Bridging Zone Length Research Articles

Toughening and Strengthening Response in Ni3Al-Bonded Titanium Carbide Cermets

Abstract Nickel aluminide (Ni3Al) was used as a binder phase to fabricate dense TiC cermets with Ni3Al contents of up to 60 vol. % and TiC grain sizes of ~ 5 to ~ 0.8 μm by either sintering of mixed powders or a melt-infiltration sintering process. These TiC–Ni3Al cermets exhibit high fracture toughness together with exceptional flexure strengths (> 1 GPa), which are retained at temperatures of ~ 1000 °C. While the flexure strength exhibited a modest increase as the Ni3Al content was raised, both the Weibull modulus (up to ~20) and the toughness ~ 18 MPa m $\sqrt m $ exhibited substantial increases. The increased toughness was found to result from a combination of interface debonding and grain cleavage that combined to enhance plastic deformation of the Ni3Al ligaments in the crack wake. Crack opening displacement measurements reveal a blunted crack profile and suggest a bridging zone length in excess of 100 microns.

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.

Experimental and numerical analysis of mode-I interlaminar fracture of composite pipes

A common industrial production process for composites is filament winding, widely used for the production of axially symmetric components. In these composite components, delamination is a predominant failure mechanism. The current work focuses on investigating experimentally the effect of the initial crack and fiber bridging length on the mode-I delamination resistance curve (R-curve) behavior of various double cantilever beam (DCB) specimens. For this purpose, the magnitudes of initiation and propagation fracture toughness (GIC-init and GIC-prop) and the compliance C are calculated. DCB specimens with a stacking sequence of [± 50]6 and various initial crack lengths of a0 = 33, 37, 59 and 70 mm are manufactured from a real composite pipe using filament winding process. In order to evaluate the critical energy release rate in mode-I, various fracture tests are conducted on these specimens. The greatest bridging zone length dues to good penetration of two adjacent layers of the delamination interface. Moreover, the results indicate that the fiber bridging length has a significant effect on the GIC and the largest value of fiber bridging causes a large fracture toughness value. Finally, numerical simulations are performed using finite element (FE) method and GIC-init measurements obtained experimentally are compared to the numerical findings. The numerical displacements and GIC-init, calculated from the numerical displacements, are found to be in good agreement compared to the experimental results.

Effect of interface fiber angle on the R-curve behavior of E-glass/epoxy DCB specimens

In this study, the effect of interface fiber angle on the R-curve behavior of double cantilever beam (DCB) specimens made of E-glass/epoxy under mode I loading is investigated experimentally. For this purpose, DCB specimens with stacking sequences of [011/θ//012] and θ=0, 30, 45, 90 are manufactured by hand lay-up method. These stacking sequences are chosen to eliminate the effect of remote ply orientation on the R-curve behavior of DCB specimens during the delamination propagation. In order to obtain the critical strain energy release rate, fracture tests are conducted on these specimens. Results show that DCB specimens with 0°//0° interface have the lowest initiation interlaminar fracture toughness and the greatest bridging zone length due to good penetration of two adjacent layers of the delamination interface. Moreover, results indicate that the interface fiber angle has significant effect on the steady-state interlaminar fracture toughness as well as the bridging zone length.

Intralaminar fracture of unidirectional carbon/epoxy composite: experimental results and numerical analysis

Fracture of carbon fiber reinforced polymers (CFRPs) is dominated by large scale fiber bridging which acts as a very important toughening mechanism. The objective of this paper is to investigate the intralaminar Mode I fracture in a unidirectional CFRP composite in double cantilever beam specimens with thickness H = 6, 10 and 14 mm with a symmetric intralaminar precrack introduced by a thin diamond wire saw. Optical fibers with 10 multiplexed Bragg grating sensors are glued onto the upper surface of selected specimens of H = 6 and 10 mm, to measure the axial strain profile during fracture. The bridging tractions are expressed as a function of the maximum bridging stress, the bridging zone length and exponential softening parameter. The measured strains are input to an inverse parametric numerical model to obtain the traction separation relation due to bridging. The optimized strain distribution corresponds to a bridging traction profile, with a maximum bridging traction of ∼8.3 MPa. This stress is 6 times larger than the corresponding in interlaminar fracture value. The resultant resistance-curves increase with sample thickness in corresponding steps of 20%. The plateau energy release rate is ∼2.3 times higher than the corresponding interlaminar one, although having the same initial fracture toughness. The calculated energy contribution of bridging agrees very well with the produced resistance-curves. The resultant bridging law is applied over a cohesive element model to reproduce the load-displacement curves.

