具损伤压电智能层合结构的非线性动力学性能与疲劳寿命研究
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摘要
纤维增强复合材料层合结构在加工与使用过程中极易产生损伤,损伤的出现及其扩展将劣化结构的力学性能,降低其使用寿命,为保证该类结构安全可靠地工作,必须根据不同的缺陷形式确定相应的损伤本构关系,建立其静、动力学模型,分析损伤对结构力学性能及其使用寿命的影响。本论文以纤维增强复合材料层合结构以及压电智能层合结构为研究对象,综合考虑结构几何非线性和压电效应等因素,研究具基体开裂、脱层、纤维与基体脱胶等不同损伤形式下,层合结构及压电智能层合结构的非线性动力响应与疲劳损伤寿命等问题,揭示其力学行为的本质特征。本论文的研究成果不仅具有较重要的学术价值,也具有较强的工程应用意义。本论文的主要研究工作如下。
研究具损伤压电粘弹性层合梁的疲劳寿命问题。基于线粘弹性理论和连续介质损伤力学,采用Boltzmann叠加原理和应变能等效原理,建立了具正交各向异性损伤的粘弹性复合材料的本构关系。设每一单层沿厚度方向有相同的损伤程度,考虑几何非线性、横向剪切效应和压电效应,根据复合材料力学和非线性层合板壳理论,建立了具损伤压电粘弹性层合梁的非线性运动控制方程,采用Kachanov型损伤演化模型表征在单次循环载荷作用下的损伤演化,应用Chaboche高周期疲劳损伤模型来描述多次循环载荷作用下的疲劳损伤累积状况,然后,综合运用有限差分法、Newmark法、Newton-Cotes法和迭代法对整个问题进行求解,并利用循环跳跃法来缩减计算量。具体地讨论了载荷参数、结构几何参数、材料参数和压电效应等因素对具损伤压电粘弹性层合梁非线性动力响应和疲劳损伤演化曲线的影响,且与非线性有限元的结果进行了比较。
研究具基体开裂损伤压电层合板的疲劳寿命问题。基于Talreja张量内变量损伤模型,应用不变量理论和不可逆热力学原理建立了适用于具基体开裂损伤纤维增强复合材料弯曲问题的损伤本构关系。考虑几何非线性和压电效应,根据Von Karman非线性板理论,建立了具基体开裂损伤压电层合板的非线性运动控制方程。采用Kachanov型损伤演化模型表征在单次循环载荷作用下的损伤演化,应用Chaboche高周期疲劳损伤模型描述多次循环载荷作用下的疲劳损伤累积状况,然后,综合运用有限差分法、Newmark法、Newton- Cotes法和迭代法对整个问题进行求解,并利用循环跳跃法来缩减计算量。具体地讨论了载荷参数、结构几何参数、材料参数和压电效应等因素对具基体开裂损伤压电层合板非线性动力响应和疲劳损伤演化的影响,且与已有文献的结果进行了比较。
研究具非对称脱层压电层合梁板的疲劳脱层扩展问题。基于非线性弹性板壳理论和可动边界变分原理,考虑脱层间的接触效应,建立了具脱层压电层合梁板的非线性运动控制方程及相应的定解条件。应用Griffith准则,建立了脱层前缘的能量释放率表达式,根据Paris的疲劳扩展准则,得到了循环荷载作用下脱层前缘的脱层扩展率,然后,应用循环跳跃法计算出脱层前缘的扩展长度。具体地讨论了电压、脱层的非对称性、脱层长度等因素对具非对称脱层压电层合梁板脱层前缘的能量释放率,以及脱层前缘扩展长度的影响。
研究具非对称脱层压电层合圆柱壳的疲劳脱层扩展问题。基于可动边界变分原理,建立了考虑脱层间非线性接触效应的具脱层压电层合圆柱壳的力学模型。首先,将脱层的上下部分视为两串连非线性弹簧来计算接触力,然后,对系统的非线性运动控制方程进行修正,从而有效地避免了脱层之间的相互贯穿。应用Griffith准则,导出了压电层合圆柱壳脱层前缘的能量释放率表达式,且根据Paris的疲劳扩展准则,得到循环荷载作用下脱层前缘的扩展长度。具体地讨论了压电效应、接触区刚度、脱层的非对称性、脱层长度等因素对具非对称脱层压电层合圆柱壳脱层前缘的能量释放率,以及脱层前缘扩展长度的影响。
研究具界面损伤复合材料层合板的非线性动力响应问题。基于Soldatos精确应力分析的广义六自由度板理论,考虑复合材料层合板铺设层间界面处的损伤效应,应用变分原理,建立了具界面损伤复合材料层合板的三维非线性运动控制方程;基于弹性力学空间问题的平衡微分方程,考虑具损伤界面的位移和应力连续条件,确定了非线性运动控制方程中的待定形函数。综合利用有限差分法、Newmark法、Newton-Cotes法和迭代法对具界面损伤简支可动层合板的层间应力以及非线性动力响应进行求解。具体地讨论了界面损伤对界面处应力场和层合板非线性动力响应的影响。
研究纤维增强复合材料界面的疲劳脱粘扩展问题。基于弹性力学的基本理论,建立了纤维增强复合材料脱粘区和未脱粘区的平稳微分方程及相应的定解条件,导出了纤维与基体中轴向正应力的计算式;应用界面脱粘的能量释放率准则,建立了复合材料脱粘的判据,根据Paris的疲劳裂纹扩展准则,得到循环荷载作用下界面脱粘的扩展率,然后应用循环跳跃法计算出界面脱粘的疲劳扩展长度。算例中,以碳/环氧复合材料为例,讨论了材料参数、几何参数、预应力、外载荷等因素对纤维/基体应力分布、界面脱粘能量释放率、疲劳扩展长度的影响。
The damages will easily emerge in fibre-reinforecd composite structures during the manufacturing and service processes. The emergence of damages and their further growth will drastically reduce the mechanical properties and service life of the structures. For the safe reliability of structures, it is necessary to establish the constitutive relations and mechanical modeling for different kinds of damage and analyze the effect of damage on the mechanical properties and service life of the structure. In this dissertation, considering fibre-reinforced composite laminated structure and piezoelastic laminated structures as the subjects investigated, the nonlinear dynamic response and fatigue damage prediction of piezoelectric laminated structure with different kind of damage, such as matrix crack, delamination and interfacial debonding, are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results are significant not only in the academic but also in the practical engineering. The main results contain as follows.
The fatigue damage life of piezoelectric viscoelastic laminated beams is investigated. Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Supposing the damage variables remain constant throughout the thickness in each layer, considering geometric nonlinearity, transverse shear deformation and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated beams with damage are derived by using the composite mechanics and nonlinear laminated theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution for the damaged piezoelectric viscoelastic laminated beams are discussed in detail.
The fatigue damage life of piezoelectric laminated plate with matrix cracks is investigated. Based on the Talreja’s damage model with tensor valued internal state variables and the invariant theory, using the thermodynamic relations, a constitutive model for fibre-reinforced composite containing matrix cracks is established. Considering geometric nonlinearity and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated plates with matrix cracks are derived by using the Von Karman’s nonlinear theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth.
Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution curve for piezoelectric viscoelastic laminated plates with matrix cracks are discussed in detail. The fatigue delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is investigated. Based on the nonlinear elastic plate’s theory and variational principle of moving boundary, the nonlinear governing equations of the piezoelectric laminated beam-plates with delamination are derived, and the corresponding boundary and matching conditions are given. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. Applying the Paris law, the delamination growth rate is arrived and using cyclic skip method, the delamination growth lengths along the delamination fronts under cycle load are finally determined. In the numerical examples, the delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is calculated, and the effects of voltages, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.
The fatigue delamination growth of piezoelectric laminated cylindrical shell with asymmetric delamination is investigated. Based on the variational principle of moving boundary, an analytic model of delaminated piezoelectric laminated cylindrical shell under the consideration of nonlinear contact effects is derived. Firstly, the contact force is calculated through regarding the two segments beside the delamination as two nonlinear springs connected in series. Then, the governing equation of transverse motion is modified by the nonlinear contact force and thus the penetration between two delaminated layers can be avoided. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. Applying the Paris law, the delamination growth lengths along the delamination fronts under cycle load are finally determined. In numerical examples, the delamination growth length of piezoelectric laminated cylindrical shell with asymmetric delamination is calculated, and the effects of voltages, stiffness factor of contact region, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.
The nonlinear dynamic response of composite laminated plate is investigated. Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis, considering the effect of interfacial damage and using the variation principle, the three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived. Then based on the equilibrium differential equation in the elastic mechanics theory, considering the displacement and stress continuity conditions, the undetermined shape functions of governing equations are obtained. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are derived by applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure. In numerical calculation, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed in detail.
