Notch Beam Research Articles

Acoustic emission characterization of fracture toughness for fiber reinforced ceramic matrix composites

The fracture toughness of a carbon fiber reinforced silicon carbide composite was investigated relating to classical critical stress intensity factor KIC, work of fracture, and acoustic emission energy. The KIC was obtained by the single edge notch beam method and the work of fracture was calculated using the featured area under the load–displacement curves. The KIC, work of fracture, and acoustic emission energy were compared for the composites before and after heat treatment and then analyzed associated with toughening microstructures of fiber pullout. It indicates that the work of fracture and acoustic emission energy can be more suitable to reflect the toughness rather than the traditional KIC, which has certain limitation for the fracture toughness characterization of the crack tolerant fiber ceramic composites.

Exploring the reduction of laboratory testing for the cohesive zone model for asphalt concrete

The cohesive zone model is a popular tool used to predict cracking in asphalt concrete. However, two of the three inputs required for the cohesive zone model, tensile stress and fracture energy, come from destructive laboratory tests. If the peak load from a fracture test (which supplies fracture energy) could be substituted for the tensile strength, the amount of laboratory testing could be halved. This research compared the peak loads from the single-edge notch beam, semi-circular bend and disk-shaped compact tension fracture tests as well as the tensile strength from the standard indirect tension (IDT) test. Even accounting for specimen geometry, the data did not indicate consistent correlation of the three fracture tests with the IDT test across various testing temperatures, loading rates or sample type (laboratory vs field samples). Therefore, no fracture test provided a sufficiently robust correlation to recommend replacing the tensile strength with the peak load of the fracture test for the cohesive zone model.

Mechanical properties of novel calcium phosphate–mullite biocomposites

Herein, the results of systematic mechanical property measurements of pressureless sintered calcium phosphate (CaP)-mullite composites are discussed. Our experimental results demonstrated how the mullite addition (upto 30 wt%) influenced hardness, elastic modulus, strength and toughness properties of the composites. In assessing each of these fundamental material properties, either a range of load or a number of complimentary techniques were used to obtain reliable measure of mechanical properties. Importantly, the results of single edge V notch beam measurements revealed that a reliable toughness value of ~1.5 MPa m(0.5) could be obtained in composites containing 20 or 30 wt% mullite. Our results clearly illustrated that a combination of elastic modulus (~80 GPa), compressive strength of more than 350 MPa, three-point flexural strength of 70-80 MPa, hardness of 4-5 GPa were achievable with the investigated composites. Such a combination of material properties, in addition to modest toughness property appeared to indicate that CaP-mullite composites could be used as a biomaterial for hard tissue replacement.

Microstructure, Fracture and Damage Mechanisms in Rare-Earth Doped Silicon Nitride Ceramics

Influence of rare-earth oxide additives on the strength, fracture toughness and tribological behaviour of hot-pressed Si3N4 and Si3N4/SiC micro/nano-composites has been investigated. Four-point bending mode and ball on disc methods have been used for strength and wear tests and Single-Edge V-Notched Beam, Chevron Notched Beam, Indentation Strength and Indentation Fracture techniques for fracture toughness measurement. Fractography has been used to characterize strength limiting defects, fracture micromechanisms and damage mechanisms during the wear test. The strength values were strongly influenced by the present processing flaws. Wear behavior is significantly influenced by the chemical composition and by the microstructure of the materials.

Laboratory Mixed-Mode Cracking of Asphalt Concrete Using the Single-Edge Notch Beam

ABSTRACT Reflective cracking is a combination of Mode I (opening) and Mode II (sliding) fracture, or Mixed-Mode fracture. The Single-Edge Notch Beam [SE(B)] test was used to analyze Mixed-Mode fracture characteristics of three asphalt concrete mixtures in the laboratory. The peak loads were similar across all three mixtures, emphasizing the importance of fracture mechanics when analyzing low temperature characteristics of asphalt concrete. The fracture work successfully differentiated the three mixtures, and showed that the fracture work increased as the level of Mode II increased. Simulations showed the damage in the mixtures evolved differently, with the more compliant mixtures showing a higher percentage of dissipated creep damage, and the more quasi-brittle mixture showing a higher percentage of dissipated fracture damage.

