Analytical model to predict multiaxial laminate fracture toughness from 0° ply fracture toughness

The prediction of nominal strength is very important in the design and evaluation of materials especially polymer matrix composites. Various cohesive laws forms are successfully used in predicting the nominal strength of laminated composite structures. For composite structures, fracture toughness is dominated parameter when using cohesive laws to predict their nominal strength. In spite of complex reported models, this study propose an easy simple model to predict the fracture toughness of multidirectional composite laminates using the fracture toughness of the 0° ply ones. This model is mainly based on the geometry of fiber orientation and linear elastic fracture mechanics and uses the fracture toughness of the 0° ply obtained from compact tension test specimens. A good prediction is obtained by comparing the model results with experimental data which are obtained from center‐cracked specimens manufactured using different lay‐ups orientations and materials. POLYM. ENG. SCI., 54:234–238, 2014. © 2013 Society of Plastics Engineers     

Development and evaluation of TiB2–AlN ceramic composites sintered by spark plasma

Titanium diboride (TiB₂) is a ceramic material with high mechanical resistance, chemical stability, and hardness at high temperatures. Sintering this material requires high temperatures and long sintering times. Non-conventional sintering techniques such as spark plasma sintering (SPS) can densify materials considered difficult to sinter. In this study, TiB₂–AIN (aluminum nitride) composites were sintered by using the SPS technique at different sintering temperatures (1500 °C, 1600 °C, 1700 °C, 1800 °C, and 1900 °C). x-ray diffraction was used to identify the phases in the composites. mechanical properties such as hardness and indentation fracture toughness was obtained using a vickers indenter. Different toughening mechanisms were identified, and good densification results were obtained using shorter times and lower temperatures than those previously reported.     

Fracture toughness evaluation of polytetrafluoroethylene

The objective of this preliminary work was to explore the fracture resistance of polytetrafluoroethylene (PTFE) (DuPont tradename Teflon) as part of materials characterization work related to the development of “reactive” material projectiles. Little mechanical property data is available on this material since it is commonly used only as a coating material with the dominant properties being its low friction coefficient and high application temperature. Additional end products of the “7C” derivative, however, includes sheet, gaskets, bearing pads, piston rings, and diaphragms. In this work, standard ASTM E1820 fracture toughness specimens were machined from a 14‐mm‐thick sheet of this material obtained from NSWC Dahlgren Laboratory. These specimens were tested at three test temperatures and four test rates to determine if fracture would occur in this material, and if so, how the fracture toughness depends on the test temperature and specimen loading rate. Standard axial tensile specimens were also tested at quasi‐static and elevated loading rates at temperatures from ambient to ?73°C. The major results are that while crack extension is difficult at ambient (20°C) temperature, for temperatures slightly below ambient, a rapid degradation of fracture resistance occurs. This reduction in fracture resistance is enhanced by rapid loading, and the material loses approximately 75% of its toughness (fracture energy absorption ability) at ?18°C if the crack opening loading rate of the C(T) specimen approaches 0.25 m/s. Further reductions in temperature or increases in the loading rate appear to result in a reduced rate of degradation of fracture toughness.     

Environmental effects on thermoplastic and elastomer toughened cyanate ester composite systems

The effects of temperature and moisture on thermal and mechanical properties of high‐temperature cyanate ester composite materials were investigated. A resin transfer molding process was used to impregnate glass fiber fabrics with matrices that underwent thermoplastic or elastomeric toughness modifications. The elastomer‐modified material obtained the highest mode I fracture toughness values primarily because the toughener did not phase separate. Extended exposure to 200°C, however, deteriorated initial toughness improvements regardless of the modifier utilized. Although the thermal stability was increased by using thermoplastic modifiers in comparison to the elastomer‐modified material, the degradation was mainly governed by the cyanate ester network. Gaseous degradation products caused delaminations and therefore reduced strength when the materials were exposed to 200°C for 1000 h. Also, upon immersion in water at 95°C, the matrices absorbed up to 3.3 wt % more than previous values reported in the literature. Fiber/matrix interfacial phenomena were responsible for this behavior because fiber/matrix adhesion also was reduced drastically as shown by the strong reduction in flexural strength. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 556–567, 2000     

