Serration and noise behaviors in materials

Serration and noise behaviors in plastically deforming solids are related to avalanches of deformation processes. In the stress-strain curves, the serration characteristics are visible as stress drops or strain jumps. In fact, similar serration characteristics are ubiquitous in many structural and functional materials, such as amorphous materials [also metallic glasses, or bulk metallic glasses (BMGs)], high-entropy alloys (HEAs), superalloys, ordered intermetallics, shape-memory alloys (SMAs), electrochemical noise, carbon steels, twinning-induced plasticity steels (TWIP steels), phase-transformation-induced plasticity steels (TRIP steels), Al-Mg alloys, nano-materials, magnetic functional materials, and so on. Because of their unique and universal properties, many researchers have focused on this field to find out what causes the serration behaviors and what can be learned about the material from the serration characteristics. For example, the serration characteristics contain information about the mechanisms of plastic deformation and the structural evolution during deformation. However, due to many factors affecting the serration behavior and some uncertain or uncontrolled factors, it’s a difficult task to give a unified picture of a vast amount of serration data. This review article summarizes the results of previous studies in this rapidly-developing field, attempting to provide a new perspective in expounding the connection between macroscopic properties and micro-mechanisms.In this review paper, serration behavior of a wide range of materials will be discussed. One of the most important goals is to investigate the factors influencing serration characteristics and deformation mechanisms. Several statistical properties, such as distributions of stress drop sizes and waiting times, are reviewed and used to quantify the serration behavior. Moreover, models and theories on the serrated flow will be discussed, which quantify the deformation mechanism and provide physical intuition for the experiments, and methods to organize experimental data. Besides discussing serrations in stress-strain curves of many solid materials, this review paper will also cover other systems with serrations and collective noise, such as crackling noise in the earth’s crust (earthquakes), volume fluctuations in a granular medium and jamming behavior in random-packing systems.     

The study of work hardening in Fe-Mn-Al-C alloys

Three austenitic Fe-Mn-Al-C alloys with different aluminium content from 0, 5.1 and to 8.5wt% are chosen for the present work hardening study. Serrated stress-strain curves with pronounced work hardening were observed during tensile testing, also the serration of stress-strain curve is found to be decreasing as the increase of aluminium content. The serration can, however, still be observed even if the aluminium content is increased to as much as 8.5wt%. According to morphology studies and electron microscopic investigations, it is found that strain-induced deformation twins are closely related to the work hardening in the present alloys. Therefore, deformation twinning is strongly suggested as a major cause of work hardening in Fe-Mn-Al-C alloys, and also plays an important role on the serration of stress-strain curve.     

Improvement of creep-fatigue life by the modification of carbide characteristics through grain boundary serration in an AISI 304 stainless steel

The modification of carbide characteristics through grain boundary serration and its subsequent effect on the creep-fatigue property at 873 K have been investigated, using an AISI 304 stainless steel. It was found that the grain boundaries are considerably serrated when a specimen is furnace-cooled. The grain boundary serration leads to a change in the carbide characteristics as well as grain boundary configuration, i.e., morphology of carbide from an acute triangular to a planar form and a lowered density. Additionally, an array of carbide particles is changed from a consistent to zigzag pattern, in terms of their preference to one grain to share the coherency. Planar carbides on serrated grain boundaries have a lower interfacial energy than that of triangular carbides on straight grain boundaries. It is suggested that the modification of carbide characteristics through the grain boundary serration has a remarkable influence on the improvement of creep-fatigue resistance.Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, South Korea.     

Effects of aging temperature and grain size on the formation of serrated grain boundaries in an AISI 316 stainless steel

The effects of aging temperature and grain size on the formation of serrated grain boundaries have been investigated in an AISI 316 stainless steel. Grain size increased slightly over aging temperature ranges of 650–870 °C, resulting in predominantly serrated grain boundaries. However, when the temperature exceeded 880 °C, the grain size significantly increased, and grain boundary serration was not observed. The initial grain size also had an influence on the occurrence of grain boundary serration. For specimen having a large initial grain size of about 200 μm, no serrated grain boundary formed after aging treatment at 760 °C. Serrated grain boundaries were observed when “normal” initial grain sizes 55 μm were employed. It was found that the frequency of low angle boundaries markedly increased as the initial grain size increased from 55 to 200 μm. From the results obtained, it is possible to describe that the grain boundary serration could be considered as a spontaneous reaction that aims to reduce the total free energy of the system, and form a new interface of lower free energy. We proposed that the competition between grain growth and grain boundary serration during aging treatment reduces the total free energy of the alloy system: at temperatures exceeding 880 °C, the dominant process is the grain growth, while grain boundary serration predominates over the range of 650–870 °C.     

