基于非线性动力系统的Portevin-Le Chatelier效应分析
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摘要
在一定的温度、应变率或适当的预变形下,多种合金材料在拉伸实验中会出现特殊的塑性失稳现象,其表现为时域上的锯齿形应力流动和空域上的应变局域化,这种现象被称为Portevin-Le Chatelier(PLC)效应。PLC效应属于一种群集性现象,其本质源于材料微细观结构演变过程中的动态应变时效现象,即可动位错与林位错、溶质原子之间动态的交互作用。在对PLC效应发生时的应力曲线的特征参量,如锯齿幅度和重加载时间进行统计时,发现随着加载应变率的增大,其分布形式由峰值分布转变为幂率分布,从非线性动力学角度看,其中暗含着不同动力模式的转变过程,因此,本文从非线性动力学的角度来探求PLC效应的动力作用机制,主要采用三种非线性分析的手段,包括重构相空间轨迹的吸引子状态分析、基于小波变换的多尺度分析及多分形分析,对PLC效应的动力学行为进行相应的研究。
采用相空间重构技术对低应变率(对应C带型)时的吸引子特征进行分析。在确定延迟时间量时,传统方法,即利用应力时间序列的自相关函数,对PLC效应应力信号分析存在着极限性。因此本文采用联合平均位移法来作为确定延迟时间量的准则,并展示了相应的相空间轨迹,结果发现给定应力序列具有混沌吸引子的特征结构。
基于小波变换技术对PLC效应进行多尺度分析中,首先探讨了PLC效应处于混沌状态时的自相似性质及其产生机制;其次,鉴于传统手段提取应力曲线特征量时难以避免的人为因素会给分析带来误差,使用小波变换这种纯粹的数学手段,能够很好地解决这一问题,并从小波系数的物理意义上对其进行了论述;最后,对不同固溶处理温度的应力时间曲线进行小波分解,发现小波系数存在非单调的变化形式,与已有的统计结果类似,进一步表明可以将小波变换这种数学手段应用到PLC效应研究领域中,达到对PLC效应的时域结构进行多尺度观测及特征参量的无误差统计。
在已有的PLC效应非线性行为研究成果下,为了区别A、B、C三种不同带型的PLC剪切带的动力学机制,本文采用了多分形分析的方法。通过计算多分形谱参数发现,不同带型在一定尺度上都存在多分形行为,其中B带型应力信号的均匀程度最高,这是因为它们的变形状态不同,B带时由变形带引起应变集中所带来的塑性应变不协调与重加载阶段内的塑性应变释放相当,其动力系统的稳定性更高。认为随加载应变率的降低,PLC效应的动力模式由自组织临界性经拟周期的过渡状态转变到混沌区域。
When in certain range of temperature and strain rate, as well as proper initial deforming, various alloy materials can display special plastic instability phenomenon in tension experiment, and it performs to be the serrated stress flow in temporal field and the localized strain band in spatial field, which is called the Portevin-Le Chatelier (PLC) effect. PLC effect belongs to some kind of collective phenomenon and is considered to originate from the dynamical strain aging effect in the meso-structure evolution process of materials, also known as the dynamical interaction among mobile dislocation, forest dislocation and solute atoms. It is found that the characteristic parameters distribution of stress curve turns out to change when strain rate increases in PLC effect, specially, which displays the crossover from peak type to scaling type. From the point of nonlinear dynamics, such change implies the transition of different dynamical modes. Therefore, this paper is mainly focused on investigating the underlying dynamical mechanism of PLC effect via nonlinear dynamics, and takes three kinds of nonlinear analysis tools including the attractor trajectory analysis of reconstructed phase space, multiscale analysis based on wavelet transform and multifractal analysis, in order to characterize dynamical behavior of PLC effect.
In section 2, it is mainly the attractor analysis in low strain rate (corresponding to type C band) by means of reconstructed phase space technology. However, it is suggested that there exists shortcomings for the traditional method which makes use of the self-correlation function in determining time lag in stress series of PLC effect. Therefore, the advanced combine average method is taken as the theorem for determination of time lag in this paper, and for comparison, it also displays the relevant trajectory in phase space. Finally, it is confirmed the given stress series posses the characteristic structure of chaotic attractor.
In section 3, it is mainly the multiscale analysis of PLC effect based on the wavelet transform technology. Firstly, the self-similarity and its source are analyzed when PLC effect displays chaotic behavior. Secondly, considered the inevitable analysis error for the obtaining characteristic parameters due to personal reasons, wavelet transform as pure mathematical tool can get rid of such problem easily, for the usage of wavelet transform in PLC effect, this paper also gives the specific discussion from the physical meaning of wavelet coefficient. Thirdly, when stress curves in different solution temperature disposed on wavelet decomposition, it can found that wavelet coefficients display non-monotonous changing type as the temperature increases, similar to the traditional statistical result, which also further proves that the feasibility of application of wavelet transform in the study of PLC effect for fulfilling multiscale investigation and errorless statistics of characteristic parameters about the temporal structure.