Delamination characteristics of multi‐directional carbon fiber/epoxy composites under high pressure

It was shown in a previous study that for unidirectional (0‐deg) graphite/epoxy composites, the fracture toughness under hydrostatic pressure increased 38% as hydrostatic pressure increased from 0.1 MPa to 200 MPa. This work investigates the compressive delamination behavior of multi‐directional graphite/epoxy laminated composites subjected to various hydrostatic pressures. Compressive delamination tests were performed under four hydrostatic pressure levels: 0.1, 100, 200, and 300 MPa Eighty‐eight‐ply dog‐bone type specimens with a single delamination at the center of the specimen were used. The stacking sequence applied was [0°/±45°/90°]_lls. The compliance and fracture load were determined from load‐displacement curves as a function of hydrostatic pressure. The results show that the compliance decreases with increasing pressure while fracture load increases with increasing pressure. The compressive delamination toughness, G_c, was determined from the compliance method as a function of applied hydrostatic pressure. The results also show that G_c is significantly affected by hydrostatic pressure and increases from 2.11 kJ/m² to 3.04 kJ/m2 (44% increase) as hydrostatic pressure increased from 0.1 MPa to 300 MPa. Visual examination of the fractured surface revealed that the increase of G_c is due to the suppression of micro‐cracks With increasing pressure. It was also found from SEM examination of delaminated surface that the G_c increase is due to more epoxy adhering to the fibers and more plastic deformation of epoxy material as applied hydrostatic pressure increases.     

Effect of Crystallites on Surface Damage and Fracture Behavior of a Glass-Ceramic

A study was conducted of the effect of crystallization on the fracture toughness, strength, and resistance to surface damage of glass-ceramic materials with a range of microstructures obtained by different heat treatments. The hardness indentation method was used as a quantitative tool to simulate mechanical surface damage. In the uncrystallized glass and in the glass-ceramic heat-treated to result in a uniform fine-grained structure, crack size increased monotonically with indentation load. In contrast, in the glass-ceramics heat-treated to result in a microstructure consisting of larger crystallites (a few micrometers) contained within a fine-grained matrix, a discontinuity in the crack size vs load curve presented evidence for crack-pinning at crack sizes which were a small multiple of the intercrystallite spacing. At the position of crack-pinning, the fracture toughness showed a discontinuous increase with increasing crack size that was attributed to crack deflection. The strength of the glass and fine-grained glass-ceramic measured in biaxial flexure decreased monotonically with indentation load. The strength at low values of indenter load of the glass-ceramic heat-treated to yield the coarser crystallites within the fine-grained matrix was independent of indentation load, indicating stable crack propagation prior to fast fracture. At the higher values of indenter load, the coarse-grained glass-ceramics exhibited a monotonic decrease in strength with increasing indentation load. The results of this study indicate that the strengthening observed on crystallization of a glass can be attributed to a combination of a decrease in flaw size achieved at a given mechanical surface treatment, an increase in fracture toughness, and a modification in the mode of crack propagation.     

High-toughness mullite ceramics fabricated by hot-press sintering of pyrophyllite and AlOOH at low temperatures

High-toughness mullite ceramics were fabricated through hot-press sintering (HPS) of pyrophyllite and AlOOH, which were wet-milled and well mixed using a planetary ball mill. The impacts of sintering temperatures and contents of AlOOH on mullite phase formation, densification, microstructure and mechanical properties in ceramic materials were investigated through XRD, SEM and mechanical properties determination. The results indicated that high-toughness mullite ceramics could be successfully prepared by HPS at temperatures higher than 1200°C for 120 min. Increasing the sintering temperature from 1000 to 1300°C significantly enhanced the flexural strength and fracture toughness of samples. The highest flexural strength of 297.97±25.32 MPa and fracture toughness of 4.64±0.11 MPa⋅m^1/2 were obtained for samples sintered at 1300°C. Further increase of temperature to 1400°C resulted in slight decrease of flexural strength and fracture toughness. Compared with the mullite ceramics prepared only using pyrophyllite as raw material, incorporation of AlOOH into raw material significantly increased the mechanical properties of final mullite ceramics. And stoichiometric AlOOH and pyrophyllite as starting material gave the best performance in fracture toughness. The high-toughness of mullite ceramics were ascribed to the high mullite phase content, fine mullite whiskers and in situ formed, intertwined three-dimensional network structure obtained through HPS at a low temperature of 1300°C.     

