Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal...Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.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
Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and...Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empiricai method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli＇s photo-elastic experiment and Isida＇s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.展开更多
基金the Special Research Fund for the National Major Science and Technology Achievement Transformation Project(No.2012GG01)the National Natural Science Foundation of China(No.51305387)the Provincial Natural Science Foundation of Hebei of China(No.E2015203103)
文摘Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.
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.
基金supported by the National Natural Science Foundation of China (No. 51179115)
文摘Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empiricai method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli＇s photo-elastic experiment and Isida＇s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.
