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In this study, numerical simulation analysis on fracture of girth welds on pipelines with crack defect and small Single Edge Notch Beam(SENB) was performed with the finite element method for accurately characterizing the correlation of apparent fracture toughness of the girth welds on high-grade steel pipelines and the small specimens. The conversion coefficient of apparent fracture toughness was introduced by comparing the difference of apparent fracture toughness of the girth welds on full-scale pipelines and the SENB specimens. Conversion coefficients between full-scale pipelines and SENB specimens under different working conditions were obtained by quantitatively studying the impact of pipe diameter, wall thickness, crack length and depth on the apparent fracture toughness of girth welds on full-scale pipelines, realizing quantitative characterization of the apparent fracture toughness of girth welds on high-grade steel pipelines based on the test results of small specimens. The results indicate that the pipe diameter has little effect on the apparent fracture toughness and its conversion coefficient. The conversion coefficient of fracture toughness increases with the increasing of wall thickness and decreases with the increasing of crack length and depth. The effect of crack depth on the apparent fracture toughness of pipelines is more obvious than other influencing factors. A relatively accurate apparent fracture toughness of girth welds on high-grade steel pipelines can be obtained based on the conversion coefficient, providing theoretical reference for accurately characterizing the apparent fracture toughness of girth welds on high-grade steel pipelines.

• The apparent fracture toughness of sandstone is significantly influenced by the cracked specimen configurations and loading types. • The difference of T-stress for various cracked specimens is the primary factor causing the disparity in apparent fracture toughness. • Positive T-stress can improve the K IC , while negative T-stress will decrease the K IC. The dependence of K IIC on the T-stress is exactly opposite to that of K IC. In order to investigate the impact of cracked specimen configurations on the apparent fracture toughness of the green sandstone, a series of fracture experiments were conducted utilizing four distinct types of specimens. The experimental results show that the cracked straight-through Brazilian disk (CSTBD) specimens observed the minimum mode I fracture toughness K IC and the maximum mode II fracture toughness K IIC. The K IC measured by notched semi-circular bending (NSCB) specimens is nearly twice that of CSTBD specimens, while the K IIC is only 77% of CSTBD specimens. It indicates that both the specimen configurations and loading conditions are significant factors influencing the apparent fracture toughness, which may be attributed to the different T-stress for different specimens. Furthermore, several fracture criteria were employed to evaluate the experimental results. Simultaneously, a theoretical framework based on the generalized maximum tangential strain (GMTSN) criterion was proposed to investigate the impact of T-stress on apparent fracture toughness. The results indicate that positive T-stress can improve the K IC , while negative T-stress can decrease the K IC. In addition, we also found that the dependence of K IIC on T-stress is exactly opposite to that of K IC. The study provides theoretical references for systematically evaluating experimental results and selecting specimens reasonably. [ABSTRACT FROM AUTHOR]

In this research, size effects on the mode I notch fracture toughness of polymeric specimens weakened by a rounded-tip V-shaped (RV) notch are investigated experimentally and theoretically. For this purpose, multiple fracture tests are performed on the RV-notched Brazilian disk (RVNBD) and RV-notched semicircular bend (RVNSCB) polymeric samples with four different scales. Then, the fracture loads measured from the experiments are converted to the notch fracture toughness using finite element analysis. The experimental results show that the mode I notch fracture toughness is significantly dependent on the nominal dimension (radius) of RVNBD and RVNSCB samples, so by increasing the sample radius, the mode I notch fracture toughness increases. In order to justify the size dependency of notch fracture toughness, a modified form of the point stress criterion is proposed. The value of critical distance rc in the modified point stress (MPS) criterion is considered to be size-dependent. Subsequently, a semiempirical relation is used for describing this size dependency. It is revealed that the MPS criterion is able to predict the size-dependent value of notch fracture toughness for both RVNBD and RVNSCB samples made of polymeric materials well. [ABSTRACT FROM AUTHOR]

The freeze–thaw damage, particularly in cold region, occurs frequently when concrete structures lose their durability. In this study, the dynamic mechanical properties of concrete after 0, 50, 100, 150 cycles of freeze–thaw are investigated. The microstructure of concrete associated with freeze–thaw damage is observed by mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) technologies. According to the experimental data, the influences of the freeze–thaw cycles and the loading rate on the dynamic mechanical properties are analysed, respectively. It is shown that the apparent dynamic splitting tensile strength and the apparent dynamic fracture toughness of the specimen both decrease with the increase of the freeze–thaw cycles and the loading rate. On the basis of MIP results, it is found that the porosity, the most probable pore size and the critical diameter of the concrete all increase with the increase of the cycles of freeze–thaw. The micrographs obtained from SEM illustrate that the development of cracks and the production of crystals are dominant performances reflecting the damage of concrete under freeze–thaw cycles. In addition, the freeze–thaw cycles can induce dissolution of the specimen, which benefits the growth of the crystal ettringite. [ABSTRACT FROM AUTHOR]

