R-curve Behavior Research Articles

On the R-curve behavior of human tooth enamel

In this study the crack growth resistance behavior and fracture toughness of human tooth enamel were quantified using incremental crack growth measures and conventional fracture mechanics. Results showed that enamel undergoes an increase in crack growth resistance (i.e. rising R-curve) with crack extension from the outer to the inner enamel, and that the rise in toughness is a function of distance from the dentin enamel junction (DEJ). The outer enamel exhibited the lowest apparent toughness (0.67 ± 0.12 MPa m 0.5), and the inner enamel exhibited a rise in the growth toughness from 1.13 MPa m 0.5/mm to 3.93 MPa m 0.5/mm. The maximum crack growth resistance at fracture (i.e. fracture toughness ( K c)) ranged from 1.79 to 2.37 MPa m 0.5. Crack growth in the inner enamel was accompanied by a host of mechanisms operating from the micro- to the nano-scale. Decussation in the inner enamel promoted crack deflection and twist, resulting in a reduction of the local stress intensity at the crack tip. In addition, extrinsic mechanisms such as bridging by unbroken ligaments of the tissue and the organic matrix promoted crack closure. Microcracking due to loosening of prisms was also identified as an active source of energy dissipation. In summary, the unique microstructure of enamel in the decussated region promotes crack growth toughness that is approximately three times that of dentin and over ten times that of bone.

R-Curve Behavior of Machinable SiC/h-BN Nano-Composites

SiC/h-BN nano-composites powder was synthesized using an in-situ reaction method and SiC/h-BN nano-composites were fabricated by hot-pressing. Damage resistance and R-curve behavior of machinable SiC/h-BN nano-composites was evaluated using the indentation- strength-in-bending technique and compared with that of SiC/h-BN micro-composites and monolithic SiC. The results showed that SiC/h-BN nano-composites have better damage resistance and R-curve behavior than SiC/h-BN micro-composites and monolithic SiC.

Damage tolerance and R-curve behavior of ZrB 2–ZrO 2 composites

Four ZrB 2 composites were prepared by hot-pressing with different content of ZrO 2, i.e., 0, 10, 20 and 30 vol%. By means of the indentation-strength method, damage tolerance and resistance-curve ( R-curve) behavior were investigated for ZrB 2–ZrO 2 composites. Under the indentation load of 196 N, retained strength of monolithic ZrB 2 was only ∼89 MPa, however, that value could reach ∼281 MPa for ZrB 2–30 vol%ZrO 2 composite. Obvious R-curve behavior was further found in ZrB 2–ZrO 2 composites compared with monolithic ZrB 2. Regarding ZrB 2–30 vol%ZrO 2, the steady-state toughness was ∼6.5 MPa m 1/2. Such improved toughening effect was attributed to the crack bridging and transformation toughening of ZrO 2.

Comparison of R-Curve Behavior of Si<sub>3</sub>N<sub>4</sub> Measured by Indentation Method and Single-Edge V-Notched Beam Technique (SEVNB)

Study compare R-curve behaviour of silicon nitride obtained using Vickers indented beam specimens and single edge V-notched beam (SEVNB). R-curve measurement realized by Vickers indented beam was reported by Krause. Crack growth using single edge V-notched beam was observed in situ. The indentation experiments, in comparison with SEVNB method revealed higher R-curve values (KR=3.3 – 4.8 MPa.m1/2). The discrepancy in the R-curve results is attributed to inaccuracy related to the determination of indentation toughness. The indentation fracture toughness may include the aspects of crack opening behaviour, residual indentation stress intensity.

Slow crack growth resistance and bridging stress determination in alumina-rich magnesium aluminate spinel/tungsten composites

The slow crack growth (SCG) resistance ( V–K I diagrams) of magnesium aluminate spinel and its tungsten composites with different metallic content (7, 10, 14 and 22 vol.%) is reported. It is found that tungsten plays a crucial role in the composite by increasing crack resistance: the higher the W content, the higher the stress intensity factor needed for crack extension at a given rate. The reinforcement is due to the bridging mechanism performed by metal particles, as it strongly affects the compliance of cracked specimens. Its magnitude is estimated by a compliance function Φ( a) from a double torsion test. From the compliance function, R-curve behaviour is predicted for the composite with highest tungsten content. It explains the effect of metal particles on SCG curves. The W–MgAl 2O 4 interface is believed to influence the reinforcement mechanism.

