Acoustic emission and the Portevin-Le Chatelier effect

Many metals and alloys which exhibit repeated discontinuous yielding (Portevin-Le Chatelier effect) also emit rather interesting acoustic energy during work hardening. Both phenomena are dramatic in dead-weight extensions of annealed specimens of brass or aluminum. The acoustic emission from such specimens was monitored and correlated with the features of the Portevin-Le Chatelier effect. It is shown that, when the discontinuous yielding subsides in aluminum, so does the acoustic emission; in fact, smooth continuous flow can occur in these materials with no detectable acoustic emission. Data are presented which are consistent with the hypothesis that, at room temperature, elastic energy released during a yield increment is proportional to the elastic energy stored since the last yield increment. This is not observed at elevated temperatures. It is concluded that additional studies of the acoustic-emission phenomena associated with plastic deformation can aid in achieving a better knowledge of the strain-hardening process for crystalline solids.     

Influence of precipitation on the Portevin-Le Chatelier effect in Al-Mg alloys

In the alloy with solute content higher than the limiting solubility, the solute atoms that have failed to dissolve will precipitate from the solid solution and form precipitations. In this study, the Portevin-Le Chatelier (PLC) effects in annealed 5456 and 5052 aluminum alloys with different precipitation contents have been investigated under different applied strain rates. The results suggest that precipitations have significant effect on the PLC effect and the more the precipitations are, the greater the influence is. Furthermore, the solute diffusion is pipe diffusion in 5052 alloy with lower precipitation content. However, for 5456 alloy with higher precipitation content, the diffusion is no longer the case but more complex.     

铝合金中PLC变形带的轨迹观察和研究

本文采用了动态数字散斑干涉法 (DSPI) ,对恒定加载应变率下铝合金试件的拉伸实验作了直接地观察和研究。实验记录了三种类型的PLC(Portevin LeChatelier)变形带 (类型A、B、C)在试件表面的产生过程 ;追踪了它们产生和传播的空间轨迹 ;探讨了在室温下出现不同类型PLC带所必需的加载应变率范围 (当 ε≥ 5× 1 0 - 4 s- 1 时 ,变形过程中以A类型的PLC带为主 ;当 ε <3× 1 0 - 5s- 1 时 ,则大量出现C类型的PLC变形带 ;而B类型的带将出现于这两者之间 ) ;并对”锯齿形”应力曲线中应力下掉的幅值进行了统计研究。同时 ,针对连续传播的A类型带和跳动传播的B类型带 ,得到了变形带的传播速度在变形过程中的递减演化趋势。实验还观察到随着塑性变形量的增加 ,变形带的倾斜方向会发生对称迁移现象。A、B带在拉伸试验过半时迁移现象发生 ,而C带在拉伸试验的初期即频繁出现     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

Al-Cu合金Portevin-Le Chatelier效应的多重分形分析

区别于传统的非线性动力学的吸引子结构分析,本文采用多重分形分析的研究方法讨论不同加载应变率条件下Al-Cu合金Portevin-Le Chatelier效应的多重分形特征,以揭示控制不同带型的内在动力机制。结果表明不管是哪种带型,都在一定尺度上存在着多重分形结构;同时发现B带的应力信号的均匀性高于A、C带,这反映了随着加载应变率的降低,动力系统由自组织临界性经拟周期状态过渡到混沌状态。     

A1-Mg合金中析出强化相对Portevin—Le Chatelier效应的影响

Portevin—Le Chatelier（PLC）效应作为广泛存在于各种合金材料中的重要塑性失稳现象一直受到研究者的广泛关注。本文对镁原子质量百分含量分别为2．5％和5％的两种铝合金一国标LF2和LF5铝合金进行宏观拉伸实验和透射电子显微镜观察实验。通过宏观和微观实验结果的对比分析表明，由于LF5合金中作为溶质的Mg原子的含量相对于LF2合金成倍增加导致析出相颗粒数量也成倍增加，进而引起PLC效应在强度和加工硬化时间的倍增，这些对应关系表明A1-Mg合金中析出相颗粒是产生并影响PLC效应的重要因素。实验结果显示虽然析出相颗粒数量在多方面影响PLC效应，但是对其飞行时间的影响却微乎其微。     

