Large-scale Bridging Research Articles

Determination of a cohesive law for delamination modelling – Accounting for variation in crack opening and stress state across the test specimen width

The cohesive law for Mode I delamination in glass fibre Non-Crimped Fabric reinforced vinylester is determined for use in finite element models. The cohesive law is derived from a delamination test based on DCB specimens loaded with pure bending moments taking into account the presence of large-scale bridging and the multi-axial state of stress in the test specimen. The fracture resistance is calculated from the applied moments, the elastic material properties and the geometry of the test specimen. The cohesive law is then determined in a three step procedure: 1) Obtain the bridging law by differentiating the fracture resistance with respect to opening displacement at the initial location of the crack tip, measured at the specimen edge. 2) Extend the bridging law to a cohesive law by accounting for crack tip fracture energy. 3) Fine-tune the cohesive law through an iterative modelling approach so that the changing state of stress and deformation across the width of the test specimen is taken into account. The changing state of stress and deformation across the specimen width is shown to be significant for small openings (small fracture process zone size). This will also be important for the initial part of the cohesive law with high stress variation for small openings (a few microns), but the effects are expected to be smaller for large-scale-bridging where the stress varies slowly over an increase in crack opening of several millimetres. The accuracy of the proposed approach is assessed by comparing the results of numerical simulation using the cohesive law derived by the above method, with those of physical testing for the standard DCB Mode I delamination test (ASTM D 5528).

Fatigue Properties of Aerospace Z-Pinned Composites

This paper presents an experimental study into the effect of through-thickness z-pin reinforcement on the in-plane and out-of-plane (delamination) fatigue properties of carbon-epoxy composites used in aerospace structures. The in-plane fatigue strength and fatigue life (load cycles-to-failure) of aerospace composite materials are reduced by z-pins. The in-plane compressive fatigue properties decrease when the volume content of z-pins is increased. Reductions to the in-plane fatigue properties are due to microstructural damage caused by the z-pins. However, the out-of-plane (delamination) fatigue properties of composites are increased greatly by z-pins. The mode I, mode II and mixed mode I/II delamination fatigue properties increase rapidly with increasing volume content of z-pins. The improvement is due to the z-pins forming a large-scale bridging zone along the delamination which resists fatigue crack growth. The work clearly reveals that a trade-off exists between the in-plane and out-of-plane fatigue properties of z-pinned composites. Improvements to the delamination fatigue properties come at the expense of lower in-plane fatigue performance, and this is a key consideration for the design of z-pinned aerospace composite structures.

Large scale fiber bridging in mode I intralaminar fracture. An embedded cell approach

Fiber reinforced composites can develop large scale bridging upon mode I fracture. This toughening mechanism depends on the constituents and the geometry of the specimen, and is especially important in unidirectional laminates when fracture is parallel to the fibers. The mode I intralaminar fracture behavior of unidirectional carbon-epoxy laminates was investigated by means of a three-dimensional multiscale model based on an embedded-cell approach. A double cantilever beam specimen was represented by an anisotropic homogeneous solid, while the bridging bundles ahead of the crack tip were included as beam elements. The failure micro-mechanisms controlling the crack propagation (namely, decohesion and subsequent failure of the bridging bundles) were included in the behavior of the different constituents. Numerical simulations were able to predict the macroscopic response, as well as the development of bridging and the growth of the crack. These results demonstrated the ability of the virtual testing approach to study complex fracture processes in composite materials. Finally, the developed model was employed to study the thickness effect and ascertain the influence of the constituents' properties on the energy released during fracture.

Comparative study of metal and composite z-pins for delamination fracture and fatigue strengthening of composites

The influence of the material properties of z-pins on the mode I delamination properties of carbon–epoxy laminates is investigated. Improvements to the delamination fracture toughness and fatigue resistance of laminates reinforced in the through-thickness direction with z-pins made of metal (copper, titanium or stainless steel) or unidirectional carbon fibre composite is determined. Irrespective of the material, the z-pins are highly effective at increasing the fracture toughness and fatigue resistance by forming a large-scale bridging zone along delamination cracks. However, the fracture toughening and fatigue strengthening capacity of the z-pins is strongly dependent on their material properties, and increased in the order: copper (least effective), titanium, stainless steel and carbon fibre (most effective). The fracture and fatigue failure modes of the z-pins are also dependent on their material properties. The study reveals that improvements to the mode I fracture toughness and fatigue resistance can be optimized via a judicious choice of the z-pin material. Z-pins with high stiffness, strength and fatigue resistance (such as carbon fibre) provide the greatest improvement to the delamination toughness and fatigue strength.

