R-curve Behavior Research Articles

R‐Curve Behavior of Si3N4–BN Composites

R‐curve behavior of Si3N4–BN composites and monolithic Si3N4 for comparison was investigated. Si3N4–BN composites showed a slowly rising R‐curve behavior in contrast with a steep R‐curve of monolithic Si3N4. BN platelets in the composites seem to decrease the crack bridging effects of rod‐shaped Si3N4 grains for small cracks, but enhanced the toughness for long cracks as they increased the crack bridging scale. Therefore, fracture toughness of the composites was relatively low for the small cracks, but it increased significantly to ∼8 MPa·m1/2 when the crack grew longer than 700 μm, becoming even higher than that of the monolithic Si3N4.

Influence of a finite notch root radius on fracture toughness

The validity of fracture toughness data from tests with V-notched bending bars depends in the notch root radius and the presence of an R-curve behaviour. In a theoretical study it is shown how the notch radius affects the formally computed conventional toughnesses. These are computed under the assumption that the introduced notch with a small crack at the notch root acts as a long crack of the same total size and, in a stronger simplification, that the crack length is identical with the depth of the notch.

On the origin of the toughness of mineralized tissue: microcracking or crack bridging?

Two major mechanisms that could potentially be responsible for toughening in mineralized tissues, such as bone and dentin, have been identified—microcracking and crack bridging. While evidence has been reported for both mechanisms, there has been no consensus thus far on which mechanism plays the dominant role in toughening these materials. In the present study, we seek to present definitive experimental evidence supporting crack bridging, rather than microcracking, as the most significant mechanism of toughening in cortical bone and dentin. In vitro fracture toughness experiments were conducted to measure the variation of the fracture resistance with crack extension [resistance–curve (R-curve) behavior] for both materials with special attention paid to changes in the sample compliance. Because these two toughening mechanisms induce opposite effects on the sample compliance, such experiments allow for the definitive determination of the dominant toughening mechanism, which in the present study was found to be crack bridging for microstructurally large crack sizes. The results of this work are of relevance from the perspective of developing a micromechanistic framework for understanding fracture behavior of mineralized tissue and in predicting failure in vivo.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

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.

Fracture of aluminium reinforced with densely packed ceramic particles: link between the local and the total work of fracture

Model composites of pure Al reinforced with 50% ceramic particles are produced by infiltration. The composite fracture energy is measured by J-integral testing. Marked R-curve behaviour is found. The J– R curves exhibit a break in their slope at a well-defined point. This point is shown to denote the onset of macroscopic crack propagation and is used to assess the composite toughness. Toughness reaches values as high as 40 MPa m . Quantitative metallography and stereoscopic reconstructions of fracture surfaces are used to estimate the local work of fracture in the process zone. The measured (total) fracture energy is about ten times the estimated local fracture energy, for all composites. The main contribution to their total fracture energy is thus from plastic dissipation around the crack-tip; however, the toughness is still dictated by the local fracture energy. This study hence experimentally substantiates the “valve” concept in fracture mechanics.

823 アルミナの疲労特性に及ぼすR曲線挙動の効果(GS-3 疲労特性)

The R-curve of alumina could be obtained from Indented beam method. Furthermore the effect of the rising R-curve behavior on the lifetime of fatigue has been investigated by comparing with the experiments and the lifetime predictions obtained by considering the crack growth resistance originated in the R-curve behavior on the K_l-V relation. It was found that the effect of stress cycling on the fatigue would be caused by the reduction of the R-curve by cycling load.

Effects of Aging on the Toughness of Human Cortical Bone: A Study from Nano to Macro Size-Scales

ABSTRACTAge-related deterioration of both the fracture properties and the architecture of bone, coupled with increased life expectancy, are factors leading to the increasing incidence of bone fracture in the elderly. In order to facilitate the development of treatments which counter this increased fracture risk, a thorough understanding of how fracture properties degrade with age is required. The present study describes ex vivo fracture experiments to quantitatively assess the effects of aging on the fracture toughness of human cortical bone in the longitudinal direction. Because cortical bone exhibits rising crack-growth resistance with crack extension, we depart from most previous studies by evaluating the toughness in terms of resistance-curve (R-curve) behavior, measured for bone taken from donors 34 to 99 years old. Using this approach, both the crack-initiation and crack-growth toughness are determined and are found to deteriorate with age; the initiation toughness decreases ∼40% from 40 to 100 years, while the growth toughness is effectively eliminated over the same age range. Evidence from x-ray synchrotron tomography is provided to support the hypothesis that the reduction in crack-growth toughness is associated primarily with a degradation in the degree of extrinsic toughening, in particular involving crack bridging at the microstructural level in the wake of the crack. Atomic force microscope-based nanoidentation of individual collagen fibers revealed changes at the collagen fibrillar level and deep-ultraviolet Raman spectroscopy showed that the cross-linking at the nanostructural level also changes with age. These results should provide for a better mechanistic understanding of the increased propensity for bone fracture with age.