Face-centred cubic (fcc-) Mo–N and Ta–N exhibit an inherent driving force for vacancy formation. To study their interaction and effects on structural evolution and mechanical properties, we synthesised Mo–Ta–N coatings by reactive magnetron sputtering using nitrogen-to-total pressure ratios, pN2/pT, of 0.32 and 0.69.Low pN2/pT results in high concentration of N vacancies, which stabilise single-phase fcc-Mo1-xTaxNy up to x = 0.76. These solid solutions follow the MoN0.5–Ta0.875N0.875 quasi-binary tie line. Compressive residual stresses, σ, indentation hardness, H, and toughness, KC, increase with Ta content, reaching their maxima of (on average) -2.0 GPa, 28 GPa, and 7.0 MPa√m, respectively, within the x range 0.38–0.69. Higher Ta contents favour higher concentration of metal vacancies deteriorating the properties.High pN2/pT favours the formation of fcc-Mo1-xTaxNy rich in metal vacancies, which however always coexists with a hexagonal phase. Within the x range 0.33–0.66, the fraction of the hexagonal phase is negligible, and σ, H, and KC deviate from −1.0 GPa, 28 GPa, and 2.9 MPa√m, respectively, within the error of measurements.The combination of experimental and theoretical studies demonstrates the power of point defects in stabilising desired crystal structures and improving mechanical properties through the thereby tuned atomic configuration.

To clarify the direction of microstructure design for improving stretch-flangeability, relationships of stretch-flangeability to microstructure and mechanical properties of ultra-high-strength dual-phase (DP) steels were investigated. Microstructure of relatively simple ferrite-martensite DP steels was modified by intercritical annealing, then the effects of microstructure modification on stretch-flangeability, tensile properties, and fracture resistance of the DP steels were systematically quantified. The hole-expansion ratio (HER) increased linearly with an increase the apparent fracture initiation energy, but was not significantly correlated with any individual microstructural properties of DP steels, which have been reported to correlate with HER (e.g., the fraction of martensite, the carbon content of martensite, or the hardness difference between ferrite and martensite). To increase the stretch-flangeability of an ultra-high-strength DP steels, its microstructure should be designed to increase its fracture toughness (i.e., microstructure with low mechanical heterogeneity). [ABSTRACT FROM AUTHOR]

This work presents experimental data to determine the apparent fracture toughness, K Q , from hydraulic fracturing in a penny-shaped crack for frozen sand. An initial crack, represented by a circular plastic, is embedded in the specimen during the preparation with a pipe positioned perpendicular to the center of the circular crack in order to inject liquid into the penny-shaped crack. In determining the K Q , the first approach directly utilizes the penny-shaped crack stress-intensity factor (SIF), which requires the hydraulic pressure and crack radius dimension. The second approach combines the volume in the penny crack with the SIF, in which K Q is determined without using the crack radius dimension. The third approach (brittleness) explores the stress in the uncracked ligament to estimate the tensile strength ( σ t ) and characteristic length ( l c h ), which is related to the apparent fracture toughness. The K Q from these hydraulic fracturing approaches are validated via three-point bend (TPB) on notched and unnotched beams for frozen sand, using the same dimensions and preparation method. The hydraulic fracturing experimental results indicated that the values of K Q , σ t , and l c h for frozen sand are 0.22–0.66 MPa√m, 7.5–9.5 MPa, and 0.8–7.6 mm, respectively, which are comparable to the TPB results. An important outcome of this work allows for the determination or estimation of K Q , σ t and l c h for a material like methane hydrate in sand that is difficult to obtain using the standard test setup under the atmospheric conditions. [ABSTRACT FROM AUTHOR]