The fatigue debonding growth of fibre-reinforecd composite with interfacial debonding is investigated. Based on the basic theory of elastic mechanics, the equilibrium differential equations of deboned and fully-bonded regions of composite are derived and the corresponding boundary conditions are given, then the calculating formulas of axial stresses in fiber and matrix are obtained. The criterion of energy release rate for interfacial debonding are obtained. Applying the Paris law, the interfacial debonding rate is arrived and using cyclic skip method, the fatigue interfacial debonding lengths under cycle load are finally determined. In numerical examples, the typical carbon/epoxy composite with interfacial debonding is calculated, and the effects of material constants, geometric constants, initial stress and external load on the distribution of stresses in fiber/matrix and interfacial debonding energy release rate and fatigue growth length are discussed in detail.
研究具损伤压电粘弹性层合梁的疲劳寿命问题。基于线粘弹性理论和连续介质损伤力学,采用Boltzmann叠加原理和应变能等效原理,建立了具正交各向异性损伤的粘弹性复合材料的本构关系。设每一单层沿厚度方向有相同的损伤程度,考虑几何非线性、横向剪切效应和压电效应,根据复合材料力学和非线性层合板壳理论,建立了具损伤压电粘弹性层合梁的非线性运动控制方程,采用Kachanov型损伤演化模型表征在单次循环载荷作用下的损伤演化,应用Chaboche高周期疲劳损伤模型来描述多次循环载荷作用下的疲劳损伤累积状况,然后,综合运用有限差分法、Newmark法、Newton-Cotes法和迭代法对整个问题进行求解,并利用循环跳跃法来缩减计算量。具体地讨论了载荷参数、结构几何参数、材料参数和压电效应等因素对具损伤压电粘弹性层合梁非线性动力响应和疲劳损伤演化曲线的影响,且与非线性有限元的结果进行了比较。
研究具基体开裂损伤压电层合板的疲劳寿命问题。基于Talreja张量内变量损伤模型,应用不变量理论和不可逆热力学原理建立了适用于具基体开裂损伤纤维增强复合材料弯曲问题的损伤本构关系。考虑几何非线性和压电效应,根据Von Karman非线性板理论,建立了具基体开裂损伤压电层合板的非线性运动控制方程。采用Kachanov型损伤演化模型表征在单次循环载荷作用下的损伤演化,应用Chaboche高周期疲劳损伤模型描述多次循环载荷作用下的疲劳损伤累积状况,然后,综合运用有限差分法、Newmark法、Newton- Cotes法和迭代法对整个问题进行求解,并利用循环跳跃法来缩减计算量。具体地讨论了载荷参数、结构几何参数、材料参数和压电效应等因素对具基体开裂损伤压电层合板非线性动力响应和疲劳损伤演化的影响,且与已有文献的结果进行了比较。
研究具非对称脱层压电层合梁板的疲劳脱层扩展问题。基于非线性弹性板壳理论和可动边界变分原理,考虑脱层间的接触效应,建立了具脱层压电层合梁板的非线性运动控制方程及相应的定解条件。应用Griffith准则,建立了脱层前缘的能量释放率表达式,根据Paris的疲劳扩展准则,得到了循环荷载作用下脱层前缘的脱层扩展率,然后,应用循环跳跃法计算出脱层前缘的扩展长度。具体地讨论了电压、脱层的非对称性、脱层长度等因素对具非对称脱层压电层合梁板脱层前缘的能量释放率,以及脱层前缘扩展长度的影响。
研究具非对称脱层压电层合圆柱壳的疲劳脱层扩展问题。基于可动边界变分原理,建立了考虑脱层间非线性接触效应的具脱层压电层合圆柱壳的力学模型。首先,将脱层的上下部分视为两串连非线性弹簧来计算接触力,然后,对系统的非线性运动控制方程进行修正,从而有效地避免了脱层之间的相互贯穿。应用Griffith准则,导出了压电层合圆柱壳脱层前缘的能量释放率表达式,且根据Paris的疲劳扩展准则,得到循环荷载作用下脱层前缘的扩展长度。具体地讨论了压电效应、接触区刚度、脱层的非对称性、脱层长度等因素对具非对称脱层压电层合圆柱壳脱层前缘的能量释放率,以及脱层前缘扩展长度的影响。
研究具界面损伤复合材料层合板的非线性动力响应问题。基于Soldatos精确应力分析的广义六自由度板理论,考虑复合材料层合板铺设层间界面处的损伤效应,应用变分原理,建立了具界面损伤复合材料层合板的三维非线性运动控制方程;基于弹性力学空间问题的平衡微分方程,考虑具损伤界面的位移和应力连续条件,确定了非线性运动控制方程中的待定形函数。综合利用有限差分法、Newmark法、Newton-Cotes法和迭代法对具界面损伤简支可动层合板的层间应力以及非线性动力响应进行求解。具体地讨论了界面损伤对界面处应力场和层合板非线性动力响应的影响。
研究纤维增强复合材料界面的疲劳脱粘扩展问题。基于弹性力学的基本理论,建立了纤维增强复合材料脱粘区和未脱粘区的平稳微分方程及相应的定解条件,导出了纤维与基体中轴向正应力的计算式;应用界面脱粘的能量释放率准则,建立了复合材料脱粘的判据,根据Paris的疲劳裂纹扩展准则,得到循环荷载作用下界面脱粘的扩展率,然后应用循环跳跃法计算出界面脱粘的疲劳扩展长度。算例中,以碳/环氧复合材料为例,讨论了材料参数、几何参数、预应力、外载荷等因素对纤维/基体应力分布、界面脱粘能量释放率、疲劳扩展长度的影响。
The damages will easily emerge in fibre-reinforecd composite structures during the manufacturing and service processes. The emergence of damages and their further growth will drastically reduce the mechanical properties and service life of the structures. For the safe reliability of structures, it is necessary to establish the constitutive relations and mechanical modeling for different kinds of damage and analyze the effect of damage on the mechanical properties and service life of the structure. In this dissertation, considering fibre-reinforced composite laminated structure and piezoelastic laminated structures as the subjects investigated, the nonlinear dynamic response and fatigue damage prediction of piezoelectric laminated structure with different kind of damage, such as matrix crack, delamination and interfacial debonding, are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results are significant not only in the academic but also in the practical engineering. The main results contain as follows.
The fatigue damage life of piezoelectric viscoelastic laminated beams is investigated. Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Supposing the damage variables remain constant throughout the thickness in each layer, considering geometric nonlinearity, transverse shear deformation and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated beams with damage are derived by using the composite mechanics and nonlinear laminated theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution for the damaged piezoelectric viscoelastic laminated beams are discussed in detail.
