Experimental data indicate that Young’s modulus of materials decreases with the decreasing of the grain size. Obviously, the primary factor of this decrease is presence of grain-boundary region, which Young’s modulu...Experimental data indicate that Young’s modulus of materials decreases with the decreasing of the grain size. Obviously, the primary factor of this decrease is presence of grain-boundary region, which Young’s modulus other than in the bulk of crystallites. There is a set of various expressions for calculation of Young’s modulus of polycrystals, obtained under the assumption, that it is possible to consider a polycrystal as a composite consisting of a crystalline matrix and a intercrystalline layers (grain-boundary region). Calculations showed incorrectness of application of a majority of these expressions and a large error in the calculations for the nanocrystalline materials. By us, on the basis of the same assumptions, is also obtained analytical expression for calculating Young’s modulus of materials with grain size more than 30 nm, which is more exact, than all others.It is necessary to consider under the calculation of effective Young’s modulus nanocrystalline materials with grain size of less than 30nm, that grain-boundary region itself is not uniform. It is reliably established, that the triple joints of grain boundaries have a structure and properties, different from the structure and the properties of grain boundaries, which these joints connect. For nanocrystalline materials the volume fraction of the triple joints in the grain-boundary region can reach 50% and even more. Therefore assumption was made, that the nanocrystalline materials should be represented as consisting of three phases (triple joints, grain boundary between the triple joints and crystallite). On the basis of this idea is obtained analytical expression for calculating of Young’s modulus nanocrystalline materials. The analysis shows that Young’s modulus calculated by this analytical expression coordinated with the theory and the experiment.展开更多
文摘Experimental data indicate that Young’s modulus of materials decreases with the decreasing of the grain size. Obviously, the primary factor of this decrease is presence of grain-boundary region, which Young’s modulus other than in the bulk of crystallites. There is a set of various expressions for calculation of Young’s modulus of polycrystals, obtained under the assumption, that it is possible to consider a polycrystal as a composite consisting of a crystalline matrix and a intercrystalline layers (grain-boundary region). Calculations showed incorrectness of application of a majority of these expressions and a large error in the calculations for the nanocrystalline materials. By us, on the basis of the same assumptions, is also obtained analytical expression for calculating Young’s modulus of materials with grain size more than 30 nm, which is more exact, than all others.It is necessary to consider under the calculation of effective Young’s modulus nanocrystalline materials with grain size of less than 30nm, that grain-boundary region itself is not uniform. It is reliably established, that the triple joints of grain boundaries have a structure and properties, different from the structure and the properties of grain boundaries, which these joints connect. For nanocrystalline materials the volume fraction of the triple joints in the grain-boundary region can reach 50% and even more. Therefore assumption was made, that the nanocrystalline materials should be represented as consisting of three phases (triple joints, grain boundary between the triple joints and crystallite). On the basis of this idea is obtained analytical expression for calculating of Young’s modulus nanocrystalline materials. The analysis shows that Young’s modulus calculated by this analytical expression coordinated with the theory and the experiment.
