桅杆结构纤绳连接拉耳风致疲劳裂纹萌生与扩展寿命预测
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摘要
桅杆结构是一种主要承受风荷载的高耸结构,由一根直立的细长杆身和3～4个方向沿高度斜向张拉的数层纤绳组成,近年来被广泛应用于无线电通讯、广播电视、海空导航、环境保护、能源开发等国民经济的重要领域。由于其复杂的工作机理尚未被人们完全认识和掌握,桅杆结构发生破坏事故的比例在土木工程界首屈一指。大量桅杆事故研究报告表明:倒塌破坏事故多数是由于疲劳损伤后引起结构失稳或结构构件应力超过极限强度而引起的。因此有必要进行桅杆结构的疲劳损伤分析及疲劳寿命预测,为桅杆结构疲劳剩余寿命评估以及疲劳损伤监测新方法的提出提供重要依据。
以裂纹萌生寿命控制结构的疲劳是对结构疲劳断裂认识不足的结果,疲劳总寿命包括裂纹萌生和裂纹扩展两部分,完整的疲劳分析既要研究裂纹的起始萌生,也要研究裂纹的扩展。本论文首先采用多轴疲劳理论估算拉耳孔边裂纹萌生寿命。采用基于FFT算法改进的谐波叠加法模拟了桅杆结构沿杆身高度分布的15条脉动风速时程并进行了相关函数与功率谱检验,通过风速风压关系转换得到与自然风基本特性一致的模拟风荷载。
建立桅杆结构非线性动力计算模型,在时域内分析桅杆结构模拟风荷载作用下的非线性动力响应,获得桅杆结构纤绳应力响应时程。由于桅杆结构的对称性仅计算了0°、30°、60°风向桅杆结构的风振响应,其余方向风振响应根据对称性得到;借助有限元软件计算确定桅杆结构局部拉耳模型疲劳危险点及其应力应变状态,对危险点应力应变状态进行坐标旋转,按一定间隔变化旋转角度搜索最大损伤参量所对应的临界损伤面位置;采用双重雨流计数法提取临界损伤面上的正、剪应变循环并基于von Mises准则合成统一的多轴疲劳损伤参量,然后依据Mason-coffin公式及Miner疲劳累积损伤准则估算桅杆结构纤绳连接拉耳各不同风向不同平均风速作用下的多轴疲劳累积损伤,由总损伤计算出裂纹萌生寿命。
本文重点采用断裂力学方法研究桅杆拉耳这个局部构造复杂结构在初始疲劳裂纹下的扩展。桅杆结构纤绳连接拉耳裂纹的扩展寿命研究主要解决两个问题:裂纹前缘应力强度因子计算与孔边裂纹扩展分析。本文采用有限元法计算三维表面裂纹前缘应力强度因子。首先借助ANSYS高级网格划分技巧解决了复杂结构裂纹体有限元建模难题;利用布尔运算、高级网格划分技巧等手段采用实体建模法创建三维裂纹体模型。基于裂纹实体建模,采用有限元法分别计算了含中心表面裂纹及孔边角裂纹平板前缘应力强度因子,并与含中心表面裂纹及孔边角裂纹平板结构的Newman&Raju应力强度因子经验公式的计算结果进行对比验证了有限元实体建模及应力强度因子求解过程的可靠性。
采用前述有限元法计算桅杆结构拉耳各种给定形状、尺寸孔边裂纹裂纹前缘Ⅰ、Ⅱ、Ⅲ型应力强度因子,将全部应力强度因子转化为便于计算的无因次应力强度因子并采用最小二乘法进行多项式拟合,为确保应力强度因子变化趋势以拟合曲线函数值代替离散无因次应力强度因子采用多参数拉格朗日插值法插值计算任意形状孔边裂纹无因次应力强度因子,由无因次应力强度因子计算任意形状孔边裂纹应力强度因子;并就某一形状裂纹的插值计算结果与有限元分析结果进行对比:插值结果与有限元求解非常接近,因此采用数值插值计算近似代替全三维有限元分析简化应力强度因子求解过程。
在上述插值求解应力强度因子的基础上考虑混合裂纹扩展模式及裂纹闭合效应,以桅杆结构下层纤绳连接拉耳孔边裂纹为例采用Paris裂纹扩展速率公式研究了孔边裂纹的扩展形状变化特性;考虑孔边裂纹扩展形状变化特性采用逐循环直接积分法分别预测了桅杆结构上、下层纤绳连接拉耳不同初始条件孔边裂纹的扩展寿命。
Guyed mast is a kind of highrising structure which mainly subjects to wind load, and consists of a slender bar body and several layer cables of 3 or 4 orientation stretching obliquely along height which has been widely used on radio communication,broadcast television,ocean and air navigation,environment protection,energy explore and other important fields of national economy.The ratio of guyed mast failure accidents is the second to none in civil engineers on account of the complicate working mechanism of guyed mast has yet not been understood and mastered completely.Reports of many guyed mast failure accidents show that most collapse and failure accidents are result of structural instability or the stress of structural member has exceeded the strength limit due to fatigue damage.So it is necessary to study fatigue damage and predict the fatigue life of guyed mast in order to provide important basis for guyed mast on evaluation of fatigue residual life and proposition of new method of fatigue damage detection.
