Fracture Toughness Of Grain Boundaries Research Articles

Effects of Pb and Bi on mechanical properties and fracture modes of bcc iron symmetrical tilt grain boundaries

The internal structural material T91 in the accelerator driven subcritical reactor system (ADS) has encountered the challenge of liquid metal embrittlement caused by Pb and Bi. Therefore, it is of utmost importance to gain a comprehensive understanding of their embrittlement mechanism. The effects of Pb and Bi on the surface energy of surfaces and separation work and fracture toughness of grain boundaries in body center cubic (BCC) Fe are examined using first-principles calculation. Pb and Bi atoms reduce the surface energy and grain boundary cohesion strength of BCC Fe, with a more significant decrease in surface energy. Meanwhile, the segregation of Pb and Bi in the grain boundary reduces the fracture toughness of the grain boundary. By comparing different surface energy and separation work, it is found that BCC pure Fe is more prone to intergranular fracture, while the presence of Pb and Bi causes cleavage fracture. This elucidates the low-temperature fracture mode of BCC-Fe and reveals the potential mechanism of brittle cleavage fracture caused by Pb and Bi in BCC-Fe. The derived results are discussed in terms of electronic structure and show good agreement with experimental results in the literature, ultimately contributing to a thorough understanding of the intrinsic mechanism of liquid metal embrittlement of T91 steel.

Effects of alloying elements on cohesion and brittleness of grain boundary of iron

First-principles calculation is performed to systematically investigate the effects of alloying elements (Cr, Mo, Ni, Pb, and Bi) on stability, cohesion strength, Young's modulus, and fracture toughness of the ∑3(111)[11‾0] grain boundary (GB) of BCC Fe. It is found that compared with Cr, Mo, and Ni, both Pb and Bi are energetically more favorable to segregate to GB and decrease the GB energy of Fe. Calculations also reveal that Pb and Bi have an important effect to significantly reduce the cohesion strength, Young's modulus, and fracture toughness of GB of Fe, and that such an effect of Bi seems bigger than that of Pb. The derived results are discussed in terms of electronic structure and are in good agreement with experimental and theoretical results in the literature, which could provide a deep understanding of the intrinsic mechanism of the effects of Pb and Bi on embrittlement of BCC Fe.

A two-set order parameters phase-field modeling of crack deflection/penetration in a heterogeneous microstructure

Modeling of crack deflection/penetration or manifested as intergranular/transgranular fracture in polycrystals has long been a challenge in both fracture mechanics and materials science. A phase-field model formulated with two-set order parameters describing the crack field and the microstructure field respectively, is herein established to investigate the competition between crack penetration and deflection at an interface. The advantages of the proposed model are three-fold: (1) the fracture toughness of grain boundaries and/or interfaces, besides single crystal properties (e.g., Young’s modulus, Poisson ratio, and fracture toughness), can be automatically incorporated, (2) cohesive interfaces are treated in one phase-field framework in comparison with the integrated phase-field and cohesive zone model in which cohesive elements have to be manually placed at the interface, and (3) two-set order parameters enable to describe the concurrent crack propagation and microstructure evolution. The proposed model is validated by comparing the simulated critical deflection angles with the results from theoretical analysis of the linear elastic fracture mechanics and the experiments. The model is then applied to a heterogeneous Silicon Nitride polycrystal to determine the effect of interface fracture toughness on the intergranular/transgranular fracture transition and the effective toughness of the materials.

Helium bubble nucleation at grain boundaries and its influence on intergranular fracture

ABSTRACTAn in-depth understanding of the formation of intergranular helium bubbles and its relation to embrittlement is an important issue in the nuclear industry. In this paper, a thermodynamic model is developed to analyze the nucleation of intergranular helium bubbles. Microstructural observation using scanning electron microscopy and electron backscatter diffraction gives a detailed description for the relation between the bubble formation and the grain-boundary (GB) misorientation in helium-implanted nickel and Inconel X750. The theoretical and the experimental results confirm that the nucleation of intergranular helium bubbles is GB structure-dependent, the helium-to-vacancy ratio plays an important role in the bubble precipitation, and the interfacial tension of bubbles cannot be approximated to be the interfacial energy. The bubble-induced intergranular embrittlement in a polycrystal is modelled. The GB misorientation distribution, the intergranular bubble nucleation and growth and the GB connectivity are the key factors affecting the GB fracture toughness. The hoop ductility of the cladding tubes containing helium is analyzed. The hoop stress-induced increase in the GB energy promotes the precipitation of bubbles at the radial GBs and lead to the loss of tube ductility. Based on this work, the complicated correlation among the intergranular helium bubbles, the GB structure, the helium concentration, the applied stress and the helium embrittlement is clarified.