Al-Mg合金中析出强化相对Portevin-LeChatelier效应的影响

Portevin-Le Chatelier(PLC)效应作为广泛存在于各种合金材料中的重要塑性失稳现象一直受到研究者的广泛关注.本文对镁原子质量百分含量分别为2.5%和5%的两种铝合金-国标LF2和LF5铝合金进行宏观拉伸实验和透射电子显微镜观察实验.通过宏观和微观实验结果的对比分析表明,由于LF5合金中作为溶质的Mg原子的含量相对于LF2合金成倍增加导致析出相颗粒数量也成倍增加,进而引起PLC效应在强度和加工硬化时间的倍增,这些对应关系表明Al-Mg合金中析出相颗粒是产生并影响PLC效应的重要因素.实验结果显示虽然析出相颗粒数量在多方面影响PLC效应,但是对其飞行时间的影响却微乎其微.     

Al-Mg合金中析出强化相对Portevin-Le Chatelier效应的影响

Portevin-Le Chatelier(PLC)效应作为广泛存在于各种合金材料中的重要塑性失稳现象一直受到研究者的广泛关注。本文对镁原子质量百分含量分别为2.5%和5%的两种铝合金-国标LF2和LF5铝合金进行宏观拉伸实验和透射电子显微镜观察实验。通过宏观和微观实验结果的对比分析表明,由于LF5合金中作为溶质的Mg原子的含量相对于LF2合金成倍增加导致析出相颗粒数量也成倍增加,进而引起PLC效应在强度和加工硬化时间的倍增,这些对应关系表明Al-Mg合金中析出相颗粒是产生并影响PLC效应的重要因素。实验结果显示虽然析出相颗粒数量在多方面影响PLC效应,但是对其飞行时间的影响却微乎其微。     

白光散斑相关法多尺度分析Portevin-Le Chatelier剪切带变形

在适当的温度、应变率或预变形下,合金材料的拉伸试验中,将会出现伴随雪崩式剪切变形带的锯齿形塑性失稳、即PLC(Portevin-Le Chatelier)效应。本文利用图像相关求位移场的方法,对恒定加载应变率下(10-4/s),拉伸铝合金(A2017)试件时出现的PLC效应从宏观剪切带变形到微观晶粒变形等多尺度进行了观察和定量化的分析。通过对PLC效应发生时采集的试件表面的白光散斑图进行相关运算,得到试件表面剪切变形区域各点的精细位移,并在此基础上计算出剪切带区域的应变分布及剪切带的宽度。实验结果显示,当PLC效应发生时,剪切带区域的应变曲线呈台阶型,带的前后边缘应变梯度较大,中间近似呈平台状,带外区域应变值接近零,塑性拉伸变形主要集中在带内。     

Relationship between Local Strain Jumps and Temperature Bursts Due to the Portevin-Le Chatelier Effect in an Al-Mg Alloy

Local strain and temperature of an AA5754-O aluminum alloy sheet have been full-field measured during monotonous tensile tests carried out at room temperature. Sharp strain increases and temperature bursts which are locally generated by the Portevin-Le Chatelier phenomenon have been measured at the same point for two strain rates: V2?=?1.9?×?10^?3?s^?1 and V10?=?9.7?×?10^?3?s^?1. A relationship, which is based on the underlying physical mechanisms, has been established between the strain and the temperature and experimentally verified for the highest strain rate V10. The discrepancy between the theoretical and experimental results for the lowest strain rate V2 suggests that the localized plastic deformations do not follow an adiabatic transformation. Such a set-up seems to offer a direct and experimental method to check the adiabatic character of localized plastic deformations.     

