Fracture toughness of glasses and hydroxyapatite: A comparative study of 7 methods by using Vickers indenter

Numerous methods have been proposed to estimate the indentation fracture toughness Kic for brittle materials. These methods generally uses formulæ established from empirical correlations between critical applied force, or average crack length, and classical fracture mechanics tests. This study compares several models of fracture toughness calculation obtained by using Vickers indenters. Two optical glasses (Crown and Flint), one vitroceramic (Zerodur) and one ceramic (hydroxyapatite) are tested. Fracture toughness and hardness are obtained by using instrumented Vickers indentation at micrometer scale. Young's moduli are obtained by instrumented Berkovich indentation at nanometer scale. Fracture toughness is calculated with models involving crack length measurements, and by models free of crack length measurements by considering critical force, chipping, pop-in. Finally, method based on the cracking energy, commonly employed for coated materials is also used.The aim of this work is to compare seven methods, which enable the facture toughness determination, on four brittle materials. To do so, it was necessary to determine some specific constant in the case of Vickers tip use.On the one hand, results show that methods using crack length, critical force, edge chipping or pop-in lead to comparable results, and the advantages and drawbacks are highlighted. On the other hand, the indentation energy method leads to underestimated results of about 20%.     

Analytical Approaches to Stress Intensity Factor Evaluation for Indentation Cracks

In the present paper, an analytical solution for the stress intensity factor in the case of cracks produced by Vickers indenters has been extended to the cases of triangular indenters, i.e., Berkovich and cube-corner. According to the adopted approach, median/radial cracks produced by indentations are modeled as loaded by either a point-force or a symmetric disk-shaped wedge. The wedge diameter is assumed to be equal to the plastic zone size whereas the wedge thickness is evaluated by comparing the wedge volume with the hardness-impression volume. The point-force and the disk-shaped wedge analyses produce an upper and a lower bound, respectively, of the geometry-dependent parameter appearing in the expression for the fracture toughness. The predictions of the present analysis are in good agreement with similar experimental and numerical results.     

Sequences of fracture toughness micromechanisms in PP/CaCO3 nanocomposites

Mechanical properties and fracture toughness micromechanisms of copolypropylene filled with different amount of nanometric CaCO₃ (5–15 wt %) were studied. J‐integral fracture toughness was incorporated to measure the effect of incorporation of nanoparticle into PP matrix. Crack‐tip damage zones and fracture surfaces were studied to investigate the effect of nanofiller content on fracture toughness micromechanisms. It was found that nanofiller acted as a nucleating agent and decreased the spherulite size of polypropylene significantly. J‐integral fracture toughness (J_c) of nanocomposites was improved dramatically. The J_c value increased up to approximately two times that of pure PP at 5 wt % of nano‐CaCO₃. The fracture micromechanisms varied from rubber particles cavitation and shear yielding in pure PP to simultaneous existence of rubber particles cavitation, shear yielding, filler particles debonding, and crazing in PP/CaCO₃ nanocomposites. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Fracture toughness of phenolphthalein polyether ketone

The static and impact fracture toughness of phenolphthalein polyether ketone (PEK-C) were studied at different temperatures. The static fracture toughness of PEK-C was evaluated via the linear elastic fracture mechanics (LEFM) and the J-integral analysis. Impact fracture toughness was also analyzed using the LEFM approach. Temperature and strain rate effects on the fracture toughness were also studied. The enhancement in static fracture toughness at 70°C was thought to be caused by plastic crack tip blunting. The increase in impact fracture toughness with temperature was attributed two different mechanisms, namely, the relaxation process in a relatively low temperature and thermal blunting of the crack tip at higher temperature. The temperature-dependent fracture toughness data obtained in static tests could be horizontally shifted to match roughly the data for impact tests, indicating the existence of a time–temperature equivalence relationship. © 1995 John Wiley & Sons, Inc.     