Fracture behavior of solid electrolyte LATP material based on micro-pillar splitting method

The NASICON type solid electrolyte LATP is a promising candidate for all-solid-state Li-ion batteries considering energy density and safety aspects. To ensure the performance and reliability of batteries, crack initiation and propagation within the electrolyte need to be suppressed, which requires knowledge of the fracture characteristics. In the current work, micro-pillar splitting was applied to determine the fracture toughness of LATP material for different grain orientations. The results are compared with data obtained using a conventional Vickers indentation fracture (VIF) approach. The fracture toughness obtained via micro-pillar splitting test is 0.89 ± 0.13 MPa?m^1/2, which is comparable to the VIF result, and grain orientation has no significant effect on the intrinsic fracture toughness. Being a brittle ceramic material, the effect of pre-existing defects on the toughness needs to be considered.     

Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with vickers indenter

Virtual crack closure technique and elastoplastic finite element method were employed to calculate the stress intensity factors (SIF) of ceramic materials on the tip of both half‐penny crack (HPC) and radial crack (RC) induced by Vickers indenter and the value of fracture toughness (K_IC) was extracted by the design of equi‐SIF contour of HPC and RC crack front. Through dimensional theorem and regressive analysis, a functional relationship between instrumented indentation parameters, crack length of Vickers impression and fracture toughness of ceramic materials was established, thus a novel methodology has been presented for measuring fracture toughness of ceramic materials by instrumented Vickers indentation. Both numerical analysis and experiments have indicated that this methodology enjoys higher measurement precision compared with other available indentation methods. The methodology is universally suitable for HPC, RC as well as transition cracks and capable of determining fracture toughness and elastic modulus in a single indentation test. In addition, it saves the effort of measuring the diagonal length of Vickers impression in case that the impression remains unclear.     

Investigation of fracture behavior of cement-bonded corundum castables using wedge splitting test and digital image correlation method

To investigate the fracture behavior of cement-bonded corundum castables, various cement contents and pre-treating temperatures have been comparatively studied using the wedge splitting method and the digital image correlation technique. The results show that the microstructure enhances the mechanical properties, so the fracture energy and the maximum load as well as the fracture modes are affected correspondingly. The castables demonstrate the highest fracture energy and maximum load at 1600 °C with cement content of 10 wt% due to an appropriate amount of CA6. At the temperatures of 110 and 1100 °C, the crack propagation within the matrix and along the interface are dominated whereas within the aggregates significantly increased at 1600 °C, leading to the brittleness of materials. However, increasing the cement content can reduce their brittleness, caused by the maximum strain in thex-direction, largest length of the main crack, and high ratio of crack propagation in the matrix.     

Brittle Fracture versus Quasi Plasticity in Ceramics: A Simple Predictive Index

Simple relations for the onset of competing brittle and quasi-plastic damage modes in Hertzian contact are presented. The formulations are expressed in terms of well-documented material parameters, elastic modulus, toughness, and hardness, enabling a priori predictions for given ceramics and indenter radii. Data from a range of selected ceramic (and other) materials are used to demonstrate the applicability of the critical load relations, and to evaluate coefficients in these relations. The results confirm that quasi plasticity is highly competitive with fracture in ceramics, over a sphere radius range 1–10 mm. Implications concerning the brittleness of ceramics in the context of indentation size effects are discussed.     

