Cohesive Zone Model Parameters Research Articles

Estimation of CZM Parameters for Investigating the Interface Fracture of Adhesively Bonded Joints Under Mode I, Mode II, and Mixed‐Mode (I/II) Loading

ABSTRACTThe mechanical performance of joints for any engineering applications requires accurate characterization of joint interfaces. This paper presents a simplified experimental procedure to estimate the cohesive zone model (CZM) parameters for predicting the interface failure of adhesively bonded joints subjected to mode I (opening) and mode II (shear) loading. The novelty of this procedure lies in predicting all CZM parameters—cohesive stiffness, strength, and cohesive energy (fracture toughness), of the bonded interface using one common experimental setup. It is observed that the cohesive strength and cohesive energy in shear loading are approximately 3.8 and 11.6 times, respectively, compared to the opening loading condition. Employing a triangular cohesive law, the CZM parameters are combined with appropriate damage initiation (quadratic stress) and evolution (power law) criteria. The proposed methodology is verified against experimental load–displacement responses of the bonded interface under mixed‐mode I/II (opening/shear) loading across a wide range of mode mixity (α = 0°, 15°, 30°, 45°, 60°, 75°, and 90°). The maximum error between the experimental and the numerical peak load is 5.11%. The acceptable agreement between the numerical and experimental results confirms the effectiveness of this method in investigating interface fracture in adhesively bonded joints under different loading conditions.

Optimization of CZM parameters of Norway spruce tested in mode I using multistart simplex method

The paper addresses the advanced fracture analysis of the SEN-TPB test on Norway Spruce in three anatomical directions: tangential (T), radial (R) and tangential–radial (TR). It utilizes reverse engineering to obtain cohesive zone model (CZM) parameters, which are then compared to the experimental values obtained using the compliance-based beam method (CBBM) and additional standard material tensile tests perpendicular to the grain. The optimization employs force–displacement curves to find their optimal fit using the multistart simplex optimization method. Results indicate that CZM modeling can be relatively problematic when realistic values are used; however, the best agreement with experimental data is observed for the group of cracks in the TR direction. A fundamental issue with CZM modeling in the elastic part has been identified and discussed. The sensitivity of the problem to various parameters was assessed, and an energy balance in the CZM at Fmax was performed. This work contributes to knowledge about realistic modeling of the interface and a fundamental understanding of fracture in wood.

Enhanced interface adhesion in shape memory alloy hybrid composites via an elastomeric interface: An experimental and numerical investigation

Shape Memory Alloy Hybrid Composites (SMAHCs) hold great promise for different applications. However, the interface between SMAs and the matrix presents challenges due to large strains associated with the martensitic transformations (MTs). Although different strategies have been proven effective in increasing interfacial strength, debonding and its prevention remain unresolved. Therefore, to enable MTs in SMAHCs, this paper proposes a novel solution using a rubber-like elastomeric interface. Pull-out SMAHC specimens were tested at different embedding lengths with and without the elastomeric interface. Specimens with the elastomeric interface showed better performance and stress-strain transfer during MT up to SMA wire breakage. The behaviour of the interface was studied using finite element analysis. A fine-tuning method was proposed for the cohesive zone model parameters. Simulated pull-out tests matched experimental data, revealing the debonding mechanisms. However, results with the elastomer underscored the need to fully represent the underlying physics of the highly deformable interface.

Cross-scale method of MD-FE for modeling mechanical damage behaviors of ferrite-cementite steels

Inspired by the experimentally observed ferrite-cementite interface damage and ferrite matrix damage, this work develops a cross-scale method using the cohesive zone model (CZM) as a bridge to study the mechanical damage behavior of ferrite-cementite steel at the micro-nano scale. The CZM parameters for the damage region of ferrite-cementite steel were obtained by molecular dynamics (MD) simulations, which were then applied to cohesive elements in the finite element (FE) framework, thus enabling crack initiation and propagation at the micro-scale. Simulation results show that the ferrite-cementite interface is more susceptible to damage resulting in cracking compared to the ferrite matrix, which is consistent with the experimental observation that there are extensive debonded voids due to interface damage. The implementation of this work provides a new way to study the micro-nano scale mechanical behavior of heterogeneous materials containing both interface damage and matrix damage.