The Effects of Cure Temperature and Time on the Bulk Fracture Properties of a Structural Adhesive

The purpose of this investigation is to determine experimentally the possibility of optimizing the room temperature bulk fracture properties of structural adhesives with respect to cure temperature, time and cool-down conditions. The model adhesive, Metlbond, is a solid film modified nitrile epoxy resin supplied in two forms: Metlbond 1113 (supported with synthetic fabric carrier cloth) and Metlbond 1113-2 (without carrier cloth). The effects of carrier cloth on the bulk fracture properties are investigated as well. The uniaxial tensile strength and rigidity values were determined over a wide range of cure temperatures and times with fast and slow cool-down conditions during a previous investigation by the authors. For the present investigation, the fracture toughness of the model adhesives, subjected to opening mode failure, are experimentally determined, with the use of single-edge-cracked specimens, for different cure and cool-down conditions. It is found that the optimum fracture toughness values are obtained at low temperature-long time cure conditions in the absence of carrier cloth when slow cool-down condition is employed. Using the elastic-plastic material behavior assumption, it is shown that an average crack tip plastic zone radius can be determined using the fracture toughness and tensile strength values obtained corresponding to a given cool-down condition. These average plastic zone radii values are used along with the available tensile rigidity values to evaluate the optimum fracture energies of the model adhesives for a number of cure schedules. It is found that the optimum fracture energy levels are obtained at high temperature-short time cure conditions, using slow cool-down in the absence of carrier cloth.     

Toughness of HDPE/CaCO3 microcomposites prepared from masterbatch by melt blend method

In this study, a series of high‐density polyethylene and micro/nanocalcium carbonate polymer composites (HDPE/CaCO₃ nanocomposites) were prepared via melt blend technique using a twin screw extruder. Nanocomposite samples were prepared via injection molding for further testing. The effect of % loading of CaCO₃ on mechanical and fracture toughness of these composites has been investigated in details. The effect of precrack length variation on the fracture toughness of the composite samples was evaluated, and the morphology of the fractured samples was also observed using scanning electron microscopy (SEM). It was found that increasing the % of CaCO₃ and precrack length decreased the fracture toughness. Fracture surface examination by SEM indicated that the diminished fracture properties in the composites were caused by the aglomerization of CaCO₃ particles which acted as stress concentrators. A finite element analysis using ANSYS was also carried out to understand the effect of agglomeration size, interaction between the particles and crack tip length on the fracture properties of these composites. Finally, a schematic presentation of the envisioned fracture processes was proposed. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Mechanical properties and indentation-induced phase transformation in 4H–SiC implanted by hydrogen ions

This paper aims to improve machining efficiency, suppress surface cracking, and reduce subsurface damage of silicon carbide (SiC). Hydrogen ions were implanted into SiC to study mechanical properties at nano and macro scales. Nanoindentation experiments were conducted using a Berkovich indenter. Firstly, the effect of ion implantation on the load-displacement curves at different indentation depths was investigated using molecular dynamics (MD) simulations. Elastic-plasticity at nanoscale was analyzed, and the values of material properties were obtained. Secondly, variability of surface morphology, phase transformation, and coordination number induced by nanoindentation with and without ion implantation was evaluated. Although ion implantation induced damage to the SiC model, the damage after nanoindentation was lower than that without ion implantation. Additionally, nanoindentation experiments were performed for small loads and high loads, respectively. The small load experiments were employed to derive material properties of the ion-implanted SiC. Improvement mechanisms of ion implantation on crack extension, fracture toughness, and elastic recovery rate were investigated under the high-load experiments. The results indicate that the amorphous structure induced by ion implantation can successfully prevent crack propagation and improve fracture toughness. The modification technology of SiC by ion implantation significantly improves the machining efficiency and the non-damage of its surface and subsurface.     

Preparation of TiO2 epoxy nanocomposites by ultrasonic dispersion and resulting properties

Nanocomposites gained more and more importance in the last few years because of their improved performance over the neat polymer matrix, that is, toughness and stiffness can be enhanced simultaneously by the addition of nanoparticles. However, the dispersion of these particles in the matrix remains a big challenge. In this study, two types of TiO₂ nanoparticles were dispersed in two different epoxy resins by means of ultrasound. The particle size development in dependence on the dispersion time was investigated by dynamic light scattering for the different material systems. Furthermore, the influence of the viscosity on the sonication process' efficiency was analyzed. The resulting nanocomposites were tested for fracture and Charpy toughness. SEM images revealed that the improved fracture toughness properties are correlated to a rougher fracture surface, whose formation dissipates more energy. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

The effect of chemical modification on the fracture toughness of montmorillonite clay/epoxy nanocomposites

The change in fracture toughness and its dependence on the content of clay nanoplatelets and adhesion at the interface between clay nanoplatelets and anhydride-cured epoxy matrix are discussed. Three clay nanoplatelets with different chemical modifications were used in this investigation. To fabricate nanocomposites, the clay nanoplatelets were sonicated in acetone for 2 h. The role of the clay nanoplatelets in the mechanical/fracture properties was investigated by transmission electron microscopy (TEM). Bright-field TEM micrographs showed excellent dispersion of clay nanoplatelets in epoxy matrix. Both intercalation and exfoliation of clay nanoplatelets were observed depending on clay modification. Compact tension specimens were used for fracture testing. The fracture toughness increased with increasing clay content. The fracture toughness of clay/epoxy nanocomposites varied with the clay morphology in the epoxy matrix. Different morphologies of the fracture surfaces, highly dependent on the morphology of dispersed clay nanoplatelets, were observed using environmental scanning electron microscopy (ESEM). The fracture toughness was found to be correlated with the fracture surface roughness measured by confocal laser scanning microscopy (CLSM).     

Microscopic analysis of single-fiber push-out tests on ceramic matrix composites performed with Berkovich and flat-end indenter and evaluation of interfacial fracture toughness

Single-fiber push-out tests performed with a Berkovich and a flat-end indenter tip were conducted on the same SiC/PyC/SiC ceramic matrix composite sample for comparison. Push-out measurements were stopped at different stages during the experiment for a detailed microscopic analysis of the front and back side of the sample, to investigate the progression of failure during push-out process. The microscopic analyses reveal differences from the established interpretations which are crucial for quantitative evaluation of interface properties. Based on the microscopic findings, a modified loading schedule comprising unloading–reloading cycles is proposed, which provides access to the dissipative and non-dissipative energy contributions during push-out test. A new energy-based approach is presented which allows for the determination of the interfacial fracture toughness, without assumptions regarding the stress distribution along the interface to be made. Presuming stable crack growth along the complete debonding length, the interfacial fracture toughness of the sample investigated amounts to 44 ± 9 J/m².     

纳米复合陶瓷

纳米复合陶瓷可分为四种类型:分散型、梯度型、被复型和纳米-纳米复合。纳米复合微粒的制备有气相法、液相法和固相法。分散型和被复型纳米复合陶瓷的室温韧性和强度约提高2～5倍,其高温硬度、韧性、强度、蠕变、疲劳断裂强度、热冲击特性等亦得到显著改善。纳米-纳米复合材料具有可加工性和超塑性等新功能。本文评价和探讨了纳米复合陶瓷的力学性能和纳米尺寸分散的作用。     

Quantitative Characterization of the Fracture Surface of Si Single Crystals by Confocal Microscopy

Experiments are conducted to study the dislocation nucleation conditions at the crack tip in {110}〈110〉 oriented Si single crystals. Specimens with surface cracks are first statically loaded at elevated temperatures for a prolonged period of time to initiate and move dislocations away from the crack tip, then cooled down to room temperature and loaded to fracture to measure the fracture toughness. Fractographic analysis of the fracture surfaces is performed. Distinct wavy patterns on the fracture surface at the initial cleavage crack front are observed, which is attributed to the existence of local mixed mode I/mode III stresses resulting from the inhomogeneous dislocation activity. Confocal microscopy is employed to quantify the fracture surface roughness. The results show that the increase of fracture toughness is directly associated with the increased area of the rough surface, which is characterized by the roughness number or the fractal dimension increment. Our results also demonstrate that dislocation nucleation can occur only at discrete sites. The spacing between these dislocation nucleation sources is of the order of 1 μm. A simple model is developed for the relationship between the fracture toughness and the surface roughness parameters, which is in good agreement with the experimental results.     

Toughening of laminated ZrB2-SiC ceramics with residual surface compression

Laminated ZrB₂-SiC ceramics with residual surface compression were prepared by stacking layers with different SiC contents. The maximum apparent fracture toughness of these laminated ZrB₂-SiC ceramics was 10.4 MPam^1/2, which was much higher than that of monolithic ZrB₂-SiC ceramics. The theoretical predictions showed that the apparent fracture toughness was strongly dependent on the position of the notch tip, which was confirmed by the SENB tests. Moreover, laminated ceramics showed a higher fracture load when the notch tip located in the compressive layer, whereas showed a lower fracture load as the notch tip within the tensile layer. The toughening effect of residual compressive stresses was verified by the appearance of crack deflection and pop-in event. The influence of geometrical parameters on the apparent fracture toughness and residual stresses was analyzed. The results of theoretical calculation indicated that the highest residual compressive stress did not correspond to the highest apparent fracture toughness.     

Toughening of unmodified polyvinylchloride through the addition of nanoparticulate calcium carbonate

PVC/CaCO₃ polymer nanocomposites of differing compositions were produced using a two-roll mill and compression molding. The morphology was observed using transmission electron microscopy, and the static and dynamic mechanical and fracture properties determined. The presence of nanometer-sized CaCO₃ particles led to a slight decrease in the tensile strength but improved the impact energy, the storage modulus and the fracture toughness. Fracture surface examination by scanning electron microscopy indicated that the enhanced fracture properties in the nanocomposites were caused by the assisted void formation at the particles. This hypothesis is supported by a microstructure-based finite element modeling based upon elastic-plastic deformation around a weakly bonded particle. Hence, this provides an explanation of both the uniaxial tensile behavior and enhanced toughness of the nanocomposites.     

Analyzing indentation behavior of LaGaO3 single crystals using sharp indenters

In this work, the mechanical properties of (1 0 0) and (0 0 1) oriented LaGaO₃ single crystals have been studied using sharp indenters. Vickers hardness values for both the (1 0 0) and (0 0 1) samples were found to be in the same range (8 GPa). The values for the indentation fracture toughness (K_R) from Vickers indentation on the (1 0 0) samples were determined to be 0.8 ± 0.2 MPa m^1/2. Different crack lengths, implying a strong anisotropy in the indentation fracture toughness values, were observed in the two mutually perpendicular directions in the indentations on the (0 0 1) samples. These measurements led to estimates of 0.5 ± 0.1 and 1.3 ± 0.3 MPa m^1/2 for the two different sets of cracks on the (0 0 1) samples. In situ nanoindentation inside the SEM using a cube-corner indenter has also been used for studying the indentation fracture response of these samples.     

Fracture toughness of bisphenol A‐type epoxy resin

The relationship between the postcuring conditions and the fracture toughness of a bisphenol A‐type epoxy resin cured with acid anhydride was investigated. The glass transition temperature and fragility parameter, derived from the thermo‐viscoelasticity, were used to characterize the epoxy resin postcured under various conditions. Relationship between these two parameters and the fracture toughness was then investigated, based on the fractography results of a microscopic roughness examination of a fractured surface. The values of the glass transition temperature and fragility greatly depended on the postcuring conditions. The glass transition temperature was approximately 400 K when the crosslinking reaction was saturated. The fragility was independent of the saturation of the reaction and varied between 50 and 180. The results of the fracture test and fractography examination showed that there was no direct correlation between the glass transition temperature, the fracture toughness, and the roughness. On the other hand, there was a correlation between the fragility, fracture toughness, and roughness when the glass transition temperature saturated (at 400 K). As the fragility decreased from 180 to 50, the fracture toughness increased from 0.6 to 1.1 MPa · m^1/2 at the same glass transition temperature. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 10: 2266–2271, 2002     

Mechanical Properties of PMMA‐Sepiolite Nanocellular Materials with a Bimodal Cellular Structure

