DCB and TDCB models in this study. This paper studies the fracture characteristics of specimens due to two kinds of configurations by comparing with the experimental results of DCB and TDCB specimens for mode 1. This study aims to apply fracture toughness to the design of adhesive joints.

Modeling effects of gas bubbles on the mechanical behaviors of Ag/Bi-2212 round wires using a double cantilever beam bridge model

Due to the larger current-carrying property, Bi2Sr2CaCu2Ox (Bi2212) superconductors have a great potential application in high field magnet. Bi2212 superconducting material can be fabricated as an isotropic round wire. However, there is 30% void space in the wire, such as gas bubbles. The void space has a larger influence on the property of the wire. In this paper, we will study the effect of gas bubble on the fracture behavior. Based on the double cantilever beam model and critical state theory, the mechanical behavior of Bi2212 wire is studied for decreasing field. Two different damage mechanisms are discussed using the strain energy release rate and strain of bridge. The results show that the large gas bubble can increase the strain of bridge. The central filaments with gas bubble are easier to be damaged than the edge filaments with gas bubble.

Fracture of a thin power-law nonlinear material with a crack using the DCB model

A thin power-law nonlinear material with a crack is studied. For a thin cracked structure, we simulate the layer with an edge crack or a center crack as a double-cantilever beam (DCB) or a double-clamped beam, respectively. A static bending solution is first solved for prescribed bending moment, concentrated force, or uniformly distributed loading. The strain energy is calculated and energy release rate near the crack tip is determined. Obtained results of the power-law singularity of the stress and strain fields is in agreement with that of the well-known HRR field for two-dimensional hardening materials. Explicit expressions for the energy release rate or J integral are obtained. The effects of the hardening exponent on crack growth are analyzed. Our results agree with previous experimental observations of a brass DCB specimen.

Investigation and verification of fatigue characteristic on the adhesive slanted interface of specimen with foaming aluminum for sliding mode

Foaming aluminum is a super light weight manufactured by adding thickener and foaming agent after dissolving aluminum ingot to be foamed in a sponge configuration. Studying on fatigue of adhesive structures configured with aluminum foam and fracture toughness for adhesive interfaces may be considered very important. In this study, DCB specimens of aluminum foam composite material were designed based on British industrial standard (BS 7991) and ISO international specification (ISO 11343), and Mode II tests were performed. Examination of graphs of loads and displacements according to fatigue cycles for the four types of specimens shows that time capable of withstanding fatigue loads is the longer, the larger the slanted angle of the tapered double cantilever beam model under the same fatigue load conditions. Since similar results to those from actual experiments were observed based on comparisons of actual experimental data with analysis data, the analysis results according to a finite element method employed in this study could be relied upon, and it is considered that structural safety could be found by imulations alone in lieu of experiments requiring much cost and time when such method as this is applied.

Brittle interfacial cracking between two dissimilar elastic layers: Part 2—Numerical verification

A thorough program of 2D finite element method (FEM) simulations is carried out parametrically on a bimaterial double cantilever beam (DCB) model in MSC/NASTRAN. The Young’s modulus ratio, the Poisson’s ratio, the thickness ratio, and the DCB tip loads are varied over their entire practically useful domains for different values of the crack extension size. Extensive comparisons are made between the results of the analytical theory that was developed in Part 1 by Harvey et al. (2015) and FEM results. This paper reports the outcome of these comparisons. The present analytical theory and the supporting mathematical techniques are thoroughly verified. Overall, excellent agreement is observed between the present analytical theory and the FEM results for the crack extension size-dependent energy release rate (ERR) components and the stress intensity factors (SIFs).

Combined effect of strain-rate and mode-ratio on the fracture of lead-free solder joints

Abstract The critical strain energy release rate for the solder joint fracture was measured as a function of the strain rate and the mode ratio of loading. These data are useful in predicting the fracture of solder joints loaded under arbitrary combinations of tension and shear during the impact conditions typical of falling portable electronic devices. In this study, strain rates from quasi-static (close to 0 s − 1 ) to 61 s − 1 were investigated at phase angles from 0 to 60°, typical of the range found in microelectronic devices. Copper–solder–copper double cantilever beam (DCB) model specimens were prepared using SAC305 solder at cooling rates and times above liquidus typical of actual ball grid arrays (BGAs). A drop tester was designed and built to achieve different strain rates at various mode ratios. The critical initiation strain energy release rate, J ci , increased about 70% from quasi-static to intermediate strain rates, before decreasing by more than 67% from intermediate strain rates to 42 s − 1 .

Effect of scale parameter on the deflection of a nonlocal beam and application to energy release rate of a crack

This article studies the influence of the nonlocal scale parameter on the deflection of a nonlocal nanobeam and crack growth. Using the Timoshenko hypothesis, a single governing equation is derived and its exact solution can be determined through appropriate end‐support conditions. Numerical calculations are carried out for a cantilever microtubule in solution at a given flow speed. The effects of nonlocal scale parameter on the deflection are discussed. Based on the obtained solutions, the double cantilever beam model is utilized to determine energy release rate near a crack tip for an edge crack and a central crack, respectively. It is found that the scale parameter plays different roles in determining stress intensity factors and energy release rates, depending on crack constraints. When neglecting shear deformation, the results for nonlocal Euler‐Bernoulli beams can be directly obtained.

Double cantilever beam model for functionally graded materials based on two-dimensional theory of elasticity

This paper extends the double cantilever beam (DCB) model to functionally graded materials (FGMs) based on two-dimensional theory of elasticity. A theoretical approach is proposed to determine strain energy release rate of a crack in a layered FGM with exponential gradient perpendicular to the crack plane. Elasticity solutions of a functionally graded cantilever subjected to a concentrated force and a bending moment are derived for thickness-wise varying Young’s modulus. Using the derived elasticity solutions, the energy release rate and stress intensity factor for an edge crack and a central crack parallel to the surface are obtained. Numerical results are given to show the influence of gradient index on fracture parameters.

Fatigue Analysis and Experimental Verification at Tapered Double Cantilever Beam(TDCB) Model of Aluminum Foam

Fatigue Analysis and Experimental Verification at Tapered Double Cantilever Beam(TDCB) Model of Aluminum Foam

A Study of Analysis on Fatigue Property at Adhesive Part of Tapered Double Cantilever Beam(TDCB) Model Composed of Aluminum Foam

A Study of Analysis on Fatigue Property at Adhesive Part of Tapered Double Cantilever Beam(TDCB) Model Composed of Aluminum Foam