Strength and fracture toughness of earth-based natural fiber-reinforced composites

This paper presents the results of a combined experimental and theoretical study of the strength, fracture toughness, and resistance-curve behavior of natural fiber-reinforced earth-based composite materials. The composites, which consist of mixtures of laterite, clay, and straw, are stabilized with controlled levels of Ordinary Portland cement. The compositional dependence of compressive, flexural/bend strength, and fracture toughness are explored for different proportions of the constituent materials using composites and crack-tip shielding models. The underlying crack-microstructure interactions associated with resistance-curve behavior were also studied using in situ/ex situ optical microscopy. This revealed evidence of crack bridging by the straw fibers. The measured resistance-curve behavior is also shown to be consistent with predictions from small- and large-scale bridging models. The implications of the results are then discussed for potential applications in the design of robust earth-based building materials for sustainable eco-friendly homes.

Fracture in the Single Cantilever Beam Test with Large Scale Bridging

A single cantilever beam test was performed on joints constituted from unidirectional carbon fiber composite flexible beam bonded to a rigid polyamide/aluminium block. The loading was following a constant separation rate rule, for which steady-state fracture energy can be obtained. In addition to the standard resistance curve we have investigated, using backface strain monitoring technique, fiber bridging effect on load distribution in the vicinity of the crack front. A big impact of the fiber bridging on the overall R-curve behaviour was confirmed with local non self-consistency of the crack propagation. The results are backed up analytically.

Specimen thickness dependence of large scale fiber bridging in mode I interlaminar fracture of carbon epoxy composite

Large scale bridging is an important toughening mechanism in composite laminates that depends on the specimen geometry as well as the constituent materials. In this work, an iterative approach is applied to identify the effect of specimen thickness on traction–separation behavior in the bridging zone. Double cantilever beam specimens (DCB) with embedded arrays of wavelength-multiplexed fiber Bragg grating (FBG) sensors are subjected to monotonic mode I fracture loading. As processed specimens with thicknesses h=2, 4, 8 and 10mm as well as specimens of h=4mm milled down from the 8 and 10mm are tested. Non-homogeneous strain distributions in the vicinity of the interlaminar crack plane are locally monitored by means of embedded FBGs. The measured strain data are used to quantify the bridging tractions associated with each specimen thickness and consequently the energy release rate (ERR) due to the bridging. The results show that the bridging zone length and the ERR at the plateau level increase with specimen thickness while the results for all specimens with h=4 are the same thus excluding any processing effects. Moreover, the maximum stress of traction-opening in the bridging zone and crack opening displacement at the end of the zone are independent of thickness. In contrast, the rate of tractions decay depends on the specimen thickness in that it decreases with thickness scaling. Thus the so-called bridging law is not a material parameter. The identified traction–separation relations are employed in a cohesive zone model to predict fracture of DCB specimens with different thicknesses.

An iterative analytical/experimental study of bridging in delamination of the double cantilever beam specimen

Large scale bridging in mode-I delamination of layered composites is an important toughening mechanism. While its extent depends on constituent materials, it is also influenced by specimen geometry. Here, an analytical approach is adopted to express the through the thickness longitudinal strains in a double cantilever beam (DCB) specimen with the applied load and bridging tractions. The expression for the strains is confronted with strain data from embedded Bragg grating sensors to obtain bridging tractions in specimens with different thicknesses. The results show that the maximum stress of traction–separation in the bridging zone and maximum crack opening displacement at the end of the bridging zone are independent of thickness. However, the form of the bridging traction depends on thickness and is not a material property. The identified bridging relations are appended in a cohesive zone model to simulate delamination. The proposed approach predicts fracture of DCB specimens with different thicknesses.

Experimental approach for mixed-mode fatigue delamination crack growth with large-scale bridging in polymer composites

An experimental apparatus utilizing double cantilever beam specimens loaded with uneven bending moments was developed to study the mixed-mode fatigue crack growth in composites. The approach is suitable when large-scale bridging of cracks is present. To illustrate the testing method, cyclic growth of delaminations in a typical fibre-reinforced polymer composite was investigated under a constant cyclic loading amplitude. Pure mode I, mode II and mixed-mode crack growth conditions were examined. The results, analysed using a J-integral approach, show that the double cantilever beam loaded with uneven bending moments configuration provides a robust approach to investigate the fatigue crack growth of composites for pure mode and mixed-mode cracking. A steady-state crack growth regime was observed for mode I and mixed-mode loading. For mode II loading, steady-state was absent, and a progressively decreasing crack growth rate observed. In addition to details concerning the equipment, a general discussion of the development of cyclic bridging laws for delamination growth in the presence of large-scale bridging is provided.

