Transgranular Fracture Mode Research Articles

Microstructural characterization and creep deformation response of an Inconel-600/Inconel-625 welded joint obtained by oscillating GMAW process.

This investigation presents the microstructural characterization and creep failure mechanism of a dissimilar weld (DW) of Inconel 600 (IN600) and Inconel 625 (IN625) at a temperature of 675 °C and different stress levels. Optical microscopy (OM), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and Vickers microhardness test were used to characterize the welded joint, the creep rupture features, and microstructural characteristics of the DW respectively. The experimental results show that the crept samples consistently broke on the base material of the IN600 side and that the failure was mainly controlled by the plastic deformation of coarser austenitic grains, dynamic recrystallization, and the coalescence and growth of microcracks that resulted from the evolution of the Cr-rich carbides along the grain boundaries that conducted to a transgranular fracture mode.

Multi-functional amorphous/crystalline interfaces rendering strong-and-ductile nano-metallic-glass/aluminum composite

Metal matrix composites (MMCs) are the materials-of-choice for a large range of important applications under harsh service conditions. However, owing to the high phase contrast between the matrix and the reinforcements, the strength-ductility conflict of MMCs is still outstanding. Here we fabricated a novel aluminum (Al) matrix composite reinforced by deformable, cobalt-zirconium-boron (CoZrB) metallic glass nanoparticles. The amorphous CoZrB/Al composite with only 2.0 vol.% particle reinforcements possessed a uniaxial tensile strength of 387.0 ± 1.2 MPa, showing over 80 % improvement over the unreinforced pure Al matrix at a similar uniform elongation. The strength-ductility synergy of the composite was also significantly superior to that of the composite reinforced by fully crystallized nanoparticles. These findings were rationalized by the unique multi-functionality of the amorphous particle/matrix interfaces, which effectively transferred the load from the matrix to the particles, coordinated the co-deformation of the nanoparticles and the matrix, and imparted a transgranular fracture mode in the composite with extensive matrix plastic deformation. The methodology developed in this study was shown to be generally effective for other matrix and metallic glass nanoparticle compositions, and our work may shed new light on the development of high-performance metal matrix composites for advanced structural applications.

Microstructural characterization and equibiaxial flexural strength of CeO2 and Ti-doped CeO2

In this study, the synthesis of CeO2 and titanium dioxide (TiO2) doped CeO2 (TDC) monoliths are investigated, and their fracture strength is assessed using an equibiaxial flexure testing technique at room temperature. Pellets were synthesized using conventional powder processing and sintering methods to produce the desired characteristics. The TiO2 dopant concentration was optimized at 0.1 wt % TiO2 to obtain dense, solid-solution pellets with an enhanced grain microstructure. A ball-on-ring fixture was used to obtain the TRS and Weibull parameters of over 30 pellets for CeO2 and 0.1 wt % TDC to compare fracture behavior. The TRS of CeO2 pellets ranged from 88 to 160 MPa and the TRS of 0.1 wt % TDC pellets ranged from 102 to 171 MPa, both being consistent with published values. Weibull parameters, such as characteristic strength and Weibull modulus, were extracted as 129 MPa and 8.5 for CeO2 and 150 MPa and 9.3 for 0.1 wt % TDC, respectively. Although Hertzian contact damage was observed on compressive surfaces, failure initiation occurred on the tensile surfaces of both types of samples. Fracture surface analysis for CeO2 indicated a predominantly intergranular fracture while 0.1 wt % TDC had a predominantly transgranular fracture mode. The TRS of 0.1 wt % TDC resulted in increased Weibull parameters when compared to CeO2, indicating sample chemistry and microstructure impact mechanical behavior for these samples.

Revealing the failure mechanism of industrial Fe-25Cr-20Ni stainless steel plate: Fine-grained segregation band and brittle phase induced delamination cracking

The use of heat-resistant stainless steel thick plates in industrial production often presents challenges due to the presence of uneven microstructure and segregation, which can pose a persistent challenge for the prolonged safe operation of critical components made from such materials. This study aimed to investigate the fracture mechanism of an industrial Fe-25Cr-20Ni stainless steel plate at room temperature through uniaxial tensile experiments and fully reversed strain-controlled tension-compression fatigue experiments. Delamination cracks were observed on the fracture surfaces of both experiments. The specimens with fracture delamination were systematically studied by detailed microstructural evolution, and the failure mechanism and main reasons of fracture delamination were analyzed. The results show that the fracture delamination is related to the fine-grained segregation band (FGSB) consisted of fine grains and sigma phase located at the center of the thickness of the stainless-steel plate. The FGSB demonstrates low transgranular and intergranular fracture modes and exhibits bamboo knobs crack during plastic deformation, leading to a mixed fracture mode of ductile and brittle fracture. Furthermore, FGSB, as an anisotropic microstructure, which has a high stress concentration with nearby grains during plastic deformation. The sigma phase fracture and the weakening of the interface strength of the microstructure in FGSB provide a potential initiation site for fatigue crack initiation, thereby contributing to the possibility of aggravating fatigue damage and deteriorating fatigue performance. It is concluded that FGSB, as a metallurgical defect in stainless steel plates, is responsible for delamination failure.

Static and dynamic fracture toughness of graphite materials with varying grain sizes

Graphite materials play critical roles as moderators, reflectors, and core structural components in high-temperature gas-cooled nuclear reactors. During the reactor operation, graphite materials may experience a variety of loads, including thermal, radiation, fatigue, and dynamic loads, potentially leading to crack initiation and propagation. Therefore, it is imperative to investigate their fracture properties. Despite this, there remains a paucity of comprehensive studies on the fracture toughness of graphite materials with varying grain sizes, particularly concerning dynamic fracture toughness. This study addresses this gap by employing a digital-image-correlation-based virtual extensometer to analyze crack propagation in graphite materials of different grain sizes, enabling precise measurement of crack propagation length and fracture toughness. Findings reveal that static fracture toughness increases with larger grain sizes, while under dynamic loading, smaller grain sizes exhibit greater fracture toughness. Additionally, dynamic fracture toughness shows a near-linear increase with impact speed. Scanning electron microscopy analysis of fracture surface morphology highlights the impact of grain size and impact speed on fracture toughness. Nuclear graphite specimens with larger grain sizes have more irregular grain and pore distributions, enhancing crack deflection and propagation resistance, thereby increasing fracture toughness. The observed loading rate dependence of dynamic fracture toughness is attributed to a gradual transition from intergranular to transgranular fracture modes with increasing impact speed.

Effects of sintering temperature on the microstructure and mechanical properties of Ni-based alloy

Ni-based alloys were prepared at different sintering temperatures in this study. The effects of sintering temperature on the volume fraction, morphology, and distribution of precipitates in Ni-based alloys, and its impact on mechanical properties were studied. The results show that the microstructure contains γ-Ni, Ni3Si, M7(B, C)3, M23(B, C)6, and a Si-rich multi element phase. The morphology of M7(B, C)3 particles undergoes an evolution of small particles → mainly strip shape → mainly small block shape and nearly spherical shape, accompanying with the dissolution-reprecipitation process of M7(B, C)3 particles caused by the diffusion of Cr element with the increasing of sintering temperature. Meanwhile, the M23(B, C)6 particle is keeping aggregating and growing. The relative density, microhardness, and bending strength of Ni-based alloys also increase. Especially these properties are found to be increase quickly between 1025 °C and 1050 °C. The increase in microhardness and bending strength is attributed to the reduction in the number of residual sintering pores and the increase in the volume fraction and size of precipitates. In addition, the transition of fracture morphology from intergranular fracture mode to a combination of intergranular and partially transgranular fracture mode also contributes to the rise in bending strength.

How are microstructural defect interactions linked to simultaneous intergranular and transgranular fracture modes in polycrystalline systems?

The major objective of this investigation is to fundamentally understand and predict how intergranular (IG) and transgranular (TG) fracture modes nucleate and propagate in f.c.c. polycrystalline systems due to defects, such as total and partial dislocation densities and grain boundary (GB) structures and misorientations. A dislocation density crystalline plasticity (DCP) formulation based on the evolution and interaction of total and partial dislocation densities was integrated with a recently developed fracture approach to investigate the fracture nucleation and propagation of simultaneous multiple fracture events, including both IG and TG fracture events. The aggregate grains and GB orientations and morphologies are based on EBSD measurements that are representative of polycrystalline copper aggregates with a broad range of random high angle and low angle GBs. The predictions indicate that dislocation density pileups induce IG fracture due to interrelated stress, slip, and total and partial dislocation density accumulations and interactions for both high angle GBs (HAGBs) and low angle GBs (LAGBs). TG fracture nucleation and propagation occurred due to normal stress accumulations, which exceeds the fracture stress, along cleavage planes. Furthermore, it is shown how IG cracks transition from the GB plane to the cleavage planes as cracks nucleate and propagate. Accumulated plastic zones due to different slip system activities can impede and blunt crack propagation and fronts. These plastic zones form due to high Lomer and Shockley partial dislocation densities. These predictions, which are consistent with experimental observations, provide a fundamental understanding of how simultaneous failure modes initiate and propagate for physically representative microstructures.

