In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, whi...In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.展开更多
The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By usin...The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.展开更多
The tensile equipment of the advanced confocal scanning laser microscope （CSLM） was used to research the high temperature mechanical properties of low carbon silicon-bearing steel by twin-roll strip casting. The res...The tensile equipment of the advanced confocal scanning laser microscope （CSLM） was used to research the high temperature mechanical properties of low carbon silicon-bearing steel by twin-roll strip casting. The results show that, at the strain rate of 0. 000 5 s ^-1, the strip clearly shows signs of brittleness at around 600 ℃ and its plasticity falls considerably between 750 ℃ and 600 ℃. This is because during the transformation from austenite to ferrite, the low strength ferrite at the austenite grain boundaries greatly reduces the steel＇ s high temperature plasticity. The subsequent strip coiling process should be controlled at less than the brittle temperature of approximately 600 ℃, so cracks at the coiling stage can be prevented.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10432030 and No. 10125209).
文摘In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.
基金Project supported by the National Natural Science Foundation of China (No.90305023)
文摘The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.
文摘The tensile equipment of the advanced confocal scanning laser microscope （CSLM） was used to research the high temperature mechanical properties of low carbon silicon-bearing steel by twin-roll strip casting. The results show that, at the strain rate of 0. 000 5 s ^-1, the strip clearly shows signs of brittleness at around 600 ℃ and its plasticity falls considerably between 750 ℃ and 600 ℃. This is because during the transformation from austenite to ferrite, the low strength ferrite at the austenite grain boundaries greatly reduces the steel＇ s high temperature plasticity. The subsequent strip coiling process should be controlled at less than the brittle temperature of approximately 600 ℃, so cracks at the coiling stage can be prevented.