The fatigue damage life of piezoelectric laminated plate with matrix cracks is investigated. Based on the Talreja’s damage model with tensor valued internal state variables and the invariant theory, using the thermodynamic relations, a constitutive model for fibre-reinforced composite containing matrix cracks is established. Considering geometric nonlinearity and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated plates with matrix cracks are derived by using the Von Karman’s nonlinear theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth.
Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution curve for piezoelectric viscoelastic laminated plates with matrix cracks are discussed in detail. The fatigue delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is investigated. Based on the nonlinear elastic plate’s theory and variational principle of moving boundary, the nonlinear governing equations of the piezoelectric laminated beam-plates with delamination are derived, and the corresponding boundary and matching conditions are given. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. Applying the Paris law, the delamination growth rate is arrived and using cyclic skip method, the delamination growth lengths along the delamination fronts under cycle load are finally determined. In the numerical examples, the delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is calculated, and the effects of voltages, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.
The fatigue delamination growth of piezoelectric laminated cylindrical shell with asymmetric delamination is investigated. Based on the variational principle of moving boundary, an analytic model of delaminated piezoelectric laminated cylindrical shell under the consideration of nonlinear contact effects is derived. Firstly, the contact force is calculated through regarding the two segments beside the delamination as two nonlinear springs connected in series. Then, the governing equation of transverse motion is modified by the nonlinear contact force and thus the penetration between two delaminated layers can be avoided. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. Applying the Paris law, the delamination growth lengths along the delamination fronts under cycle load are finally determined. In numerical examples, the delamination growth length of piezoelectric laminated cylindrical shell with asymmetric delamination is calculated, and the effects of voltages, stiffness factor of contact region, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.
The nonlinear dynamic response of composite laminated plate is investigated. Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis, considering the effect of interfacial damage and using the variation principle, the three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived. Then based on the equilibrium differential equation in the elastic mechanics theory, considering the displacement and stress continuity conditions, the undetermined shape functions of governing equations are obtained. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are derived by applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure. In numerical calculation, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed in detail.
The fatigue debonding growth of fibre-reinforecd composite with interfacial debonding is investigated. Based on the basic theory of elastic mechanics, the equilibrium differential equations of deboned and fully-bonded regions of composite are derived and the corresponding boundary conditions are given, then the calculating formulas of axial stresses in fiber and matrix are obtained. The criterion of energy release rate for interfacial debonding are obtained. Applying the Paris law, the interfacial debonding rate is arrived and using cyclic skip method, the fatigue interfacial debonding lengths under cycle load are finally determined. In numerical examples, the typical carbon/epoxy composite with interfacial debonding is calculated, and the effects of material constants, geometric constants, initial stress and external load on the distribution of stresses in fiber/matrix and interfacial debonding energy release rate and fatigue growth length are discussed in detail.
引文
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