R-curve Behavior Research Articles

Effect of Poling Direction on R‐Curve Behavior in Lead Zirconate Titanate

R‐curves of lead zirconate titanate (PZT) have been measured with compact tension (CT) specimens for different poling conditions and grain sizes. Depending on poling direction the plateau value of the R‐curves ranged from 1.13 to 1.54 MPa·m1/2 for a grain size of 6.4 μm and from 1.14 to 1.30 MPa·m1/2 for a grain size of 5.2 μm. Poling in the thickness direction yielded the material with the highest fracture toughness while the direction parallel to the loading direction led to the lowest fracture toughness.

Microstructural evolution and mechanical properties of Si3N4–SiC (nanoparticle)–Si3N4 (whisker) composites

The effects of SiC-nanoparticle and Si3N4-whisker additions on the microstructural evolution and mechanical properties of Si3N4 were investigated. The addition of SiC nanoparticles suppressed Si3N4 grain growth, leading to an improvement in the flexural strength. On the other hand, Si3N4 whiskers in the specimen promoted the formation of large elongated grains, which were found to be beneficial to the fracture toughness of the material. When both SiC nanoparticles and Si3N4 whiskers were added concurrently, large grains were formed in fine matrix grains. The microstructure of Si3N4 was controlled by adjusting the relative concentrations of SiC nanoparticles and the Si3N4 whiskers added. These compositional and microstructural variations of the Si3N4 had significant influence on the mechanical properties, such as strength, fracture toughness, R-curve behavior, and high-temperature strength.

R‐Curve Behavior and Crack‐Closure Stresses in Barium Titanate and (Mg,Y)‐PSZ Ceramics

R‐curves, process zones, and shielding stresses of barium titanate (BaTiO3) and partially stabilized zirconia (PSZ) have been studied using compact‐tension (CT) specimens. BaTiO3 and PSZ exhibited pronounced R‐curves that rose over similar crack lengths and showed steady‐state toughnesses of 0.7 and 6.4 MPa·m1/2, respectively. Both steady‐state toughnesses were ∼80% larger than the initial fracture toughnesses. Ferroelastic domain switching was the main toughening mechanism in BaTiO3, whereas, in PSZ, transformation toughening was the main toughening mechanism. The crack process zone and crack‐opening‐displacement (COD) profile of each material was studied in detail using atomic force microscopy. Crack‐closure‐stress distributions were extracted from the COD profiles, using weight‐function methods. The resulting stress profiles indicated that compressive residual stresses of 40 MPa in BaTiO3 and 400 MPa in PSZ acted in a limited region behind the crack tip. In the PSZ, crack bridging seemed to be a competing mechanism to transformation toughening.

Comparison of R‐Curves from Single‐Edge V‐Notched‐Beam (SEVNB) and Surface‐Crack‐in‐Flexure (SCF) Fracture‐Toughness Test Methods on Multilayered Alumina–Zirconia Composites

The single‐edge V‐notched‐beam fracture testing method was used to measure the short‐crack R‐curve behavior of a 90‐vol%‐alumina–10‐vol%‐ceria‐doped zirconia multilayered composite. The initiation and extension of short cracks from the V‐notch tip were observed in situ via optical microscopy. Initial crack lengths of 15–50 μm were obtained repeatedly. The resulting R‐curve was similar to the R‐curve that was measured using the surface‐crack‐in‐flexure testing method. The ability to control the position of the V‐notch tip within a material permits study of the influence of specific microscopic features on the fracture behavior.

Crack growth resistance of Cr3C2/Al2O3 composites

The crack resistance of Cr 3 C 2 /Al 2 O 3 composites was investigated. The indentation/strength technique was used to determine the R-curve behaviors. The small (2 μm) Cr 3 C 2 particles were found to have a better toughening effect than that of large (7 μm) Cr 3 C 2 particles in Cr 3 C 2 /Al 2 O 3 composites. The R-curve behaviors in Cr 3 C 2 /Al 2 O 3 composites could be attributed to the mechanisms of crack-deflection and crack-branching. Materials exhibiting R-curve behavior also had narrower strength distribution and larger Weibull modulus than those of Griffith materials.