Experimental estimation and numerical validation of cohesive zone parameters in hydroxyl functionalized MWCNTs‐reinforced CFRP under pure mode II loading

AbstractThe present study concerns the interface mode II fracture of hydroxyl functionalized multi‐walled carbon nanotubes (MWCNTs) reinforced carbon fiber epoxy composites. The well‐known cohesive zone model (CZM) is employed for investigating crack propagation. The major difficulty in applying the CZM is the parameter identification. In this work, the CZM's strength and energy parameters are determined reliably from the Short beam shear (SBS) and End‐notched flexure (ENF) tests, respectively, for pristine and three MWCNTs variations—0.1 wt.%, 0.2 wt.%, and 0.3 wt.%. The derived CZM parameters from the tests are imputed to a bilinear cohesive law to simulate the global load vs. displacement responses, which correlate well with the experimental findings. It is observed that the addition of 0.2 wt.% of MWCNTs increases the cohesive strength and fracture energy up to 14.14% and 17.78%, respectively, when compared to the pristine composites. Finally, the field emission scanning electron microscopy (FESEM) analysis is carried out to investigate the fracture mechanisms.Highlights Cohesive properties under mode II are estimated using standard fracture tests. The homogenization technique is used to calculate the effective properties of CFRP. The maximum % error among the experimental and the numerical peak load is 3.01%. A higher density of hackles with an increase of MWCNTs up to 0.2 wt.%.

Inverse parameter identification framework for cohesive zone models based on multi-island genetic algorithm

Composite interfaces are commonly simulated by cohesive zone models with the key challenge being the calibration of interfacial parameters. A novel inverse identification framework is presented in this paper to determine the interface parameters of cohesive zone models. This approach employs the multi-island genetic algorithm to obtain the key parameters of cohesive zone model which can reproduce the experimental observations. Utilizing two independent metrics, namely the load-displacement response and the debonding length history, an objective function is formulated to give the framework inherent robustness. The interface debonding length is used to uniquely determine the debonding properties of the specimen. To demonstrate the feasibility of the proposed framework, the strength-based cohesive zone model is taken as an example. The inverse algorithm is adopted to identify the interface parameters of both the double cantilever beam (DCB) experiments and the fixed-ratio mixed-mode (FRMM) tests. The robustness, accuracy and sensitivity of the framework are validated through the double cantilever beam test. The findings indicate that the numerical results align closely with the experimental data, confirming that the interface parameters identified by the proposed framework can reproduce the experimental results.

Deep neural network aided cohesive zone parameter identifications through die shear test in electronic packaging

AbstractThe die shear test is a feasible and conventional method to characterize the shear strength of die‐attaching layer materials in electronic packaging. A new method for determining cohesive zone model (CZM) parameters using deep neural networks (DNN) and die shear tests is proposed, different from classical fracture framework or lap shear test‐based methods. With the sintered nano‐silver die shear test, the results show that the bilinear CZM inversion results agree well with the experimental results. It is found that the DNN model has high accuracy in predicting and identifying the maximum shear traction strength τmax, separation displacement of the interface δf, and the interface stiffness k1 of CZM parameters for sintered nano‐silver adhesive layer through die shear test load versus displacement curves. The presented DNN‐aided inverse identifying method through the die shear test in this paper could provide an alternative and convenient method for extracting CZM parameters of various kinds of adhesive materials in electronic packaging.

Inverse identification of cohesive zone parameters for sintered nano-silver joints based on dynamic convolution neural network

The inverse identification of cohesive zone parameters is an important topic in the field of fracture mechanics. In this paper, three data-driven models, including multilayer perceptron (MLP), convolutional neural network (CNN), and dynamic convolutional neural network (DCNN), were presented to predict the cohesive zone parameters of sintered nano-silver end notched flexure (ENF) joints. Based on the construction of experimental and numerical datasets of load versus displacement curves, bilinear cohesive zone model (CZM) parameters of sintered silver joints are adopted as the prediction target. The investigation shows that MLP, CNN, and DCNN are all valid for predicting CZM parameters through load versus displacement curves with reasonable accuracy. However, DCNN has better prediction accuracy and performance than those of CNN and MLP models based on loss analysis, statistical indicator comparison, and K-fold cross-validation. DCNN can be adopted as the suitable surrogate model for CZM parameters inverse identification with high prediction accuracy. Otherwise, DCNN is also not sensitive to the load versus displacement curves data length. However, the computation efficiency of DCNN during the training process is not as high as that of MLP. Those three methods presented in this paper are very hopeful to be adopted for other inverse identifications of CZM parameters for various kinds of adhesive joints.

