Steady-state Fracture Toughness Research Articles

A multi-linear constitutive relation considering the temperature effect on quasi-static mode I delamination in UD/MD laminates

In this study, a multi-linear constitutive relation taking into account temperature and fiber bridging is proposed for characterizing delamination behavior in composite laminates under various temperature conditions. An approach combining analytical solution and J-integral is also established for determining the cohesive parameters in the multi-linear constitutive relation. To validate the proposed constitutive relation, mode I quasi-static delamination experiments of unidirectional (UD) and multidirectional (MD) carbon/bismaleimide laminates are carried out at 25 ℃ (room temperature), 80 °C and 130 ℃. The experimental results show that the increasing temperature resulted in a monotonic increase in the fracture toughness of the UD laminates while affect the fracture toughness of MD laminates slightly. A FE model is established with the implementation of the proposed multi-linear constitutive relation using UMAT subroutine. Good agreements between the experimental and simulated results demonstrate the validity of the proposed constitutive relation, with the relative difference of peak load between predicted and experimental values less than 8.2 % and the relative difference of initial and steady-state fracture toughness between predicted and tested results less than 15 %. This study provides the possibility to numerically study the temperature effect on the delamination behavior of laminates and has promising applications in the damage tolerance design of composite structures.

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.

Investigation of the mode-I delamination behavior of Double-Double laminate carbon fiber reinforced composite

Double-Double (DD) laminate, consisting of a repeat of a 4-ply sub-laminate [±Φ/±Ψ], has attracted widespread attention. The delamination damage of composites is always a significant failure problem in the application and a challenge for DD laminate. However, the mode-I delamination propagation behavior and fracture toughness of DD laminate with different interface angles were seldom reported. In this study, the interface angles of DD laminate were variable and could be classified into two types: Ψ/Φ and –Ψ/Φ interfaces. The effect of interface angle on the delamination propagation of DD laminate was explored using the double cantilever beam test. The delamination damage mechanisms of the above interfaces were revealed using macroscopic and microscopic characterization methods. The results showed that the initial fracture toughness values of laminates at the 0°/0°, 90°/0°, Ψ/Φ, and –Ψ/Φ interfaces were similar, and the steady-state fracture toughness values of laminates at the Ψ/Φ interfaces were at least 20% higher than that of the –Ψ/Φ interfaces. Moreover, the maximum bridging stresses at Ψ/Φ and –Ψ/Φ interfaces were approximately equal, while the final failure displacements at Ψ/Φ interfaces were about 1.4–1.5 times than that at –Ψ/Φ interfaces.

Influence of curing pressure on the mode I static and fatigue delamination growth behavior of CFRP laminates

Curing conditions affect the mechanical properties of manufactured composite structures. However, the effect of curing pressure on the delamination behavior of laminates is still lack of investigation. This work studies the mode I static and fatigue delamination of carbon/epoxy laminates prepared at curing pressures of 1 MPa and 3 MPa. Delamination tests are conducted using double cantilever beam set-up. Test results show that more bridging fibers present in the laminates cured at 3 MPa, with more significant R-curve behavior, higher values of steady-state fracture toughness and maximum bridging stress than those in the laminates cured at 1 MPa. SEM images show that the laminates cured at 3 MPa mainly occur interlaminar damage while the major failure mechanism in the laminates cured at 1 MPa is the fiber/matrix debonding. A normalized model is proposed to describe the fatigue delamination behavior of laminates with fiber bridging effect. It shows that all fatigue data can be characterized by a single linear curve and curing pressure affects the slope of the linear curve. Furthermore, simulation for the delamination growth is conducted based on a tri-linear cohesive zone model. Good agreements between experimental and predicted load–displacement responses are achieved, illustrating the applicability of the established FE model.

On the use of the Combined Loading Compression fixture to estimate the intralaminar compressive fracture toughness of composites

This study reassesses the constraint effect provided by a Combined Loading Compression (CLC) fixture on notched specimens used to measure the compressive intralaminar fracture toughness of composite materials. An experimental campaign is carried out to determine whether a variation in the specimen gauge section length would result in a significant change in the nominal strength of Double Edge Notch CLC specimens. Following the testing of six sets of different specimen geometries for both a uni-directional thermoplastic and a bi-directional woven thermoset composite, the effect of the gauge length is analysed using the size-effect method. Results show that nominal notched strength variation is minimal, suggesting that the CLC clamp does not effectively constrain the gripped sections against in-plane deformations. This assessment proves that the correction factor used in the determination of the R-curve needs to be computed considering the entire specimen geometry, including the gripped regions. Furthermore, the results reveal that previous characterisation campaigns conducted using end-loaded Double Edge Notch Compression specimens could have led to a significant underestimation of the steady-state fracture toughness.