Taking crack germination life as fatigue criterion is the result of having no enough knowledge of fatigue fracture.Fatigue total life includes crack germination and crack propagation,and complete fatigue analysis should not only study crack germination but also crack propagation.This dissertation studied crack germination lift with multi-axial analytic theory.15 series of wind load along the height of the guyed mast have been simulated with harmonic wave superpose method improving by introducing FFT algorithm.Also the cross-correlation function and power spectrum have been checked and simulated wind load with the same characteristic of natural wind has been obtained by transformation wind velocity to wind pressure.
A nonlinear dynamic model has been established and the nonlinear dynamic response has been analyzed via Newmark-βdirect integration combining to Newton-Raphson integration,so we can get the stress response time history of cable. On account of the symmetry of guyed mast only 0°、30°、60°orientation of wind responses have been calculated and wind response of other orientation can be obtained according to symmetry.The stress or strain state of dangerous point of fatigue on guyed mast's ear plate has been calculated via finite element software. Rotate the coordination of stress or strain with angle changes per certain interval to search the critical plane relation to maximum damage.The shear and normal strain cycle of critical plane are extracted with double rain-flow counting method and be composed a unified multi-axial fatigue damage parameter basing on Von-Mises rule. Then The multi-axis fatigue accumulative damages of different wind orientation and wind average velocity of guyed mast's ear plate connecting with sub-layer cable have been evaluated on basis of Mason-coffin formula and Miner fatigue accumulative damage rule.And germination life of crack has been calculated according to total damage.
The emphasis of this dissertation is studying the propagation of initial fatigue crack of complicate structure guyed mast's ear plate with fracture mechanics.The research of crack propagation of ear-plate connecting guyed mast to cable should solve two problems:the calculating of stress intensity factors along crack front and the analysis of crack propagation.Stress intensity factors along 3-D surface crack have been calculated with finite element method.In view the difficulty on modeling 3-D crack,a solid modeling method has been proposed.This method decreases modeling word greatly by adopting Boolean operation and some super mesh skills which can be used to model all kinds of cracked finite element model with complex configuration.Stress intensity factors of central surface crack and crack at hole have been calculated with finite element method basing on solid modeling method.They are compared with the results deriving from Newman & Raju stress intensity factor empirical formula.By that the procedures of solid modeling and solving of stress intensity factor have been validated.
With previous described finite element method we calculatedⅠ,Ⅱ,Ⅲtype of stress intensity factor along front of given shape and size crack at hole of guyed mast's ear-plate and transform them all to the form of no-dimension stress intensity factors which are convenient for calculation.Simulate no dimension stress intensity factor with polynomial by least square method.In order to maintain the changing trend of no-dimension stress intensity factor we replace the dispersed no-dimension stress intensity factor with data of polynomial function to calculate no-dimension Stress intensity factors of any shape crack at hole by multi-parameter Lagrange interpolation method.And then calculate stress intensity factor of any shape crack at hole.There is a comparison between interpolation value and the finite element analytical results of a certain shape crack which shows that they are close to each other.So we can replace whole 3-D finite element analysis with numerical interpolation calculation approximately.