Thermal and mechanical properties of Sc2O3–CeO2 co-stabilized zirconia ceramic as promising thermal barrier coating material

CeO₂ and Sc₂O₃ co-stabilized ZrO₂ ceramics have attracted much attention as potential thermal barrier coatings (TBCs) materials for applications above 1300 °C. In this study, a series of Sc_0.04Ce_xZr_0.96-xO_1.98 (SCZ, x = 0.08, 0.10, 0.12, 0.16) ceramic materials were synthesized with the solid-state method and their phase stability, microstructures and thermo-physical properties were systemically investigated by x-ray diffraction (XRD), Raman spectra, field emission scanning electron microscopy (SEM), thermal dilatometer, laser flash apparatus (LFA), and Vickers hardness tester. The results showed that Sc_0.04Ce_0.12Zr_0.84O_1.98 (4S12CZ) and Sc_0.04Ce_0.16Zr_0.80O_1.98 (4S16CZ) ceramic materials still maintained stable tetragonal phase structure after 100 h high temperature treatment at 1500 °C. SCZ had a high thermal expansion coefficient (TEC), low thermal conductivity, and high fracture toughness. The TEC of the ceramics increased with CeO₂ addition because lattice energy reduced with increasing substitution of Zr⁴⁺ by bigger Ce⁴⁺ while thermal conductivity decreased due to the increase of lattice distortion. Compared with 4S12CZ, 4S16CZ exhibited a higher fracture toughness of 6.48 ± 0.04 MPa m^1/2 and showed the better anti-sintering property. Besides, the thermal conductivity, TEC and thermal cycling lifetime of 4S16CZ were optimal. The comprehensive performance of 4S16CZ suggested it could be explored as a promising TBC material for high-temperature application.     

An acoustic emission study on the fracture behavior of continuous glass fiber/polypropylene composites based on commingled yarn

The fracture behavior of continuous glass fiber reinforced polypropylene composites made of commingled yarn in the form of biaxial (±±45°) noncrimp warp‐knitted fabric, twill woven fabric, and swirl mat, respectively, was investigated by virtue of single edge notched tensile (SEN‐T) specimens. These composite laminates were manufactured by compression molding and cooled at two different rates (1°C/min and 10°C/min) during the last processing phase of the laminates. The failure mechanisms were studied by acoustic emission (AE) analysis. AE amplitude ranges corresponding to the individual failure modes have been identified. For biaxial noncrimp fabric reinforced materials, the failure mechanisms involved in the fracture procedure are governed by the interface related failure events. Higher cooling rate, which is accompanied by better fiber/matrix adhesion, results in not only the increase in the relative proportion of high‐amplitude failure events, but also the occurrence of a large quantity of fiber fracture events. For woven fabric and mat reinforced composites, fiber‐dominated failure mechanisms result in the higher fracture toughness when compared with biaxial noncrimp fabric composites. Under this circumstance, the change in cooling rate only results in the difference in the relative frequency of the individual failure modes. In addition, it is found out that the initiation fracture toughness of SEN‐T specimens can be easily assessed by marking the load value which corresponds to the first point of AE signals emitted stably in AE events‐displacement curves. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

Failure characterization of polypropylene block copolymer welded joints

The failure behavior of polypropylene block copolymer double-V welded joints was investigated. Joints were prepared using the hot-gas welding technique at varying gas temperatures in the range of 230–260°C. Uniaxial tensile tests, fracture mechanics experiments, several microscopy techniques, and complementary FEM analysis were carried out to assess the quality of filler rods and welding interfaces. The developed interfaces were weaker than the parent material as a consequence of polymer chains segregation during the welding process. The hot-gas temperature had a marked effect on the failure behavior of the welds. The highest interface toughness was attained at the highest gas welding temperature used at which, polymer chains were able to quickly diffuse into the parent material enlarging the distance of penetration and hence the micro-deformation capability of the joint. POLYM. ENG. SCI., 47:1062–1069, 2007. © 2007 Society of Plastics Engineers     

Analytical estimation of fracture toughness for circumferential cracks in thin hard films on ductile substrates