Damage resistance and R-curve behavior of multilayer Al 2O 3/SiC ceramics

Damage resistance and R-curve behavior of multilayer Al 2O 3/SiC ceramics were evaluated in bending by the indentation-strength and the single-edge-notched-beam methods. Due to the crack deflection at the Al 2O 3/SiC interfaces, a plateau indentation strength response was achieved, suggesting an exceptional resistance to contact-induced damage. Moreover, fracture toughness was observed to increase from 8.0 to 15.5 MPa m 1/2 with increasing notch depth from 0.5 to 2.0 mm, indicative of a strong R-curve behavior.

Alumina-mullite-zirconia composites obtained by reaction sintering: Part I. Microstructure and mechanical behaviour

Zirconia particles can be added to the matrix to overcome the brittleness inherent in ceramic materials, thereby strengthening the material through tetragonal-monoclinic phase transformation of the zirconia. This work focuses on the effect of the percentage of zirconia and mullite in the mechanical and thermomechanical properties of alumina-mullite-zirconia composites that were obtained by reaction sintering of alumina and zircon. Different samples were processed, resulting in composites with an alumina matrix, which was always volumetrically predominant. A percentage of alumina and mullite with maximized mechanical and thermomechanical properties was observed. This maximization is discussed in terms of the microstructure obtained for the composites mentioned above. The toughening mechanisms provided by zirconia and mullite inclusions, based not only on the R-curve behaviour but also on the analysis of the fracture surface, are also discussed in this report. An additional paper will be forthcoming, containing detailed discussions concerning the R-curve behaviour of the same composites.

Alumina-mullite-zirconia composites obtained by reaction sintering Part II. R-Curve behavior

Applying Linear Elastic Fracture Mechanics equations and sample compliance variation to quantify the instantaneous crack length, the R-curve behavior of alumina-mullite-zirconia composites obtained by reaction sintering, was evaluated as a function of zirconia and mullite content. Changes in the R-curve profile as a function of the notch geometry (Chevron and straight-through notch) was observed and discussed, based on the analysis of the y(α) function applied to each notch type. The influence of the y(α) function in the R-curve shape was observed in both the initial and the final crack propagation region where, in the latter, the R-curves presented a sharp increase. In order to suppress these effects, the R-curve values for pure alumina were deducted from those obtained for the different composites produced. The analysis of the resulting curves highlights the influence of the amount of zirconia and mullite inclusions in these composites.

Characterization of Mode I Delamination Growth in Glass/Epoxy Composite Cylinders

Mode I delamination growth in filament wound composite cylinders has been examined analytically and experimentally. Beam specimens with the axis parallel to the cylinder axis were machined from the cylinders. The specimen contained an aluminum film at one end to define a starter delamination. A beam model incorporating elastic foundation effects and curved cross sections of the sub-beams of the delamination region was developed for the beam specimens configured for a DCB test from laminated beam theory derived from a shallow shell formulation. An experimental study on [±016 and [±0112, glass/epoxy DCB specimens employing contoured loading tabs accommodated to the curved cross-section was conducted. The delaminations were initially at the mid-surface, and the angles 0 were 300, 550 and 850. Analytical predictions of the compliance were in agreement with experimental data over the range of crack lengths, beam thicknesses, and ply angles examined. The fracture toughness corresponding to propagation straight from the insert increased slightly with increased angle 0 at the ±0 interface. The propagation fracture toughness increased steeply with crack length and then dropped. The increasing resistance, i.e., R-curve behavior, is attributed to the work associated with bridging and fracture of angle-ply fiber bundles, and the drop is attributed to crack jumping to another interface. For all laminates, the crack propagated in a non-uniform manner across the width of the specimen.

