Bridging Tractions Research Articles

Temperature-dependent R-curve and traction-separation relation in mode-I fracture of GFRP laminates

The R-curve and fiber bridging phenomenon in mode-I fracture of glass-fiber reinforced laminates at different temperatures are investigated in this study, aiming to reveal their changes with temperature. The mode-I fracture experiments are carried out by adopting double cantilever beam (DCB) configuration at −55 ℃, 23 ℃ and 80 ℃. Fiber bridging is observed during the tests. The R-curve and bridging traction are quantitatively analyzed, from which the relationship between the R-curve and fiber bridging phenomenon, and temperature is obtained. It is found that fiber bridging effect is enhanced with the increase of temperature. The bridging traction of specimens tested at 80 ℃ is significantly higher than that at −55 ℃ and 23 ℃. An R-curve model considering both temperature and fiber bridging effects is proposed. In addition, bilinear and tri-linear traction-separation relations (TSLs) are utilized to establish a numerical model for the simulation of delamination growth behavior with the consideration of the temperature-dependent effect on the mechanical properties of composite materials. When using the bilinear TSL, the fiber bridging is considered by integrating the resulted R-curve into finite element model via a user-defined USDFLD subroutine. Effects of initial interface stiffness, interface strength and viscosity coefficient on simulated results are numerically investigated. Finally, applicability of the established numerical models is illustrated by comparisons between the simulations and the test results.

Effect of Selective Z-Pinning on the Static and Fatigue Strength of Step Joints between Composite Adherends

The z-pinning reinforcement technique, which involves inserting thin pins through the body of a laminate, has proven highly effective in enhancing the strength of various composite joint configurations. This investigation aims to explore the enhancements achievable through selective z-pinning at very low pin contents on both the static and fatigue performance of composite joints. Single-step joints between carbon/epoxy adherends were reinforced using steel pins arranged in two, three, or four rows of pins parallel to the edges of the overlap, resulting in pin contents ranging from 0.2% to 0.4%. Joint panels were manufactured through co-curing, and coupons were extracted from the panels for static and fatigue tensile testing. The experimental tests show that z-pinning improves the static strength (by about 15%) and extends the fatigue lives of the joints. The ultimate failure of both unpinned and pinned joints is due to the unstable propagation of a crack at the bond line. The superior performances of pinned joints are mainly due to the bridging tractions imposed between the crack faces by z-pins, which delay the growth of the debonding crack. The enhancements in static and fatigue strength achieved by z-pinning were essentially independent of the number of pin rows, and the pins positioned near the joint edges were found to play a dominant role in controlling the structural performance of pinned joints.

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.

Using z-pinning to improve the low-velocity impact performance of composite skin/stringer structures

This paper investigates the effect of the z-pin pre-hole inserted (ZPI) process on the impact resistance and post-impact flexural properties of skin/stringer composite structure with different z-pin parameters. The responses of the specimens are characterized in terms of impact denting & cracking length, load-carrying capacity, energy absorption and so on. Experimental results demonstrate that the z-pin cannot inhibit the initiation of debonding cracks at the skin/stringer interface. However, the z-pin forms a bridging traction zone across the cracking and prevent it from developing, which ensures the skin/stringer structure preserve higher peak loading and impact resistance. The specimens with the highest z-pin density have better impact resistance and outstanding residual flexural post-impact properties. Moreover, z-pins play a bridging role through its own failure. One is the inter-fiber debonding and splitting or shear failure of z-pins due to “snubbing effect,” the other is the sliding friction of z-pins and z-pins’ elastic deformation. These results could provide some guidance for designing z-pinning connection of composite skin/stringer structure.

Experimental and numerical study on the influence of cure process on the bridging traction mechanism of z-pins

This paper focuses on the bridging mechanism of individual z-pins embedded in carbon/epoxy laminates with curing effects into account. Based upon experiments, partial debonding exists in the vicinity of z-pins before pullout loading. Despite scatter, bi-linear relationship from load–displacement data is collected to characterize the bridging responses of z-pins. Complete pull-out is the dominant failure mode of z-pins after loading, due to inferior interfacial adhesion. A representative volume element (RVE) model of a single z-pin reinforced composite laminates is established, with resin-rich pockets and interfacial behavior into consideration. A qualitative analysis is presented to evaluate the influence of curing defects on the bridging ability of z-pins. The variations of cure-dependent properties are explicitly modeled. Cohesive elements are applied to the z-pin and interface regions in terms of bi-linear constitutive law. The predictions show reasonably well agreement with the experiments. Remarkably, the mismatched curing residual stresses are responsible for the generation of interfacial cracking around z-pins. The pre-existing cracking provides a reduction of physical interfacial contact, thus adversely controlling the effectiveness of z-pin reinforcement. Furthermore, the influence of cure process on the bridging behavior of z-pins is explored using a parametric method.

Experimental study on the low-velocity impact and post-impact flexural properties of curved CFRP laminates reinforced by pre-hole Z-pinning (PHZ) technique

This paper presents an experimental investigation into the effect of Z-pin on the low-velocity impact response and flexural properties after impact of the curved CFRP laminates. The Z-pinned specimens are produced using a low-damage pre-hole Z-pinning (PHZ) technique. Unpinned and Z-pinned [0/45/–45/90]4S specimens are both subjected to low-velocity impacts. Nondestructive inspection technique is used to evaluate the internal damage after impact. Subsequently, three-point bending tests are performed to characterize the flexural properties of the impacted specimens. Experimental results indicate that Z-pinned laminate, due to the bridging traction across the delamination cracks provided by pins, can provide an efficient crack arrest mechanism both in impact and bending after impact tests. Compared with the unpinned specimens, the delamination damage projection area (DDPA) is reduced by 28.5–63.5%, depending on the diameter and volume fraction of Z-pin. In addition, Z-pin could improve the residual flexural strength significantly. The specimens with a high Z-pin volume fraction have excellent damage tolerance, leading to an 18.1–76.1% improvement in the residual flexural strength compared with unpinned specimens.

Influence of glass fibre reinforced polymer composite pin reinforcement on shear and dynamic behaviour of composite joint manufactured through co-cure technique

The co-cure technique efficiently joins composite components in wings, ailerons, skins, ribs and spars in aeronautical applications. The present study investigates the effect of through-thickness reinforcement of glass fibre reinforced polymer composite pin on shear and dynamic properties of co-cured composite joints. The experimental results exhibited that through-thickness reinforcement with 2% composite pin volume significantly improved the shear strength and elongation limit by 38.4% and 102.4% compared to unpinned joints. Furthermore, composite pin reinforcement changed the catastrophic failure of co-cured joints to progressive failure due to the tougher bridging traction of composite pins. The comparison of fractured surfaces exposed that debonding, composite pin pull-out and shear fracture of pins are the major failure mechanisms involved in enhanced shear strength and progressive failure of co-cured composite joints. The experimental modal analysis avowed that through-thickness reinforcement with 2% composite pin volume improved the fundamental natural frequency of the co-cure joints, while co-cure joint reinforced with higher volume (4%) of composite pins had higher damping value due to excessive fibre damage, which increased interaction between composite adherent and adhesive.

An efficient semi-analytical method to extract the mode II bridging-traction law in ENF tests directly from the experimental load displacement data

Large scale fiber bridging ahead of the crack tip of ENF specimen is one of the most common toughening mechnisms, leading to a significant resistance phenomenon on the fracture toughness. In order to account for the toughening effect of the fiber bridging to accurately model the delamination of composite laminates, a physically semi-analytical method is presented to determine the mode II bridging law with the assumption of linear form directly from the experimental load displacement curve. The method includes the deflection analysis of the ENF specimen based on the beam theory considering the closing force introduced by fiber bridging and the inverse method iteratively determining the bridging law parameters. To validate the proposed method, the identified bridging tractions by the current method are integrated in the traditional cohesive law to simulate the whole delamination propagation process of undirectional laminates with different materials and multidirectional laminates. Good agreements between the numerical results and experimental ones indicate the accuracy and the applicability of the current method. The major advantage of the proposed method is that it reduces the instructmentation needed in the delamination test and it can be adopted as an efficient method to investigate the delamination behaviour of specimens.

Multi-scale strengthening of co-cure joints through multiwall carbon nanotube modified adhesive and GFRP pins

The present work reports a multi-scale method to strengthen the co-cure lap joints by reinforcing MWCNT nano-filler and glass fibre pins. Shear analysis indicated that incorporating MWCNTs into the epoxy adhesive and transversely embedding fibreglass pins enhanced the shear strength due to intrinsic and extrinsic strengthening processes. The results avowed that concurrent reinforcement of MWCNTs and glass fibre pins promotes higher shear properties under static loading, with a 92.7% increase in shear strength compared to unreinforced co-cured lap joints. The examination of failure surfaces revealed that dual-reinforcement transformed the unstable failure of co-cure joints into a stable mode due to multiplicative effects, including creating a rough surface, shear bands, crack path deviance, and stronger bridging traction of fibrous pins.