On adhesively bonded joints with a mixed failure mode—An experimental and numerical study

Cohesive zone model (CZM) has been extensively used to study interfacial failure behaviors such as fracture of adhesively bonded joints (ABJs). Accurate and efficient identification of traction–separation law (TSL) in CZM signifies an important issue for design and analysis of adhesive structures. In this study, a modified Arcan fixture was developed and employed to investigate the mixed mode failure behaviors of ABJs for carbon fiber reinforced plastic (CFRP) substrates under a tensile-shear coupling load, in which the double cantilever beam (DCB) test was carried out to characterize fracture toughness for benchmark data. With the help of digital image correlation (DIC) technique, the interfacial displacement field was obtained. The virtual crack closure technique (VCCT) was adopted to decouple the mode mixture at different tension-shear angles of the Arcan specimens. Based on the traction–separation law for each mixed ratio of failure mode, a refined CZM was established. In this study, the Arcan and DCB specimens bonded with a flexible adhesive of 3M DP190 were prepared and tested. The experiments were carried out for the ABJs with two adhesive layer thicknesses of 0.3 mm and 1 mm, respectively, to investigate the influence of bonding thickness. Based on the extracted CZM parameters, a finite element (FE) analysis model was developed and validated with the experimental results. Unlike the traditional predetermined damage evolution law, a new CZM was established without a priori cohesive damage evolution; and the effectiveness of the proposed model for the TSL extraction was verified. By using this method, the mechanical response of the bonding interface under complex stress state was well predicted and the FE modeling of ABJ’s fracture was accurately achieved. The study is anticipated to gain new understanding and fundamental data on mixed failure mode, thereby enabling better design of ABJs for engineering applications.

Investigation of damage mechanisms related to microstructural features of ferrite-cementite steels via experiments and multiscale simulations

Spheroidized ferrite-cementite steel (SFC) is susceptible to micro-defects owing to the mismatched deformation between the ferrite and cementite during cold forming, which seriously deteriorates the fatigue life. However, the damage mechanism related to microstructural features in the SFC steel during cold deformation has not been fully investigated, hindering control of the microstructure and forming process. This study presents a method coupled with experiments and multiscale simulations to research the damage mechanisms and the dependence of microstructure features under uniaxial tension in SFC steel. In situ tensile test revealed three damage mechanisms in SFC steel under uniaxial tension: cementite cracking, ferrite/cementite interface debonding, and ferrite cracking. In particular, the final fracture was mainly dominated by the ferrite/cementite interface debonding. In multiscale simulations, the macroscale tensile and nanoindentation simulations were carried out to obtain the strain history and mechanical properties of the mesoscale simulations, respectively. The mesoscale IP-based RVE and CP-based unit cells simulations were performed to capture the driving forces from the three damage mechanisms and the dependence of microstructural features, respectively. The nanoscale molecular dynamics simulation was conducted to identify the model parameters of cohesive zone model (CZM) in the mesoscale simulations. The numerical results indicated that particle-cracking void occurred when the internal von Mises stress exceeded the ultimate strength of the cementite particles. Interface-debonding void nucleated when the load on the particle was insufficient to resist its strength. Matrix-cracking should be attributed to the stress concentration caused by the dislocation pile-up or the crossing of multiple slip bands. In addition, interfacial debonding were more likely to occur in the stable orientations and high-angle grain boundaries of ferrite matrix. Compared with a circular cementite particle, an elliptical particle was more prone to cause interfacial debonding. Also, the ferrite/ferrite grain boundary showed earlier interfacial debonding perpendicular to the loading direction than parallel to the loading direction.