This work examines the susceptibility of methane hydrate in sand to fracture. The task is made difficult because of two challenges: (1) the means to conduct hydraulic fracturing experiments under high pressure and low temperature conditions, and (2) the formation of high saturation hydrate-bearing sand. The apparent fracture toughness ( K Q ) of a material is usually determined via conducting standard tests such as three-point bend on notched beams or pull test on compact specimens. In Part I, Too et al. (2018) , hydraulic fracturing in a penny-shaped crack was found able to determine K Q and estimate the tensile strength of frozen sand. As such, experiments were conducted using the similar approach on the synthesized high saturation methane hydrate-bearing sand specimens (approximately 50–75%) with sample size of 80 mm in diameter and 150 mm in length. The range of K Q determined is between 0.3 and 1.4 MPa√m while the tensile strength estimated ranges between 6 and 12.5 MPa for the hydrate saturation range. The possibility of creating artificial fractures in synthetic methane hydrate-bearing sand may present an opportunity to improve the gas production from natural occurring hydrate-bearing sand. [ABSTRACT FROM AUTHOR]

Multipass friction stir processing (FSP) was performed on as-cast (AC) AZ91 magnesium alloy with different tool probe lengths to introduce layered microstructure through the thickness. Three microstructural variations were developed. They were, half thickness fine grain microstructure (HFG), surface modified-fine grain microstructure (SFG) and full thickness fine grain microstructure (FFG). FSP was performed at tool rotation rate of 720 rpm and transverse speed of 150 mm/min. The coarse α-Mg dendrites of 100 μm were refined to approximately 2 μm. Network of β-Mg 17 Al 12 interdendritic particles were broken and distributed uniformly after multipass FSP. Tensile test and notch fracture toughness test were conducted to understand the effect of layered microstructure on mechanical properties. The tensile properties, namely, yield strength, tensile strength and percentage elongation of AC material were found to be 92 MPa, 100 MPa and 0.8% respectively and the corresponding values for FFG were improved to 242 MPa, 327 MPa and 4.7%. For HFG and SFG, these values were found to follow the rule of mixture. Similarly, apparent fracture toughness (K Q ) values of single edge notch bend (SENB) specimen without precrack were compared and the results showed improvement from 6.2 MPa√m in AC to 12.3 MPa√m in FFG. [ABSTRACT FROM AUTHOR]

The paper analyses the fracture behaviour of several rocks, namely a sandstone, a limestone and two marbles, one of them being a Carrara marble. The experimental program comprises in total 216 fracture specimens, tested in 4-point bending conditions and including specimens with notch radii varying from 0.15 mm up to 15 mm. The notch effect is analysed through the evolution of the apparent fracture toughness and the application of the Theory of Critical Distances. The present study aims to generalize a previous study on a granite and a limestone to a broader range of rocks. The point and line methods of the Theory of the Critical Distances successfully explain the notch effect on the fracture specimens. The value of the critical distance of these rocks is of the order of mm. Finally, the results show a correlation between the microstructural features of the rocks, specifically the grain size, and their critical distances. [ABSTRACT FROM AUTHOR]

When the structural integrity of notched components is analysed, it is generally assumed that notches behave as cracks, something which generally provides overconservative results. Thus, it is necessary to derive models that take into account the higher fracture resistance developed by structural materials when notches (and not cracks) are present. In this sense, the use of the Theory of Critical Distances (TCD) for the estimation of the apparent fracture toughness ( K N c ) observed in notched components has been validated for different types of materials, such as ceramics, polymers, composites and metals. The estimations, for U-shaped notches, arise from the combination of the TCD with the Creager-Paris stress distribution ahead of the notch tip, and apply a notch correction factor to the material fracture toughness observed in cracked conditions ( K c ). Such correction only depends on the geometry (notch radius) and the material critical distance ( L ). The latter is the critical issue when applying the TCD, given that it generally requires calibration through experimental results and simple statistics (best fitting), or through a combination of experimental results with finite elements modelling. This paper provides some default safe values of the material inherent strength that may be used to derive safe estimates of the corresponding value of L , without any further calibration, to be finally used in the apparent fracture toughness predictions and subsequent structural integrity assessments. [ABSTRACT FROM AUTHOR]

The relation of the non-singular opening stress component with apparent fracture toughness was investigated for unidirectional carbon-fiber laminates by means of double cantilever beam experiments in which laminate thickness was varied. It was found that a sample configuration with smaller thickness related to a higher apparent fracture toughness measurement. This result was explained by the presence of a negative non-singular opening stress component, which was found to decrease with thickness. The experimental procedure utilized first crack propagation from the initial polytetrafluoroethylene insert to avoid ambiguity of defining crack location due to crack curving, resulting in a wider crack front and fiber bridging. The two dimensional finite element analyses were used to calculate the corresponding singular and non-singular stress components and the energy release rates. Based on the experimental results a two parameter linear elastic fracture mechanics model was calibrated to incorporate the thickness dependence of the apparent fracture toughness. [ABSTRACT FROM AUTHOR]