Robust Elevation Prefiltering Method for Non-Side Looking Airborne Radar

When the airborne early warning (AEW) radar transmits signal with medium or high pulse repetitive frequency (PRF), range ambiguity occurs at the receiver. For non-side looking airborne radar (non-SLAR), the short-range ambiguous clutter suffers from serious range dependence. As a result, the clutter plus noise covariance matrix cannot be correctly estimated, and the performance of clutter suppression obtained by space-time adaptive processing (STAP) degrades greatly. A robust elevation prefiltering method is proposed. This method can suppress the ambiguous short-range clutter by exploiting multi-elevation angles constraint, resulting in a deep and wide beam notch in the elevation angle corresponding to the short range. Moreover, the method offers potential robustness to combat the platform height with uncertain errors. Simulation results show the validity of the method.

Influence of notch on the elastic–plastic response of clamped beams subjected to low velocity impact

In the present paper, experimental and numerical results on deformation and failure of clamped mild steel beams with and without notches subjected to low velocity impact are reported. Three sets of mild steel beams are used in experiments: (i) Beams without notch (ii) beams with 3.0 mm wide rectangular notch and (iii) beams with 0.35 mm wide rectangular notch. The response of the beam is studied in terms of maximum permanent deflection and strain history during contact period. High-speed digital camera was used to capture the impact phenomena of beam specimens. The effect of notch depth, notch width and impact location on the beam response is studied. The presence of notch in beams increases the permanent deflections, and increases the chances of initial tearing failure at the notch location. It is observed from experiments that, the extent of notch influence on dynamic response depends on notch depth and location. In the notched beam, the crack started at the notch corner and extended upwards resulting in failure. The numerical simulations of the experimental impact tests were carried out using the commercial finite element software (ANSYS) and good agreement between numerical and experimental permanent deflection values was observed. The instantaneous distributions of curvature profiles of beam computed numerically are presented for both notched and unnotched beams.

Mechanical behavior of La 0.8Sr 0.2Ga 0.8Mg 0.2O 3 perovskites

This paper examines the important mechanical properties of commercially purchased La 0.8Sr 0.2Ga 0.8Mg 0.2O 3 at room temperature and 800 °C. Sr and Mg-doped lanthanum gallates (LSGM) are strong candidates for use as solid electrolytes in lower temperature solid oxide fuel cells operating at or below 800 °C. The material was found to be phase pure with a Young's modulus value of ∼175 GPa. The four point bending strength of the LSGM samples remained almost constant from 121 ± 35 MPa at room temperature to 126 ± 20 MPa at 800 °C. The fracture toughness, as measured by the single edge V notch beam (SEVNB) method, was 1.22 ± 0.06 MPa√m at room temperature, 1.04 ± 0.09 MPa√m at 700 °C followed by a small increase 1.31 ± 0.16 MPa√m at 800 °C. We also report, for the first time, the static subcritical (or slow) crack-growth (SCG) behavior of natural cracks in LSGM performed in four point bending tests at room temperature. The exponent of a power-law representation in the SCG tests was found to be n = 15, a rather low value showing LSGM to be highly susceptible to room temperature SCG.

Parallel nanogap fabrication with nanometer size control using III–V semiconductorepitaxial technology

A nanogap fabrication process using strained epitaxial III–V beams is reported. Theprocess is highly reproducible, allowing parallel fabrication and nanogap sizecontrol. The beams are fabricated from MBE-grown (GaAs/GaP)/AlGaAs strainedheterostructures, standard e-beam lithography and wet etching. During the wet etchingprocess, the relaxation of the accumulated stress at the epitaxial heterostructureproduces a controlled beam breakage at the previously defined beam notch. Afterthe breakage, the relaxed strain is proportional to the beam length, allowingnanogap size control. The starting structure is similar to a mechanically adjustablebreak junction but the stress causing the breakage is, in this case, built into thebeam. This novel technique should be useful for molecular-scale electronic devices.

Microstructural characterization and fracture behavior of a microhybrid and a nanofill composite

Objectives To characterize the microstructure and composition of two different composites, and to determine their influence on the physical properties and fracture behavior. Methods The microstructure and composition of a microhybrid (Filtek Z250™-Z2) and a nanofill (Filtek Supreme™-SU) composite were analyzed using scanning electron microscopy (SEM) and electron dispersive spectroscopy (EDS). Filler wt% was determined by thermogravimetric analysis. Hardness ( H) and degree of conversion (DC) were evaluated at top and bottom surfaces of 2-mm thick specimens, and the dynamic elastic modulus ( E) was determined with ultrasonic waves. Bar specimens ( n = 30) were subjected to flexure loading and flexural strength ( σ f) was calculated (MPa). Fractographic analysis (FA) was performed to determine the fracture origin ( c) for calculation of fracture toughness ( K Ic), and these results were compared to those from the single edge notch beam (SENB) method. Results were statistically analyzed using two-way ANOVA, Student's t-test and Weibull analysis ( α = 0.05). Results Z2 had higher filler wt%, H, E and DC at 2-mm depth as compared with SU. The fracture behavior ( σ f and K Ic) and the structural reliability ( m) of the composites were similar. Results of K Ic tested by SENB or calculated from fracture surfaces from flexure testing were similar. Significance The microstructural organization of the composites determines their physical properties, in spite of the similar filler content. In contrast, the microstructure did not influence the fracture behavior and the structural reliability of these highly filled composites. FA was shown to be a reliable method for determining the K Ic of composites.