R-curve behavior and toughening mechanisms of resin-based dental composites: Effects of hydration and post-cure heat treatment

Objectives To test the hypothesis that the fracture resistance of two different particulate resin composites degrade after water hydration and improve after post-cure heat treatment, and to correlate those changes with salient failure micromechanisms. Methods Two composites with different filler morphology were selected, denoted microhybrid (Filtek™ Z250) and nanofill (Filtek™ Supreme plus). Following initial light curing, hydrated samples were aged in water for 60 days at room temperature while post-cured samples were heat treated at 120 °C for 90 min. Fracture resistance was assessed using fracture resistance curves ( R-curves) utilizing pre-cracked compact tension, C(T), specimens. The flexural strength of the hydrated composites also was evaluated in four-point bending using unnotched beams. Scanning electron microscopy (SEM) of crack paths and fracture surfaces was performed to determine the micromechanisms of fracture and toughening. The results were compared by two-way ANOVA and Tukey's multiple comparison test ( p ≤ 0.05). Results SEM observations revealed a predominantly interparticle matrix crack path for all cases except the hydrated nanofill composite, which showed evidence of particle matrix debonding. Hydration lowered the strength for both composites and the peak toughness for the nanofill composite. The strength decrease was attributed to resin matrix plasticization and hydrolytic degradation in both cases, with additional interfacial degradation causing a larger strength decline and concomitant peak toughness decrease in the nanofill composite. The post-cure heat treatment noticeably changed the R-curve shape causing the peak toughness to be reached after shorter amounts of crack extension. Such changes help explain the increases in strength reported in other studies and is attributed to improved resin matrix properties. Significance Results from this study provide new insight into the micromechanisms of fracture in resin-based dental composites which should aid the future development and improvement of these materials.

OS0744 金属薄膜法を用いたアルミナセラミックスの繰返し疲労寿命予測(構造用材料の疲労挙動と寿命評価,オーガナイズドセッション)

In order to predict the cyclic fatigue life of alumina ceramics, a new method was proposed. First, to monitor the small crack growth behavior during static fatigue, a thin metal film method was proposed. Second, based on the crack growth data, crack growth characteristics and R-curve behavior were evaluated. Then, cyclic fatigue life was predicted, and predicted results were compared with cyclic fatigue test results. As the results, it is found that crack growth behavior can be monitored over wide range of crack growth rate by using the thin metal film method. And it is confirmed that the cyclic fatigue life of ceramics can be predicted by using proposed method.

R-curve behavior and micromechanisms of fracture in resin based dental restorative composites

The fracture properties and micromechanisms of fracture for two commercial dental composites, one microhybrid (Filtek™Z250) and one nanofill (Filtek™Supreme Plus), were studied by measuring fracture resistance curves ( R -curves) using pre-cracked compact-tension specimens and by conducting both unnotched and double notched four point beam bending experiments. Four point bending experiments showed about 20% higher mean flexural strength of the microhybrid composite compared to the nanofill. Rising fracture resistance was observed over ∼1 mm of crack extension for both composites, and higher overall fracture resistance was observed for the microhybrid composite. Such fracture behavior was attributed to crack deflection and crack bridging toughening mechanisms that developed with crack extension, causing the toughness to increase. Despite the lower strength and toughness of the present nanofill composite, based on micromechanics observations, large nanoparticle clusters appear to be as effective at deflecting cracks and imparting toughening as solid particles. Thus, with further microstructural refinement, it should be possible to achieve a superior combination of aesthetic and mechanical performance using the nanocluster approach for dental composites.

Strength scaling of adhesive joints in polymer–matrix composites

The fracture of adhesive joints between two glass-fibre laminates was studied by testing double cantilever beam test specimens loaded by uneven bending moments. A large-scale fracture process zone, consisting of a crack tip and a fibre bridging zone, developed. The mixed mode fracture resistance increased with increasing crack length, eventually reaching a steady-state level ( R-curve behaviour). The steady-state fracture resistance level increased with increasing amount of tangential crack opening displacement. Cohesive laws, obtained from fracture resistance data, were used for prediction the load carrying capacity of 2-m long “medium size” adhesive joint specimens subjected to four point flexure. Medium size specimens were manufactured and tested. A good agreement was found between the predicted and measured strength values of the medium-size specimens. Thus, the scaling from small specimens to medium-size specimens was successfully achieved.

Correlation of wear behavior and indentation fracture resistance in silicon nitride ceramics hot-pressed with alumina and yttria

Nine kinds of silicon nitrides with different microstructures were fabricated by controlling both sintering conditions and amounts of sintering additives, Al 2O 3 and Y 2O 3. The wear behavior of the various Si 3N 4 ceramics was investigated in sliding contact test without lubricant. The specific wear rate varied notably from 6 × 10 −6 to 4 × 10 −4 mm 3 N −1 m −1 depending on the microstructures, whose ranking was difficult to predict directly from the hardness or fracture resistance obtained by the indentation fracture (IF) technique as well as the single-edge-precracked beam (SEPB) method. A good correlation was obtained between the specific wear rate and both mechanical properties when a lateral-crack chipping model was applied as the material removal process. However, the correlation was lost when the fracture toughness obtained by the SEPB method was employed, indicating that the conventional long-crack toughness is inappropriate for analyzing the wear behavior of Si 3N 4 exhibiting a rising R-curve behavior.