Mechanistic Aspects of Fracture of Human Cortical Bone

AbstractThere has been growing interest of late in the fracture properties of human bone. As understanding such properties in the context of the hierarchical microstructure of bone is of obvious importance, this study addresses the evolution of the in vitro fracture toughness with crack extension (Resistance-curve behavior) in terms of the salient mechanisms involved. Fracture-mechanics based measurements were performed on compact-tension specimens hydrated in Hanks' Balanced Salt Solution using cortical bone from mid-diaphyses of 34-41 year-old human humeri. Post-test observations of the crack path were made by optical microscopy and three-dimensional X-ray computed tomography. The fracture toughness was found to rise linearly with crack extension with a mean crack-initiation toughness of Ko ∼ 2.0 MPa√m for crack growth in the proximal-distal direction. The increasing cracking resistance had its origins in several toughening mechanisms, most notably crack bridging by uncracked ligaments. Uncracked-ligament bridging, which was observed by tomography in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed Rcurve behavior through compliance-based experiments. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging stress distribution. The results obtained in this study provide an improved understanding of the mechanisms associated with the failure of cortical bone, and as such are of importance from the perspective of developing a realistic framework for fracture risk assessment, and for determining how the increasing propensity for fracture with age can be prevented.

Modelling of R-curve behaviour in ceramic–metal laminates

In materials that display R-curve behaviour, the magnitude of the bridging stress is dependent on the local crack opening. Therefore, the bridging stress distribution and consequently, the toughness can be quite different for different crack geometries and crack lengths, even if the same bridging law is applied. In the present study, using the exact stress–displacement function ( σ( u)) of the constrained metal layer and a weight-function-based approach, it was possible to obtain the crack opening profile ( u( x)), and hence the bridging stress distribution along the bridging zone. The calculated displacement profiles using the weight function were checked by comparison with that obtained using the Finite Element Method at different crack sizes. Predicted fracture toughness resistance curves were compared to experimental results for different ceramic–metal combinations. The effect of different properties of the bridging layer (thickness, ductility, strength and debonding) on the predicted R-curve has been studied by their effect on the bridging traction-displacement relationship.

Crack blunting, crack bridging and resistance-curve fracture mechanics in dentin: effect of hydration

Few studies have focused on a description of the fracture toughness properties of dentin in terms of resistance-curve (R-curve) behavior, i.e., fracture resistance increasing with crack extension, particularly in light of the relevant toughening mechanisms involved. Accordingly, in the present study, fracture mechanics based experiments were conducted on elephant dentin in order to determine such R-curves, to identify the salient toughening mechanisms and to discern how hydration may affect their potency. Crack bridging by uncracked ligaments, observed directly by microscopy and X-ray tomography, was identified as a major toughening mechanism, with further experimental evidence provided by compliance-based experiments. In addition, with hydration, dentin was observed to display significant crack blunting leading to a higher overall fracture resistance than in the dehydrated material. The results of this work are deemed to be of importance from the perspective of modeling the fracture behavior of dentin and in predicting its failure in vivo.

R-curve behavior of laminated SiC/BN ceramics

Laminated SiC/BN ceramics with a perfect layered structure was fabricated by tap-casting process and hot-pressing sintering. Damage resistance and R-curve behavior of laminated SiC/BN ceramics were evaluated using the indentation-strength-in-bending technique, and compared with those of monolithic SiC ceramics. The results showed that the indentation strengths for monolithic SiC ceramics decreased steeply with indentation load, while for laminated SiC/BN ceramics reduced slightly with indentation load, suggesting an exceptional damage resistance. Moreover, a rising R-curve behavior was demonstrated for laminated SiC/BN ceramics, a plateau R-curve behavior for monolithic SiC ceramics. The excellent damage resistance and pronounced R-curve behavior of laminated SiC/BN ceramics were attributed to crack deflection, crack branching and crack delamination at the SiC/BN weak interfaces.

Damage Resistance and R-Curve Behavior of Laminated SiC/BN Ceramics

Damage Resistance and R-Curve Behavior of Laminated SiC/BN Ceramics

R-curve behavior of alumina toughened with molybdenum and zirconia particles

Alumina matrix was added with metal molybdenum and different amounts of zirconia's particles. R-curves were measured during stable crack propagation and a piezo-spectroscopic technique has been used to assess the bridging stresses developed along the crack wake at the critical condition for crack propagation. The theoretical R-curves calculated from the average (microscopic) bridging stress distribution obtained by in situ Raman spectroscopy were in good agreement with the experimental data. If the molybdenum content is kept constant but the ZrO 2 amount is increased, the toughening due to t- m transformation increases, but at the same time the metal/ceramic interface is weakened by the presence of zirconia and the toughening due to metal particles bridging decreases. As a result of that, the presence of zirconia has only a limited beneficial influence on the overall toughness. The overall composite toughness is due to transformation and bridging toughening mechanisms, however, the two mechanisms do not have synergistic effects and crack bridging by molybdenum particles appears to be the dominant toughening mechanism.