利用动态DSPI及其时域位相分析研究Portevin—Le Chatelier滑移带

Portevin—Le Chatelier(PIC)效应是一种典型的塑性失稳现象，我们提出了一种新方法对合金材料中的PIC效应进行直接的观察和定量化的研究，这种方法的原理基于干涉散斑图样的位相差是一个与时间相关的单调函数，当PIC效应发生的时候，干涉散斑图序列被高速采集记录下来进行时域位相分析，同时通过动态散斑干涉法补偿位移，利用这种方法可以得到PIC滑移带及周围区域沿拉伸方向的位移分布并估算由滑移引起的试件的伸长。     

Piobert–Lüders plateau and Portevin–Le Chatelier effect in an Al–Mg alloy in simple shear

The jerky flow in an Al–Mg alloy is studied during simple shear tests at room temperature and various strain rates. Direct observations of the sample surface using digital image correlation allow the study of the type and the dynamics of bands associated to plastic instabilities as a function of shear strain and shear strain rate. The paper features that both Piobert–Lüders and Portevin–Le Chatelier phenomena can be observed for a simple shear stress state at room temperature. The nucleation, growth and movement of the bands are described: it is shown that the kinematics of the bands is similar to those observed in tension but that the orientation of the bands varies with the shear strain.     

On the propagation and pulsation of Portevin-Le Chatelier deformation bands: An experimental study with digital speckle pattern metrology

The Portevin-Le Chatelier (PLC) effect is closely associated with inhomogeneous deformation, which is characterized by the band of strain localization. In this work, the spatio-temporal dynamics of the Portevin-Le Chatelier deformation bands are investigated by a novel digital speckle pattern metrology technique consisting of digital speckle pattern interferometry (DSPI) and digital speckle correlation (DSC). A series of tension process of a commercial aluminum alloy (A2017) under different imposed strain rates in a range from 10⁻⁶ to 10⁻³ s⁻¹ are monitored in real time with this technique. The formation of the PLC band, the evolution of the band structure and the propagation of the band are visualized and followed by fringe patterns. The distribution of the deformation in the specimen containing the band is measured precisely. It is shown that even for a tensile test, an elastic shrinkage deformation, which is caused by the avalanche-like shearing deformation within the band, occurs outside the band.     

Complexity analysis of a Cournot–Bertrand duopoly game with different expectations

In this paper, we consider a Cournot–Bertrand mixed duopoly model with different expectations, where the market has linear demand and the firms have fixed marginal cost functions. Two firms choose output and price as decision variables, respectively, under the assumption that there is a certain degree of differentiation between the products offered by firms to avoid the whole market is occupied by the one that applies a lower price. The two players are considered to have bounded rational and static expectations. The existence and local stability condition of Nash equilibrium is investigated. We find the stability region of Cournot–Bertrand system is bigger than that of Cournot or Bertrand system under the same conditions. Furthermore, there are two different kinds of bifurcations when the parameters pass through the different boundary curves of the stability region, which is different from the Cournot or Bertrand model. Numerical simulation method is used to display the dynamic behaviors of the dynamical system, such as periodic cycles, bifurcation diagrams and strange attractors of the systems. The economic explanations of the complex dynamic behaviors are also given.     

Evaluating cavitation regimes in an internal orifice at different temperatures using frequency analysis and visualization

Experiments on a water cavitating orifice were conducted to investigate the influence of pressure and temperature on flow regime transition due to cavitation. The thermal effects could be important in cases with cryogenic cavitation or hot fluid injection. The investigations were based on CCD observations and a pressure fluctuations frequency analysis.The high-speed photographic recordings were used to analyze the cavitation evolution and individuate the frequency content of the two-phase flow by processing the pixel-intensity time-series data.The cavitating structures showed different behaviors and characteristics with variations in operating conditions, as the pressure inside the orifice and the flow temperature .The flow regime map for the cavitating flow was obtained using experimental observations to analyze the occurrence of the different two-phase flow regime transitions at various operating conditions.As the pressure at the orifice inlet increased, at the same downstream pressure, cavitation inception occurred. The decrease of the cavitation number brought a significant increase in cavitation zone extension. As the pressure drop inside the orifice increased, the cavitation was characterized by an evident increase in cavitation zone length to the outlet of the orifice. With a further cavitation number decrease, the transition to jet cavitation was evident.The temperature influenced both the cavitation intensity and the cavitation number at which different two-phase flow regime transitions occurred, which tended to increase with temperature.The vapor fraction was estimated using an image processing algorithm.The frequency content given by the pressure fluctuations was analyzed and compared with the frequency spectra obtained from the visual observations. The behavior of the different cavitating flows could be correlated to the frequency spectrum of the pressure fluctuations measured upstream and downstream of the orifice. The cavitation number reduction and consequent increase in cavitating area width were related to a corresponding significant increase in the amplitude of typical frequency components. The transition to jet cavitation was characterized by a significant increase in the first peak in the frequency spectrum; weaker spectral peaks were also present at high cavitation numbers.     

