In addition to enhancement of the resuits near the point of appiication of a concentrated ioad in the vicinity of nano-.size defects, capturing surface effects in smaii structures, in the framework of second strain gradient eiasticity is of particuiar interest. In this framework, .sixteen additionai material constants are reveaied, incorporating the roie of atomic .structures of the eiastic soiid. In this work, the analytical formuiations oftiiese constants corresponding to fee metáis are given in terms of the parameters of Sutton-Chen interatomic potentiai function. The constants for ten fee metáis are computed and tabuiized. Moreover, the exact dosed-form soiution of the bending of a nano-size Bernoulli-Euler beam in second strain gradient eiasticity is provided: the appearance of the additionai constants in the corresponding formuiations, through the governing equation and boundary conditions, can .serve to deiineate tiie true behavior of the materiai in uitra .smaii eiastic structtves. having very iarge swface-to-voiume ratio. Now that the vaiues of the materiai constants are avaiiabie, a nanoscopic study of the Keivin probiem in .second strain gradient theory is performed, and the result is compared quantitativeiy with those of the first strain gradient and traditionai tlwories.
Hydrogen ingress into a metal is a persistent source of embrittlement. Fracture surfaces are often intergranular, suggesting favorable cleave crack growth along grain boundaries (GBs) as one driver for embrittlement. Here, atomistic simulations are used to investigate the effects of segregated hydrogen on the behavior of cracks along various symmetric tilt grain boundaries in fcc Nickel. An atomistic potential for Ni-H is first recalibrated against new quantum level computations of the energy of H in specific sites within the NiΣ5(120)⟨100⟩ GB. The binding energy of H atoms to various atomic sites in the NiΣ3(111) (twin), NiΣ5(120)⟨100⟩, NiΣ99(557)⟨110⟩, and NiΣ9(221)⟨110⟩ GBs, and to various surfaces created by separating these GBs into two possible fracture surfaces, are computed and used to determine equilibrium H concentrations at bulk H concentrations typical of embrittlement in Ni. Mode I fracture behavior is then studied, examining the influence of H in altering the competition between dislocation emission (crack blunting; "ductile" behavior) and cleavage fracture ("brittle" behavior) for intergranular cracks. Simulation results are compared with theoretical predictions (Griffith theory for cleavage; Rice theory for emission) using the computed surface energies. The deformation behavior at the GBs is, however, generally complex and not as simple as cleavage or emission at a sharp crack tip, which is not unexpected due to the complexity of the GB structures. In cases predicted to emit dislocations from the crack tip, the presence of H atoms reduces the critical load for emission of the dislocations and no cleavage is found. In the cases predicted to cleave, the presence of H atoms reduces the cleavage stress intensity and makes cleavage easier, including NiΣ9(221)⟨110⟩ which emits dislocations in the absence of H. Aside from the one unusual NiΣ9(221)⟨110⟩ case, no tendency is found for H to cause a ductile-to-brittle transformation for cracks along GBs in Ni, either according to theory or simulation for initial equilibrium H segregation and with no, or limited, H diffusion near the newly-created fracture surfaces. The NiΣ3(111) twin boundary does not absorb H at all, suggesting that embrittlement is more difficult in materials with higher fraction of such twin boundaries, as found experimentally. Experimental observations of cleavage-like failure are thus presumably caused by mechanisms involving H diffusion or dynamic crack growth.
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