摘要
承受复杂荷载的工程结构、构件和零件多用金属材料制成,要保证它们的安全服役,需要透彻了解复杂加载条件下金属材料的塑性行为并建立合理的本构模型。由于变形机制的复杂性,金属在复杂加载情形下塑性行为还很难准确描述。原因是现有本构模型对屈服面的演化及与之相关的塑性流动规律的描述不够合理,还需在大量的实验、理论和数值研究的基础上加以完善。
本文分别采用单试样和多试样方法对45号钢、多晶铜和多晶铝进行拉扭复杂加载条件下屈服面演化规律的试验研究。对单试样和多试样方法进行了对比分析,探讨了用单试样法测试屈服面的局限性,用大量试样开展了多试样法屈服面演化的试验研究,证明了多试样法的可靠性。采用Chaboche粘塑性模型,通过对工程实际应用材料45号钢进行了拉扭试验的宏观数值模拟,检验了经典塑性本构模型对屈服面的描述能力。提出了完整试样宏观联合拉扭模拟结合三维多晶集合体代表性单元子模型的屈服面演化模拟计算方法,在此基础上对材料结构相对简单的多晶铜和多晶铝材料进行了晶体塑性行为分析的细观数值模拟研究。
本文主要研究结论和创新点总结如下：
1.对确定材料后继屈服面的单试样和多试样试验方法开展了比较研究。研究表明,单试样法屈服点的测试顺序和测试点数对所测得的屈服面的形状有很大影响。第一测试点与预加载方向相反时,所得屈服面会出现“内凹”现象,反之,则不出现“内凹”现象。说明用单试样法确定的后继屈服面因测试路径不同而不同,结果明显不合理且与塑性基本理论相悖。而采用多试样法得到的后继屈服面不出现“内凹”现象,且屈服测试点与加载顺序无关,分散性可控制在一定范围,理论上合理。本文研究得到了采用多试样法研究屈服面演化更为合适的结论,为证实当前被国外很多学者应用的单试样法的不合理性提供了测试实例。
2.采用多试样试验方法对45号钢进行了拉扭加载条件下的后继屈服面与塑性流动规律的系统研究。通过研究预加载路径、卸载范围、屈服定义和预变形程度对屈服面演化规律的影响,表明后继屈服面的“尖角”方向与预加载方向相同,在预加载相反方向屈服面趋于扁平。屈服定义和预加载路径对屈服面的形状和塑性流动方向均有显著影响,目标平移应变较大的屈服定义所得屈服面较接近圆柱面,且塑性流动方向与屈服面近似正交。平移应变越小,所得屈服面越小、“尖角”现象越显著,且塑性流动方向与屈服面正交方向的偏离角越大。这一结论表明经典塑性理论对屈服面形状的描述在塑性变形较小时与实际情形有较大误差,不利于疲劳分析。
3.探讨了Chaboche模型关于背应力和屈服半径描述的合理性。推导了考虑粘塑性和非线性硬化的本构模型隐式积分算法,在此基础上编写了ABAQUS/UMALT材料用户子程序。用它对45号钢的单轴拉伸和不同应变幅拉压循环试验进行了数值模拟,从宏观角度探讨了多试样法测试45号钢后继屈服面的过程。研究结果表明：Chaboche塑性本构模型能够描述较大平移应变定义的屈服面的膨胀和移动,但不能描述小平移应变定义的屈服面的“尖角”、“钝尾”等形状演变的现象。
4.提出了完整试样宏观联合拉扭模拟结合三维多晶集合体代表性单元子模型的屈服面演化模拟计算方法：首先采用宏观弹塑性本构模型模拟试样尺度上的力学响应,得到试样指定位置处子模型多晶集合体代表性单元的位移边界条件,运用晶体塑性本构模型对多晶集合体代表性单元的力学行为进行分析。该子模型计算方法实现了宏观试样尺度与晶粒尺度的跨尺度分析,降低了材料力学行为模拟的计算量,能描述细观尺度上材料非均匀变形的行为和过程。
5.针对预拉伸和预扭转变形后的拉扭组合试验,用子模型法建立多晶集合体单元,结合晶体塑性理论对多晶铜进行了晶粒尺度的屈服特性研究,探讨不同加载路径和不同屈服点定义对材料后继屈服描述的影响；通过对不同加载路径多晶铜非均匀性的统计分析,探讨加载历史对多晶材料细观塑性变形不均匀性的影响。对试验的数值计算表明,运用子模型的晶体塑性模拟与后继屈服试验的实测结果有较好的吻合。
6.结合对多晶铝进行的复杂循环加载下后继屈服面试验研究,考虑非线性运动硬化,用多晶集合体代表性单元结合子模型的计算方法实现了后继屈服面演化的晶粒尺度数值模拟。发现和证实了考虑多晶材料微结构特性和晶粒变形方式的多晶代表性单元模型的数值模拟能够合理呈现屈服面演化的方向差异-“前尖后扁”现象,且与试验观察结果比较吻合。说明本文方法可为往复加载条件下材料晶粒尺度的塑性变形规律研究提供有效的分析工具,并可为改进现有材料塑性行为的描述提供参考。
Metal materials have been widely used in engineering structures, components and parts subjected to complex loading. In order to insure the safety of them, the plastic behavior of metal materials should be comprehensively understood and reasonably described by constitutive model. Metal plastic behavior under complex loading is still difficult to be accurately described because of the intricacies of deformation mechanisms. This is leading to that the yield surface evolution and the associated plastic flow law cannot be expressed reasonably by the conventional constitutive models. Therefore, in order to improve the constitutive description, large quantities of experimental, theoretical and numerical studies are demanded.
In this thesis, the experimental analyses of the yield surface evolution of a45steel, polycrystalline copper and pure aluminium are carried out by using single-specimen and multiple-specimen methods. The limitations of single-specimen method were investigated, and the reliability of multiple specimens'test was proven by experimental numerical comparative analysis. The description ability on yield surfaces of conventional plastic theory, taking Chaboche visco-plastic model, for example, was investigated. A sub-model method was proposed for the cross-scale analyses considering the global specimen and the local polycrystalline aggregate. The macro mesoscopic plastic behavior was researched with crystal plasticity theory and classical plasticity theory.
The main conclusions and achievements obtained as follows:
1. The single-specimen method and multiple-specimen method to determine a yield surface were compared. The results show that the shape of the yield surface with the single-specimen method is related to the loading sequences and the number of testing points. The yield surface appears "concave" feature when the first yield point is tested in the opposite to preloading direction, otherwise this phenomenon will not occur. The shape of yield surface with the single-specimen method was affected by loading path, and the result is obviously unreasonable and deviates from the plastic basic theory. The yield surface tested by multiple-specimen methods will not lead to "concave" feature. It was proven that multiple-specimen method is more reasonable to test yield surface. This research provides test cases to question the single-specimen method that adopted by many foreign scholars.
2. Using the multiple-specimen method, the evolution of the subsequent yield surface and the plastic flow rule of a45steel were presented under tension-torsion loading. The effects of preloading paths, unloading points, yield definitions and prescribed pre-strain on the subsequent yield surface were explored. The experimental results of yield surface for a45steel are as follows:the shape of the subsequent yield surfaces strongly depends on the preloading direction; the curvature of the subsequent yield surfaces in the loading direction is larger than that in the opposite direction. The plastic flow directions are not always normal to the subsequent yield surfaces, and are related to the yield definitions. By the yield definitions with smaller offset strain, the distortion of the subsequent yield surfaces becomes more prominent, and the plastic flow directions have larger deviation from the normal directions of yield surface. Based on the larger plastic strain definition, the subsequent yield surfaces are close to a column surface. The results reveal that the conventional plastic theory cannot reasonably predict yield surface determined by a fairly small offset strain, and not fit to fatigue analysis.
3. The rationality of Chaboche model, including back-stress and yield radius, was discussed. The integral algorithm of the model which considering visco-plasticity and the nonlinear kinematic hardening was deduced, and the user subroutine UMAT for ABAQUS was compiled. The simulation confirmed that the present model can be applied to describe the hysteresis of a45steel under the cyclic loading with different strain amplitude. The experiments of subsequent yield surfaces of a45steel were simulated with Chaboche model by single-specimen and multiple-specimen methods. The results demonstrated it can reasonably predict the translation and expansion of yield-surface, but can not describle the distorsion, such as "sharp corner" and "blunt rear", when yield was defined by a fairly small offset strain.
4. A sub-model method was developed to investigate the plastic behavior considering a global test specimen and polycrystalline aggregate model. The global specimen was analyzed by the macroscopic elasto-plastic constitutive model, the displacement boundary conditions were applied to the representative volume element (RVE) with polycrystalline aggregate. The cross-scale analysis was implemented from macro-specimen scale to micro-grain scale based on the crystal plasticity theory and classical plastic plasticity theory. This calcalation method can obviously reduce the total computing time and simulate precisely the micro-inhomogeneity of deformation.
5. Combined tension-torsion test under pre-tension and pre-torsion deformation, the yield characteristic of polycrystalline copper in grain scale was investigated by applying crystal plasticity theory associated with polycrystalline aggregate model. Through the research on the shape and the evolution of the subsequent yield surface, the effects of different loading paths and different yield definitions on the subsequent yield surface were explored. The heterogeneous statistical analysis of the polycrystalline copper under different loading paths is also performed. And further more, the effect of loading history on subsequent yield surface, and on micro heterogeneous distribution were estimated. The results by the analysis based on crystal plasticity calculation combined with the sub-model method were compared with experimental results, and they were in reasonable agreement.
6. Comparing to the experimental processes of subsequent yield surfaces of a pure aluminium under complex cyclic loading, the the evolution of subsequent yield surface were simulated at grain scale by applying crystal plasticity theory associated with polycrystalline aggregate model, which considering the microstructural characteristics and grain deformation of polycrystalline materials. It was confirmed that numerical simulation of polycrystalline aggregate RVE model can reasonably estimate the distortion of the yield surface evolution along different directions—"sharp corner and blunt rear", and the results coincide reasonably with experimental observations. It indicated that the method proposed by author can be applied to present the plastic deformation under cyclic loading at grain scale. In addition, this research provides a reference for improving the description of the present plastic behavior.
引文
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