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The interaction between hydraulic fracture (HF) and natural fracture (NF) in naturally fractured rocks is critical for hydraulic fracturing. This paper aims to focus on investigating the development of tensile and shear debonding zone on the NF caused by the stresses produced by HF, and the influence of NF’s debonding behavior on the interaction between HF and NF.

Theoretically, tensile and shear debonding modes of NF are considered, two dimensionless parameters are proposed to characterize the difficulty of tensile and shear failure of NF, respectively. Numerically, a finite element model combining the extended finite element method and cohesive zone method (CZM) is proposed to study NF’s debonding behavior and its influence on the interaction between HF and NF.

Both theoretical analysis and numerical simulation show the existence of two debonding modes. The numerical results also show that the HF can cross, offset or propagate along the NFs depending on the parameters’ value, resulting in different fracture network and stimulated reservoir volume. When they are large, the NF’s debonding area is small, HF tends to cross the NF and the fracture network is simple; when they are small, the NF’s debonding area is large, HF will propagate along the NF. In addition, HF is easier to propagate along with NF under tensile debonding mode while it is easier to pass through NF under shear debonding mode.

The theoretical and numerical considerations are taken into account in the influence of the debonding of NFs on the interaction between HFs and NFs and the influence on the formation of the fracture network.

Since failure of laminated composites by delaminations is common, the purpose of this paper is to present a numerical procedure to check the stability of delaminations in fiber metal laminate (Glare), with different possible damage configurations, under uni-axial tension. Deformation behavior of the laminate is also examined. Influence of the type and the extent of damage, represented by varying sizes and number of delaminations, on delamination driving force and laminate deformation is found.

Delaminated Glare is modeled by finite element method. Interface cohesive elements are used to model the delaminations. Finite element results provide the deflection/deformation characteristics of the laminate. Driving forces of delaminations are estimated by J integrals that are numerically obtained over cyclic paths near delamination tips. Laminates with different types of delaminations are also fabricated and externally delaminated for measurement of their interlaminar fracture toughness. The delamination is considered to be stable if its driving force is less than corresponding interlaminar fracture toughness of the laminate.

Delaminations are found to be stable in laminates with lower number of delaminations and unstable in laminates with higher number of delaminations. Increase in size of delaminations increases the deformations but reduces the delamination driving force whereas increase in number of delaminations increases both deformations and driving forces. The trends change in case of laminates with symmetrical damage. Shape of delamination is also found to influence the deformations and driving forces. The finite element model is validated.

There is scope for validating the numerical results reported in the paper by theoretical models.

Checking the stability of delaminations and their effect on deformation behavior of the laminate helps is assessment of safety and remaining life of the laminate. If failure is predicted, preemptive action is taken by using repair patch ups at identified critical locations in order to avoid failures in service conditions.

The paper offers the following benefits: use of cohesive zone method that is readily possible in finite element procedures and is relatively simple, fast and reasonably accurate is demonstrated; suitability of using J integrals over paths crossing non-homogeneous and property mismatched material layers is tested; and influence of the type and the extent of damage in the laminate on its deformation behavior and delamination driving forces is found. This type of work has not been reported so far.

The purpose of this paper is to predict the response and perforation of fibre metal laminates (FMLs) subjected to impact by projectiles at different velocities.

A finite element (FE) model is constructed in which recently proposed dynamic constitutive models for fibre reinforced plastic (FRP) laminates and metals are used. Moreover, a recently developed dynamic cohesive element constitutive model is also used to simulate the debonding between FRP laminates and metal sheets. The FE model is first validated against the test data for glass laminate aluminum reinforced epoxy (GLARE) both under dropped object loading and ballistic impact, then used to perform a parametric study on the influence of projectile nose shape on the perforation of FMLs.

It is found that the present model predicts well the response and perforation of GLARE subjected to impact loading in terms of load-time history, load-displacement curve, residual velocity and failure pattern. It is also found that projectile nose shape has a considerable effect on the perforation of GLARE FMLs and that the ballistic limit is the highest for a flat-ended projectile whilst for a conical-nosed missile the resistance to perforation is the least.

Recently developed constitutive models for FRPs and metals, together with cohesive element model which considers strain rate effect, are used in the FE model to predict the behaviour of FMLs struck by projectiles in a wider range of impact velocities; the present model is advantageous over such existing models as Johnson-Cook (JC) + Chang-Chang and JC (+BW) + MAT162 in terms of failure pattern though they produce similar results for residual velocity.

