不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.

UNIFIED SOLUTIONS OF LIMIT INTERNAL PRESSURE FOR THICK-WALLED CYLINDER WITH DIFFERENT BEHAVIOUR IN TENSION AND COMPRESSION

Thick-walled cylinder is widely used in practical engineerings. If the limit internal pressure is calculated accurately, it is great significance to prevent accidents and reduce risk. There are many engineering materials that the tensile strength and tensile modulus are different. These differences have a significant effect on the ultimate internal pressure. Previous studies have shown that only considering one aspect of the tension and compression strength and the modulus of tension and compression has a certain error with the actual situation. With consideration of the intermediate principal stress and the different elastic modulus and different strength in tension and compression, elastic and plastic stress distribution, the unified analytical solutions of the elastic limit internal pressure, the plastic limit internal pressure and the shakedown limit internal pressure of thick-walled cylinder under internal pressure are deduced based on twin shear unified strength theory. The correctness of the calculation results is proved through the verification and comparative analysis with other literatures. The influence of radius ratio, unified strength theory parameter, tension-compression ratio and coefficient of tensile-compression modulus of materials on the solutions is analyzed. It is shown that each unified solution increases with increasing the radius ratio and unified strength theory parameter but decreases with increasing the tension-compression ratio. The elastic limit internal pressure decreases with increasing the coefficient of tension-compression modulus. When the wall thickness increases to a certain value, the shakedown limit internal pressure decreases with increasing the coefficient of tension-compression modulus. The different elastic modulus and strength in tension and compression have significant influence on the stability of the thick-walled cylinders. The consideration of the intermediate principal stress effect can make materials give full play to their potential. The variable law of the limit internal pressure with radius ratio provides reference for selecting reasonable wall thickness. The conclusion furnishes some theoretical basis for the engineering application of thick-walled cylinders.