A modified cohesion method considering fiber bridging

The fiber bridging characteristics of multidirectional laminates are more obvious than those of unidirectional laminates, which means more fibers will be pulled out of multidirectional laminates. The existence of bridging phenomenon will have a greater impact on the interlaminar fracture toughness. However, the traditional cohesive model cannot characterize the features of fiber bridging well. In this paper, a new modified cohesive model is proposed by considering the nonlinear degradation of the mechanical response of the fibers to the matrix and the bridging stress, modify the mode I cohesive model from the theoretical point of view as well. Based on the modified model, a new functional model is developed to characterize the interlaminar fracture toughness and the traction-separation relationship. Meanwhile, the maximum bridging stresses at different interfaces are calculated. Compared with the original functional model, the modified functional model has a higher fitting accuracy with the steady-state fracture toughness experimental values and can better characterize the traction-separation relationship at different interfaces, which provides a theoretical basis for the modified cohesive model.

Study on mode I interlaminar fracture toughness of laminated plates considering interface angle

Multidirectional laminates are more widely used in practical engineering, and their fiber bridging characteristics are more obvious than unidirectional laminates. Due to the deficiency of research on the relationship between interface angle and interlaminar fracture toughness of multidirectional laminates, the numerical model of interface mode I fracture toughness of multidirectional laminates related to interface angle is modified by analyzing the difference between steady-state fracture toughness and initial fracture toughness of each interface. Meanwhile, the mode I interlaminar fracture toughness of multidirectional composite laminates under five interface modes is studied. Based on the finite element software, the cohesion model is established and verified. The analytical results are in good agreement with the experimental data, and the modified model can better verify the relationship between interface angle and interlaminar fracture toughness. At the same time, the fiber bridge force in the process of delamination along different interfaces is calculated, which provides a basis for the modified model.

Experimental and numerical investigations on the mode I delamination growth behavior of laminated composites with different z-pin fiber reinforcements

Z-pinning can effectively improve delamination growth resistance of fiber reinforcing laminated composites and attracts much attention. Material and geometrical characteristics of z-pins have effects on the delamination behavior. Numerous studies have been conducted to investigate the effect of volume fraction, diameter, shape, surface treatment and angle of z-pin, insertion length and areal density. However, the effect of elastic modulus of z-pins on the delamination behavior is still lack of investigation. In this work, the delamination behavior of two kinds of z-pinned laminates is experimentally and numerically studied. The laminates are reinforced by z-pins with different elastic moduli, including carbon fiber pin and polyimide fiber pin. It is found the elastic modulus of z-pins has effects on the steady-state fracture toughness, the bridging zone length and the micro failure mechanism. A bilinear cohesive zone model is applied for the simulation of delamination in composite laminates and discrete nonlinear spring elements are used for the characterization of the mechanical behavior of z-pins. The FE model is validated by comparing the predictions with the experimental results. Validated FE model is further applied to numerically investigate the density, the distribution distance and the distribution form of z-pins on the mode I delamination behavior.

Quantitative prediction of the fracture toughness of amorphous carbon from atomic-scale simulations

Fracture is the ultimate source of failure of amorphous carbon (a-C) films, however it is challenging to measure fracture properties of a-C from nano-indentation tests and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions on fracture of a-C. Systematic large-scale K-field controlled atomic-scale simulations of crack propagation are performed for a-C samples with densities of $\rho=2.5, \, 3.0 \, \text{ and } 3.5~\text{g/cm}^{3}$ created by liquid quenches for a range of quench rates $\dot{T}_q = 10 - 1000~\text{K/ps}$. The simulations show that the crack propagates by nucleation, growth, and coalescence of voids. Distances of $ \approx 1\, \text{nm}$ between nucleated voids result in a brittle-like fracture toughness. We use a crack growth criterion proposed by Drugan, Rice \& Sham to estimate steady-state fracture toughness based on our short crack-length fracture simulations. Fracture toughness values of $2.4-6.0\,\text{MPa}\sqrt{\text{m}}$ for initiation and $3-10\,\text{MPa}\sqrt{\text{m}}$ for the steady-state crack growth are within the experimentally reported range. These findings demonstrate that atomic-scale simulations can provide quantitatively predictive results even for fracture of materials with a ductile crack propagation mechanism.