Three-point bending fracture characteristics of three-dimensional-C/SiC with single-edge notch beam specimens

Abstract Loading–unloading properties of three-dimensional-C/SiC composites at ambient temperature were studied by three-point bending experiments with single-edge notch beam specimens. Crack growth was examined by scanning electron microscopy. The whole propagation process of a notch consists of a transient state and a steady state. The crack growth resistance is derived based on energy evaluation by a graphical method taking into account the non-linear fracture of the composites. The maximum value of the crack growth resistance, corresponding to the transition of the notch into cracks, reaches about 303.7 kJ m−2 when the ratio of equivalent crack length to sample thickness amounts to 0.13. The energy for the steady crack growth is about 20 kJ m−2.

Fracture toughness of Si3N4 processed by gas pressure sintering and hot pressing

This present work evaluates the influence of microstructure on the fracture toughness of two types of silicon nitride. The two microstructural types of silicon nitride were processed using the gas pressure sintering (GPS) and hot pressing (HP) pathways. The fracture toughness was measured using the Single Edge V-Notch Beam (SEVNB) and Chevron Notch Beam (CNB) methods. The results from both methods for the two forms were in close agreement (with a maximum variation of 5.8%); the KIc of the material processed by HP was 35% higher than that of GPS and the grain length had a direct influence on the fracture toughness.

Carbon-fibre-reinforced carbon composite filled with SiC particles forming a porous matrix

A carbon-fibre-reinforced carbon (C/C) composite filled with silicon carbide (SiC) particles was produced, using the winding technique. A porous matrix consisting of glassy carbon, SiC particles and small pores in homogeneous distribution was produced, ensuring a damage-tolerant fracture behaviour. Neither fibre coatings nor further infiltration steps were necessary for the preparation of the composite, which makes this a low-cost process making no limitations on wall thickness. The microstructure and homogeneity of the material is shown using micrographs, mercury porosimetry and BET measurements. Bending tests, as well as single-edge notch beam (SENB) tests point to high values for the bending strength and formal fracture toughness. A damage-tolerant fracture behaviour is demonstrated by the load–displacement curves and fracture surfaces.

Fracture toughness measurements of LPS-SiC: a comparison of the indentation technique and the SEVNB method

Many methods are currently used to measure the fracture toughness of ceramic materials. Methods based on crack-length measurements of cracks introduced into the sample surface by the Vicker's indentor have the advantage that they are easy to use, but are very unreliable due to subcritical crack growth and the difficulty in determining the exact length of the cracks. Furthermore, depending on the crack shape there are many equations to calculate K Ic. Other methods like the Chevron Notch or Single Edge Pre-cracked Beam (SEPB) are often difficult to execute or expensive. The simple and inexpensive Single-Edge-V-Notched Beam (SEVNB) on the other hand gives reliable values of fracture toughness of ceramic materials. In this method a saw cut is tapered to a sharp V-notch using a razor blade sprinkled with diamond paste. Thus, it is possible to introduce a sharp crack with a notch width of less than 20 micrometers, necessary to conduct valid tests. In this investigation, fracture toughness measurements on LPS-SiC materials carried out by the indentation technique and the SEVNB method have been compared.

Fictitious crack modelling of polymethyl methacrylate porous material

Fracture tests were performed on a granular polymethyl methacrylate porous material used as a mould for white ware castings. Two types of sample geometry (single-edge notch beam and wedge opening load) and two types of environment (dry at room temperature and in water at 45 °C) were used and the force–displacement curves were measured. The fictitious crack model with a bilinear softening curve was used to fit the experimental data resulting in an excellent agreement for all types of test. From the values of the fracture energy it is concluded that the measurement of the fracture toughness cannot be performed through a maximum peak load experiment for the given sample size and geometry. A comparison of the fracture surfaces under both conditions is made and an explanation for the different types of morphology is proposed.

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorKCand a second parameterT orA3,whereT andA3are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateGCis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.