Fracture Toughness Test with a Sharp Notch Introduced by Focussed Ion Beam

The validity of fracture toughness data obtained from tests with V-notched bending bars is affected by the notch root radius and the presence of R-curve behavior. A macroscopic test specimen has been developed that contains a notch introduced by focused ion beam machining. This produces a notch root radius of less than 0.1 μm, so that notch effects can be ignored for most ceramics. Also, due to the very small notch depths the influence of a rising R-curve should be very close to that of natural cracks. First tests, carried out on a Ce-doped zirconia ceramic resulted in a toughness of KIc ≈ 5.9 MPa√m.

Modeling crack propagation in wood and wood composites. A review COST Action E35 2004–2008: Wood machining – micromechanics and fracture

AbstractPredictive simulation of crack growth and fracture of wood and wood composites has always been difficult, and it has been limited by the availability of appropriate fracture models. As summarized herein, progress has been made on several fronts. First, a variety of fictitious crack model refinements have been made, along with the corresponding effects on bulk load-deformation response andR-curve behavior. Second, progress has been made on several different discrete element approaches that can explicitly represent material heterogeneity and variability. While progress has been substantial, a universal fracture law for wood remains elusive.

Understanding the mechanical properties of hot pressed Ba-doped S-phase SiAlON ceramics

In this contribution, we report the analysis and interpretation of the mechanical property measurements for a new class of SiAlON ceramic. The hardness and indentation fracture toughness were measured on the hot pressed Ba-doped S-SiAlON ceramic using Vickers indentation at varying loads (up to 300 N). An important observation was that all the investigated S-SiAlON exhibited the characteristic rising R-curve behavior with a maximum toughness of up to 10–12 MPa m 1/2 for ceramics, hot pressed both at 1700 and 1750 °C. Crack deflection by large elongated S-phase grains and crack bridging by β-Si 3N 4 needles has been found to be the major toughening mechanisms for the observed high toughness. Theoretical estimates, using a toughening model based on crack bridging and deflection by platelet shaped ‘S’-phase grains and β-Si 3N 4 needles, reveal the interfacial friction of around 200 MPa. Careful analysis of the indentation data reveals the average (apparent) hardness modestly increases with indent load in all S-SiAlON samples, with more significant effect for S-SiAlON, hot pressed at 1600 °C. This effect has been analyzed in the light of the established model of ‘indentation-induced cracking’ phenomenon. Our experimental results suggest that a modest combination of average hardness of 15 GPa and indentation toughness of around 12 MPa m 1/2 could be achieved in Ba-S-SiAlON ceramic and further improvement requires microstructural tailoring.

Mode II Interlaminar Fracture and Damage Evaluation of GFRP Woven Laminates at Cryogenic Temperatures using the 4ENF Specimen

This article focuses on understanding the Mode II interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures. A four point bend, end notched flexure (4ENF) test is performed at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4K), and an R-curve characterization is conducted for determining the mode II cryogenic fracture properties of GFRP woven laminates. The test configuration is also analyzed by finite element analysis coupled with damage. The damage distributions within the 4ENF specimens are predicted, and the effect of damage on the Mode II energy release rate is examined. This work is the first application of failure criteria (Hoffman criterion and maximum strain criterion) to the description of the R-curve behavior and interlaminar fracture toughness values of woven laminate ENF specimens at cryogenic temperatures.

Interface Effects on the Quasi-Static and Impact Toughness of Discontinuously Reinforced Aluminum Laminates

Trilayer laminates consisting of two layers of aluminum alloy 7093 surrounding one layer of 7093/SiC/15p were produced via two roll-bonding techniques as well as by adhesive bonding. The effects of systematic changes in interface characteristics (i.e., weak bond via roll bonding with a thin ductile interlayer material, stronger bond via roll bonding without a thin ductile interlayer, and strongest bond via adhesive bonding with a semibrittle material) on the subsequent laminate toughness was studied. The fracture resistance of the laminates and the constituent materials was examined via instrumented Charpy notched impact testing in the crack-arrester orientation as well as by fracture-toughness testing of bend bars tested in the crack-divider and the crack-arrester orientations. The notched impact resistance of the trilayer crack-arrester laminates was found to be greater than both monolithic 7093/SiC/15p and 7093 samples of similar global thickness. The laminated structure promoted crack arrest, deflection, and large-scale deformation of the unreinforced layers, producing R-curve behavior. The tendency for interface delamination was predicted and confirmed based on recent mechanics-based analyses. The trilayer laminate structures tested in the crack-divider orientation exhibited a greater R-curve than either of the 7093/SiC/15p or 7093 samples tested at similar global thickness. Both types of roll-bonded laminates (i.e., stronger interface and weak interface containing a thin metal interlayer) exhibited a greater enhancement in Charpy impact toughness and mode I fracture toughness than did the adhesively bonded (i.e., semibrittle interface) laminates. These relative improvements in toughness were rationalized by estimating the contributions to energy absorption by the delamination and crack bridging in these systems and by the effects of the interface type on these processes. These results are generally relevant to the performance of these materials under impact and under certain blast loading and penetration situations.