This paper analyses the structural integrity of components containing U-shaped notches by combining Failure Assessment Diagrams and the Line Method correction for notch effects. With this objective, the experimental results obtained in 555 fracture tests are homogeneously evaluated in the same Failure Assessment Diagram, with and without applying the Line Method notch corrections, and covering a wide range of materials such as PMMA, Al7075-T651, four different structural steels (S275JR, S355J2, S460M and S690Q) tested at different temperatures from the Lower Shelf up to the ductile-to-brittle transition zone, and two rocks (granite and limestone). It is demonstrated that the proposed methodology generally produces significant reductions in the conservatism associated to notch effects, yet providing safe predictions. [ABSTRACT FROM AUTHOR]

This paper analyses the capacity of the Line Method to provide evaluations of the apparent fracture toughness, which is the fracture resistance exhibited by materials in notched conditions. With this aim, the experimental results obtained in 555 fracture tests are homogeneously presented and compared to the Line Method evaluations. It is remarked that the Line Method provides adequate estimates of the apparent fracture toughness, and also that it conveniently addresses the physics of the notch effect. All this makes the Line Method a valuable scientific and engineering tool for the fracture assessment of materials containing notches. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of the notch effect in two ferritc-pearlitic steels: S275JR and S355J2. The research is based on the development and analysis of an experimental programme composed of 336 CT specimens, combining 6 different notch radii, and testing temperatures from the lower shelf up to the upper shelf of the two materials. The notch effect is analysed through the evolution of both the load bearing capacity and the apparent fracture toughness, and also through the relation between these two variables and the failure micromechanisms. The results reveal a clear notch effect in both materials. In the case of the load bearing capacity, this notch effect has its maximum at lower shelf temperatures. The notch effect in the apparent fracture presents a maximum at the lower temperatures of the ductile-to-brittle transition zone. Finally, the Scanning Electron Microscopy fractographies have justified the previous observations. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the analysis of the notch effect on granite and limestone fracture specimens. The research is based on the results obtained in an experimental programme composed of 84 fracture specimens, combining the two materials and 7 different notch radii varying from 0.15mm up to 10mm. The notch effect is analysed through the evolution of the apparent fracture toughness and the application of the Theory of the Critical Distances. The results reveal a significant notch effect in the limestone, whereas the notch effect in the granite is negligible for the range of notch radii analysed. Both observations are justified by the corresponding critical distance of the material. [Copyright &y& Elsevier]

Highlights: [•] It is performed an analysis of the notch effect in two ferritic–pearlitic steels operating in the lower shelf. [•] Apparent fracture toughness predictions provided by the Theory of Critical Distances are validated. [•] This theory provides reasonable predictions of the material apparent fracture toughness. [•] It is also shown a direct relation between fracture mechanisms and apparent fracture toughness. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis of the notch effect in the load bearing capacity, the apparent fracture toughness and the fracture mechanisms of four different materials: polymer PMMA, aluminium alloy Al7075-T651, and structural steels S275JR and S355J2 within their corresponding ductile-to-brittle transition zone. Concerning the load bearing capacity and the apparent fracture toughness, a clear notch effect has been observed. In the case of the apparent fracture toughness, this has been adequately predicted here through the Theory of Critical Distances. As for fracture mechanisms, it is shown how these progressively change with the notch radius, from basically brittle ones in cracked conditions, to non-linear mechanisms observed for higher notch radii. This evolution has been observed in the four analysed materials and, in all cases, has justified the corresponding consequences of the notch effect on both the load bearing capacity and the apparent fracture toughness. [Copyright &y& Elsevier]

Abstract: The Theory of Critical Distances is actually a group of methodologies, all of them using a characteristic material length parameter when performing fracture assessments on any kind of stress risers. In this paper, the application of the Theory of Critical Distances on Polymethyl methacrylate is analysed, the parameters involved in the analysis are calibrated, and the different versions of this theory are applied, with satisfactory results, to the prediction of the notch effect on the apparent fracture toughness measured on notched specimens. Also, a Scanning Electron Microscopy analysis is performed, establishing relations between the fracture mechanisms and the predictions provided by the Theory of Critical Distances. [Copyright &y& Elsevier]