Delamination in carbon fiber epoxy DCB laminates with different stacking sequences: R-curve behavior and bridging traction-separation relation

R-curve and traction-separation relation are commonly used to characterize the fiber bridging, which is significant toughening mechanism in composite laminates. Current investigations are mainly focused on unidirectional laminates. However, the dependence of the R-curve and traction-separation relation on the stacking sequence is still lack of comprehensive studies. Here, the effect of stacking sequence on the R-curve and traction-separation relation in unidirectional and multidirectional CFRP DCB laminates with designed generic +θ°/−θ° and 0°/θ° interfaces were systematically investigated, and interpreted combining with the fractographical analysis of failed fracture surface. Experimental results showed the fiber bridging length, steady-state fracture toughness and maximum bridging stress were strongly influenced by the stacking sequence. However, there was no clear relationship between them and the stacking sequence. In addition, the maximum bridging stress increased with the flexural modulus while a reverse trend presented in the relation between the maximum COD at the end of the fiber bridging zone and the flexural modulus. The obtained traction-separation relations were finally integrated into a tri-linear cohesive zone model. Numerical results from this model agreed well with the test results, which illustrated that the proposed cohesive zone model was applicable for delamination modelling in composite laminates with the effect of fiber bridging.

Ultra-tough and in-situ repairable carbon/epoxy composite with EMAA

Preforming is a common process in the manufacture of net-shaped composites, and there is a critical need for technologies that improve manufacturing speed without adversely impacting the interlaminar fracture toughness. Furthermore, composite structures that are repairable in-situ have potential for significant cost and performance benefits. This paper presents a new multi-functional composite system that combines ultra-high interlaminar fracture toughness with exceptional repair efficiency and is seamlessly integrated into the braiding process for rapid preform manufacture. The co-braided repair agent, EMAA, is shown to improve the interlaminar fracture toughness by over threefold, while enabling full recovery of the fracture properties via a thermal repair process. The resistance to crack initiation and crack propagation were strongly influenced by the geometric shape and spatial distribution of the EMAA which, in turn, was dictated by the preforming time. A new strategy is developed to produce a 3D fused EMAA network that enables the effective delivery of the repair agent into the delamination cracks and a greater than 100% recovery to the steady-state fracture toughness following delamination repair. The EMAA composites developed in this study exhibited repeated (at least three cycles) in-situ delamination repair abilities.

A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture formulation, inspired by first principles calculations. The theoretical model is numerically implemented using a mixed finite element formulation and several boundary value problems are addressed to gain physical insight and showcase model predictions. The results reveal the critical role of plastic strain gradients in rationalising decohesion-based arguments and capturing the transition to brittle fracture observed in hydrogen-rich environments. Large crack tip stresses are predicted, which in turn raise the hydrogen concentration and reduce the fracture energy. The computation of the steady state fracture toughness as a function of the cohesive strength shows that cleavage fracture can be predicted in otherwise ductile metals using sensible values for the material parameters and the hydrogen concentration. In addition, we compute crack growth resistance curves in a wide variety of scenarios and demonstrate that the model can appropriately capture the sensitivity to: the plastic length scales, the fracture length scale, the loading rate and the hydrogen concentration. Model predictions are also compared with fracture experiments on a modern ultra-high strength steel, AerMet100. A promising agreement is observed with experimental measurements of threshold stress intensity factor Kth over a wide range of applied potentials.

Poroelastic effects on steady state crack growth in polymer gels under plane stress

Fracture experiments on polymer gels are often conducted with thin specimens, which are close to plane stress in two-dimensional models. However, many of the previous theoretical and numerical studies on fracture of polymer gels have assumed plane strain conditions. The subtle differences between the plane stress and plane strain conditions are elucidated in this paper based on a linear poroelastic formulation for polymer gels, including the asymptotic crack-tip fields and finite element simulations of steady-state crack growth in long strip specimens. Moreover, a poroelastic cohesive zone model is adopted to study the rate-dependent fracture process of polymer gels. It is found that, without the cohesive zone model, the normalized crack-tip energy release rate at the fast crack limit is greater than the slow crack limit, suggesting reduced poroelastic toughening for fast crack growth under plane stress conditions, while the two limits are identical under plane strain conditions. With a solvent-permeable cohesive zone for the case of immersed specimens, solvent diffusion within the cohesive zone enhances the poroelastic toughening significantly as the crack speed increases, leading to a rate-dependent traction-separation relation. On the other hand, with no solvent diffusion in the cohesive zone for the not-immersed case, the poroelastic toughening effect diminishes as the crack speed increases. Based on the present study, the intrinsic steady-state fracture toughness of a poroelastic gel can be determined using long-strip pure-shear specimens, which in general is smaller than the applied energy release rate.

R-curve behaviour of the mixed-mode I/II delamination in carbon/epoxy laminates with unidirectional and multidirectional interfaces

To successfully predict the delamination behaviour of the laminated composite structures with fibre bridging, the R-curve has to be studied. This work experimentally investigates the complete R-curve behaviour of the unidirectional and multidirectional carbon/epoxy composite laminates. The delamination tests use the double cantilever beam (DCB), mixed-mode bending (MMB) and end-notched flexure (ENF) specimens for mode I, mixed-mode I/II and mode II loading, respectively. The test results show that the interfacial ply and mode mixity (φ-ratio) have significant influences on the initial fracture toughness, steady-state fracture toughness and fibre bridging length. The ratio between the steady-state fracture toughness and its initial value is approximately same for both interfaces, which indicates a similar enhanced effect of the fibre bridging on the fracture toughness. The Benzeggagh-Kenane (B-K) criterion is capable of representing the relation between the fracture toughness and the φ-ratio. Based on the DCB and MMB test results, the predicted values of the mode II fracture toughness via the B-K criterion are very close to the experimental ones, which illustrates the possibility of determining the mode II fracture toughness without executing the mode II delamination tests. Furthermore, a semi-empirical expression is proposed, which can well predict the mixed-mode I/II delamination behaviour.

Experimental characterization of delamination in off-axis GFRP laminates during mode I loading

This work experimentally investigates the influence of the off-axis angle between the lamina orientation and the crack growth direction in mode I delamination of GFRP laminates having R-curve behaviour due to large scale bridging. Initial and steady-state fracture toughness are characterized for different configurations of two laminate designs using moment loaded DCB specimens. In layup design 1, the layers adjacent to the initial delamination are parallel and the off-axis angle is varied. For layup design 2, only the off-axis angle of layers adjacent on one side of the initial delamination is varied. Microscopy, fractography, and comparisons of R-curves are used as tools to classify the cracking behaviour. All off-axis configurations tested experienced crack migration from the initial crack plane. In layup design 1, a significant difference in initial fracture toughness are found as opposed to layup design 2 in which an insignificant difference in initial fracture toughness and steady-state fracture toughness, respectively, are found. The off-axis configurations of layup design 2 are associated with crack migration and intraply crack propagation. The transition from interlaminar to intraply crack propagation correlates with the location of off-axis fibers not supported by the initial delamination indicating a free edge effect of the DCB specimen.

Enhancing the Fracture Toughness Properties by Introducing Anchored Nano-Architectures at the Metal–FRP Composite Interface

This paper presents a novel technique for improving aluminium–glass/epoxy composite interfacial bonding through the generation of metallic nano-architectures on the metal surface. Silver nanowires (AgNWs) deposited via solution casting at varying concentrations and annealed at different temperatures in an air atmosphere improved the aluminium-glass/epoxy composite fracture toughness as measured via mode I experiments. For AgNW concentrations of 1 and 3 g/m2 deposited via a single-stage process and annealed at 375 °C, the initiation fracture toughness of the aluminium-glass/epoxy composite improved by 86% and 157%, respectively, relative to the baseline composite without AgNWs. The corresponding steady-state fracture toughness of these nano-modified fibre metal laminates (FMLs) were at least seven times greater than the baseline composite. The FML variant in which AgNWs were deposited at a concentration of 3 g/m2 through a two-stage process followed by annealing at 375 °C and 300 °C, respectively after each deposition, achieved the highest steady-state fracture toughness of all nano-modified composites—a fracture toughness value that was 13 times greater than the baseline composite. Intrinsic and extrinsic toughening mechanisms dictated by the morphology of the silver nano-architectures were found to be responsible for the improved initiation and steady-state fracture toughness in nano-modified FMLs.

