Fibre Bridging Phenomenon Research Articles

Numerical Investigation of the R-Curve Effect in Delamination of Composite Materials Using Cohesive Elements

This paper presents a numerical investigation of the R-curve effect in delamination propagation in composite materials. The R-curve effect refers to the phenomenon whereby resistance to crack propagation increases with the advancement of the delamination, due to toughening mechanisms, such as fiber bridging. Numerical models often neglect this effect assuming a constant value of the fracture toughness. A numerical approach based on cohesive elements and on the superposition of two bilinear traction-separation laws is adopted here to accurately predict the R-curve effect in skin-doubler composite specimens subjected to three-point bending tests. The carbon-epoxy material presents two different sensitivities to the fiber bridging phenomenon resulting in two different R-curves. Comparisons with literature experimental data, in terms of load and delaminated area vs. applied displacement, and ultrasonic C-scan images show the effectiveness of the adopted approach in simulating the R-curve effect. The predicted numerical stiffness aligns with the experimental scatter, although the maximum load is slightly underestimated by approximately 15% compared with the average experimental results. The numerical model accurately predict the R-curve effect observed in the experimental data, demonstrating a 31% increase in the maximum load for the material configuration exhibiting greater sensitivity to fiber bridging.

Fracture toughness and fiber bridging mechanism for mode-I interlaminar failure of spread-tow woven composites

Given the current lack of research data on the delamination behavior of spread-tow woven composites, this study aims to systematically characterize the mode-I interlaminar fracture behavior of plain weave spread-tow fabrics (STFs) composites. DCB tests were conducted to investigate the influence of different ply thicknesses, unit cell sizes, and interface angles on delamination behavior and fiber bridging. The experimental results revealed a stick–slip crack propagation behavior in mode-I delamination of studied material, and a detailed analysis was performed on the influence mechanism of unit cell size on this behavior. Fiber bridging was found to be the primary mechanism responsible for the increased interlaminar fracture toughness in the plain weave STFs composites. Fractography analysis indicated that regions rich in fibers and resin in thicker-ply laminates promote fiber bridging, while an interface angle inconsistent with the direction of crack propagation inhibits fiber bridging. The concept of average steady-state fracture toughness (average Gs) was introduced as a means to assess propagation fracture toughness and two methods were proposed to obtain bridging tractions for characterizing the fiber bridging phenomenon. The bridging tractions and average Gs were used as key parameters to establish a trilinear cohesive zone model (CZM) for simulating mode-I delamination. The numerical results aligned well with the experimental results, demonstrating the applicability of the parameter determination strategy based on the average Gs and bridging tractions for the selection of parameters to use in the CZM.

Cohesive Zone Modeling of the Interface Fracture in Full-Thermoplastic Hybrid Composites for Lightweight Application.

With the increasing demand for lightweight and high-performance materials in the automotive and aerospace industries, full-thermoplastic hybrid composites have emerged as a pivotal solution, offering enhanced mechanical properties and design flexibility. This work aims to numerically model the fracture strength in full-thermoplastic hybrid composites made by forming and overmolding organosheets. The mode I fracture was investigated by modeling the behavior of T-joint specimens under a tensile test following the cohesive zone modeling (CZM) approach. The sample was designed to replicate the connection between the laminate and the overmolded part. Double cantilever beam (DCB) specimens were manufactured with organosheets and tested to mode I opening to determine the interlaminar fracture toughness. The fracture toughness out of the mode I test with DCB specimens was used to define the CZM parameters that describe the traction-separation law. Later, due to the particular geometry of the T-join specimens that under tensile load work close to pure mode I, the cohesive parameters were determined by inverse analysis, i.e., calibrating the theoretical models to match experimental results. The fracture resistance T-joint specimens appeared dependent on the fiber-bridging phenomenon during the delamination. In particular, the presence of fiber-bridging visible from the experimental results has been replicated by virtual analyses, and it is observed that it leads to a higher energy value before the interface's complete breakage. Moreover, a correspondence between the mode I fracture toughness of the DCB specimen and T-joint specimens was observed.

Investigation of crack propagation in filament wound composite samples of Mode-I by using acoustic emission technique

A common industrial method of fabricating composite structural is filament winding, which is widely used to manufacture axisymmetric components. One of the most prevalent damage mechanisms in these composite structures is delamination, which occurs in various types of loading. In this research, the mechanical behavior and propagation of the initial crack of Mode-I in carbon/epoxy filament wound (FW) composite curve beams have been investigated via the acoustic emission (AE) method. For this purpose, at first, a composite tube was made with considering the artificial interlayer separation, and the beam specimens were cut from the longitudinal direction. At first, the initiation of the failures was determined using the AE method. Then, the growth and spread of interlayer delamination were investigated by the energy of AE signals and the sentry function. By determining the speed of the AE waves and providing a method to filter unwanted signals, the momentary position of the interlayer delamination tip during growth is predicted. The results showed that the fiber bridging phenomenon was due to the penetration of the two regions adjacent of the separation interface, and the fiber bridging length considerably affected the Mode-I delamination fracture toughness. In addition, the fracture toughness increased as the fiber bridging zone enlarged. Finally, good agreement was observed between the fracture toughness values obtained from the AE method and those found in the standard ASTM D5528.

Asymmetric bending characteristics and failure mechanism of bamboo under different loading directions

Bamboo has a special microstructure, its fiber content decreases gradually from the outside to the inside. This kind of gradient distribution results in obviously asymmetric bending characteristics of bamboo, and shows different bending properties and failure modes in different bending directions. In this study, bending properties of moso bamboo (Phyllostachys pubescens) in three different directions (type A: outward bending, type B: tangential bending, type C: inward bending) were tested. Digital image correlation (DIC) and scanning electron microscopy (SEM) were used to analyze the failure process, strain field change and failure morphology of bamboo, and summarized the failure mechanism of bamboo bending in different directions. Results indicated that the tangential bending have the highest modulus of rupture (MOR) and modulus of elasticity (MOE), and the inward bending has the best flexural toughness. The failure mechanism of the three bending directions was different. For type A, the initial crack appeared in the parenchyma tissue in the tensile region where the fiber content was less, so the crack rapidly expanded inside the parenchyma tissue, forming a neat failure section, then led to low toughness of bamboo. For type B, the initial crack appeared in the parenchyma tissue in the tensile region. Due to the moderate fiber content in the tensile region, the fiber bridging phenomenon appeared in the fracture section, led to the higher elastic modulus and strength of the type B. For type C, the initial crack appeared in the parenchyma tissue in the compression region. Because of the more fiber content in the tensile region, the cracks in this part propagated transversely and formed the failure morphology of interlayer separation, which increased the toughness of the specimen. This study is helpful to understand the asymmetric bending characteristics of bamboo, and provide guidance for the use of bamboo as a structural material and the preparation of composite materials.

Experimental and Numerical Research of Delamination Process in CFRP Laminates with Bending-Twisting Elastic Couplings.

This paper aims at experimental and numerical research of delamination process in carbon/epoxy composite laminates with different fiber orientation angles in stacking sequence exhibiting the bending-twisting elastic couplings. Experimental specimens were subjected to the double cantilever beam (DCB) tests according to the ASTM D5528 regulations. Values of the mode I strain energy release rates were calculated by using three different data reduction schemes: the modified beam theory, the compliance calibration method and the modified compliance calibration. Determination of delamination initiation point was conducted in twofold way: by visual observation of crack tip using high resolution camera and by utilization of the acoustic emission technique. Numerical analyss were prepared in Abaqus/CAE Software environment by using the virtual crack closure technique (VCCT). The numerical beam model consisted of SC8R continuum shell elements. Obtained outcomes revealed that extensive fiber bridging phenomenon occurring during delamination process pronouncedly affected propagation values of strain energy release rate (GIprop) and numerically obtained load-displacement curves. Nevertheless, in initial stage of delamination, results obtained by using the VCCT were in agreement with experimental data. The greatest value of the mode I fracture toughness equal 0.56 N/mm was obtained for the BT45 laminate.

Experimental study on interface failure behavior of 3D printed continuous fiber reinforced composites

Additive manufacturing (or 3D printing) for continuous fiber composite exhibits great potential for fabrication of next-generation lightweight sophisticated structural components. Nevertheless, understanding of interface characteristics of printed parts has remained an open research question for broader applications of this new technology in engineering practice. This study aimed to evaluate the interfacial quality of 3D-printed carbon fiber reinforced plastic (CFRP) composites from two aspects: interlaminar fracture toughness in a pure mode and interfacial failure mechanism in a mixed mode. Prior to the experimental tests, the microstructural quality of the 3D printed specimens was characterized, which showed that the void content and shape of different materials are different. There is a clear boundary line where the short fiber matrix layer and the continuous fiber reinforced layer are in contact, while the interface formed between the same material layers has no evident connection traces. The standard specimens were printed for testing pure mode I and mode II interlaminar fracture toughness, through which the G Ι C and G IIC of interface between continuous carbon fiber layers was characterized. It was found that the fiber bridging phenomenon presented in the double cantilever beam (DCB) experiments, resulting in a higher initial mode I fracture toughness. The end notched flexure (ENF) tests found that the fracture toughness of initial mode II in between the 0° continuous carbon fiber layers was relatively low. The scanning electron microscope (SEM) analysis revealed that the separated surface had only a small area of the matrix being sheared. The single lap specimen printed directly was proposed as a simplified model for simulating complex structural parts subjected to mixed stress of peel and shear. The mechanical responses and failure characteristics of the interfaces composed of different materials and different fiber angles under mixed stress were studied. It is found that each specimen presented some mixed failure modes, and the interface characteristics of different materials and different fiber orientations were completely different. The results gained in-depth understanding on the interfacial properties of 3D printing fiber reinforced structures, thereby providing key data and knowledge for practical applications. • Different layering methods with different interlayer morphology and void shape. • The critical strain energy release rates of type I and typeⅡwere obtained. • Continuous fiber bridging enhances type I fracture toughness. • The shear resistance of the interface between continuous fibers and matrix is very weak. • Reinforcement materials and fiber angles affect the interfacial bond strength and failure.

Transformation-induced plasticity in SMA composites experiencing fiber bridging phenomenon

The present study aims to investigate the fiber bridging phenomenon in the fracture of a composite sheet reinforced with shape memory alloy wires undergoing transformation-induced plasticity in pseudoelastic loading. To this end, the Entchev-Lagoudas thermomechanical model is used, and the necessary equations to describe the adiabatic conditions of nitinol fibers are extracted considering the transformation-induced plasticity. The formulation needed for the numerical implementation of the constitutive model of the shape memory alloy is then developed using the convex cutting plane algorithm. The force effect of the bridging fibers on the crack edges of the composite specimen is applied directly, and the extended finite element method is used to study the fracture of the cracked composite specimen. The present research examines the effects of temperature conditions, fiber volume fraction, matrix material, and residual stresses on the results.

Experimental and Numerical Assessment of Fibre Bridging Toughening Effects on the Compressive Behaviour of Delaminated Composite Plates.

Increasing the Mode I inter-laminar fracture toughness of composite laminates can contribute to slowing down delamination growth phenomena, which can be considered one of the most critical damage mechanisms in composite structures. Actually, the Mode I interlaminar fracture toughness (GIc) in fibre-reinforced composite materials has been found to considerably increase with the crack length when the fibre bridging phenomenon takes place. Hence, in this paper, the fibre bridging phenomenon has been considered as a natural toughening mechanism able to replace embedded metallic or composite reinforcements, currently used to increase tolerance to inter-laminar damage. An experimental/numerical study on the influence of delamination growth on the compressive behaviour of fibre-reinforced composites characterised by high sensitivity to the fibre bridging phenomenon has been performed. Coupons, made of material systems characterised by a variable toughness related to a high sensitivity to the fibre bridging phenomenon and containing artificial through-the-width delaminations, were subjected to a compressive mechanical test and compared to coupons made of standard material system with constant toughness. Out-of-plane displacements and strains were monitored during the compression test by means of strain gauges and digital image correlation to assess the influence of fibre bridging on delamination buckling, delamination growth and on the global buckling of the specimens, including buckling shape changes. Experimental data were combined with a numerical study, performed by means of a virtual crack closure technique based procedure, named SMart Time XB – Fibre Bridging (SMXB-FB), able to mimic the crack bridging effect on the toughness properties of the material system. The combination of numerical results and experimental data has allowed the deformations and the buckling shape changes to be correlated to the onset and evolution of damage and, hence, contributes to improving the knowledge on the interaction of the failure mechanisms in the investigated composite specimens.

Numerical study on the toughening effect of the fiber bridging on delaminated composite stiffened panel

In this paper, the debonding behavior of a fiber reinforced composite panel, under flexural loading conditions, is numerically studied. Two material systems, respectively insensitive and sensitive to the fiber bridging phenomenon, are considered. The toughening effect of the fiber bridging phenomenon, on the debonding propagation, is analyzed. An innovative numerical procedure, able to consider GIc variations with the crack length, is proposed. The results of numerical models are compared to evaluate the fiber bridging sensitivity effects on the maximum attained load and on the delaminated area.

Cross-Influence between Intra-Laminar Damages and Fibre Bridging at the Skin-Stringer Interface in Stiffened Composite Panels under Compression.

In this paper, the skin–stringer separation phenomenon that occurs in stiffened composite panels under compression is numerically studied. Since the mode I fracture toughness and, consequently, the skin–stringer separation can be influenced by the fibre bridging phenomenon at the skin–stringer interface, in this study, comparisons among three different material systems with different fibre bridging sensitivities have been carried out. Indeed, a reference material system has been compared, in terms of toughness performance, against two materials with different degrees of sensitivity to fibre bridging. A robust numerical procedure for the delamination assessment has been used to mimic the skin–stringer separation. When analysing the global compressive behaviour of the stiffened panel, intra-laminar damages have been considered in conjunction with skin–stringer debonding to evaluate the effect of the fibre and matrix breakage on the separation between the skin and the stringer for the three analysed material systems. The latter are characterised by different toughness characteristics and fibre bridging sensitivities, resulting in a different material toughness.

Numerical Investigation on Delamination Growth in Composite Panels Including Fibre-Bridging Effect

In this work, the delamination onset and propagation in composite panels with induced defects is numerically investigated by means of a robust numerical procedure, called SMXB-FB and implemented in ANSYS FEM code by Ansys Parametric Design Language. The used methodology is based on the Virtual Crack Closure Technique (VCCT) and is able to avoid the time-step and mesh dependency issues of the standard VCCT based delamination growth approaches. In addition the proposed model takes into account the Fibre Bridging phenomenon by considering the real variation of the Critical Energy Release Rate associated to the Mode I failure mechanisms (peeling). A sensitivity analysis has been performed to assess the influence of the geometrical parameters on the delamination growth and the carrying load capability of a composite plate with a through-width delamination under compression in the presence of the fibre bridging phenomenon. Three different material models have been adopted: high sensitive, sensitive, and insensitive to the fibre bridging phenomenon to better point out how the fibre bridging phenomenon can delay the delamination growth and influence the compressive behaviour of the composite plate.