Abstract: Argillites are considered worldwide as potential host rock for high level radioactive waste given the low permeability and strong adsorption potential. However, the excavation of the galleries of a repository would produce a disturbed zone around the boundaries rich of new fractures which may enhance the conductivity of the rock along the gallery axis. Several mine-by experiments have been performed in underground rock labs to investigate the features of the disturbed zone. In Mont Terri URL (Kanton Jura, Switzerland) the EZ-B experiment was specifically conceived for the measurement of excavation induced fractures around a small chamber. The host rock of the URL is a particularly compact and resistant argillite, known as the Opalinus Clay (OPA) excavated and OPA samples were subjected to fracture mechanics tests at the rock mechanics lab of IGAG-CNR in Torino, Italy. The tests aimed at the understanding aspects of the fracturing process occurring in OPA of Mont Terri, which may be considered a transversely isotropic geomaterial, whose planes of isotropy coincide with the bedding. [Copyright &y& Elsevier]

Abstract: The Point Method and the Line Method are two approaches derived from the Theory of Critical Distances, used in conjunction with a characteristic material length parameter when performing fracture assessments on any kind of stress risers, including notches. This paper analyses the application of both the Point Method and the Line Method for the prediction of the notch effect on the aluminium alloy Al7075 in T651 conditions. The parameters involved in the analysis are calibrated through a combination of experimental tests and finite elements modelling, and a comparison is made between the experimental results and the predictions provided by these two approaches. Also, a Scanning Electron Microscopy analysis is performed, establishing relations between the fracture mechanisms and the predictions provided by the Theory of Critical Distances. The results obtained demonstrate the suitability of the Point Method and the Line Method for the analysis of notches. [Copyright &y& Elsevier]

Abstract: This paper illustrates the need to develop specific methodologies for the assessment of notched structural components. These are usually analysed under the assumption that notches behave as cracks, providing results that may be overconservative. The proposal consists, on the one hand, in the application of the Theory of Critical Distances for the estimation of the apparent fracture toughness, and for the conversion of the notched situation into an equivalent cracked situation in which the material develops a higher fracture resistance (the apparent fracture toughness). On the other hand, once the apparent fracture toughness has been defined, the assessment is performed using the Failure Assessment Diagram methodology, and assuming that the notch effect on the plastic collapse load is negligible. The methodology has been applied to notched fracture specimens made of PMMA and Al7075-T651, providing satisfactory results and a noticeable reduction in the overconservatism derived from analyses in which the notch effect is not considered. [Copyright &y& Elsevier]

Abstract: This study describes the effect of FGM coating thickness on apparent fracture toughness (AFT) of a thick-walled cylinder containing two diametrically-opposed edge cracks emanating from the inner surface of the cylinder. The incompatible eigenstrain developed in the cylinder due to nonuniform coefficient of thermal expansion because of cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress intensity factor (SIF) addressed in a previous study, an approach is developed to calculate AFT. Some numerical results of AFT are presented for a TiC/Al2O3 FGM coating at the inner surface of an Al2O3 thick-walled cylinder. [ABSTRACT FROM AUTHOR]

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to KII and non-singular T-stresses T x and T y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2 T x = T y ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model. [ABSTRACT FROM AUTHOR]

Abstract: The paper presented deals with the fracture behaviour of ceramic laminates. The residual stresses in individual layers of Al2O3/5vol.%t-ZrO2 (ATZ) and Al2O3/30vol.%m-ZrO2 (AMZ) are determined. Assumptions concerning linear elastic fracture mechanics and small scale yielding are considered. In this frame the procedure based on a generalization of Sih’s strain energy density factor to the case of a crack touching the interfaces between two dissimilar materials is used for determination of effective values of the stress intensity factor on material interfaces. An important increase of fracture toughness at the AMZ/ATZ interface was predicted in comparison to the fracture toughness of individual material components. Predicted values were compared with data available in the literature and mutual good agreement was found. The procedure suggested can be used for estimation of resistance to crack propagation through multilayered structures and its design. The procedure can contribute to enhancing the reliability and safety of structural ceramics or, more generally, of layered composites with strong interfaces. [Copyright &y& Elsevier]

