裂纹扩展与损伤演化理论与应用研究
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摘要
在长寿命结构的设计过程中,结构或构件的耐久性与损伤容限设计是极为重要的设计环节。而构件或材料的抗断裂性能是耐久性与损伤容限设计所考察的重要力学指标之一。目前,对这方面的研究还缺乏坚实的理论基础。因此,对含裂纹构件尤其是含非穿透裂纹构件抗断裂性能的研究不仅具有学术研究价值,而且也具有工程应用价值。
本文对含裂纹构件的抗断裂性能进行了较为全面的理论研究和必要的实验研究,并且取得了一定的成果,全文共涉及三个方面的内容:
第一部分研究了二维含穿透裂纹构件在两种失效模式(裂纹扩展与韧带屈服)下的载荷与位移关系。
本文基于能量差率原理、余能原理、计及厚度效应的断裂韧度与阻力曲线理论以及塑性本构关系,得到二维含穿透裂纹构件载荷-位移曲线的解析闭合解;为了验证该解析闭合解的有效性,进行了二维含穿透裂纹构件的准静态单调加载试验研究。
第二部分从裂纹扩展动力与裂纹扩展阻力两个方面,研究了含非穿透裂纹三维有限大体的裂纹扩展问题。
在裂纹扩展动力研究方面,改进了已有的基于能量差率原理求解含非穿透裂纹三维有限大体应力强度因子与能量释放率的方法,并得到与有限元法计算结果基本一致的显示闭合解。
在裂纹扩展阻力研究方面,基于热力学原理,给出了重复加载下含非穿透裂纹三维构件的疲劳裂纹扩展速率的理论表达式;在此基础之上,给出了预测疲劳裂纹扩展寿命的数值方法。同时,建立了以热力学定律为基础的单调加载下含非穿透裂纹三维构件的裂纹扩展微分方程组,并给出由方程组绘制疲劳裂纹扩展阻力曲线的数值方法。
第三部分应用基于损伤力学原理的疲劳裂纹形成寿命的封闭解预估某型号民机加压舱的疲劳裂纹形成寿命。
在有限元细节应力分析结果的基础上,结合塑性理论与损伤力学原理得到疲劳裂纹形成寿命预估模型,给出机身加压舱结构的概率疲劳寿命,该方法的计算结果与全尺寸等压舱结构的疲劳试验结果基本一致。
In the design process of long term structures, the damage-tolerance and durability design are very important design links. The behaviors against fracture of materials and structural members are key indexes of above designs. However, there are no solid theoretical foundations in these aspects. Therefore, the topic of this dissertation have important significance in academic research and engineering application.
In this dissertation, comprehensive theoretical studies and necessary experimental works are performed. The relevant achievements can be divided into following three parts.
PartⅠ, the closed form analytical solutions of nonlinear load-deflection curves of two dimensional structural members with through thickness cracks under the conditions of crack growth and ligament yielding are provided and verified by experimental results.
PartⅡ, an improved closed form solution of stress intensity factors and energy release rates of three dimensional structural members with non-through thickness cracks are carried out on the basis of energy method and checked by finite element computions..
Furthermore, the theoretical expressions of fatigue crack growth rates of three dimensional structural members with non-through thickness cracks under repeated loading are established on the foundation of thermodynamics and fatigue crack growth lives are predicted by these expressions with numerical method. Similarly, the system of differential equations of crack growth of three dimensional structural members with non-through thickness cracks under monotonic loading is founded on the basis of themodynamics also and resistance curves can be drawn by this system of differential equations through numerical method.
PartⅢ, a closed form solution of probabilistic fatigue crack initiation life prediction based upon the conservative integral principle of damage mechanics, finite element method and theory of plasticity is applied to the pressurized cabin of certain type civil aircraft. The computational result agree with the result given by the full scale fatigue test of the pressurized cabin.
本文对含裂纹构件的抗断裂性能进行了较为全面的理论研究和必要的实验研究,并且取得了一定的成果,全文共涉及三个方面的内容:
第一部分研究了二维含穿透裂纹构件在两种失效模式(裂纹扩展与韧带屈服)下的载荷与位移关系。
本文基于能量差率原理、余能原理、计及厚度效应的断裂韧度与阻力曲线理论以及塑性本构关系,得到二维含穿透裂纹构件载荷-位移曲线的解析闭合解;为了验证该解析闭合解的有效性,进行了二维含穿透裂纹构件的准静态单调加载试验研究。
第二部分从裂纹扩展动力与裂纹扩展阻力两个方面,研究了含非穿透裂纹三维有限大体的裂纹扩展问题。
在裂纹扩展动力研究方面,改进了已有的基于能量差率原理求解含非穿透裂纹三维有限大体应力强度因子与能量释放率的方法,并得到与有限元法计算结果基本一致的显示闭合解。
在裂纹扩展阻力研究方面,基于热力学原理,给出了重复加载下含非穿透裂纹三维构件的疲劳裂纹扩展速率的理论表达式;在此基础之上,给出了预测疲劳裂纹扩展寿命的数值方法。同时,建立了以热力学定律为基础的单调加载下含非穿透裂纹三维构件的裂纹扩展微分方程组,并给出由方程组绘制疲劳裂纹扩展阻力曲线的数值方法。
第三部分应用基于损伤力学原理的疲劳裂纹形成寿命的封闭解预估某型号民机加压舱的疲劳裂纹形成寿命。
在有限元细节应力分析结果的基础上,结合塑性理论与损伤力学原理得到疲劳裂纹形成寿命预估模型,给出机身加压舱结构的概率疲劳寿命,该方法的计算结果与全尺寸等压舱结构的疲劳试验结果基本一致。
In the design process of long term structures, the damage-tolerance and durability design are very important design links. The behaviors against fracture of materials and structural members are key indexes of above designs. However, there are no solid theoretical foundations in these aspects. Therefore, the topic of this dissertation have important significance in academic research and engineering application.
In this dissertation, comprehensive theoretical studies and necessary experimental works are performed. The relevant achievements can be divided into following three parts.
PartⅠ, the closed form analytical solutions of nonlinear load-deflection curves of two dimensional structural members with through thickness cracks under the conditions of crack growth and ligament yielding are provided and verified by experimental results.
PartⅡ, an improved closed form solution of stress intensity factors and energy release rates of three dimensional structural members with non-through thickness cracks are carried out on the basis of energy method and checked by finite element computions..
Furthermore, the theoretical expressions of fatigue crack growth rates of three dimensional structural members with non-through thickness cracks under repeated loading are established on the foundation of thermodynamics and fatigue crack growth lives are predicted by these expressions with numerical method. Similarly, the system of differential equations of crack growth of three dimensional structural members with non-through thickness cracks under monotonic loading is founded on the basis of themodynamics also and resistance curves can be drawn by this system of differential equations through numerical method.
PartⅢ, a closed form solution of probabilistic fatigue crack initiation life prediction based upon the conservative integral principle of damage mechanics, finite element method and theory of plasticity is applied to the pressurized cabin of certain type civil aircraft. The computational result agree with the result given by the full scale fatigue test of the pressurized cabin.
引文
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