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

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

A novel magnesium hydroxide sulfate hydrate whisker-reinforced magnesium silicate hydrate composites

Magnesium hydroxide sulfate hydrate (MHSH) whiskers are used to reinforce magnesium silicate hydrate (M-S-H) cement mortars as novel microfibrous materials because of their similar pH. The microstructure, mechanical performance, and reinforcement mechanism were investigated, and the results showed that the addition of between 1 and 5 wt% MHSH whiskers improved the compressive and flexural strengths of M-S-H cement mortars. The optimal compressive and flexural strengths were obtained at MHSH whisker contents between 3 and 4 wt%. The MHSH whiskers had a limited effect on the toughness of M-S-H cement, and mortars reinforced with MHSH whiskers exhibited brittle failure due to the small size of MHSH whiskers and low fiber bridging traction. Scanning electron microscopy (SEM) revealed that the microscale reinforcement mechanism of MHSH whiskers involved whisker pullout, crack deflection, whisker-cement coalition pullout, and whisker fracture. These mechanisms helped dissipate energy and optimize the stress distribution and transfer, which were crucial to improving the flexural strength. The SEM images revealed the rough and grooved surfaces of MHSH whiskers, and X-ray photoelectron spectroscopy (XPS) showed the presence of polar functional groups on the surface which resulted in the adhesion of M-S-H gel on MHSH whiskers due to good interfacial bonding. The mercury intrusion porosimetry (MIP) results indicated that the addition of MHSH whiskers reduced the porosity of M-S-H cement mortars, which also contributed to the increased compressive strength.

An efficient method for fiber bridging traction identification based on the R-curve: Formulation and experimental validation

Fiber bridging is one of the main toughening mechanisms in mode I interlaminar and intralaminar fracture of laminated composites. Intact fibers exert closing forces on both faces of the crack, restraining crack propagation. An effective identification procedure is required to characterize bridging tractions and to develop accurate prediction models. The method proposed in this work is based on the resistance (R)-curve and assumes fiber bridging tractions decreasing non-linearly with respect to the crack opening displacement, following a parametric function. The distribution parameters are identified by a fixed-point iterative procedure where the energy release rate computed in a numerical model is matched with the values obtained experimentally in two points of the R-curve. The method is applied and validated through three cases, from low bridging intensity in thin-ply delamination to high bridging intensity in intralaminar fracture.

Dependency of bridging traction of DCB composite specimen on interface fiber angle

In this paper, the role of interface fiber angle on the bridging traction of double cantilever beam (DCB) specimens is investigated experimentally. In order to eliminate the effect of the remote ply orientation on the bridging traction during delamination initiation and propagation, DCB specimens with stacking sequences of [011/θ//012] where θ=0, 30, 45 and 90 were considered. An experimental test set-up was established for measuring the Initial crack tip opening displacement (ICTOD) using image processing method and conducting the fracture tests. The J-integral approach was used for obtaining the bridging laws from the experimental data. The experimental results show that by increasing the interface fiber angle, the maximum bridging traction in the bridging zone increases, but the ICTOD at the end of the bridging zone is independent of the interface fiber angle. Finally, the measured bridging laws were used with cohesive elements in ABAQUS software to model the delamination propagation in DCB specimens accurately.

Influence of Z-pin embedded length on the interlaminar traction response of multi-directional composite laminates

The work in this paper investigated the performance of composites through-thickness reinforcing Z-pins as a function of their embedded length in pre-preg laminates. Single Z-pins were inserted into multidirectional carbon fibre laminates with increasing thicknesses, corresponding to embedded lengths from 1mm to 10mm and tested through a range of mixed mode displacement ratios to investigate their interlaminar bridging traction response. Detailed analysis of the tests revealed a non-linear tangential friction response and its strong dependence on the embedded length of the Z-pin. Using a new power law empirical relationship for the tangential friction force per unit length, a modified Z-pin bridging traction analytical model was proposed, giving good predictions of the full mixed mode bridging mechanics of a CFRP Z-pin in a multidirectional composite laminate of varying thickness. Several characteristics of the model are discussed and their influence on predicting the Z-pin bridging energy response have been analysed.

Effects of large scale bridging in load controlled fatigue delamination of unidirectional carbon-epoxy specimens

Fatigue delamination growth in composites is accompanied by large scale bridging (LSB) that yields important toughening effects. However, the extent of this mechanism depends on the laminate geometry rendering its modeling a challenging task. This work presents a combined experimental/numerical study on characterization of specimen thickness dependence of LSB in fatigue delamination. Double cantilever beam specimens of different thicknesses (h = 2, 4 and 8 mm), equipped with arrays of multiplexed fiber Bragg grating sensors, are subjected to mode I fatigue loads. Measured strain data with the sensors are employed to identify the bridging tractions and subsequently compute the energy release rate (ERR) due to the bridging as well as the ERR at the crack tip. The obtained results confirm that fatigue delamination growth strongly depends on the specimen geometry when LSB prevails. It is shown that both the extent of bridging and critical ERR at failure increase by increasing the specimen thickness while the maximum bridging traction at the crack tip is found independent of the specimen geometry. The identified traction-separation relations serve to establish a power correlation, between the crack growth rate and ERR at the crack tip which is independent of the specimen thickness.