This study focuses on the analysis of apparent fracture toughness of a thick-walled functionally graded material (FGM) cylinder with two diametrically opposed edge cracks emanating from the inner surface of the cylinder. The crack surfaces and the inner surface of the cylinder are subjected to an internal pressure. The incompatible eigenstrain developed in the cylinder due to non-uniform coefficient of thermal expansion after cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress-intensity factor developed in our previous study, an approach is presented to evaluate apparent fracture toughness. To demonstrate the approach, some numerical results of apparent fracture toughness are presented for a TiC/Al2O3 FGM cylinder. The effects of material distribution, cylinder wall thickness, application temperature and number of cracks on apparent fracture toughness are investigated in details. It is found that all these factors play an important role in controlling apparent fracture toughness of a thick-walled FGM cylinder. [ABSTRACT FROM AUTHOR]

TiN-matrix coating was prepared by reactive high velocity oxygen fuel (HVOF) spraying on carbon steel based on the self-propagating high temperature synthesis (SHS) technique in air. The phase composition, structures, and properties of TiN-matrix coating were analyzed using XRD, EDS, SEM and Vickers microhardness equipment. The anti-corrosion property in nearly neutral 3.5 wt% NaCl electrolytic solution was measured. The Weibull distribution of Vickers microhardness at different loads and their linear fitting were analyzed. The apparent fracture toughness of the coating was also calculated. The coating is composed of main phases (TiN, TiN0.3), minor phases (Ti2O3, TiO2), and porosity. The anti-corrosion property of an HVOF-sprayed TiN-matrix coating in electrolytic solution is superior to that of AISI 316L stainless steel. The microhardness values from 1137HV0.05 to 825HV1 are relatively high and have indentation size effect (ISE). With the increment of m, which increases with the increment of applied load, the microhardness values are more concentrated. The average value of apparent fracture toughness K IC is $$ 4.62\,\hbox{MPa} \cdot m^{{\frac{1} {2}}} $$. It is higher than that of reactive plasma sprayed (RPS) TiN coating, which reflects the good toughness of a TiN-matrix coating deposited by reactive HVOF spraying. [ABSTRACT FROM AUTHOR]

Abstract: This study concerns the inverse problem of evaluating the optimum material distribution for desired fracture characteristics in a thick-walled functionally graded material (FGM) cylinder containing two diametrically-opposed edge cracks emanating from the inner surface of the cylinder. The thermal eigenstrain developed in the cylinder material due to nonuniform coefficient of thermal expansion as a result of cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress intensity factors developed in a previous study, an inverse method is developed to optimize material distribution intending to realize prescribed apparent fracture toughness in the FGM cylinder. To present some numerical results, a TiC/Al2O3 FGM cylinder is considered and the inverse problems are solved to evaluate material distributions for two examples of prescribed apparent fracture toughness. The effect of cylinder wall thickness on the material distribution and comparison of material distributions corresponding to a single and two cracks are also discussed. The numerical results reveal that the apparent fracture toughness of FGM cylinders can be controlled by choosing the material distributions properly. [Copyright &y& Elsevier]

In this study, the intrinsic static/dynamic fracture toughness of advanced glass ceramic is evaluated from the apparent static/dynamic fracture toughness of a notched specimen. A critical average stress fracture model is suggested to establish the relationship for predicting the intrinsic fracture toughness from the apparent fracture toughness of a notched specimen. The critical average stress fracture model is established using the relationship between the notch root radius and the effective distance calculated by finite element analysis. The effective distance is the major characteristic describing stress distributions ahead of the notch tip. Therefore, the effective distance can be used to evaluate the behavior of structures containing notches. It is concluded that the true fracture toughness can be estimated from test results of apparent fracture toughness measured by using a notched specimen. Also, the effective distance can be used to evaluate the failure criterion of structures with notches. [ABSTRACT FROM AUTHOR]

Abstract: Two different Si3N4–TiN based micro-laminates were successfully designed and manufactured (by tape casting) with a rising R-curve behaviour. These laminates were successfully designed to have maximum apparent fracture toughnesses of 10.5 and 18.0MPam1/2. Thin compressive Si3N4 layers of 50μm thickness were used to control the residual stresses and hence the apparent fracture toughness in the micro-laminates. No ‘edge cracking’, crack deflection or crack bifurcation was observed in the two designs of micro-laminates studied. [Copyright &y& Elsevier]