Evaluation by Vickers indentation of fracture toughness of a phosphate biodegradable glass.

Indentation tests are commonly used for the evaluation of fracture toughness of brittle materials, particularly glasses and ceramics, because this technique requires only a small polished area on the specimen surface from which a large number of data points can be generated rapidly. However, a wide variety of equations for the calculation of fracture toughness of ceramic materials by means of Vickers indentation are available. Such equations are obtained phenomenologically and their parameters adjusted in such a way that the KIC values obtained are in good agreement with those obtained by conventional methods. This is the reason why it is necessary to check which type of equation reproduces more accurately the results obtained by means of conventional methods for the material which is going to be investigated. In the present work seven different fracture toughness equations widely used in glass and ceramic studies are considered and the results are compared with those obtained by conventional methods, such as single-edge notch beam (SENB) specimens tested in three-point bending. The role played by the applied indentation load is considered.

Fracture Toughness of TiB2 and B4C Using the Single‐Edge Precracked Beam, Indentation Strength, Chevron Notched Beam, and Indentation Strength Methods

The mode I fracture toughness (KIc) of boron carbide (B4C) and titanium diboride (TiB2) was determined using four competing techniques. The indentation strength (IS), chevron notched beam (CNB), and indentation fracture (IF) methods are common techniques that were compared to the recently standardized single‐edge precrack beam (SEPB) method. The SEPB method was more difficult to apply, but it represents the most rigorous method for KIc determination, because it uses few assumptions and requires a direct measurement of crack length. The IS method was an expeditious and economical alternative when low indentation loads were used. CNB KIc values were virtually rate‐independent when displacement rates less than or equal to 0.5 mm/min were used. The IF method was the least satisfactory technique, because of high variability in Kc values and because of the low differentiation between the two materials studied.

Slow crack growth in aerogels

The chemical susceptibility was measured by a dynamic method on aerogels immediately after supercritical drying and after oxidation treatment. Five loading speeds between 10 μm/min and 100 mm/min were used. After oxidation treatment, the Weibull modulus increased, which indicates a narrowing of the strength distribution. Toughness of the aerogels was measured by the single edge notch beam technique. ‘As-prepared’ aerogels did not show slow crack propagation. However, as the oxidized materials exhibit a stress corrosion phenomenon, the crack propagation rate was evaluated using the median value of strengths obtained with the highest crosshead speed. The lifetime prediction is estimated as a function of failure probability and from a proof testing experiment.

Hardness and fracture toughness of tetragonal zirconia single crystals

Yttriaand ceria-stabilized tetragonal zirconia attract great interest due to their exceptional mechanical properties. Hardness tests of such materials exhibit a stress-induced martensitic transformation of metastable tetragonal ZrO 2 to the stable monoclinic form [1, 2]. The compressive stress arising around the indentation improved the mechanical properties of tetragonal zirconia as compared to the completely stabilized (cubic) zirconia (CSZ). The dilatation associated with phase transformation also causes surface uplift around the indentation, which was revealed by phase contrast optical microscopy [3]. Another possible mechanism for increasing the toughness of tetragonal zirconia is a stress-induced reorientation of ferroelast domains [4, 5]. Major investigations of such materials were performed using ceramics and polycrystals. The mechanical properties of tetragonal zirconia single crystals have not been adequately studied. We studied the hardness and fracture toughness of 3.3 mol % yttria-0.3 mol % ceria and 3.3 mol% yttria-0.3 mol% terbia-stabilized tetragonal zirconia crystals (Y-Ce-TZC and Y-Tb-TZC, respectively). The tests were performed on the (0 01) plane of crystals grown by the scull-melting technique. Single crystals doped with yttria and ceria were red, crystals grown with yttria and terbia additions were yellow. Raman spectroscopy revealed only tetragonal phase in these crystals. Fracture toughness was determined by indentation and three-point single edge notch beam (SENB) bending. Three-point bending tests were performed on 3.5 mm × 5.0 mm × 25 mm rectangular specimens, the sides of which were coincident with the (001) plane. The hardness tests were performed on a Matsuzawa MXT70 microhardness tester at 0 .1 -10N loads and on a TP-2 Vickers hardness tester at 50-300 N loads. The indentation diagonals were parallel to the (100) and (110) directions (henceforth ( 10 0) and (1 10) indentations). Indentation size and radial crack length were measured by a NU-2E microscope (Carl Zeiss Iena, Germany) using the phase contrast technique. Indentation fracture toughness was determined according to the expressions given by Anstis et al. for half-penny radial cracks [6]: