循环硬化材料高温非比例循环棘轮行为的本构描述及其有限元实现
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摘要
棘轮效应是在非对称应力控制循环加载下塑性变形的循环累积。棘轮效应可能导致疲劳寿命的减少或使结构的变形超过限制而不能正常工作,是实际工程结构设计中需要考虑的一个重要问题。近20年来,国内外学者已对金属材料的棘轮行为进行了大量的实验和理论研究,在材料的循环本构模型、棘轮效应的预测等方面取得了较大的进展。但是,对金属材料的棘轮效应,尤其是材料的高温非比例多轴棘轮效应进行准确的预测仍是一个很大的挑战。因此,对金属材料的非比例多轴棘轮行为及与其相关的应变循环变形行为进行系统深入的实验研究,继而发展能较为精确的对其进行描述的本构模型,对固体力学及其相关学科具有非常重要的理论意义,对工程构件更可靠的设计和使用也具有重要的应用价值。此外,随着计算机技术的迅速发展,现在已经可以采用有限元软件对各种工程构件的变形行为进行模拟和预测。然而,现有的一些大型有限元程序中使用的循环本构模型对棘轮效应等循环变形行为的预测不够精确,因此有必要将新发展的本构模型进行数值实现,并将其移植到现有的有限元软件中,进而对一些工程结构的循环变形行为进行准确的数值模拟。这可以促进先进模型在结构分析和寿命评估中的应用,具有较高的工程应用价值。
为了对循环硬化材料在高温下的非比例多轴棘轮行为和应变循环特性进行深入系统的研究并对其进行较为精确的本构描述,本论文开展了如下工作:
1.在350℃和700℃下,对材料在单轴和多种加载路径下的非比例多轴棘轮行为和应变循环特性进行了系统的实验研究。通过对实验数据的研究分析,得到了材料在高温下的非比例棘轮行为和应变控制循环变形行为的基本特性,为相关本构模型的建立奠定了基础。
2.在统一粘塑性循环本构的框架下,改进和发展了一个新的本构模型,对材料的高温非比例多轴棘轮行为和应变循环变形行为进行了统一描述。该模型给出了一个新的背应力演化方程,引入了非比例度参量,并且还考虑了最大塑性应变幅值记忆效应和温度效应的影响。与模型相配套,采用了一套合理的方法确定材料参数。模型的模拟结果与实验结果的比较表明,新发展的本构模型对SS304不锈钢高温非比例多轴循环变形行为的描述比较合理。
3.利用隐式积分方法,推导出简化本构模型的应力积分公式和整体迭代所需的一致性切线刚度矩阵,借助大型有限元软件ABAQUS的用户子程序,将模型移植到有限元分析软件中。采用移植后的ABAQUS软件对材料在不同加载路
When the structure components are subjected to a cyclic stressing with non-zero mean stress, a cyclic accumulation of inelastic deformation will occur, which is called ratcheting. Ratcheting can shorten the fatigue life of components or induce the components not to work normally because of the exceed-limit deformation. It is important to consider ratcheting in designing engineering structures. In the last two decades, lots of experimental and theoretic research on ratcheting for metallic materials has been done. The cyclic constitutive models of ratcheting and prediction of ratcheting have advanced significantly. However, the accurate prediction of ratcheting for metallic materials is still a challenge, especially for the multiaxial ratcheting at high temperature. We should do more deep and comprehensive research on the non-proportionally multiaxial ratcheting and the relatively strain-controlled cyclic behavior, and then develop a constitutive model which can simulate them more accurately. This research is then a topic with theoretical significance for solid mechanics and other interrelated subject and application value for designing and using engineering components credibly. In the other hand, with the development of computer technology, we can simulate and predict the deformation of engineering structure by using finite element programs now. But the constitutive models used in existing programs can not simulate ratcheting accurately. So it is necessary to implement the new constitutive models to finite element programs and simulate the cyclic deformation of engineering structure well and truly. This work can accelerate the application of advanced constitutive models, and it is also of great engineering application value.In order to carry out an in-depth research on the non-proportionally multiaxialratcheting and strain-controlled cyclic behavior for cyclic hardening material at hightemperature and develop a constitutive model which can simulate them moreaccurately, this thesis is mainly concerned with the following studies:1. An experimental study was carried out on the uniaxial and non-proportionallymultiaxial cyclic deformation at high temperatures. The ratcheting behavior andcyclic hardening/softening behavior of SS304 stainless steel were experimentallystudied under several non-proportionally multiaxial loading paths at 350℃ and
700'C. Some significant results are obtained by analyzing the experimental data, which are very useful to construct a corresponding constitutive.2. Based on the experimental study, a new constitutive model was developed in the unified visco-plastic frame, which can describe the non-proportionally multiaxial ratcheting and strain-controlled cyclic behavior uniformly. In this model, a new kinematic hardening equation was used;the non-proportionality, the effect of temperature and memorization for the maximum plastic strain amplitude were also considered. Correspondingly, a reliable and fairly method to determine the parameters of the model is proposed. The cyclic deformation behavior of SS304 stainless steel at 350'C and 700"C were simulated by the developed model. It is shown from the simulated result that the developed model can describe the non-proportional multiaxial deformation behavior of SS304 stainless steel at high temperature reasonably.3. The simplified constitutive model was implement into the finite element program ABAQUS by user-subroutine UMAT. Based on radial method and back Eular integration, a new implicit stress integration algorithm was proposed. Simultaneously, a new expression of consistent tangent modulus was also derived. Numerical examples and ratcheting simulation for simple structure at high temperatures were given. The computational results showed that the finite element implementation was successful, and the constitutive model has great engineering application value.