Take guyed mast' ear plate connecting with sub-layer cable as objects,we studied the characteristic of crack propagation shape by adopting Paris propagation velocity formula with consideration of mix crack propagation pattern and crack close phenomenon on the basis of above solving of stress intensity factor.Propagation life of crack at hole of different initial situation of ear-plates connecting with guyed mast's upper and lower layer cables have been predicted with one by one cycle direct integration method with the consideration of the characteristic of crack propagation shape.
以裂纹萌生寿命控制结构的疲劳是对结构疲劳断裂认识不足的结果,疲劳总寿命包括裂纹萌生和裂纹扩展两部分,完整的疲劳分析既要研究裂纹的起始萌生,也要研究裂纹的扩展。本论文首先采用多轴疲劳理论估算拉耳孔边裂纹萌生寿命。采用基于FFT算法改进的谐波叠加法模拟了桅杆结构沿杆身高度分布的15条脉动风速时程并进行了相关函数与功率谱检验,通过风速风压关系转换得到与自然风基本特性一致的模拟风荷载。
建立桅杆结构非线性动力计算模型,在时域内分析桅杆结构模拟风荷载作用下的非线性动力响应,获得桅杆结构纤绳应力响应时程。由于桅杆结构的对称性仅计算了0°、30°、60°风向桅杆结构的风振响应,其余方向风振响应根据对称性得到;借助有限元软件计算确定桅杆结构局部拉耳模型疲劳危险点及其应力应变状态,对危险点应力应变状态进行坐标旋转,按一定间隔变化旋转角度搜索最大损伤参量所对应的临界损伤面位置;采用双重雨流计数法提取临界损伤面上的正、剪应变循环并基于von Mises准则合成统一的多轴疲劳损伤参量,然后依据Mason-coffin公式及Miner疲劳累积损伤准则估算桅杆结构纤绳连接拉耳各不同风向不同平均风速作用下的多轴疲劳累积损伤,由总损伤计算出裂纹萌生寿命。
本文重点采用断裂力学方法研究桅杆拉耳这个局部构造复杂结构在初始疲劳裂纹下的扩展。桅杆结构纤绳连接拉耳裂纹的扩展寿命研究主要解决两个问题:裂纹前缘应力强度因子计算与孔边裂纹扩展分析。本文采用有限元法计算三维表面裂纹前缘应力强度因子。首先借助ANSYS高级网格划分技巧解决了复杂结构裂纹体有限元建模难题;利用布尔运算、高级网格划分技巧等手段采用实体建模法创建三维裂纹体模型。基于裂纹实体建模,采用有限元法分别计算了含中心表面裂纹及孔边角裂纹平板前缘应力强度因子,并与含中心表面裂纹及孔边角裂纹平板结构的Newman&Raju应力强度因子经验公式的计算结果进行对比验证了有限元实体建模及应力强度因子求解过程的可靠性。
采用前述有限元法计算桅杆结构拉耳各种给定形状、尺寸孔边裂纹裂纹前缘Ⅰ、Ⅱ、Ⅲ型应力强度因子,将全部应力强度因子转化为便于计算的无因次应力强度因子并采用最小二乘法进行多项式拟合,为确保应力强度因子变化趋势以拟合曲线函数值代替离散无因次应力强度因子采用多参数拉格朗日插值法插值计算任意形状孔边裂纹无因次应力强度因子,由无因次应力强度因子计算任意形状孔边裂纹应力强度因子;并就某一形状裂纹的插值计算结果与有限元分析结果进行对比:插值结果与有限元求解非常接近,因此采用数值插值计算近似代替全三维有限元分析简化应力强度因子求解过程。
在上述插值求解应力强度因子的基础上考虑混合裂纹扩展模式及裂纹闭合效应,以桅杆结构下层纤绳连接拉耳孔边裂纹为例采用Paris裂纹扩展速率公式研究了孔边裂纹的扩展形状变化特性;考虑孔边裂纹扩展形状变化特性采用逐循环直接积分法分别预测了桅杆结构上、下层纤绳连接拉耳不同初始条件孔边裂纹的扩展寿命。
Guyed mast is a kind of highrising structure which mainly subjects to wind load, and consists of a slender bar body and several layer cables of 3 or 4 orientation stretching obliquely along height which has been widely used on radio communication,broadcast television,ocean and air navigation,environment protection,energy explore and other important fields of national economy.The ratio of guyed mast failure accidents is the second to none in civil engineers on account of the complicate working mechanism of guyed mast has yet not been understood and mastered completely.Reports of many guyed mast failure accidents show that most collapse and failure accidents are result of structural instability or the stress of structural member has exceeded the strength limit due to fatigue damage.So it is necessary to study fatigue damage and predict the fatigue life of guyed mast in order to provide important basis for guyed mast on evaluation of fatigue residual life and proposition of new method of fatigue damage detection.