R-curve behaviour and microstructure of liquid-phase sintered α-SiC

R-curves for two liquid-phase sintered α-SiC (SC-A and SC-B), of different microstructures, were characterized using indentation-strength method. Silicon carbide SC-B, with its coarser microstructure and 8 MPa · m1/2 toughness, showed higher resistance to crack growth and more damage tolerance than silicon carbide SC-A, with its finer microstructure and 4.5 MPa · m1/2 toughness. These results suggest that a coarse microstructure is beneficial to toughening and damage tolerance while a fine microstructure is beneficial to strengthening.

Microstructural influence on the R-curve behavior of a 70%Si3N4-30% barium aluminum silicate self-reinforced composite

Fracture toughness and crack growth resistance (R-curve) behavior of several microstructures of 70%Si3N4-30%BAS composite are characterized using the indentation and modified compact tension methods, at room temperature. Both the whisker morphology and matrix properties contribute to the fracture resistance behavior. Crack deflection, whisker bridging and pullout are regarded as the dominant toughening mechanisms.

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76 mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125 mm/min (0.005 in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G 1). There is a well pronounced general trend observed: G 1 increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G 1 increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G 1, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.

Fabrication of Al2O3/TiC/Ni Functionally Graded Materials by Pulsed-Electric Current Sintering and Their Mechanical Properties.

Dense Functionally Graded Materials (FGMs) in the systems of Al2O3/TiC/Ni and (Al2O3-WC/Co)/TiC/Ni were fabricated at 1300°C and 10 minutes by pulsed-electric current sintering method. The grain growth was effectively prevented and fine microstructure could be obtained by this rapid sintering. The residual stress produced in the outer Al2O3 and Al2O3-WC/Co layers of FGMs, which was induced by the thermal expansion mismatch between the inner TiC/Ni layer and the outer layers, was in the range of-180 MPa to-300 MPa. The compressive stress and the dispersion of WC/Co particles enhanced the toughness of the outer ceramic layers, and developed steep R-Curve behavior.

Prediction of the fracture toughness of fibrous composites

A statistical/micromechanical model is developed for the prediction of the fracture toughness of fibrous composites. The fracture resistance of the material is assumed to be related to the statistical distribution of the fiber pull-out length. The distribution of the fiber pull-out length is derived from the fiber strength distribution. The R-curve behavior of the fibrous composite is predicted and interpreted based on the present model. The limiting fracture toughness is predicted to be proportional to the square root of the ineffective length, or proportional to the square root of the fiber length if the fiber length is less than the ineffective length.

A Progressive Damage Methodology for Residual Strength Predictions of Notched Composite Panels

The translaminate fracture behavior of carbon/epoxy structural laminates with through-penetration notches was investigated to develop a residual strength prediction methodology for composite structures. An experimental characterization of several composite materials systems revealed a fracture resistance behavior that resembles the R-curve behavior exhibited by ductile metals. Fractographic examinations led to the postulate that the damage growth resistance was primarily due to fractured fibers in the principal load-carrying plies being bridged by intact fibers of the adjacent plies. The load transfer associated with this bridging mechanism suggests that a progressive damage analysis methodology will be appropriate for predicting the residual strength of laminates with through-penetration notches. A progressive damage methodology developed by the authors was used to predict the initiation and growth of matrix cracks and fiber fracture. The residual strength predictions for different panel widths, notch lengths, and material systems were in reasonable agreement to the experimental failure loads.