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.

OS14-2-4 Mode-I Interlaminar Fracture Behavior of Heat-Resistant Composite Materials at High Temperature

In order to develop a High Speed Civil Transport, weight reduction by the use of advanced composite materials is one of the most important technical issues. However, composite laminates have very low interlaminar fracture resistance. Therefore, the interlaminar fracture toughness of composites has consequently become a critical design parameter for the aircraft structures. In this research, mode-I interlaminar fracture behavior of heat-resistant polyimide CFRP (Carbon Fiber Reinforced Plastics) was investigated by way of the double-cantilever-beam (DCB) test at high temperature up to 200℃. In the DCB tests at high temperature, fiber cross-over bridging was observed. In order to evaluate the influence of the bridging zone length on the crack growth resistance curve (R-curve), the DCB tests were conducted using specimens with different thicknesses. Fractographic observations of the fracture surface were performed in order to assess the crack growth behavior. The bridging characteristics were evaluated using a bridging law which describes the relationship between the crack closure traction resulting from the bridging fibers and the local crack opening displacement.

Mechanistic aspects of fracture and R-curve behavior in human cortical bone

An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K 0 of ∼2 MPa√m for crack growth in the proximal–distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of ∼2×10 −9 m/s at stress intensities ∼35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.

Combined mode-I and mode-II fracture of ceramics with crack-face grain and/or whisker bridging

Crack-face grain and/or whisker bridging in ceramics was investigated under combined mode-I and mode-II loading. A novel technique for analysing the stress shielding at the crack tip caused by the bridging was proposed, in which the critical values of the local mode-I and mode-II stress intensity factors were numerically derived from an azimuthal angle at the onset of noncoplanar crack extension using the mixed-mode failure criteria. The wedging effect, which induced local mode-I crack opening at the tip, was identified under the combined-mode loading on polycrystalline alumina as well as an alumina matrix composite reinforced with silicon carbide whiskers. The effect was accelerated with the increase in the mode-II component of nominally applied loading and the decrease in the bridging zone length. It was also found that the stress shielding due to the whisker bridging was not only effective for mode-I but also for mode-II crack opening.

Stress states and growth behavior of bridged cracks at creep regime

In this study growth behavior of bridged cracks, resulting from the growth of pre-nucleated creep cavities with diffusional and dislocation-assisted mechanisms, is investigated numerically. The elements bridging the crack are assumed to be elastic; the bridging behavior ranges from full development of the bridging zones to failure of the bridging elements during the course of crack growth. The results indicate that the bridging traction significantly relaxes even with the overall creep deformation alone. The rate of this relaxation is not influenced by the rate of crack growth. However, the rate of change in the bridging zone length or the density of the bridging elements in the bridging zone strongly affects both the maximum value and the distribution of the traction in the bridging zone. A much weaker stress singularity than the ones described by K or C * was found ahead of the bridged cracks in the creep regime. In this weak singularity region the cavities, located at increasing distance from the crack tip, grow at similar high rates to each other.