Taking crack germination life as fatigue criterion is the result of having no enough knowledge of fatigue fracture.Fatigue total life includes crack germination and crack propagation,and complete fatigue analysis should not only study crack germination but also crack propagation.This dissertation studied crack germination lift with multi-axial analytic theory.15 series of wind load along the height of the guyed mast have been simulated with harmonic wave superpose method improving by introducing FFT algorithm.Also the cross-correlation function and power spectrum have been checked and simulated wind load with the same characteristic of natural wind has been obtained by transformation wind velocity to wind pressure.
A nonlinear dynamic model has been established and the nonlinear dynamic response has been analyzed via Newmark-βdirect integration combining to Newton-Raphson integration,so we can get the stress response time history of cable. On account of the symmetry of guyed mast only 0°、30°、60°orientation of wind responses have been calculated and wind response of other orientation can be obtained according to symmetry.The stress or strain state of dangerous point of fatigue on guyed mast's ear plate has been calculated via finite element software. Rotate the coordination of stress or strain with angle changes per certain interval to search the critical plane relation to maximum damage.The shear and normal strain cycle of critical plane are extracted with double rain-flow counting method and be composed a unified multi-axial fatigue damage parameter basing on Von-Mises rule. Then The multi-axis fatigue accumulative damages of different wind orientation and wind average velocity of guyed mast's ear plate connecting with sub-layer cable have been evaluated on basis of Mason-coffin formula and Miner fatigue accumulative damage rule.And germination life of crack has been calculated according to total damage.
The emphasis of this dissertation is studying the propagation of initial fatigue crack of complicate structure guyed mast's ear plate with fracture mechanics.The research of crack propagation of ear-plate connecting guyed mast to cable should solve two problems:the calculating of stress intensity factors along crack front and the analysis of crack propagation.Stress intensity factors along 3-D surface crack have been calculated with finite element method.In view the difficulty on modeling 3-D crack,a solid modeling method has been proposed.This method decreases modeling word greatly by adopting Boolean operation and some super mesh skills which can be used to model all kinds of cracked finite element model with complex configuration.Stress intensity factors of central surface crack and crack at hole have been calculated with finite element method basing on solid modeling method.They are compared with the results deriving from Newman & Raju stress intensity factor empirical formula.By that the procedures of solid modeling and solving of stress intensity factor have been validated.
With previous described finite element method we calculatedⅠ,Ⅱ,Ⅲtype of stress intensity factor along front of given shape and size crack at hole of guyed mast's ear-plate and transform them all to the form of no-dimension stress intensity factors which are convenient for calculation.Simulate no dimension stress intensity factor with polynomial by least square method.In order to maintain the changing trend of no-dimension stress intensity factor we replace the dispersed no-dimension stress intensity factor with data of polynomial function to calculate no-dimension Stress intensity factors of any shape crack at hole by multi-parameter Lagrange interpolation method.And then calculate stress intensity factor of any shape crack at hole.There is a comparison between interpolation value and the finite element analytical results of a certain shape crack which shows that they are close to each other.So we can replace whole 3-D finite element analysis with numerical interpolation calculation approximately.
Take guyed mast' ear plate connecting with sub-layer cable as objects,we studied the characteristic of crack propagation shape by adopting Paris propagation velocity formula with consideration of mix crack propagation pattern and crack close phenomenon on the basis of above solving of stress intensity factor.Propagation life of crack at hole of different initial situation of ear-plates connecting with guyed mast's upper and lower layer cables have been predicted with one by one cycle direct integration method with the consideration of the characteristic of crack propagation shape.
引文
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