Determination of Toughness Variation and Cohesive Zone Parameters for De-bonding of Adhesively Bonded PMMA and Steel Using the Shaft-loaded Blister Test

ABSTRACT In this work, the shaft-loaded blister test (SLBT) is employed to investigate the de-bonding of a poly-metha-methyl-acrylate (PMMA) layer adhesively bonded to a steel layer. During de-bonding, the mode-mixity does not remain constant in this test; hence, the variation of mode-mixity with the change in de-bond size (blister radius) and the out-of-plane displacement of the PMMA layer is established through Finite Element Analysis (FEA). Experiments are performed in which the load, load-point displacement, and de-bond size is recorded synchronously. Three different thicknesses of PMMA layer are considered in experiments. The variation in toughness as a function of mode-mixity is evaluated. FE simulations with embedded cohesive zone model (CZM) are carried out, and the mixed-mode cohesive zone modelling parameters are identified by comparing the numerical results with experimental observations. By using this approach, the toughness variation as a function of mode-mixity and the CZM parameters is determined using the SLBT.

Influence of cohesive zone model parameters of polymer lugs with metal bushing on their geometrical and mass characteristics

Influence of cohesive zone model parameters of polymer lugs with metal bushing on their geometrical and mass characteristics

Bondline thickness effect on fracture and cohesive zone model of sintered nano silver adhesive joints under end notched flexure tests

AbstractBondline thickness effect on fracture behaviors and cohesive zone model (CZM) is an important topic for adhesive joints. In this paper, the fracture and CZM of sintered nano silver adhesive joints are investigated based on end notched flexure (ENF) test. Results show that load versus displacement curves of sintered silver adhesive joints is sensitive to the bondline thickness. With compliance‐based beam method (CBBM), the shearing fracture toughness of sintered silver bonded joints heightens with the increase of bondline thickness, which indicates that shearing fracture toughness is highly dependent on bondline thickness. R curves increase steeply for short equivalent crack length and become plateau for long equivalent crack length. The cracking morphology shows that the cracking paths are mainly interfacial and interlayer types. The bilinear CZM is also presented. The bondline thickness effect on CZM parameter is presented and discussed. The CZM given in this paper can be adopted for reliability analysis in power devices.

A robust fatigue parameter determination method for a local fatigue cohesive zone model

In this work, a robust method for determining the input fatigue parameters of a fatigue cohesive zone model recently developed by Dávila is presented. The method is based on surrogate modelling and multi objective optimization. Experimental data from delamination tests is used for the parameter determination, highlighting the phenomenological nature of the model. The ability to simulate both fatigue onset and propagation is verified for two different monotonic cohesive laws. The predictive capability of the methodology is validated against the experimental results of a partially reinforced double cantilever beam specimen (R-DCB) with non-self-similar crack propagation.

A review on the application of cohesive zone model in hydraulic fracturing

Hydraulic fracturing is an effective measure to increase production and injection and blockage removal in oil and gas field development. Accurate prediction of fracture morphologies is the key to the optimized design of hydraulic fracturing. The cohesive zone model (CZM) has been widely used in the numerical simulation of fracture initiation and propagation during hydraulic fracturing. The fractures formed by the numerical simulation vary significantly with different CZMs. In the current numerical simulation, the CZM generally adopts the bilinear model, which is more suitable for describing brittle fracture, while rocks are quasi-brittle materials and have nonlinear CZMs. This deviation should be corrected. Moreover, the CZM parameters are generally determined based on experience, without a reliable basis and standard determination method. This article focused on the CZM, systematically introduced its concept and classification, and clarified the correlation between the types of CZMs and the brittleness, quasi-brittleness, and ductility of rock fracture. The application of CZM in hydraulic fracturing was reviewed, and the existing problems, corresponding countermeasures and future research trends were presented. An integrated method of combining laboratory experiments, data mining and numerical simulation to determine the CZMs of mode I, mode II, and I/II mixed mode cohesive cracks was proposed.