In section 4, based on the achievements of PLC effect study from the point of nonlinear dynamics, this paper employs multifractal analysis to classify the underlying dynamical mechanism for different types of PLC bands including type A, type B and type C. The result suggests, whatever the type is, there exists multifractal behavior in certain scales, and specifically, the signal of type B band owns the highest homogeneity, which can be explained by the different deforming conditions, for the reason that when type B band exists, the plastic strain incompatibility can be homogenized by the release of strain within the reloading interval, and therefore, the stability of dynamical in type B band is higher than the other types. Such phenomenon can be ascribed to the fact that the crossover from self-organization to quasi-periodicity and finally to chaos for the dynamical system when strain rate decreases.
采用相空间重构技术对低应变率(对应C带型)时的吸引子特征进行分析。在确定延迟时间量时,传统方法,即利用应力时间序列的自相关函数,对PLC效应应力信号分析存在着极限性。因此本文采用联合平均位移法来作为确定延迟时间量的准则,并展示了相应的相空间轨迹,结果发现给定应力序列具有混沌吸引子的特征结构。
基于小波变换技术对PLC效应进行多尺度分析中,首先探讨了PLC效应处于混沌状态时的自相似性质及其产生机制;其次,鉴于传统手段提取应力曲线特征量时难以避免的人为因素会给分析带来误差,使用小波变换这种纯粹的数学手段,能够很好地解决这一问题,并从小波系数的物理意义上对其进行了论述;最后,对不同固溶处理温度的应力时间曲线进行小波分解,发现小波系数存在非单调的变化形式,与已有的统计结果类似,进一步表明可以将小波变换这种数学手段应用到PLC效应研究领域中,达到对PLC效应的时域结构进行多尺度观测及特征参量的无误差统计。
在已有的PLC效应非线性行为研究成果下,为了区别A、B、C三种不同带型的PLC剪切带的动力学机制,本文采用了多分形分析的方法。通过计算多分形谱参数发现,不同带型在一定尺度上都存在多分形行为,其中B带型应力信号的均匀程度最高,这是因为它们的变形状态不同,B带时由变形带引起应变集中所带来的塑性应变不协调与重加载阶段内的塑性应变释放相当,其动力系统的稳定性更高。认为随加载应变率的降低,PLC效应的动力模式由自组织临界性经拟周期的过渡状态转变到混沌区域。
When in certain range of temperature and strain rate, as well as proper initial deforming, various alloy materials can display special plastic instability phenomenon in tension experiment, and it performs to be the serrated stress flow in temporal field and the localized strain band in spatial field, which is called the Portevin-Le Chatelier (PLC) effect. PLC effect belongs to some kind of collective phenomenon and is considered to originate from the dynamical strain aging effect in the meso-structure evolution process of materials, also known as the dynamical interaction among mobile dislocation, forest dislocation and solute atoms. It is found that the characteristic parameters distribution of stress curve turns out to change when strain rate increases in PLC effect, specially, which displays the crossover from peak type to scaling type. From the point of nonlinear dynamics, such change implies the transition of different dynamical modes. Therefore, this paper is mainly focused on investigating the underlying dynamical mechanism of PLC effect via nonlinear dynamics, and takes three kinds of nonlinear analysis tools including the attractor trajectory analysis of reconstructed phase space, multiscale analysis based on wavelet transform and multifractal analysis, in order to characterize dynamical behavior of PLC effect.
In section 2, it is mainly the attractor analysis in low strain rate (corresponding to type C band) by means of reconstructed phase space technology. However, it is suggested that there exists shortcomings for the traditional method which makes use of the self-correlation function in determining time lag in stress series of PLC effect. Therefore, the advanced combine average method is taken as the theorem for determination of time lag in this paper, and for comparison, it also displays the relevant trajectory in phase space. Finally, it is confirmed the given stress series posses the characteristic structure of chaotic attractor.
In section 3, it is mainly the multiscale analysis of PLC effect based on the wavelet transform technology. Firstly, the self-similarity and its source are analyzed when PLC effect displays chaotic behavior. Secondly, considered the inevitable analysis error for the obtaining characteristic parameters due to personal reasons, wavelet transform as pure mathematical tool can get rid of such problem easily, for the usage of wavelet transform in PLC effect, this paper also gives the specific discussion from the physical meaning of wavelet coefficient. Thirdly, when stress curves in different solution temperature disposed on wavelet decomposition, it can found that wavelet coefficients display non-monotonous changing type as the temperature increases, similar to the traditional statistical result, which also further proves that the feasibility of application of wavelet transform in the study of PLC effect for fulfilling multiscale investigation and errorless statistics of characteristic parameters about the temporal structure.
In section 4, based on the achievements of PLC effect study from the point of nonlinear dynamics, this paper employs multifractal analysis to classify the underlying dynamical mechanism for different types of PLC bands including type A, type B and type C. The result suggests, whatever the type is, there exists multifractal behavior in certain scales, and specifically, the signal of type B band owns the highest homogeneity, which can be explained by the different deforming conditions, for the reason that when type B band exists, the plastic strain incompatibility can be homogenized by the release of strain within the reloading interval, and therefore, the stability of dynamical in type B band is higher than the other types. Such phenomenon can be ascribed to the fact that the crossover from self-organization to quasi-periodicity and finally to chaos for the dynamical system when strain rate decreases.
引文
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