In this study, the fracture toughness of circumferential crack caused by indentation effect of a rigid indenter on a thin and elastic coating deposited on the elastic substrate was calculated. In the coating and substrate, the analytical solution of displacement and stress field was used. The complete adhesion was considered for the coating on the substrate. The location of maximum circumferential stress was investigated using the analytical calculation of the stress and it was found that this place was located at a distance away from the center of the indenter. Then, the stress intensity factor and energy release rate for plane strain state was determined, and consequently, the energy release rate for a channel crack was calculated. Finally, the fracture toughness was calculated with energy release rate curves for plane strain crack and crack channeling. This method was used to calculate the fracture toughness of TiN/TiCrN ceramic multilayer coating which was deposited on the GTD450 substrate using the Cathodic Arc PVD method. To validate the results, the analytically calculated crack radius was compared with the experimental crack radius in the fracture load and the difference between the radiuses was in the acceptable range.     

Fracture Toughness of Porous Material of LSCF in Bulk and Film Forms

Fracture toughness of La_0.6Sr_0.4Co_0.2Fe_0.8O_3‐δ (LSCF) in both bulk and film forms after sintering at 900°C to 1200°C was measured using both single‐edge V‐notched beam (SEVNB) 3‐point bending and Berkovich indentation. FIB/SEM slice‐and‐view observation after indentation revealed the presence of Palmqvist radial crack systems after indentation of the bulk materials. Based on crack length measurements, the fracture toughness of bulk LSCF specimens was determined to be in the range 0.54–0.99 MPa·m^1/2 (depending on sintering temperature), in good agreement with the SEVNB measurements (0.57–1.13 MPa·m^1/2). The fracture toughness was approximately linearly dependent on porosity over the range studied. However, experiments on films showed that the generation of observable indentation‐induced cracks was very difficult for films sintered at temperatures below 1200°C. This was interpreted as being the result of the substrate having much higher modulus than these films. Cracks were only detectable in the films sintered at 1200°C and gave an apparent toughness of 0.17 MPa·m^1/2 using the same analysis as for bulk specimens. This value is much smaller than that for bulk material with the same porosity. The residual thermal expansion mismatch stress measured using XRD was found to be responsible for such a low apparent toughness.     

Fracture toughness of single grains and polycrystalline Li7La3Zr2O12 electrolyte material based on a pillar splitting method

In the present study an advanced pillar splitting method is used to determine the fracture toughness of a garnet-type Li₇La₃Zr₂O₁₂ (LLZO) electrolyte. The obtained results are compared to data derived on the basis of conventional Vickers indentation. Furthermore, potential micro-pillar size effects are investigated. The estimated fracture toughness values for single grains and polycrystalline LLZO material obtained via both methods are in good agreement, yielding ∼ 1 MPa m^0.5, hence the data indicate that LLZO exhibits relatively low fracture toughness and has a brittle behavior.     

Fracture behavior of die‐drawn toughened polypropylenes

The Leeds die‐drawing process has been used to make oriented sheets of toughened polypropylenes. Die‐drawn oriented sheets were produced by drawing at 110°C to draw ratios of 4, 6, and 10. Comparative measurements have been undertaken of the plane stress fracture toughness at room temperature using the essential work of fracture method for isotropic and oriented polypropylene homopolymer and the two polypropylene blends containing 10 and 25% of a polyethylene‐based elastomer. In the isotropic state, the blend containing 25% elastomer exhibited higher fracture toughness than the homopolymer and the 10% blend. The oriented sheets were tested both parallel (cracks perpendicular to the draw direction) and perpendicular (cracks parallel to the draw direction). For the latter case of cracks parallel to the draw direction, the fracture toughness of all the materials decreased with increasing draw ratio and up to a draw ratio of 4 the 25% blend exhibited higher fracture toughness than the other two materials. At higher draw ratios, however, the unfilled polypropylene was tougher than the blends. When tested parallel to the draw direction, all three materials failed with the cracks growing slowly initially followed by sudden rupture. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1336–1345, 2003