AN INDENTATION METHOD FOR ADHESIVE STRENGTH EVALUATION OF POLYMER COATINGS

An indentation method was developed for adhesive strength evaluation of a polymer coating using the example of an epoxy composition with titanium alkoxide deposited on the surface of low-carbon steel. The method is based on the numerical implementation of the fracture mechanics approach in experimental data processing. It was found that the penetration of a Rockwell indenter perpendicular to the coating surface causes annular delamination buckling of the coating around the indentation, which is due to adhesive bond breaking as a result of radial shear when the coating material is forced out from under the indenter. A controlled parameter in finite element modeling was the experimentally determined width of the coating delamination zone at a fixed indentation depth at which delamination occurred. The adhesive contact conditions were set using the bilinear law of the cohesive zone model, which describes the relationship between the adhesive shear stress and adhesive bond stretching during shear of interacting surfaces in the contact plane. The limiting specific surface energy of adhesive failure was used as a quantitative evaluation criterion for adhesive strength. The optimal value of the limiting specific surface energy of adhesive coating failure was determined for the cohesive zone model parameters that provide the best convergence of the numerical and experimental data.

Direct measurement and verification of cohesive zone model parameters for basalt/PProds using the transverse tensile test and virtual double cantilever beam test

AbstractTo further our understanding of failure in thermoplastic‐based composite rods, the mode I‐governed cohesive zone model parameter of a basalt fiber reinforced polypropylene composite rod is evaluated. The relations between stress and strain, the maximum normal traction and final separation displacement are examined using a transverse tensile test method. The measured traction is verified by three‐dimensional finite element analysis of rod‐shaped double cantilever beam specimens. The numerical results show the close relation between the crack length and cube root of compliance, and yields a representative value of the mode I‐governed critical fracture energy.

Evolution law of crack propagation and crack mode in coral aggregate concrete under compression: Experimental study and 3D mesoscopic analysis

Coral aggregate concrete (CAC) is one of the typical quasi-brittle materials, which is of great significance to explore the damage process of CAC under load from the perspective of fracture mechanics. Therefore, the Cohesive Zone Model (CZM) was introduced to simulate the physical mechanism of crack propagation in CAC materials at the mesoscale adopting the discrete crack method. The main work included test and simulation parts. The tests included CT scanning and mechanical tests, which were used to calibrate the model parameters of CZM and verify the rationality of the meso-mechanical model. Numerical simulation was used to reveal the internal damage and fracture mechanism of CAC. According to the defined damage variables, it was found that the crack growth rate inside the CAC material evolves regularly with the axial strain during compression failure. The crack of CAC with higher strength grade showed oblique sliding shear failure and was more likely to form fracture surfaces, and the aggregate damage was more significant. The revealing of the cracking modes in each strain stage of CAC provides a theoretical basis for guiding the corresponding crack prevention measures. For example, in the stage of significant shear failure, targeted improvement of shear strength and toughness will bring more significant gains.

Determination of cohesive zone model parameters for tape delamination based on tests and finite element simulations

Determination of cohesive zone model parameters for tape delamination based on tests and finite element simulations

A Numerical Approach for the Efficient Concept Design of Laser-Based Hybrid Joints

Laser-based plastic–metal joints have high potential to enable cost-efficient lightweight structures in multi-material design. By an appropriate load-optimized positioning of the microstructure on the joining zone, cost- and strength-optimized joints can be realized. However, there are no design methods and models to efficiently develop these tailored microstructures. Currently, time-consuming experiments are necessary to find the optimum microstructure concepts. These experiments must be repeated when requirements change, e.g., dimensions of the components. To provide a simple and efficient design tool, this paper presents an automated numerical method for the development of cost- and strength-optimized microstructure concepts for laser-based joining zones. The basis for the approach is a new numerical model which generates concepts for microstructures automatically based only on the stress tensor in the joining zone. A new finite element cohesive zone model (CZM) was developed to estimate the joint strength. The CZM parameters were efficiently derived from a finite element model of a single cavity. To determine the costs, a new model is presented that calculates the production time and the cost for any given microstructure. The models were interconnected in a combined optimization procedure and a genetic algorithm was used to determine cost- and strength-optimized microstructure concepts. The approach was applied to a demonstration example where the laser costs were reduced by up to 67% compared with benchmarks with surface-covering parallel linear cavities. The approach shows high potential for the efficient design of cost- and strength-optimal laser-based hybrid joints since it is fully based on simulation models and iterative experiments in the design stage are eliminated.