Influence of notch radius and R-curve behaviour on the fracture toughness evaluation of WC–Co cemented carbides

In this work the apparent fracture toughness of different grades of WC–Co cemented carbides has been evaluated by means of the single edge V-notched beam (SEVNB) method. The results are analysed, as a function of both the binder mean free path and the maximum steady-state crack shielding value, following a theoretical approach which assumes the existence of a small crack at the notch tip. The experimental findings indicate that larger defects at the notch tip and/or existence of R-curve behaviour imply higher (i.e. less restricted) values of the minimum notch radius required in SEVNB specimens for a reliable assessment of the fracture toughness of cemented carbides.

In situ observation of interfacial crack propagation in GF/epoxy model composite using bifiber specimens in mode I and mode II loading

Interfacial fracture behavior for GF/epoxy model composites was investigated under static loading using the bifiber shear (BFS) and the bifiber open (BFO) methods. Two E-glass fiber filaments were bonded with bisphenol A type epoxy. The specimens were specially designed for the in situ observation of the crack propagation in a scanning electron microscope. Three dimensional finite element analyses were carried out to obtain the complex stress intensity factors at interface, K 1 and K 2, and the energy release rate. The initial values of the fracture toughness were defined as the initiation of crack growth after pop in type crack onset at meniscus region, and the rising R-curve behavior was observed for both specimens. The difference in the shape of the R-curves and the toughness values in each specimen indicated the existence of the difference in toughness along a single filament. The comparison of the results of the BS and BO tests depicts that the fracture criterion under different fracture mode ratio is roughly expressed as K 1 2 + K 2 2 = const . The mechanism of interfacial fracture under different fracture modes were discussed in conjunction with fractrographic observation.

Mechanical property and R-curve behavior of the B4C/BN ceramics composites

The B4C/BN ceramics composites were fabricated by the hot-pressing process. In this paper, the mechanical property and R-curves behavior of the B4C/BN composites were investigated. The fracture strength and fracture toughness of the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increasing content of h-BN. The fracture strength and fracture toughness of the B4C/BN nanocomposites were significantly improved in comparison with the B4C/BN microcomposites. The damage resistance and R-curves behavior of the B4C monolith and the B4C/BN composites were evaluated by the indentation-strength in bending technique (ISB). The fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increase of the indentation load. The B4C/BN nanocomposites retained relative higher fracture strength in comparison with the B4C monolith and the B4C/BN microcomposites under the equivalent indentation load. The B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all exhibited the rising R-curves behavior. The B4C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. The toughness mechanisms of the composites were investigated. The B4C/BN composites with the h-BN content more than 20wt.% exhibited excellent machinability. The slowly rising R-curves behavior remarkably improved the machinability of the composites.

Preparation and R-curve properties of laminated Si/SiC ceramics from paper

Laminated Si/SiC ceramics were synthesized from paper via impregnation with phenolic resin, followed by lamination and carbonization of the paper–resin laminates and subsequent infiltration and reaction with liquid silicon at a temperature of 1550 °C for 10–90 min. Due to the capillarity infiltration and in situ reaction with liquid silicon, intrinsic micro- and macrostructure in the carbon preform was retained within the final ceramics. The XRD, TGA, and microscopy analysis indicated that the final material exhibited a distinguished laminar structure with alternating arrangement of SiC and silicon layers. The thick SiC layer was composed of beta-SiC and a little of free silicon and un-reacted carbon. Studies on the evaluation of R-curves behavior by the indentation-strength method indicated a strong R-curve behavior for the Si/SiC composites.

Crack resistance curve in glass matrix composite reinforced by long Nicalon® fibres

Theoretical micromechanical analysis of bridged crack development at chevron-notch tip of three-point bend specimens has been applied to determine the crack resistance curve for a composite made of a glass matrix reinforced by continuous Nicalon® fibres. Fracture toughness (KIC) values were determined using the chevron-notch technique at room temperature. The theoretical predictions were based on micromechanical analysis exploiting weight functions. Detailed FEM analysis using the ANSYS package was applied to determine numerically the weight functions for orthotropic materials. Appropriate bridging models for the theoretical prediction of the R-curve behaviour typical of the investigated composite were applied together with the weight functions. Experimental observations confirmed the theoretical calculations.