Steady-state fracture toughness of elastic-plastic solids: Isotropic versus kinematic hardening

The fracture toughness for a mode I/II crack propagating in a ductile material has been subject to numerous investigations. However, the influence of the material hardening law has received very limited attention, with isotropic hardening being the default choice if cyclic loads are absent. The present work extends the existing studies of monotonic mode I/II steady-state crack propagation with the goal to compare the predictions from an isotropic hardening model with that of a kinematic hardening model. The work is conducted through a purpose-built steady-state framework that directly delivers the steady-state solution. In order to provide a fracture criterion, a cohesive zone model is adopted and embedded at the crack tip in the steady-state framework, while a control algorithm for the far-field, that significantly reduces the number of equilibrium iterations is employed to couple the far-field loading to the correct crack tip opening. Results show that the steady-state fracture toughness (shielding ratio) obtained for a kinematic hardening material is larger than for the corresponding isotropic hardening case. The difference between the isotropic and kinematic model is tied to the non-proportional loading conditions and reverse plasticity. This also explains the vanishing difference in the shielding ratio when considering mode II crack propagation as the non-proportional loading is less pronounced and the reverse plasticity is absent.

Fracture toughness and crack resistance curves for fiber compressive failure mode in polymer composites under high rate loading

This work presents an experimental method to measure the compressive crack resistance curve of fiber-reinforced polymer composites when subjected to dynamic loading. The data reduction couples the concepts of energy release rate, size effect law and R-curve. Double-edge notched specimens of four different sizes are used. Both split-Hopkinson pressure bar and quasi-static reference tests are performed. The full crack resistance curves at both investigated strain rate regimes are obtained on the basis of quasi-static fracture analysis theory. The results show that the steady state fracture toughness of the fiber compressive failure mode of the unidirectional carbon-epoxy composite material IM7-8552 is 165.6kJ/m2 and 101.6kJ/m2 under dynamic and quasi-static loading, respectively. Therefore the intralaminar fracture toughness in compression is found to increase with increasing strain rate.

Pin pull-out behaviour for hybrid metal-composite joints with integrated reinforcements

Hybrid metal-composite joints that integrate pins on the metal adherend are a novel joining concept, and knowledge regarding single pin performance and correlation to multi-pin joint behaviour is critically lacking. Here, we investigate Selective Laser Melting manufactured titanium with pins adhered to carbon fibre-reinforced polymer composite. Single pin specimens under pull-out loading and Mode I crack growth specimens were investigated using experimental, finite element (FE) and analytical methods. We found the pin-composite interfacial strength was 3.5 times higher than comparable carbon fibre z-pins due to excellent adhesion characteristics of the as-manufactured pin surface. Consequently, the pins enabled a 365% increase in Mode I steady-state fracture toughness. We also determined that the enhanced bonding increased the maximum pin load and Mode I initiation fracture toughness by around 250%, with no pin-composite debonding during cure. We lastly show FE models using the pull-out response characterised in single pin tests give excellent predictions of experimental behaviour in multi-pin joints with no additional calibration. The work provides new correlation between pin behaviour in isolation and in multi-pin joints, highlights the importance of strong pin-composite adhesion for joint performance, and demonstrates an analysis methodology suitable for design of pin-reinforced composites and metal-composite hybrid joints.

Multi-scale interlaminar fracture mechanisms in woven composite laminates reinforced with aligned carbon nanotubes

Abstract Aligned nanoscale fibers have been shown to provide inter and intralaminar reinforcement of fiber-reinforced polymer composites. In one hierarchical architecture, aligned carbon nanotubes (CNTs) grown on advanced microfibers in a woven ply creates a ‘fuzzy fiber’ reinforced plastic (FFRP) laminate. Here, the mechanisms of Mode I fracture toughness enhancement for such laminates are elucidated experimentally by varying the type of epoxy and aligned CNT length. Reinforcement effectiveness is found to vary from reduced initiation toughness to over 100% increase in steady-state fracture toughness, depending upon the interlaminar fracture mechanisms. Fracture-surface morphology investigations reveal that interlaminar toughness enhancement is significantly less for an aerospace infusion resin than that for a much tougher hand lay-up marine epoxy. Long (∼20 micron) aligned CNTs add significant toughness in steady state (>1 kJ/m2 increase for marine epoxy) via CNT pullout and by driving the crack through tortuous paths around and through microfiber bundles/tows, whereas shorter CNTs produce less toughening (or even reduced toughness in aerospace epoxy), which is attributed to increased microfiber–matrix cohesive failure. These findings reveal the multi-scale nature of the aligned-CNT reinforced composite ply interface, and the mechanisms at work at the micro and nanoscales that influence the macroscopic behavior. These new insights provide impetus for using aligned CNTs to tailor microfiber polymer composites by adjusting microfiber orientation, steering cracks through tortuous paths, and maximizing fracture surface area through both microfiber and nanofiber pullout.