Effect of SiC Addition on R-Curve Behaviour of Alumina and ZTA Ceramics

Effect of SiC Addition on R-Curve Behaviour of Alumina and ZTA Ceramics

The mechanical behavior of ceramic–metal laminate under thermal shock

A new material system for applications involving thermal shock is proposed. The system consists of thin layers of ceramics and thinner metallic interlayers. In this study, a ceramic/metal laminate was constructed from Coor's ADS96R thin plates alternating with thinner Wesgo Cusil Active Braze Alloy interlayer foils and joined in active brazing. The maximum brazing temperature was 845 °C. Square laminated plates were quenched in room-temperature distilled water, where a very large heat transfer coefficient exists, and therefore, severe conditions of thermal shock occur. The laminated plates, initially at temperatures of 600 and 800 °C, were quenched at their bottom surface only in a specially designed apparatus. The temperatures at the top and the bottom surfaces of the specimens were measured by means of two thermocouples during quenching. The basic features of this architecture are described. The dominant behavior was the absence of interaction between the biaxial cracking mechanisms in a ceramic layer with those in an adjacent ceramic layer, and localization of the damage to those layers that experienced sufficient tensile stresses. The result was a dramatic increase of the residual strength after thermal shock. In addition, R-curve behavior upon mechanical loading caused by plastic deformation of the metallic interlayer was observed.

Mechanical properties of PZT ceramics with tailored microstructure

PZT ceramics with tailored microstructure were fabricated using 3 and 5 valence ions as dopants. It was shown that the type of additive does not influence the microstructural development. Vacancies in the Pb-lattice are being formed for all dopants to assure charge equilibrium. Thus, Pb-vacancies are identified to dominate the microstructural development of PZT ceramics. Samples with 2 mol% additive which were sintered to near theoretical density exhibit a homogeneous microstructure with an average grain size of 2 μm. The morphotropic phase boundary (MPB) of doped PZT is shifted towards higher PbZrO 3 content as compared to undoped PZT. This effect is explained in terms of crystallographic considerations. The investigations on the mechanical properties are focused on the area of the MPB that is relevant for industrial applications due to the extraordinary high electrical properties. For the first time an entire evaluation of the mechanical properties have been conducted considering the fracture toughness of poled and unpoled samples, R-curve behavior, temperature dependent bending strength and ferroelastic behavior. From these measurements the influence of domain switching processes on the mechanical properties are deduced and a correlation between mechanical, ferroelastic and ferroelectric behavior and the microstructure is supposed.

Toughness of aluminium alloy foams

The fracture behaviour of closed cell aluminium-based foams (trade-name “Alulight”) is characterized for the compositions Al–Mg1–Si0.6 and Al–Mg1–Si10 (wt%), and for a relative density in the range 0.1–0.4. The toughness testing procedures are critically analysed, and the origins of the observed R-curve behaviour for metal foams are explored. A major contribution to the observed increasing crack growth resistance with crack advance is in the development of a crack bridging zone behind the crack tip. The crack bridging response is quantified in terms of a crack traction vs extra displacement curve by performing independent tests on deep notch specimens. The area under the bridging traction vs extra displacement curve from the deep notch tests is approximately equal to the measured initiation toughness J IC, in support of the crack bridging concept. A line spring model is then used to interpret the fracture response. The effect of material composition and relative density upon the initiation toughness is measured, and the accuracy of an existing micromechanical model for the fracture toughness of a brittle foam is assessed. Finally, the reduction in tensile and compressive strengths due to the presence of an open hole is determined; it is found that the Alulight foams are notch-insensitive, with the net section strength equal to the unnotched strength.

Fracture Testing and Analysis of a Layered Functionally Graded Ti/TiB Beam in 3-Point Bending

This paper presents a methodology for testing and analyzing a layered functionally graded beam consisting of Ti and TiB phases. The test specimen is a single edge notch bending (SENB), with composition varying from a TiB-rich layer at the bottom to commercially pure (CP) Ti at the top. The crack front is aligned parallel to the material gradation and it grows along this direction (mode I). For this crack orientation, average R-curve behavior is investigated in order to understand the mechanics of crack growth. The beam is modeled using two-dimensional finite elements considering elastoplastic behavior. Properties of the mixed phase interlayers are approximated using a rule-of-mixtures approach, and the validity of this approach is discussed. Characteristic response quantities are investigated such as the mechanical fields, crack mouth opening displacement, and J integral.