Prediction of mode I delamination resistance of z-pinned laminates using the embedded finite element technique

A new finite modelling approach is presented to analyse the mode I delamination fracture toughness of z-pinned laminates using the computationally efficient embedded element technique. In the FE model, each z-pin is represented by a single one-dimensional truss element that is embedded within the laminate. Each truss is given the material, geometric and spatial properties associated with the global crack bridging traction response of a z-pin in the laminate; this simplification provides a computationally efficient and flexible model where pin elements are independent of the underlying structural mesh for the laminate. The accuracy of the FE modelling approach is assessed using mode I interlaminar fracture toughness data for a carbon-epoxy laminate reinforced with z-pins made of copper, titanium or stainless steel. The model is able to predict with good accuracy the crack growth resistance curves and fracture toughness properties for the different types of z-pinned laminate.

Characterization of intralaminar mode I fracture of AS4/PPS composite using inverse identification and micromechanics

A detailed experimental-numerical study of large scale bridging during intralaminar fracture of AS4/PPS uniaxial thermoplastic composite is reported. Identification of bridging tractions is carried out using: (a) An inverse identification method based on quasi-distributed strain data from fiber Bragg gratings, FE modeling and optimization; both small and large displacements are considered in the simulations resulting in negligible differences between the bridging tractions and of about 4% between the energy release rates in the steady state. (b) A micromechanics based virtual testing using the embedded cell approach. Bridging tractions from both methods agree very well and are used in a cohesive model to reproduce fracture. Also the data from these models are used to obtain the energy release rate (ERR) due to bridging. Comparison of these data with experimental ERR values are in good agreement.

An analytical solution for evaluating the effect of steel bars in cracked concrete

An analytical solution is proposed for investigating the mechanical behavior of a crack in steel-reinforced concrete. In this solution, an elastic–plastic constitutive law was assumed to satisfactorily describe the behavior of the steel bar, and the bridging traction was deduced from the deformation of steels. The curves of the load versus crack mouth opening displacement predicted by the proposed method could be fitted to experimental results. It was analytically demonstrated that the ultimate load-carrying capacity calculated by the developed method is not sensitive to the shape of the softening curve for a large beam with high reinforcement ratio.

Measuring and modeling fiber bridging: Application to wood and wood composites exposed to moisture cycling

We propose a new method for determining fiber-bridging, cohesive laws in fiber-reinforced composites and in natural fibrous materials. In brief, the method requires direct measurement of energy released during crack growth, known as the R curve, followed by a new approach to extracting a cohesive law. We claim that some previous attempts at determining cohesive laws have used inappropriate, and potentially inaccurate, methods. This new approach was applied to finding fiber bridging tractions in laminated veneer lumber (LVL) made from Douglas-fir veneer and four different adhesives. In addition, the LVL specimens were subjected to moisture exposure cycles and observations of changes in the bridging cohesive laws were used to rank the adhesives for their durability. Finally, we developed both analytical and numerical models for fiber bridging materials. The numerical modeling was a material point method (MPM) simulation of crack propagation that includes crack tip propagation, fiber bridging zone development, and steady state crack growth. The simulated R curves agreed with experimental results.

Experimental determination of the mode I delamination fracture and fatigue properties of thin 3D woven composites

The mode I delamination fracture toughness and fatigue strength of thin-section three-dimensional (3D) woven composite materials is experimentally determined. The non-crimp 3D orthogonally woven carbon–epoxy composites were thin (2mm) and consequently their through-thickness z-binder yarns were inclined at a very steep angle (about 70°) from the orthogonal direction. The steep z-binder angle has a marked effect on the delamination toughening and fatigue strengthening mechanisms. Experimental testing revealed that the fracture toughness and fatigue resistance increased progressively with the volume content of z-binders. However, the steep angle caused the z-binder yarns bridging the delamination crack to deform and fail in shear and through-thickness tension, rather than in-plane tension which usually occurs in thick 3D woven composites. Mode I pull-off tests on a single woven z-binder yarn embedded within the composite revealed that the crack bridging traction load, strain energy absorption and failure mechanism were strongly affected by the steep angle.