In‐situ SEM observation of the fracture behaviour of titanium carbide/nickel aluminide composites

A range of experimental titanium carbide (TiC)/nickel aluminide (Ni3Al) composites have been developed. The Ni3Al content has been varied from 15 to 40 vol.%, for two different alloy compositions. The fracture behaviour of these composites was assessed in situ, within the chamber of a field emission gun scanning electron microscope. An applied moment double cantilever beam test geometry was employed, which allowed determination of the materials fracture resistance curve (or R‐curve), while simultaneously monitoring crack–microstructure interactions. All of the tested materials exhibited a pronounced R‐curve, with fracture resistance increasing with increasing crack length, up to a steady‐state plateau value. The highest steady‐state toughness values (up to 15 MPa m−1/2) were obtained for composites prepared with the highest Ni3Al binder content. In addition, these materials exhibited the highest strength and Weibull modulus. In‐situ examination of the fracture process demonstrated considerable crack wake bridging by ductile Ni3Al ligaments, with bridging zone length of >100 μm often observed. The use of a displacement mapping technique has demonstrated that Ni3Al plastic deformation is highly localized around the crack, typically within one TiC grain width (i.e. ≈3–5 μm) away from the crack.

A simple approach for modelling the heterogeneity of crack tip plastic zones

An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K0 of ∼2 MPa√m for crack growth in the proximal–distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of ∼2×10−9 m/s at stress intensities ∼35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.

Analysis of Fiber-bridging by Extended Dagdale Model.

A simple Dagdale model for fiber bridging processes and mechanisms of unidirectionally fiber-reinforced brittle matrix composites is addressed. The model, the most primitive and the simplest one, has great advantages in analytical solutions and practical considerations, although it is not enough for quantitatively explaining experimental results. It is emphasized that the details of crack-face constitutive relation (crack bridging tractions vs. crack opening displacement relationship) are not essential for describing the toughness increment of fiber bridging systems, but that the averaged bridging traction and the bridging zone length are the most important in the considerations of crack-bridge toughening.

Extrinsic factors in the mechanics of bridged cracks

Calculations for single-edge notch specimens under uniform remote tension are used to demonstrate the profound influence of the extrinsic factors of specimen shape and load distribution on the propagation of bridged cracks when the bridging zone length is comparable to any of the dimensions of the crack or the specimen. The influence of the extrinsic factors is so strong that there is a grave risk of seriously nonconservative predictions of strength and reliability if standard engineering methods are used for materials exhibiting such bridged cracks. However, this difficulty can be resolved by regarding the relationship between the bridging tractions p and the crack opening displacement u as a fundamental material property. Extensive calculations are summarized for one class of relations p( u) that rise to a peak corresponding to ligament failure and then fall gradually to zero at large u. Resistance curves of great variety are displayed. The central role of the “bridging length scale,” the initial crack extension over which the bridging zone matures, is demonstrated. The roles of various features of p( u) in determining the transition from noncatastrophic (or ductile) failure to catastrophic (or brittle) failure are examined.

Large scale bridging in brittle matrix composites

The influence of the bridging zone length on the resistance curve behavior of three brittle-matrix composites is examined. The experimental measurements are correlated with models of crack bridging (taking into account the finite specimen dimensions) and compared with the resistance curves expected when small-scale bridging conditions prevail. The results demonstrate that the resistance curves of composite materials strongly depend on both the absolute length of the bridging zone and the length of the bridging zone relative to the total crack length and the specimen width. The latter effects are due to large-scale bridging. The results suggest that the resistance curves of toughness measurements obtained from small test specimens may overestimate the true behavior and thus, caution must be exercised in interpreting some of the recently published data. The implications for future resistance curve measurements are discussed.

Evaluation of Bridging Stress from R‐Curve Behavior for Nontransforming Ceramics

Bridging stresses at the crack interface behind the crack tip are calculated for nontransforming ceramics which show increasing toughness with crack extension (R‐curve behavior). With this approach, bridging stresses can be related analytically to the experimental R curve. Sample calculations for SiC‐whisker‐reinforced Al2O3, with a bridging‐zone length of >0.5 mm, are shown in the present study. The results indicate that the bridging stress has a maximum value within a short distance (<0.01 mm) behind the crack tip and then decreases to 0 or levels off to a finite value at the end of the bridging zone depending upon the nature of the R‐curve behavior.