Finite element modeling of mode I delamination growth in laminated DCB specimens with R-curve effects

This paper proposes a three-linear cohesive zone model (CZM) to capture the mode I delamination initiation and propagation behavior of unidirectional DCB specimens under large-scale fiber bridging conditions (R-curve behavior). This CZM is produced by superposing two bilinear CZMs and the required parameters are obtained from the experimental R-curve of a DCB specimen only knowing the initiation fracture toughness (Gi), the fiber bridging length (lFPZ) and the steady state toughness (Gss). The proposed method does not need the measurement of the crack tip opening displacement during the experiments and, therefore, it eliminates the current difficulties of the traditional CZMs in the simulation of delamination propagation under large-scale bridging.

On acquiring data for large-scale crack bridging at high strain rates

Numerical simulations are used to design test geometries and loading histories that are suitable for probing the large-scale bridging effects of through-thickness reinforcement that is shearing at high strain rates. The bridging effects are represented by a cohesive law and tests are sought that will determine any rate dependence in its parameters. The end-notched flexure test is studied, because it allows easy application of time-dependent loading and has proven to be an information-rich test in the quasi-static case. However, dynamic conditions greatly complicate fracture behavior, with possible regimes of hammering and multiple cracking, which should be avoided when maximum information is sought. Information content is addressed by focusing on regimes within the full computed solution space where crack growth is approximately steady state and the information content of experiments can be most easily assessed. Numerical results show that the hypothetical rate dependence in the cohesive law causes strong and measurable changes in the regime of steady-state behavior, if the tests are properly selected to vary the crack sliding speed. The estimates of information content are conservative, because the information available from all possible tests of specimens designed by analysis of the steady-state regime will necessarily exceed the information deduced by analyzing the steady-state regime alone.

Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.

Self-healing of delamination fatigue cracks in carbon fibre–epoxy laminate using mendable thermoplastic

This article examines the self-healing repair of delamination damage in mendable carbon fibre–epoxy laminates under static or fatigue interlaminar loading. The healing of delamination cracks in laminates containing particles or fibres of the mendable thermoplastic poly[ethylene-co-(methacrylic acid)] (EMAA) was investigated. The results showed that the formation of large-scale bridging zone of EMAA ligaments along the crack upon healing yielded a large increase (~300%) in the static mode I interlaminar fracture toughness, exceeding the requirement of full restoration. The mendable laminates retained high healing efficiency with multiple repair cycles because of the capability of EMAA to reform the bridging zone under static delamination crack growth conditions. Under fatigue loading, healing by the EMAA was found to restore the mode I fatigue crack growth resistance, with the rates of growth being slightly less than that pertinent to the unmodified laminate. The EMAA bridging zone, which generated high toughness under static loading conditions, does not develop under fatigue loading because of rapid fatigue failure of the crack bridging ligaments. Similar to the multiple healing capability of EMAA under static loading, multiple healing of delamination fatigue cracks is confirmed, with the fatigue crack growth rates remaining approximately unchanged. This study shows that EMAA was capable of full recovery of fatigue crack growth resistance and superior healing efficiency for static loading.

Fracture and resistance-curve behavior in hybrid natural fiber and polypropylene fiber reinforced composites

This article presents the results of a combined experimental and theoretical study of fracture and resistance-curve behavior of hybrid natural fiber- and synthetic polymer fiber-reinforced composites that are being developed for potential applications in affordable housing. Fracture and resistance-curve behavior are studied using single-edge notched bend specimens. The sisal fibers used were examined using atomic force microscopy for fiber bundle structures. The underlying crack/microstructure interactions and fracture mechanisms are elucidated via in situ optical microscopy and ex-situ environmental scanning microscopy techniques. The observed crack bridging mechanisms are modeled using small and large scale bridging concepts. The implications of the results are then discussed for the design of eco-friendly building materials that are reinforced with natural and polypropylene fibers.

A dynamic model to predict crack propagation in z-pinned composite structures

A dynamic model to predict crack growth phenomena in z-pinned reinforced composite structures is proposed. The formulation is based on a novel technique, which is able to couple Fracture Mechanics concepts with a strategy based on a moving mesh methodology. The former is utilized to predict the crack growth, whereas the latter defines the way to take into account the geometry changes on the basis of the invoked fracture parameters. The presence of the z-pins is simulated by means of a large-scale bridging approach, introducing along the delaminated interfaces normal and tangential traction forces depending on the dynamic characteristics of the pull-out mechanism. In order to evaluate the fracture parameters, which govern the crack evolution, the J-integral decomposition procedure is utilized, providing new expressions in the framework of a large-scale bridging crack growth. A numerical modeling based on the finite element procedure is implemented and comparisons with experimental results are reported to validate the proposed formulation. Moreover, a parametric study is developed to investigate the influence of z-pins on the crack growth mechanisms.