Enhancing the fracture toughness of polycrystalline diamond by adjusting the transgranular fracture and intergranular fracture modes

Enhancing the fracture toughness of polycrystalline diamond (PCD) is challenging because of its inherent brittleness and the absence of a toughness mechanism. Elucidating the transgranular fracture (TF) and intergranular fracture (IF) modes in PCD is urgent for fabricating robust PCDs. In this study, the toughness of PCD was optimised by adjusting the IF and TF modes. The high pressure and high temperature method (HPHT) was used to fabricate PCDs with different grain sizes (nano- to micro-scale) to modulate the IF and TF modes. The results indicate that a mixture of the IF and TF modes yields an optimum toughness in PCD compared to the single fracture mode, which yielded a high hardness (114.6 GPa) and high toughness (13.0 MPa∙m0.5). The toughness was approximately three times that of single-crystal diamonds (SCDs) and comparable to that of pure nanotwinned diamonds (NtDs). The mixed modes induce a toughening mechanism of high frequency large crack deflection, crack bridging, pull-out, and crack branching, which increases the toughness of the PCD. This work provides new insights into optimising the toughness of PCD, which is significant for fabricating robust PCDs for future applications.

Influence of temperature on deformation and damage mechanisms of wire + arc additively manufactured 2219 aluminum alloy

This work investigates the deformation and damage mechanisms of wire + arc additive manufacturing (WAAM) 2219 aluminum alloy over a broad temperature range of 77 K to 523 K. It is found that the strength and work hardening rate increase significantly with decreasing the temperature from 523 K to 77 K, and the fracture mode transitions from transgranular fracture mode to a mixture of intergranular and transgranular fracture ones. The large elongations to fracture are very similar for the specimens tested at 77 K and 523 K. This is mainly attributed to higher uniform elongation before necking at 77 K and higher post-necking elongation at 523 K. The cracking of α-Al + θ (Al2Cu) eutectics is the primary mechanism of micro-void nucleation, independent of the test temperature. The nucleated micro-voids, along with larger gas pore defects introduced by WAAM, extend along the tensile direction. In addition, as the temperature increases from 77 K to 523 K, the fracture mechanism transitions from high strain localization to extensive necking, leading to higher dislocation density, more grain fragmentation and micro-void nucleation, and more significant grain elongation and void growth. True stress and strain responses over the studied temperature range (77 ∼ 523 K) and strain rate range (0.0001 ∼ 0.01 s−1) are well predicted using an improved Arrhenius-type constitutive model, by considering the activation energy of deformation as a function of temperature.

Enhancing properties of Li2TiO3/Li4SiO4 tritium breeding ceramics by chitosan addition

Li2TiO3/Li4SiO4 ceramics have been regarded as promising tritium breeders due to their numerous merits. In this work, chitosan was employed as an effective binder to provide adhesion of Li2TiO3 particles to Li4SiO4 particles, resulting in Li2TiO3/Li4SiO4 ceramics with improved performance. Chitosan could be removed during the sintering process and had little influence on the phase composition. The resulting Li2TiO3/Li4SiO4 ceramics had higher density (92.5%T.D.), greater crushing loads (115.2 ± 20.8 N) and superior thermal properties (3.61 W/m∙K) when compared to the samples prepared without chitosan. SEM analyses displayed a dual-scale structure and the inter- and trans-granular fracture mode. Thermal cycling tests revealed that the phase composition was stable but the crushing load fell slightly. The crushing load remained at 92.4 ± 17.1 N after 12 cycles. Overall, chitosan plays an important role in the amelioration of interface combination between Li4SiO4 and Li2TiO3, and thus significantly improve density, crushing load and thermal conductivity of Li2TiO3/Li4SiO4.