In this study, intrinsic static/dynamic fracture toughness of Al 7175-T74 and 17-4PH casting steel are evaluated from the apparent static/dynamic fracture toughness of notched specimen. Fracture toughness tests are conducted using an instrumented impact and three-point bending testers. The critical average stress fracture model is used to establish the relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-cracked specimen. The critical average stress fracture model is suggested using the relationship between the notch root radius and the effective distance calculated by FE analysis. The results show that fracture toughness decreases as the notch root radius decreases until a limiting of critical radius. However, fracture toughness is independent of notch root radius below the limiting critical notch root radius. It is concluded that the true fracture toughness can be predicted from test results of apparent fracture toughness measured by using a notched specimen. Also, with the critical average stress fracture model, the equation predicting relation of notch root radius and apparent fracture toughness can be calculated. [Copyright &y& Elsevier]

This work experimentally measures the apparent fracture toughness of the interfaces between epoxy-based underfill materials and various substrates including aluminum, polyimide, BCB, and printed wiring boards (FR-4) with solder mask. A small amount of silane coupling agent is added to the base underfill in order to form various underfill derivatives, and double layer specimens with preexisting interfacial cracks are prepared for four-point bending tests. The measurements are qualitatively correlated to each silane additive. The purpose of adding silane additives was to enhance the adhesion; the enhancement of interfacial toughness was found to strongly depend on the type of substrate. The results of this study have important implications in flip-chip reliability where interfacial cracking is one of the major failure modes [ABSTRACT FROM PUBLISHER]

Face-centred cubic (fcc-) Mo–N and Ta–N exhibit an inherent driving force for vacancy formation. To study their interaction and effects on structural evolution and mechanical properties, we synthesised Mo–Ta–N coatings by reactive magnetron sputtering using nitrogen-to-total pressure ratios, p N2 / p T , of 0.32 and 0.69. Low p N2 / p T results in high concentration of N vacancies, which stabilise single-phase fcc-Mo 1- x Ta x N y up to x = 0.76. These solid solutions follow the MoN 0.5 –Ta 0.875 N 0.875 quasi-binary tie line. Compressive residual stresses, σ , indentation hardness, H , and toughness, K C , increase with Ta content, reaching their maxima of (on average) -2.0 GPa, 28 GPa, and 7.0 MPa√m, respectively, within the x range 0.38–0.69. Higher Ta contents favour higher concentration of metal vacancies deteriorating the properties. High p N2 / p T favours the formation of fcc-Mo 1- x Ta x N y rich in metal vacancies, which however always coexists with a hexagonal phase. Within the x range 0.33–0.66, the fraction of the hexagonal phase is negligible, and σ , H , and K C deviate from −1.0 GPa, 28 GPa, and 2.9 MPa√m, respectively, within the error of measurements. The combination of experimental and theoretical studies demonstrates the power of point defects in stabilising desired crystal structures and improving mechanical properties through the thereby tuned atomic configuration. [Display omitted] • Experimental and first principle insights into the barely explored MoN–TaN. • Magnetron sputtered MoN–TaN films with a wide composition range. • Role of vacancies in favouring the cubic structure over other polymorphs. • 140% toughness enhancement through cubic-structured Mo 1- x Ta x N y solid solutions realised by nitrogen vacancies. [ABSTRACT FROM AUTHOR]

• Scaling effect on mixed mode I/II fracture toughness of notched samples is studied. • Extensive fracture tests are performed on BD and SCB specimens at various scales. • PS criterion with two various FPZ lengths is employed to estimate the test results. • Notch fracture toughness increases significantly by increasing the specimen scale. • PS criterion with both FPZ lengths can estimate the test results successfully. In this study, the mixed mode I/II notch fracture toughness (NFT) of polymeric (PMMA and GPPS) specimens weakened by U- and key-hole notches is assessed experimentally and theoretically. For this aim, first, by performing experiments, the apparent fracture toughness values of cracked polymeric semi-circular bending (SCB) and Brazilian disk (BD) specimens with four different radii are specified. Next, multiple fracture experiments are conducted on the notched polymeric SCB and BD specimens at four different scales, from which the critical loads are measured and converted to the NFT values. Then, the critical radius of the fracture process zone (FPZ) for the notched polymeric specimens is acquired using two different equations already suggested in literature for cracks. A well-established stress-based failure model, namely the point stress (PS) criterion, is employed for anticipating the NFT values of the specimens tested at various scales, by taking advantages of two different critical distance formulas. The results show that at all of the four scales, the fracture toughness values of U- and key-hole notches achieved from PS criterion are in good agreement with the experimental results. Also, shown in this research is that the mixed mode NFT is considerably dependent on the nominal radius of the specimen, such that, as the specimen radius increases, the mixed mode NFT increases significantly. Moreover, it is exhibited that for the present specimens tested, both the critical distance formulas give almost the same predictions, proposing that each of them can be arbitrarily chosen for the NFT prediction. [ABSTRACT FROM AUTHOR]