Influence of the specimen geometry on R-curve behavior and roughening of fracture surfaces

Recently the R-curve behavior observed on quasi-brittle materials was proposed to be related to the roughness development of fracture surfaces. However, many experiments have shown that the R-curve behavior is not a material property but depends on the specimen shape. It is also expected that the roughening of fracture surfaces is influenced by the specimen geometry and so R-curve behaviors related to this roughening. From mode I fracture tests on wood specimens of three different shapes, R-curves are estimated and the morphology of the crack surfaces are analysed. We show that the scaling exponents of the anomalous scaling law used to describe accurately the roughness development of crack surfaces, are not influenced by the specimen geometry and appear as material dependent parameters. Nevertheless, the fracture surfaces exhibit a roughness growth region that reduces with the average stiffness of the specimens. Accordingly, the maximum roughness magnitude of fracture surfaces is a function of the initial stiffness: the higher the stiffness, the smaller the maximum magnitude of the roughness. We show that the analytical R-curves deduced from the roughnening of fracture surfaces provide good fits of the experimental macroscopic R-curves. However, if the scaling exponents obtained from the R-curve fits are close to those measured from the microscopic roughness analysis, the description of the experimental R-curves requires a magnification of the real area of the main crack. This magnification can be explained by the weakness of the assumption of an energy only dissipated by a single crack and not by a process zone. Finally, we argue that an approach where the energy is dissipated by a set of microcracks that follow the same anomalous scaling, could fully explain the experimental R-curves.

Experimental and Theoretical Investigation of R-Curve Behaviour in Al/Al<sub>2</sub>O<sub>3</sub> Functionally Graded Materials

Experimental and Theoretical Investigation of R-Curve Behaviour in Al/Al<sub>2</sub>O<sub>3</sub> Functionally Graded Materials

Resistance-curve and fracture behavior of Ti–Al 3Ti metallic–intermetallic laminate (MIL) composites

The R-curve and fracture toughness behavior of single-edge notch beams of Ti–Al 3Ti metallic–intermetallic laminate (MIL) composites has been investigated. Composites with 14, 20, and 35% volume fraction Ti, with a corresponding intermetallic layer thickness of ~540, ~440, and ~300 microns, respectively, were tested in crack arrester and crack divider orientations. In the arrester orientation, the R-curve could not be determined for the two highest Ti volume fraction compositions as the main crack could not be grown through the test samples. In the divider orientation, R-curves were determined for all three Ti volume fractions tested. The laminate composites were found to exhibit more than an order of magnitude improvement in fracture toughness over monolithic Al 3Ti. Crack bridging and crack deflection by the Ti layers were primarily responsible for the large-scale bridging conditions leading to the R-curve behavior and enhanced fracture toughness. Estimates of steady-state toughness under small-scale bridging conditions were in close agreement with experimental results.

Study of the toughening mechanisms in bone and biomimetic hydroxyapatite materials using Raman microprobe spectroscopy.

A Raman microprobe spectroscopy characterization of microscopic fracture mechanisms is presented for a natural hydroxyapatite material (cortical bovine femur) and two synthetic hydroxyapatite-based materials with biomimetic structures-a hydroxyapatite skeleton interpenetrated with a metallic (silver) or a polymeric (nylon-6) phase. In both the natural and synthetic materials, a conspicuous amount of toughening arose from a microscopic crack-bridging mechanism operated by elasto-plastic stretching of unbroken second-phase ligaments along the crack wake. This mechanism led to a rising R-curve behavior. An additional micromechanism, responsible for stress relaxation at the crack tip, was recognized in the natural bone material and was partly mimicked in the hydroxyapatite/silver composite. This crack-tip mechanism conspicuously enhanced the cortical bone material resistance to fracture initiation. A piezo-spectroscopic technique, based on a microprobe measurement of 980 cm(-1) Raman line of hydroxyapatite, enabled us to quantitatively assess in situ the microscopic stress fields developed during fracture both at the crack tip and along the crack wake. Using the Raman piezo-spectroscopy technique, toughening mechanisms were assessed quantitatively and rationally related to the macroscopic fracture characteristics of hydroxyapatite-based materials.

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance ( R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ ∗=−72 ° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack ( θ ∗=−70.5 °). A crack-initiation toughness envelope was constructed on a K I– K II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.

R-curve behavior in fracture of notched porous ceramics

Notched specimens of porous silicon carbide (SiC) with porosity 37% were fractured under four-point bending. A single edge notch with six depths ranging from 0.1 to 2.8 mm was introduced to the specimen with a height of 7 mm. The fracture of specimens with a notch depth of 0.1 mm did not start from the notch, but from the intrinsic defect. The size of the non-damaging notch is about 0.1–0.2 mm and roughly equal to the size of SiC particles. When the notch depth was larger than 0.4 mm, the fracture started from the notch for all specimens. The record of the strain gage glued on the compression surface of the specimen as a function of the load showed nonlinearity before reaching the maximum load. The critical stress intensity factor was nearly constant for crack initiation from the notch. The resistance curve was constructed by estimating the crack length from the compliance change of the specimen, and was used for determining the maximum load point in bending tests. Fractographic observations showed the fracture path along the binder phase between silicon particles.