Dynamic response of the TiB2–SiC/B4C composite ceramic under dynamic loading

AbstractTiB2–SiC/B4C composite ceramics have application as lightweight armor ceramic material, and therefore, it is particularly important to research their dynamic mechanical properties and fracture behavior under high strain rates. In the present research, the dynamic compression strength and Hugoniot elastic limit (HEL) of these composite ceramics were determined by split Hopkinson pressure bar technology and plate impact equipment, respectively. The experimental investigation results illustrated that the composite ceramic exhibited outstanding dynamic compression strength (2750 MPa) and displayed a remarkable strain‐rate strengthening effect. The HEL was calculated as 18.49 GPa, and the commonly used P–μ form of the Hugoniot curve was derived from the calculated data of the shock velocity and particle velocity. The dynamic fracture morphologies of the TiB2–SiC/B4C composite ceramic and monolithic B4C ceramic (correlation data) at macro and micro scales were observed and analyzed in detail. The dynamic fracture mechanisms were summarized in‐depth into the following three points. First, the strengthening mechanism offered by the in situ second phases could significantly improve the comprehensive property. Second, the mixed‐inter/transgranular fracture mode was conducive to energy absorption. Third, the anchoring effect and thermal expansion coefficient mismatch contributed to the energy dissipation and fracture toughness improvement. This work provides the foundation for the application and development of lightweight armor ceramic materials.

The effect of Mn containing dispersoids on the distribution of slip and fracture mode in Al-Mg-Si-Mn alloys

Improvements in the fracture performance of Al-Mg-Si extrusions are required to meet the demands of the automotive market. The fracture mode and the associated ductility results from competition between transgranular and intergranular fracture paths where intersection of slip bands and grain boundaries plays a significant role. In this study, the distribution of plastic strain within grains for microstructures with different spacings of Mn dispersoids was quantified using high resolution digital image correlation. It was observed that plastic strain was organized into slip bands where the magnitude of local shear strain decreased with reduced inter particle spacing of the dispersoids. It is proposed that this leads to a lower stress concentration on the grain boundary, decreasing the propensity for intergranular fracture. This was consistent with the findings that intergranular fracture was dominant in the dispersoid free material whereas low and high densities of dispersoids gave rise to a transgranular fracture mode.

Effect of heat treatment on microstructures and mechanical properties of Inconel 718 additively manufactured using gradient laser power

To achieve high-performance nickel-based superalloys by laser powder deposition for applications in the aviation industry, post-heat treatments are always indispensable. We prepared two typical as-deposited microstructures by constant laser power deposition (CLP) and gradient laser power deposition (GLP), respectively. A systematic research on the room-temperature microstructural evolution, hardness, tensile property and fracture morphology of Inconel 718 after three kinds of heat treatments is performed. The as-deposited microstructure and segregation ratio (SR) can significantly influence the microstructure evolution. The as-deposited GLP samples with fine discrete Laves phases and a low SR can achieve a relatively uniform element distribution and γ′′ and γ′ phase precipitation after standard solution treatment plus aging (STA), while CLP samples with coarse long-chain Laves phases and high SR require a high-temperature homogenization plus STA (HSTA) heat treatment to achieve the uniform element distribution. Differences in heat treatments have a greater impact on the fracture mechanism. With the transformation of heat treatments from direct aging, STA to HSTA, the fracture mode of both CLP and GLP samples transforms from a ductile transgranular fracture mode to a mixed mode of transgranular and intergranular fractures.

Significantly elevated strength of W-Ni3Al alloy by adding trace boron element

W-Ni3Al alloys have potential application in kinetic energy penetrator, but there are some problems such as high sintering temperature, large tungsten grain size, and poor mechanical properties. In this study, fine-grained W-Ni3Al-B alloys with excellent mechanical properties were successfully fabricated at a low temperature of 1150 °C by adding trace boron powder (B) and using spark plasma sintering (SPS). For the addition of B in the W-Ni3Al alloys, the low melting point B2O3 phase was formed and its thermite reaction released extra heat, promoting the sintering of the alloys. However, with the increasing of B content (0.1–0.7 wt%), the more hard brittle phases were formed, damaging the strength of sintered alloys; at the same time, the more B2O3 phase was evaporated due to the more released heat, causing occurrence of pores. Among all B-containing W-Ni3Al alloys, the 0.1B alloy exhibited the optimal mechanical properties with the bending strength of 1375.88 ± 19.20 MPa (higher 99.32% than that of the 0B alloy) and a high hardness value of 71.6 ± 0.29 HRA. By analyzing 0.1B alloy's microstructure, its good mechanical properties were related to the small tungsten grain size, heterostructural binder phase, minimal formation of hard brittle phases, dislocation movements being obstructed by the Al2O3 phase, and the tungsten transgranular cleavage fracture mode.

Microchemical homogeneity and quenching-induced property enhancement in BiFeO3–BaTiO3 ceramics

BiFeO3–BaTiO3 (BF-BT) solid solutions are promising as the basis for high temperature dielectric and piezoelectric materials, but their microstructural aspects have received relatively little attention. This study evaluates the influence of different processing procedures on the micro-chemical heterogeneity and functional properties of 0.67BF-0.33BT ceramics prepared by solid state reaction. It is shown that the use of high energy planetary ball milling after calcination is an effective method to improve chemical homogeneity and circumvent the core-shell type features found in conventional vibration-milled materials. BF-BT ceramics prepared by high energy milling exhibit enhanced remnant polarization, piezoelectric charge coefficient and coupling factor values of 0.34C m−2, 105 pC/N and 0.24, in comparison with those of vibration milled materials (0.30 C m−2, 73 pC/N and 0.19 respectively). Further improvements in functional properties were achieved by application of an air quenching process, which also led to an increase of 50 °C in both the Curie point and depolarization temperature; these modifications were correlated with increased structural distortion and volume fraction of the rhombohedral phase. Quenched BF-BT ceramics also exhibited mixed inter- and trans-granular fracture modes, whereas that of the as-sintered materials was predominantly inter-granular.

Influence of pre-stretching on the tensile strength, fatigue properties and the in-plane anisotropy in Al-Cu-Li alloy AA2099

The influence of pre-stretching prior to artificial aging on microstructure, tensile properties, and fatigue behavior of AA2099-T8 sheets was investigated. The results showed that increased pre-strain level from 1% to 6% resulted in a more uniform distribution and increasing density of the T1 phase. The localized plastic deformation during pre-stretching led to the formation of dense precipitation bands (DPBs) and precipitation free bands (T1-PFBs) in the sheets with the 1% pre-strain. The non-uniform distribution of the T1 phase with T1-PFBs and DPBs resulted in a decrement in elongation and a strong in-plane anisotropy of tensile properties. An appropriate level of pre-strain should be executed aiming to improve elongation and reduce the tensile anisotropy by promoting a uniform distribution of the T1 phase. In-plane anisotropy of yield strength due to the presence of DPBs and T1-PFBs was quantitatively analyzed by the modified Hall-Petch formula. The results of the calculation for the modified model showed good agreement with the experiment. In addition, resistances of fatigue crack propagation (FCP) in the same orientation were gradually decreased with the increment of pre-strain due to the increment in yield strength and more uniform distribution of the T1 phase. For the in-plane anisotropy of FCP resistance, the main reasons were the development of rough fracture surfaces and the transgranular fracture modes in L-T orientation.

Achieving High Tensile Strength of Heat-Resistant Ni-Fe-Based Alloy by Controlling Microstructure Stability for Power Plant Application

A new, wrought Ni-Fe-based alloy with excellent creep rupture life has been developed for 700 °C-class advanced ultra-supercritical (A-USC) steam turbine rotor application. In this study, its tensile deformation behaviors and related microstructure evolution were investigated. Tensile tests were carried out at room temperature, 700 °C, and 750 °C. The results show that the Ni-Fe-based alloy has excellent yield strength at 700 °C, which is higher than that of some other Ni-based/Ni-Fe-based alloys. The fracture surface characteristics indicate trans-granular and intergranular fracture modes at room temperature, 700 °C, and 750 °C. However, the intergranular fraction mode became dominant above 700 °C. Dynamic recrystallization occurred at 700 °C and 750 °C with increasing average misorientation angles. The volume fraction of the γ′ precipitate was around 20%, and the average size of the γ′ precipitates was around 30 μm, which had no noticeable change after the tensile tests. The predominant deformation mechanisms were planar slip at room temperature, bypassing of the γ′ precipitates by the Orowan mechanism, and dislocation shearing at 700 °C and 750 °C. The tensile properties, fracture characteristics, and deformation mechanisms have been well-correlated. The results are helpful in providing experimental evidence for the development and optimization of high-temperature alloys for 700 °C-class A-USC applications.