• Scaling effect on mode I notch fracture toughness of graphite specimens is studied. • Original fracture tests are performed on notched SCB specimens at different scales. • PS criterion with two various FPZ lengths is employed to estimate the test results. • Notch fracture toughness increases significantly by increasing the specimen scale. • PS criterion with both FPZ lengths can estimate the test results well. In this paper, the mode I notch fracture toughness of graphite specimens weakened by notches of different shapes is investigated experimentally and theoretically. For this purpose, first, by conducting experiments, the apparent fracture toughness values of cracked semi-circular bending (SCB) graphite specimens with four various radii are determined. Next, numerous fracture experiments are performed on the notched SCB graphite specimens in four various scales. Then, the critical radius of the fracture process zone (FPZ) for the notched graphite specimens is obtained using two various equations already proposed in literature for cracked bodies. A well-known stress-based failure model, namely the point stress (PS) criterion, is employed for estimating the notch fracture toughness values of the specimens tested at different scales, taking advantages of two different critical distance formulas. The results show that the fracture toughness values of various notches obtained from PS criterion are in good agreement with the experimental results. Also, found in this research that the notch fracture toughness is considerably dependent on the nominal dimension (radius) of the specimen, such that, as the specimen radius increases, the mode I notch fracture toughness increases. Furthermore, it is revealed that for the present specimens tested, both the critical distance formulas provide almost identical predictions, suggesting that each of them can be arbitrarily selected for prediction. [ABSTRACT FROM AUTHOR]

• A common mistake in hydraulic fracture modeling is using the fracture toughness measured from the unconfined laboratory testing, which does not consider the effect of confining stress and fluid lag at the fracture tip. If these effects are fully considered, a cohesive zone model should be utilized and it is very computational expensive. As a result, the idea of apparent fracture toughness with LEFM was first proposed by Rubin (1993) to take into account the effect of fluid lag and confining stress effect in a more cost effective method. In this manuscript, we validated the apparent fracture toughness in two approaches. • The first method, we compared the stress state near the fracture tip by comparing the cohesive zone method and the apparent fracture toughness. We found that the stress state from the apparent fracture toughness matches well with cohesive zone method, but the fracture toughness from the unconfined laboratory testing underestimates the near-tip stress magnitude. • In the second approach, we compared the fracture energy analytically and proved that the fracture energy of the apparent fracture toughness matches well with the cohesive zone method. • In this manuscript, we validated that LEFM with the apparent fracture toughness is an appropriate method in fracture modeling. Compared to the cohesive zone method, it is more cost effective. Compared with the fracture toughness measured from unconfined laboratory testing, the apparent fracture toughness is more accurate for hydraulic fracture modeling since it considers the effect of confining stress and fluid lag. Linear Elastic Fracture Mechanics (LEFM) is a widely applied theory to numerically simulate hydraulic fracture initiation and propagation in the subsurface. However, LEFM with the typical fracture toughness measured from unconfined laboratory tests does not apply to hydraulic fracturing applications under subsurface conditions because the fracture toughness is affected by the confining stress and fluid lag at the fracture tip. Thus, the apparent fracture toughness was proposed by Rubin (1993) to consider the contributions of fluid lag and confining stress. The main objective of this study is to validate the applicability of LEFM with the apparent fracture toughness in simulating hydraulic fracture under subsurface conditions. We utilized the finite element models to compare the near-tip stress state between the LEFM approach and the cohesive zone model (CZM), which considers the effect of confining stress and fluid lag. In addition, we compared the analytical solutions of fracture energy between LEFM and CZM. This study showed that the near-tip stress state of CZM outside the fluid lag and cohesive zone is comparable to the stress field predicted by LEFM with the apparent fracture toughness. However, LEFM with the fracture toughness measured from standard unconfined laboratory tests underestimates the near-tip stress state of fractures under confining stress. This study also revealed that the fracture energy of fluid-driven fractures calculated by CZM is identical to the fracture energy estimated from the approach of LEFM with the apparent fracture toughness. Thus, this study demonstrated that LEFM with the apparent fracture toughness is an appropriate and accurate method to simulate hydraulic fracture propagation in the subsurface. [ABSTRACT FROM AUTHOR]