Inelastic stress-responses of an aluminium alloy in non-proportional deformations at elevated temperature

Some characteristics of strain-induced anisotropy and effects of strain-rate on them are experimentally investigated under non-proportional loadings at elevated temperature. By applying combined loadings of axial force and internal pressure to thin-walled tubes of an aluminium alloy at 200°C, inelastic stress-responses are observed at several constant strain-rates along bilinear strain trajectories. It is found that a softening of material and a non-coaxiality between stress and inelastic strain-increment deviators occur after the corner of bilinear strain trajectory. These phenomena appear more markedly and then decay more gradually with the increase of corner angle and/or strain-rate. Experimental results are qualitatively discussed in terms of the activation of piled-up dislocations as well as the so-called back stress and drag stress.     

A perturbation analysis of the unstable plastic flow pattern evolution in an aluminum alloy

In the tensile loading of sheet metals made from some polycrystalline aluminum alloys, a single deformation band appears inclined to the elongation axis in the early stage of deformation, and symmetric double bands are observed in the later stage. This evolution of spatial characteristics of such an unstable plastic flow pattern in a polycrystalline aluminum alloy has been analyzed by a perturbation method. A small number of slip modes are taken to describe the tensile strain. A rate-dependent constitutive equation is used for each slip mode to account for the interaction between dislocations and solute atoms in dynamic strain aging. Unconstrained and constrained models are used to impose appropriate loading conditions at the early and later deformation stages, respectively. Both plane-strain and plane-stress cases are considered. It is found out that the change of boundary conditions and material inhomogeneity during the course of plastic deformation are closely related to the evolution of spatial characteristics of shear band (the Portevin–Le Chatelier band) patterns observed in experiments.     

An investigation of the microporosity formation in an Al–4.1% Cu alloy casting in microgravity and in standard gravity

 The microporosity formation in a vertical unidirectionally solidifying Al–4.1%Cu alloy casting is modeled in both microgravity and standard gravity as well as in the conditions of decreased (Moon, Mars) and increased (Jupiter) gravity. Due to the unique opportunities offered by a low-gravity environment (absence of metallostatic pressure and of natural convection in the solidifying alloy) future microgravity experiments will significantly contribute to attaining a better physical understanding of the mechanisms of microporosity formation. One of the aims of the present theoretical investigation is to predict what microporosity patterns will look like in microgravity in order to help plan a future microgravity experiment. To perform these simulations, the authors suggest a novel three-phase model of solidification that accounts for the solid, liquid, and gas phases in the mushy zone. This model accounts for heat transfer, fluid flow, macrosegregation, and microporosity formation in the solidifying alloy. Special attention is given to the investigation of the influence of microporosity formation on the inverse segregation. Parametric analyses for different initial hydrogen concentrations and different gravity conditions are carried out. Received on 14 April 2000     

A finite element analysis of the morphology of the twinned-to-detwinned interface observed in microstructure of the Cu–Al–Ni shape memory alloy

A detailed morphology of the twinned-to-detwinned interface in microstructure of 2H-martensite phase of the Cu–Al–Ni shape memory alloy is observed by optical methods (optical microscopy, white-light interferometry). Based on these observations, a finite element model of the transition layer is constructed and applied to calculate the elastic stress distribution inside the observed microstructure. The results show that the real micromorphology does not correspond to the minimum of the sum of the elastic and surface energy, and that the maxima of the stress field necessary for the existence of this morphology are comparable to the elasticity limits of the 2H-martensite.     

Complexity analysis of the time series using inverse dispersion entropy

Nonlinear Dynamics - The primary object of this study is to measure the complexity of different types of signals. We undertake the experiment to support the hypothesis of inverse dispersion entropy...