Development and application of a numerical procedure for the simulation of the “Fibre Bridging” phenomenon in composite structures

In this paper, a novel numerical procedure for delamination growth simulation able to evaluate the Fibre Bridging effect has been used to numerically investigate the mechanical behaviour of stiffened composite panels. The proposed methodology, implemented in ANSYS® FEM code by Ansys Parametric Design Language (APDL), allows to take into account the real variation of the Critical Energy Release Rate associated to the Fibre Bridging phenomenon. A first numerical application has been performed for preliminary validation purposes, simulating the flexural behaviour of representative section of a stiffened composite plate. The considerable agreement between the obtained numerical results and the literature experimental data confirms the effectiveness and the accuracy of the proposed model. Finally, a parametric analysis has been carried out in order to study the influence of the geometrical parameters of single stiffened composite panels in terms of skin-stringer debonding including Fibre Bridging.

A Numerical Assessment of Fibre Bridging Influence on Composite Panels Skin-stringer Debonding

Numerical simulations on stiffened composite panels have been performed in order to investigate the influence of fibre bridging phenomenon on the onset and on the evolution of skin-stringer debonding. A novel numerical procedure for delamination growth simulation, implemented in ANSYS® FEM code by Ansys Parametric Design Language and enhanced to take into account GIc variations related to the fibre bridging phenomenon, has been used to numerically simulate the skin-stringer separation. Indeed, fibre-reinforced composites can develop high fibre bridging under mode I (peeling) delamination growth due to the additional resistance to crack opening offered by delaminated fibres, leading to a significant increase of mode I critical strain energy release rate. Within the present paper, a limited sensitivity analysis is presented to assess the influence of geometrical parameters of stiffened composite panels on the fibre bridging relevance in skin-stringer debonding in terms of debonded area.

XFEM analysis of fiber bridging in mixed-mode crack propagation in composites

In this work, the extended finite element method (XFEM) is further generalized to study the fiber bridging phenomenon in fracture analysis of unidirectional composites. Treating composites as a biphase material, fibers effects on increasing fracture toughness are modeled by non-linear springs integrated in the XFEM formulation of displacement discontinuity. Combining the capability of XFEM in modeling arbitrary crack path with the traction-separation representation of the fracture process zone in the crack-bridged zone model, this formulation allows for simulation of fiber bridging in a crack propagation process without a priori knowledge of the crack path. Moreover, the criterion originally proposed for predicting the crack propagation path in orthotropic solids is modified to incorporate the effects of fiber orientation. Several numerical simulations of mode I and mixed-mode problems are provided, and the corresponding force–displacement curves are analyzed to address the accuracy and efficiency of the proposed method.

Beam analysis of the double cantilever beam specimen with fibre bridging

The fibre bridging phenomenon commonly seen in double cantilever beam tests is considered an artifact of the standard unidirectional specimen. Therefore, it limits the scope of the test to the measurement of the critical strain energy release rate GI c for crack initiation. This paper presents a beam model based on a linear traction–separation law that has been shown to be a good approximation to the early stages of fibre bridging. The present model enables the evaluation of accurate propagation GI c values through the fitting of experimental load–displacement curves. Furthermore, fairly good fits can be obtained without employing sophisticated optimization algorithms by considering simple relations between model parameters and curve features. Therefore, the present model is able to extract a broader set of results from a single test, thereby increasing the confidence in toughness measurements.

A study of the interlaminar fracture toughness of a carbon-fiber/epoxy composite containing surface-modified short kevlar fibers

Short Kevlar fibers (SKF) were distributed in the mid-plane of a continuous carbon-fiber/epoxy laminate before processing at the point where an initial crack is introduced in an interlaminar fracture toughness test. Two extreme cases of SKF/epoxy interfaces were obtained by oxygen-plasma-treated SKF (P-SKF) or silicone-release-agent-treated SKF (S-SKF). The mode I (G IC) and mode II (G IIC) interlaminar fracture toughnesses of the modified carbon-fiber/epoxy composites were then investigated. The fracture surface was studied by scanning electron microscopy and optical microscopy. The interfacial shear strengths of the SKF/epoxy interfaces were measured by fiber pull-out tests. G IIC increased with increasing crack length because of the presence of SKF bridging in the wake of the propagating crack. The fiber-bridging phenomenon may be influenced by the amount and orientation of SKF. However, fiber bridging was not observed in mode-II tests on P-SKF and S-SKF composites, irrespective of the amount of Kevlar fibre. G IC showed no significant effect with SKF, P-SKF and S-SKF with no fiber bridging.