Bimodal cellular poly(methyl methacrylate) with micro‐ and nano‐sized (300–500 nm) cells with up to 5 wt% of sepiolite nanoparticles and porosity from 50% to 75% are produced by solid‐state foaming. Uniaxial compression tests are performed to measure the effect of sepiolite concentration on the elastic modulus and the yield strength of the solid and cellular nanocomposites. Single edge notch bend tests are conducted to relate the fracture toughness of the solid and cellular nanocomposites to sepiolite concentration. The relative modulus is independent of sepiolite content to within material scatter when considering the complete porosity range. In contrast, a mild enhancement of the relative modulus is observed by the addition of sepiolite particles for the foamed nanocomposites with a porosity close to 50%. The relative compressive strength of the cellular nanocomposites mildly decreases as a function of sepiolite concentration. A strong enhancement of the relative fracture toughness by the addition of sepiolites is observed. The enhancement of the relative fracture toughness and the relative modulus (at 50% porosity) can be attributed to an improved dispersion of the particles due to foaming and the migration of micro‐sized aggregates from the solid phase to the microcellular pores during foaming.     

Studies of epoxy resin systems: Part D: Fracture toughness of an epoxy resin: A study of the effect of crosslinking and sub-Tg aging

The fracture toughness of an epoxy resin system, diglycidyl ether of butanediol, DGEB, cured with 4-4′ diaminodiphenyl sulphone, DDS, has been studied by varying the crosslinking density and state of aging. A stable, but rough, crack propagation was observed with specimens that were 99 percent cured and quenched. When the extent of curing was less than 99 percent or the material was aged for more than 20 min at 62°C, crack propagation was of the unstable stick-slip nature. Aging was found to decrease the initiation fracture toughness dramatically, but the arrest fracture toughness was almost unchanged. This result was associated with a change of relaxation strength of the primary, a, transition with aging. An increase of crosslinking density was found initially to reduce the fracture toughness of this epoxy resin, but the fracture toughness increased after 87 percent of curing. The initial decrease of the fracture toughness was attributed to a decrease of relaxation strength of the primary transition (i.e., the area under the α-relaxation peak), while the increase of the fracture toughness after 87 percent curing was explained by the onset of the stablerough crack propagation, Micrographs taken by scanning electron microscopy-showed possible existence of blunting during crack propagation and a decrease of blunting with the extent of aging.     

Mechanical and elastic properties of fine-grained polycrystalline scandia and erbia as determined by indentation techniques

The Young's moduli, E, and nanoindentation, NI, stress-strain curves of fine-grained scandia, Sc₂O₃, and erbia, Er₂O₃, were determined using spherical indenters with radii of 1.4 μm and 5 μm. The Young's moduli measured with the spherical indenters, were comparable to those measured by a Berkovich tip, and by ultrasound. This work further validates the use of S vs. a plots to measure the Young's moduli of polycrystalline ceramics. A major advantage of using this technique is the possibility of determining NI stress-strain curves and concomitant yield points, apparent strain hardening rates, etc. for the first time. Both the elastic moduli and the yield stresses were affected by the degree of surface polishing and tip size. The most reproducible and reliable results were obtained with the sharper nanoindenter and the best surface finish. The Vickers hardness and indentation fracture toughness values extracted from the Vickers indentations are comparable to the literature results.     

Accurate measurement of fracture toughness in structural ceramics

The measured values of fracture toughness for ceramics are closely correlated with the sharpness of notch tips, which in turn influences the accurate measurement of fracture toughness. Here, typical structural ceramics, i.e., 3 mol% yttria-stabilized tetragonal zirconia polycrystal (3Y-TZP), ZrB₂, ZrB₂-SiC and ZrB₂-SiC-Grapite, were used for the measurement of fracture toughness, and the effect of notch tip radius on the fracture toughness values of these typical structural ceramics was investigated. Ultra-sharp notches with a tip radius less than 1 μm can be fabricated by laser, lower than the critical notch tip radius in ceramics below which the fracture toughness value almost remains constant, and improved accuracy and consistency of fracture toughness measurement can be obtained by this method compared with traditional method.