In this work, the cohesive zone model (CZM) developed by some of the authors to simulate the propagation of fatigue defects in two dimensions is extended in order to simulate the propagation of defects in 3D. The paper aims to discuss this issue.

The procedure has been implemented in the finite element (FE) solver (Abaqus) by programming the appropriate software-embedded subroutines. Part of the procedure is devoted to the calculation of the rate of energy release per unit, G, necessary to know the growth of the defect.

The model was tested on different joint geometries, with different load conditions (pure mode I, mode II pure, mixed mode I/II) and the results of the analysis were compared with analytical solutions or virtual crack closure technique (VCCT).

The possibility to simulate the growth of a crack without any re-meshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the CZM attractive also for the fatigue crack growth simulation. However, differently from VCCT, three-dimensional fatigue de-bonding/delamination with CZM is not yet state-of-art in FE softwares.

One of the major concerns of the constrained-surface stereolithography (SLA) process is that the built-up part may break because of the force resulting from the pulling-up process. This resultant force may become significant if the interface mechanism between the two contact surfaces (i.e. newly cured layer and the bottom of the resin vat) produces a strong bonding between them. The purpose of this paper is to characterize the separation process between the cured part and the resin vat by adopting an appropriate and simple mechanics-based model that can be used to probe the pulling-up process.

In this paper, the time-histories of the pulling-up forces are measured using FlexiForce® force sensors. The experimental data are analyzed and used to estimate the constitutive parameters of the separation mechanism. Here, the separation mechanism is modeled based on the concept of cohesive zone model (CZM) that is well-studied in the field of fracture mechanics. By using the experimentally measured pulling-up force, this paper proposes a very efficient inverse technique to estimate the constitutive parameters for the CZM. The constitutive laws for the CZM facilitate in relating the separation force at the interface between the cured part and the resin vat in terms of the pulling-up velocity. Unlike work proposed earlier, computationally expensive full-scale finite element runs are not essential in the current work while estimating the required parameters of the constitutive laws. Instead, mechanics-based computationally efficient surrogate model is proposed to readily estimate these constitutive parameters.

Two constitutive laws are compared on the basis of their predictions of the separation force profile. Excellent match is obtained between the measured and the predicted separation force profiles.

This paper selects a suitable mechanics-based model that can characterize the separation process and proposes a computationally efficient scheme to estimate the required constitutive parameters. The proposed scheme can be used to reliably predict the separation force for the constrained-surface SLA process, leading to improved productivity and reliability of the SLA processes in fabricating the built-up parts.

Hydrofracturing technology has been widely used in tight oil and gas reservoir exploitation, and the fracture network formed by fracturing is crucial to determining the resources recovery rate. Due to the complexity of fracture network induced by the random morphology and type of fluid-driven fractures, controlling and optimising its mechanisms is challenging. This paper aims to study the types of multiscale mode I/II fractures, the fluid-driven propagation of multiscale tensile and shear fractures need to be studied.

A dual bilinear cohesive zone model (CZM) based on energy evolution was introduced to detect the initiation and propagation of fluid-driven tensile and shear fractures. The model overcomes the limitations of classical linear fracture mechanics, such as the stress singularity at the fracture tip, and considers the important role of fracture surface behaviour in the shear activation. The bilinear cohesive criterion based on the energy evolution criterion can reflect the formation mechanism of complex fracture networks objectively and accurately. Considering the hydro-mechanical (HM) coupling and leak-off effects, the combined finite element-discrete element-finite volume approach was introduced and implemented successfully, and the results showed that the models considering HM coupling and leak-off effects could form a more complex fracture network. The multiscale (laboratory- and engineering-scale) Mode I/II fractures can be simulated in hydrofracturing process.

Based on the proposed method, the accuracy and applicability of the algorithm were verified by comparing the analytical solution of KGD and PKN models. The effects of different in situ stresses and flow rates on the dynamic propagation of hydraulic fractures at laboratory and engineering scales were investigated. when the ratio of in situ stress is small, the fracture propagation direction is not affected, and the fracture morphology is a cross-type fracture. When the ratio of in situ stress is relatively large, the propagation direction of the fracture is affected by the maximum in situ stress, and it is more inclined to propagate along the direction of the maximum in situ stress, forming double wing-type fractures. Hydrofracturing tensile and shear fractures were identified, and the distribution and number of each type were obtained. There are fewer hydraulic shear fractures than tensile fractures, and shear fractures appear in the initial stage of fracture propagation and then propagate and distribute around the perforation.

The proposed dual bilinear CZM is effective for simulating the types of Mode I/II fractures and seizing the fluid-driven propagation of multiscale tensile and shear fractures. Practical fracturing process involves the multi-type and multiscale fluid-driven fracture propagation. This study introduces general fluid-driven fracture propagation, which can be extended to the fracture propagation analysis of potential fluid fracturing, such as other liquids or supercritical gases.

The purpose of this paper is to assess a numerical tool to simulate and predict the onset and the propagation of the delaminations in a composite structure.

The approach to the work is done through the cohesive zone model technique applied to the finite element method.

Double cantilever beam, end notched flexure and mixed mode bending tests have been performed and correlated to benchmark cases, in order to validate the procedure. Numerical test campaign on specimens of the skirts with delaminations has been performed to analyze the behaviour under compressive load and the buckling.

This tool is applied to the study of the behaviour of some components in carbon/epoxy composite of a space structure in which one or more delaminations are eventually present following impact damage or manufacturing process. The components in particular are the booster's skirts of a small class launcher, subjected to a compressive load.

The behavior of joints has a significant effect on the stability of water conveyance tunnel. The purpose of this paper is to study the contact and friction at the joint of the tunneling segment lining and establish its contact friction model. At the same time, the stress and deformation characteristics at the joint of the segment under hydrostatic load are analyzed.

In this study, the contact and friction in a bolted joint are examined using shear testing. The feasibility of the proposed model is verified by a numerical simulation of tests and a theoretical analysis. Accordingly, the effect of joints on the lining is explored under internal hydrostatic loading.

The results show that the openings of tunnel segments in joints gradually expand from the positions of the inner and outer edges to the location of the bolt. Moreover, the stress concentration zone is formed at the bolt. Under hydraulic loading, the opening displacement at the joint increases as the water pressure increases; nevertheless, it does not exceed engineering requirements. When the water pressure of the tunnel lining joint reaches 0.5 MPa, the opening of the joint slowly increases. When the water pressure exceeds 0.7 MPa, the opening of the joint rapidly and significantly increases.

Contact and friction in a bolted joint were examined using shear testing. A cohesive zone model of bolted joints was proposed based on test results. The influence of joint behavior on the stability of water conveyance tunnel was studied.

This paper aims to study the benefits of use of bi-adhesive (combination of two different adhesives) over conventional single adhesive in bonded lap joints. Characterise damage severity due to cohesive and adherent failure as feedback for operating load levels that assist in developing damage tolerance design of the adhesively bonded joints.

Single lap joint where the adherent plate is made up of aluminium alloy joined together with bi-adhesives is analysed. The nature of adhesives ranges from brittle, elastic-plastic, moderately ductile to largely ductile. Numerical analysis is performed considering the material and geometric non-linear behaviour of the joint. The optimum bond ratio of bi-adhesives and the effect of the location of adhesive on the stress distribution are studied. The cohesive zone modelling (CZM) is adopted to account for the cohesive failure of the joint. The adherent plate failure is also addressed by modelling and studying the behaviour of the crack at different locations in the plate using modified virtual crack closure integral (MVCCI).

The results obtained from the stress analysis show some important characteristic behaviour of the bi-adhesive joint. Although bi-adhesive is expected to result in improved joint strength, the purpose gets defeated if a brittle adhesive is used at the corners and ductile adhesive at the middle. The joint strength based on CZM, evaluated for a single adhesive, is in good comparison with the experimental results from the literature. Also, the location of the crack in the adherent plate plays a significant role in the failure of the joint.

Estimating joint strength for the bi-adhesive model using CZM and evaluating damage severity in the presence of de-bond and crack in the bi-adhesive lap joint model assists in developing robust damage tolerance design models of such joints.

The combined numerical-experimental approach has been presented. The purpose of this paper is to determine the critical rupture load of the notched components based on the cohesive zone modeling (CZM).

The 42CrMo4 steel (in normalized state) state has been tested and modeled using an eXtended finite element method (xFEM) philosophy with the CZM approach. In order to validate the numerically obtained critical load forces the experimental verification was performed.

The critical loads were determined for various notch configurations. The numerical and experimental values were compared. Based on this, a good agreement between experimental and numerical data is achieved. The relative error does not exceed 7 percent.

The presented procedure and approach is effective and simple for engineering applications. It is worth to underline that the obtained critical load values for notched components require only the static tensile test results and implementation of the presented route in numerical FEM, xFEM environment.

The presented methodology is actual and still developed. The scientific and engineering value of the presented numerical procedure is high.