为了对循环硬化材料在高温下的非比例多轴棘轮行为和应变循环特性进行深入系统的研究并对其进行较为精确的本构描述,本论文开展了如下工作:
1.在350℃和700℃下,对材料在单轴和多种加载路径下的非比例多轴棘轮行为和应变循环特性进行了系统的实验研究。通过对实验数据的研究分析,得到了材料在高温下的非比例棘轮行为和应变控制循环变形行为的基本特性,为相关本构模型的建立奠定了基础。
2.在统一粘塑性循环本构的框架下,改进和发展了一个新的本构模型,对材料的高温非比例多轴棘轮行为和应变循环变形行为进行了统一描述。该模型给出了一个新的背应力演化方程,引入了非比例度参量,并且还考虑了最大塑性应变幅值记忆效应和温度效应的影响。与模型相配套,采用了一套合理的方法确定材料参数。模型的模拟结果与实验结果的比较表明,新发展的本构模型对SS304不锈钢高温非比例多轴循环变形行为的描述比较合理。
3.利用隐式积分方法,推导出简化本构模型的应力积分公式和整体迭代所需的一致性切线刚度矩阵,借助大型有限元软件ABAQUS的用户子程序,将模型移植到有限元分析软件中。采用移植后的ABAQUS软件对材料在不同加载路
When the structure components are subjected to a cyclic stressing with non-zero mean stress, a cyclic accumulation of inelastic deformation will occur, which is called ratcheting. Ratcheting can shorten the fatigue life of components or induce the components not to work normally because of the exceed-limit deformation. It is important to consider ratcheting in designing engineering structures. In the last two decades, lots of experimental and theoretic research on ratcheting for metallic materials has been done. The cyclic constitutive models of ratcheting and prediction of ratcheting have advanced significantly. However, the accurate prediction of ratcheting for metallic materials is still a challenge, especially for the multiaxial ratcheting at high temperature. We should do more deep and comprehensive research on the non-proportionally multiaxial ratcheting and the relatively strain-controlled cyclic behavior, and then develop a constitutive model which can simulate them more accurately. This research is then a topic with theoretical significance for solid mechanics and other interrelated subject and application value for designing and using engineering components credibly. In the other hand, with the development of computer technology, we can simulate and predict the deformation of engineering structure by using finite element programs now. But the constitutive models used in existing programs can not simulate ratcheting accurately. So it is necessary to implement the new constitutive models to finite element programs and simulate the cyclic deformation of engineering structure well and truly. This work can accelerate the application of advanced constitutive models, and it is also of great engineering application value.In order to carry out an in-depth research on the non-proportionally multiaxialratcheting and strain-controlled cyclic behavior for cyclic hardening material at hightemperature and develop a constitutive model which can simulate them moreaccurately, this thesis is mainly concerned with the following studies:1. An experimental study was carried out on the uniaxial and non-proportionallymultiaxial cyclic deformation at high temperatures. The ratcheting behavior andcyclic hardening/softening behavior of SS304 stainless steel were experimentallystudied under several non-proportionally multiaxial loading paths at 350℃ and
700'C. Some significant results are obtained by analyzing the experimental data, which are very useful to construct a corresponding constitutive.2. Based on the experimental study, a new constitutive model was developed in the unified visco-plastic frame, which can describe the non-proportionally multiaxial ratcheting and strain-controlled cyclic behavior uniformly. In this model, a new kinematic hardening equation was used;the non-proportionality, the effect of temperature and memorization for the maximum plastic strain amplitude were also considered. Correspondingly, a reliable and fairly method to determine the parameters of the model is proposed. The cyclic deformation behavior of SS304 stainless steel at 350'C and 700"C were simulated by the developed model. It is shown from the simulated result that the developed model can describe the non-proportional multiaxial deformation behavior of SS304 stainless steel at high temperature reasonably.3. The simplified constitutive model was implement into the finite element program ABAQUS by user-subroutine UMAT. Based on radial method and back Eular integration, a new implicit stress integration algorithm was proposed. Simultaneously, a new expression of consistent tangent modulus was also derived. Numerical examples and ratcheting simulation for simple structure at high temperatures were given. The computational results showed that the finite element implementation was successful, and the constitutive model has great engineering application value.
引文
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