Al－Li单晶体锯齿流变的动力学特征

研究了Ａｌ－Ｌｉ单晶体锯齿流变的动力学特征，结果表明：锯齿的频率和幅度与时效状态、变形温度和加载的晶体学位向相关，并与δ′粒子被切割和固溶Ｌｉ原子对位错的钉扎有关。     

Al—Li单晶体锯齿流变的动力学特征

研究了Ａｌ－Ｌｉ单晶体锯齿流变的动力学特征，结果表明：锯齿的频率和幅度与时效状态，变形和加载的晶体学位向相关，并与δ粒子被切割和固溶Ｌｉ原子对位错的钉扎有关。     

Texture effect on serrated flow in 2090 Al‐Li alloy

Tensile specimens of 1×6×25 mm in gauge dimension were cut from the surface and centre of 12.7 mm thick 2090 Al‐Li alloy plate, which were solution treated at 550 °C for 30 min, peak‐aged at 190 °C for 18 h, or reversion‐treated at 275 °C for 2 min. The flow stress of the centre layer was higher than that of the surface layer, regardless of the heat treatments. The textures of the surface and centre layers were approximated by the {001}<110> and {011}<211> orientations, respectively. The solution‐treated specimens gave rise to extensive serrations in their flow curves at a strain rate of 2×10^‐4 s^‐1. The serration amplitude was drastically reduced after the specimens were peak‐aged or reversion‐treated. However, for the peak‐aged alloy, the surface‐layer specimens underwent complex, serrated flows, whereas the flow curve of the centre‐layer specimen was almost devoid of serration. The serration, especially fine‐type serration in the peak‐aged and reversion‐treated specimens tended to disappear with increasing strain rate. The tensile behavior was explained in terms of the texture and strain rate.     

A study on the mechanism of serrated grain boundary formation in an austenitic stainless steel

Measurement of the activation energy for the formation of serrated grain boundaries (GB) has been carried out to understand its underlying formation mechanism in an AISI 316 stainless steel. The apparent incubation time necessary to initiate grain boundary serration was obtained at different aging temperatures, and the apparent activation energy for serration was carefully calculated from the Arrhenius relationship between incubation time and aging temperature. The activation energy for GB serrations in this alloy was measured to be approximately 148 ± 20 kJ mole⁻¹, which is consistent with the activation energy for lattice diffusion of carbon in γ-iron (142 kJ mole⁻¹). This result indicates that GB serration could be controlled essentially by the lattice diffusion of carbon to grain boundaries. Based on the through-thickness observation of serrated GBs, a straight boundary began to serrate from the surface at an early stage of the aging treatment, and then the serrated parts propagated throughout the entire grain boundary.     

Investigation of serrated flow behaviour in Al–10Mg alloy

Abstract

In view of reported anomalies in the serrated flow behaviour of aged Al–8.6Mg alloy, characteristics of serrated flow were investigated in an Al–10Mg alloy after solution treatment as well as after aging. The material was prepared by melting and casting, and then it was extruded, solution treated, and aged at either 150 or 200°C. Strain rate sensitivity, types of serration, onset strain of serrated flow, magnitude of serrations, and frequency of serrations were studied as a function of aging and strain rate. It was found that the alloy exhibited all the usual features of serrated flow except one, i.e. the magnitude of serration increased in the overaged condition after decreasing up to peak aging.     

Serrated yielding in Cu-1 wt-%Cd alloy

Abstract

The influence of grain size and temperature on the serration patterns of the Portevin-Le Chatelier (PLC) effect and on the yield and flow stresses in a Cu-1 wt-%Cd alloy was investigated in the temperature range 150 to 360 ° C. Two kinds of serration patterns were observed in this alloy. Type I occurred at lower temperatures and its yield points are moderately spaced. Type II consists of regular jerky flow observed athigher temperatures. The Hall-Petch equation is obeyed over the temperature range in which jerky flow occurs. The Hall-Petch parameter k (?) is observed to show a local maximum in the temperature range where serrated flow is first observed. The PLC effect is associated with the solute- dislocation interactions, implying that k (?) contains a component associated with grain size dependent dislocation storage.     

DEALER INVENTORY MANAGEMENT SYSTEMS

This paper presents a model for analyzing inventory control policies for dealers that support the sales and service of manufactured goods. The environment faced by dealers is characterized by multiple stochastic demand classes (prioritized into emergency and regular), a principal source for boui emergency and regular requirements, multiple secondary sources for expedite requirements, and constraints on the lead time and service performance. We are concerned, in particular, with how dealers manage their inventory stockpiles and select expedite sources for replenishment when they have the option of prioritizing customers. The analysis is based on a periodic review, stochastic demand, (s,S) inventory model of dealer stock control. Exact Markov processes and approximate renewal based models are derived based on Cohen, Kleindorfer and Lee [4] and Cohen and Lee [5]. An approximation is used to develop a heuristic algorithm. Extensive numerical testing indicates that the algorithm generates solutions with acceptable cost and service penalties.     