Structure design and experimental study on ultrasonic vibration–assisted induction brazing cubic boron nitride abrasive tools

Brazed superabrasive tool has been widely used in machining of difficult-to-cut materials to improve the machining efficiency and quality. However, the severe wear and associated short service life have to be faced for conventional induction brazed (CIB) abrasive tools during machining processes, owing to its weak bonding strength between abrasive grains and metal-bonded phases. In this case, the method of ultrasonic vibration–assisted induction brazing (UVAIB) was proposed to fabricate tools, through introducing ultrasonic vibration into brazing process to improve the abrasive bonding strength. Here, a novel UVAIB device was developed, and the geometric designation parameters were optimized using a finite element simulating method. In addition, the performance of UVAIB device was tested in terms of the impedance and amplitude. Subsequently, the comparative experiment trials were performed with the brazed abrasive tools under the CIB and UVAIB method. Results show that the ultrasonic energy loss of UVAIB device can be reduced, and then, the amplification value and vibration uniformity reach 8 and 92%, respectively. In addition, a large number of pores and macro-cracks inside tool’s metallic matrix for CIB can be observed, whereas the number of pores is reduced by 75%, and only fewer and smaller micro-cracks are found for UVAIB. Furthermore, compared with the grains’ intergranular fracture for CIB, UVAIB exhibits the transgranular fracture mode due to its higher bonding strength after adopting the ultrasonic vibrating method.

Insights on mechanical properties of dual-phase high entropy alloys via Y introduction

AlCoCrFeNi high entropy alloy (HEA) with a dual-phase A2+B2 structure has received significant research interests due to its favorable mechanical properties. In order to further optimize the mechanical properties of the dual-phase AlCoCrFeNi HEA, we design several types of (AlCoCrFeNi)100-xYx (x = 0, 0.05, 0.1, 0.5 and 1, at%) HEAs and explore the microstructure evolution as well as mechanical behaviors as a function of the Y addition. Adding Y element into the (AlCoCrFeNi)100-xYx HEAs tailors the phase composition, where Y-0.05 HEA is of the single BCC solid solution, similar to Y-0 HEA. And when Y addition is equal to or higher than 0.1 at%, (Ni, Y)-rich HCP phase is identified except for the BCC phase, coinciding with a δ-Ω phase selection model. Meanwhile, Y introduction can lighten the intragranular dendrite segregation. The volume fraction of HCP phase follows a growing trend from 0 vol% to 10.33 vol% with an increment of Y introduction, which is beneficial to enhancing the yield strength (from 1302 to 1447 MPa) and microhardness (from 517 to 597 HV). Furthermore, the fracture mechanism from a transgranular fracture mode to an intergranular fracture mode is also revealed.

Hydrogen-enhanced grain boundary vacancy stockpiling causes transgranular to intergranular fracture transition

The attention to hydrogen embrittlement (HE) has been intensified recently in the light of hydrogen as a carbon-free energy carrier. Despite worldwide research, the multifaceted HE mechanism remains a matter of debate. Here we report an atomistic study of the coupled effect of hydrogen and deformation temperature on the pathway to intergranular fracture of nickel. Uniaxial straining is applied to nickel Σ5(210)[001] and Σ9(1-10)[22-1] grain boundaries with or without pre-charged hydrogen at various temperatures. Without hydrogen, vacancy generation at grain boundary is limited and transgranular fracture mode dominates. When charged, hydrogen as a booster can enhance strain-induced vacancy generation by up to ten times. This leads to the superabundant vacancy stockpiling at the grain boundary, which agglomerates and nucleates intergranular nanovoids eventually causing intergranular fracture. While hydrogen tends to persistently enhance vacancy concentration, temperature plays an intriguing dual role as either an enhancer or an inhibitor for vacancy stockpiling. These results show good agreement with recent positron annihilation spectroscopy experiments. An S-shaped quantitative correlation between the proportion of intergranular fracture and vacancy concentration was for the first time derived, highlighting the existence of a critical vacancy concentration, beyond which fracture mode will be completely intergranular.