Department of Physics, Utkal University, Bhubaneswar 751004, India.
Materials Research Centre, Indian Institute of Science, Bangalore 560012, India.
Phys Rev E. 2018 Jan;97(1-1):012201. doi: 10.1103/PhysRevE.97.012201.
Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum spread for the type C bands and decreasing with types B and A. We further show that the acoustic emission signals associated with Lüders-like band also exhibit a power-law distribution and multifractality.
在几种塑性变形材料中，声发射信号的标度不变幂律分布普遍存在。然而，在具有光滑应力-应变曲线的 hcp 和 fcc 单晶和多晶样品以及具有不连续流动的稀金属合金等明显不同的塑性变形情况下，声发射能量的幂律分布有所报道。这令人惊讶，因为这两种类型的变形的底层位错机制非常不同。到目前为止，还没有预测不连续流动的幂律统计的模型。此外， jerky 流动中的声发射信号的统计甚至更加复杂，需要多重分形度量来进行适当的特征描述。也没有模型可以解释复杂的统计数据。在这里，我们解决了与三种 Portevin-Le Chatelier 带相关的声发射信号的统计特征化问题。根据我们最近提出的计算声发射的通用框架，我们为具有塑性应变速率作为源项的弹性自由度建立了波动方程。声发射期间耗散的能量由瑞利耗散函数表示。使用来自 Portevin-Le Chatelier 效应的 Ananthakrishna 模型获得的塑性应变速率，我们计算与三种 Portevin-Le Chatelier 带和 Luders 带相关的声发射信号。使用所计算的声发射信号进行进一步的统计特征描述。我们的结果表明，该模型预测与三种 Portevin-Le Chatelier 带相关的所有声发射信号的幂律统计，其指数值随应变速率的增加而增加。与三种带类型相关的声发射信号的计算多重分形谱具有 C 型带的最大展宽，并随 B 型和 A 型带减小。我们进一步表明，与 Luders 带相关的声发射信号也表现出幂律分布和多重分形性。