Fracture Mechanics Applied to Glass Fibre/Epoxy Matrix Interface Characterization

The possibility of the application of mode I and mode II fracture mechanics to the characterization of the glass fibre/epoxy matrix interface has been studied here. The aim is to find out a method much more sensitive and reliable than the commonly used methods such as single filament tests which could allow a separate analysis of cracks initiation and potion phenomena that are involved in the damage of composite structures. One original contribution of this comparative analysis on materials differing only in their fibre sizing is the attempt to use the whole resistance curve of the materials including the propagation phase by assuming that some differences in the amplitude of the well known fibre bridging phenomenon are directly induced by differences in interface quality, which is the only parameter that is not kept constant. Both mode I and mode II tests have revealed a high sensitivity to the fibre/matrix interface quality: According to the property which is considered, variations are noted in a range of 150% to 300% for a modification of the interface by different sizing and in a range of 150% to 700% for an artificial modification of the interface by hydrothermal aging. Nevertheless mode II tests offered rather limited information (only about cracks initiation). On the other hand the interest of mode I fracture mechanics as fibre/matrix interface characterization method has appeared, in so far as this technique makes it possible to separate cracks initiation and then cracks extension phenomena, on which the fibre/matrix interface quality has a specific incidence, that is translated by variations of cracks initiation and propagation energies, of cracks growth rates and of acoustic emissions.

Weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Analysis of fiber bridging phenomenon in the composites and determination of stress intensity factors due to non-uniform stress distributions such as residual and thermal stresses generally require the use of a weight function. This paper describes the development and verification of a weight function for the single edge cracked geometry with clamped ends. Finite element analyses were conducted to determine the stress intensity factors (K) and crack opening displacements (COD) due to different types of stress distributions. The weight function was developed using the K and COD solution for a constant stress distribution. K and COD predicted using this weight function correlated well with the finite element results for non-uniform crack surface stress distributions.

On the fiber-bridging of cracks in fiber-reinforced composites

A formulation is systematically derived for a fully or partially bridged straight crack in anisotropic elastic materials such as fiber reinforced composites. Following Ting's (1988, Phys. Stat. Sol. (b) 145, 81–90) use of new sum rules for Stroh formalism, the governing equation of fiber bridging of cracks is formulated explicitly in real form. The straight crack is in terms of the superposition of dislocation density distributions and the bridging force is linearly or nonlinearly dependent on the crack opening displacement (COD). Along the crack, there may be an arbitrary variation of the stiffness of the bridging materials due to partially failed fibers or ligaments. Additionally, the crack may have any orientation with respect to the axis of the material symmetry. Finally, the solution is explicitly made in terms of Chebychev polynomials for the linear case and can be compared with that calculated by the boundary element method. In the case of a linear relation between COD and bridging traction the numerical solution is in excellent agreement with the analytic solution. This can be regarded as justification for the numerical scheme. For an oblique crack, both mode I and mode II fracture exist. In the case of a nonlinear relation between COD and bridging traction, only a numerical solution is available. By adopting Hsueh's fiber-pull-out model we know that the interfacial properties σ d , σ c and μ play important roles in the debonding, sliding and crack opening steps in fiber bridging phenomenon. The dependence of COD and K I on σ d , σ c and μ have been analyzed. Since the larger σ d , vb σ c vb and μ are, the larger bridging tractions fibers can offer, COD and K I decrease as the values of σ d , σ c and μ increase.