A cohesive zone model for predicting delamination suppression in z-pinned laminates

This paper presents a cohesive zone model based finite element analysis of delamination resistance of z-pin reinforced double cantilever beam (DCB). The main difference between this and existing cohesive zone models is that each z-pin bridging force is governed by a traction–separation law derived from a meso-mechanical model of the pin pullout process, which is independent of the fracture toughness of unreinforced laminate. Therefore, two different traction–separation laws are used: one representing the toughness of unreinforced laminate and the other the enhanced delamination toughness owing to the pin bridging action. This approach can account for the large scale bridging effect and avoid using concentrated pin forces, thus removing the mesh dependency and permitting more accurate analysis solution. Computations were performed using a simplified unit strip model. Predicted delamination growth and load vs. displacement relation are in excellent agreement with the prediction by a complete model, and both models are in good agreement with test measured load vs. displacement relation. For a pinned DCB specimen, the unit strip model can reduce the computing time by 85%.

Tailoring Sandwich Face/Core Interfaces for Improved Damage Tolerance—Part I: Finite Element Analysis

Various modifications of the face/core interface in foam core sandwich specimens are examined in a series of two papers. This paper constitutes part I and describes the finite element analysis of a sandwich test specimen, i.e. a DCB specimen loaded by uneven bending moments (DCB-UBM). Using this test almost any mode-mixity between pure mode I and mode II can be obtained. A cohesive zone model of the mixed mode fracture process involving large-scale bridging is developed. Results from the analysis are used in Part II, which describes methods and results of a series of experiments.

In-plane fracture of laminated fiber reinforced composites with varying fracture resistance: Experimental observations and numerical crack propagation simulations

A series of experimental results on the in-plane fracture of a fiber reinforced laminated composite panel is analyzed using the variational multiscale cohesive method (VMCM). The VMCM results demonstrate the influence of specimen geometry and load distribution on the propagation of large scale bridging cracks in the fiber reinforced panel. Experimentally observed variation in fracture resistance is substantiated numerically by comparing the experimental and VMCM load–displacement responses of geometrically scaled single edge-notch three point bend (SETB) specimens. The results elucidate the size dependence of the traction-separation relationship for this class of materials even in moderately large specimens, contrary to the conventional understanding of it being a material property. The existence of a “free bridging zone” (different from the conventional “full bridging zone”) is recognized, and its influence on the evolving fracture resistance is discussed. The numerical simulations and ensuing bridging zone evolution analysis demonstrates the versatility of VMCM in objectively simulating progressive crack propagation, compared against conventional numerical schemes like traditional cohesive zone modeling, which require a priori knowledge of the crack path.

Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending

The interaction of multiple delaminations in a laminated composite plate loaded dynamically under plane strain conditions (cylindrical bending) is studied by a simple but accurate model that represents the delaminated plate as a set of Timoshenko beams joined by cohesive interfaces. Behavioral maps are derived, which distinguish conditions under which multiple delaminations tend to propagate with equal lengths from those under which one of them tends to grow as a dominant crack with relatively high velocity. In homogeneous systems, equal length growth is favored when the delaminations are equally spaced through the thickness. While the behavioral maps are similar to those for static loading conditions, significant dynamic effects arise in the details of propagation: the maximum energy release rate depends strongly on the loading rate, duration and profile; dynamic effects and crack-interaction effects are generally coupled; and strong hammering effects (chaotic collisions of sub-laminates) can occur during the free wave motions that arise after the load is removed. The hammering effect can be suppressed by imposing a large-scale bridging mechanism (bridging extending far in the crack wake, as from pins or stitches), whereupon energy release rates tend to show smooth oscillations associated with waves propagating on the scale of the whole specimen. The energy absorbed during failure will depend significantly on whether conditions favor multiple delaminations propagating with equal lengths or a single delamination growing dominantly.

Fracture behavior and damage mechanisms identification of SiC/glass ceramic composites using AE monitoring

Large Scale Bridging in SiC/MAS-L (ceramic glass matrix) composites was investigated by using DEN specimens under tensile loading conditions with in situ Acoustic Emission monitoring. The AE data were successfully classified using Unsupervised Pattern Recognition Algorithms and the resulted clusters were correlated to the dominant damage mechanisms of the material. The evolution in time of the different damage mechanisms is feasible after the pattern recognition classification. Microscopic examination was used to correlate the clusters to the damage mechanism they correspond and thus to provide the failure mode identification based on AE data.