Atomic-scale mutual integrals for mixed-mode fracture: Abnormal fracture toughness of grain boundaries in graphene

In this study, we developed a computational scheme based on the atomic-level J-based mutual integral (or two-state conservation integral) to analyze the mixed-mode fracture along grain boundaries (GB) in polycrystalline solids. Discrete atomic information, obtained from molecular dynamics simulation of crack propagation along GBs in polycrystalline solids, is incorporated with asymptotic singular fields near an interfacial crack tip between dissimilar materials in the atomic-level J-based mutual integral, to extract the individual stress intensity factors of modes I and II. As a model problem, crack propagation along GBs in polycrystalline graphene, an ordered array of non-hexagonal defects, is analyzed. In the model, GBs are considered to be the most favorable paths for crack propagation, as the carbon atoms along the GBs experience less-ordered interatomic interactions than those in pristine graphene. When a mixed-mode loading is applied to a crack running along a graphene GB, as the mode mixity increases, the fracture toughness of GBs in graphene gradually increases. However, if the mode mixity is greater than 8°, the fracture toughness gradually decreases, which can be considered a unique characteristic of GBs in graphene. This abnormally-low fracture toughness of GBs in graphene for high mode mixity, may be interpreted as the competition between bond-rotation and bond-breaking mechanisms of carbon atoms, in conjunction with the Stone–Wales transformation and nonagon structures at the crack tip along GBs in graphene.

Local Fracture Toughness of Si3N4 Ceramics Measured using Single‐Edge Notched Microcantilever Beam Specimens

Local fracture toughness gives us useful and important information to understand and improve mechanical properties of bulk ceramics. In this study, the local fracture toughness of silicon nitride (Si3N4) ceramics was directly measured using single‐edge notched microcantilever beam specimens prepared by the focused ion beam technique. The measured fracture toughness of grain boundary of the Si3N4 ceramics is higher than the fracture toughness of SiAlON glass, which exists in the grain boundaries of Si3N4 ceramics. It is also shown that the fracture toughness of grain boundary depends on the rare earth oxide added as a sintering aid, which is expected in terms of the difference in the grain‐boundary structure. The fracture toughness of a single β‐Si3N4 grains is higher than the grain‐boundary fracture toughness. It was also higher than the value estimated from ab initio calculations and surface energy, which means that any dissipative energy should be included in the fracture toughness of a grain in spite of the brittle fracture in Si3N4. The fracture toughness of polycrystals of Si3N4 ceramics measured using single‐edge notched microcantilever beam specimens is intermediate between those of grains and grain boundaries, and it agrees with the estimated initial value of the Rcurve, KI0, in Si3N4 ceramics.

Measuring Local Mechanical Properties using FIB Machined Cantilevers

AbstractMicro-scale Focused Ion Beam (FIB) machined cantilevers were manufactured in single crystal copper, polycrystalline copper and a copper-bismuth alloy. These were imaged and tested in bending using a nanoindenter. Cantilevers machined inside a single grain of polycrystalline copper were tested to determine their (anisotropic) Young's modulus: results were in good agreement with values calculated from literature values for single crystal elastic constants. The size dependence of yield behavior in the Cu microcantilevers was also investigated. As the thickness of the specimen was reduced from 23μm to 1.7μm the yield stress increased from 300MPa to 900MPa. Microcantilevers in Cu-0.02%Bi were manufactured containing a single grain boundary of known character, with a FIB-machined sharp notch on the grain boundary. The cantilevers were loaded to fracture allowing the fracture toughness of grain boundaries of different misorientations to be determined.