Analysis of fracture failure of fir-tree serrations of stage II turbine disks

This paper presents an analysis of fracture failure of fir-tree serrations in stage II turbine disks in a certain type of engine. On the basis of statistical analysis, basic fracture features and fracture mechanisms of stage II turbine disk serrations have been summarized. The reasons for the serration fracture failure are: (a) the first order bending resonance k=5 in the turbine blade occurring at the speed of 9700 rpm; (b) the unreasonable design of the five-serration structure, which causes each serration to bear non-uniform stresses; (c) the disk being made of the alloy GH2036 having a low fatigue resistance; (d) the high intergranular corrosion sensitivity of GH2036. Finally, measures, i.e. the change of the five-serration structure into a three-serration structure and the replacement of GH2036 with GH2132, have been given to prevent the fracture failures, and the application has indicated that these measures are effective.     

On the γ′ precipitates of the normal and inverse Portevin-Le Châtelier effect in a wrought Ni-base superalloy

The Portevin-Le Châtelier (PLC) effects in a wrought Ni-base superalloy with different γ? precipitates contents have been investigated. Detailed analysis on the serration type of the tensile curves indicates that the γ? precipitates have a decisive influence on the transformation from normal to inverse PLC behavior, which is rarely proposed in other works. It is considered that the γ? precipitates play the same role in PLC effect as temperature and strain rate for the investigated wrought Ni-base superalloy.     

EFFECT OF FACTOR OF BLUE BRITTLE OF LOW-CARBON STEEL FOR TENSILE DEFORMATION

本文研究了形变温度、形变速率及材料晶粒度等因素对10~零钢拉伸形变时蓝脆现象的影响。结果表明,温度改变着PL 效应区的锯齿波型,晶粒尺寸增加和高的拉伸形变速率可提高PL 效应区的起始温度T(?)及终止温度T(?),改变材料出现蓝脆现象的温度及其范围。位错结构变化证实,在PL效应区内,溶质原子对运动位错的钉扎存在着由弱至强的转化过程。     

The influence of porosity on the fatigue crack growth behavior of Ti–6Al–4V laser welds

The effect of porosity––a common welding defect––on the fatigue crack growth rate (FCGR) in Ti–6Al–4V laser welds was investigated. The experimental results reveal that porosity was present in partial penetration welds over a narrow fusion zone (FZ) with martensite structure. The FCGR of the FZ was lower than that of the base plate. The fracture surface morphology of weld metal was much rougher as compared to that of the base plate. Randomly oriented martensite in the FZ led to local cleavage fracture along a preferred plane, thus, altering the crack growth direction significantly out of the primary crack plane. The zigzag crack path in the FZ resulted in a reduced FCGR at a given ΔK compared to the base plate. Besides, the porous weld showed a serration on the crack growth curve, and behaved the similar crack growth characteristics as the defect free one. SEM fractography revealed that the deflection of crack path around porosity together with local notch blunting as the crack tip pierced into porosity, balanced the increased FCGR for the occurrence of instant crack advance as the crack front reached the porosity at a low stress ratio. In contrast, the serration and drop in FCGR occurred sparingly at a high stress ratio as the crack front met the porosity.     

激光多道熔覆温度场的计算与分析

以45钢板材上熔覆三道Ni60自熔性合金粉末为例,对送粉式激光熔覆多道搭接情况下的温度场进行计算,得到了熔覆过程中基体上各点的温度变化规律及固定时刻熔覆层的温度分布曲线,分析了多道熔覆时温度场的变化规律.计算结果表明基体表面激光经过的中心点温度变化呈锯齿状,而离激光光源较远的基体上各点温度达到最大值存在一个滞后时间.多道搭接情况下,熔池内的最高温度,后两道熔覆层要略高于第一道熔覆层,且对于后两道熔覆层起熔时刻和熔覆结束时刻熔池内的最高温度明显高于熔池内的平均最高温度.     

The energy band model for bismuth: Resolution of a theoretical discrepancy

The Lax two-band model contains a term linear in wave vector which is missing in the Abrikosov-Falkovsky model. It is shown that this term is recovered if the Abrikosov-Falkovsky development is carried to second order. It is argued from the results of energy band calculations and from experiment that the term in question is as important as the term second order in wave vector which was introduced by Cohen and by Abrikosov and Falkovsky. From a study of cyclotron resonance and de Haas-van Alphen effect it is concluded which second-order terms in the general Cohen model must be kept in order to obtain agreement with experiment.     

Aging Effect on Elapsed Time of Serrations in Al-Li Single Crystals

Elapsed time of serrations in Al-Li single crystals was investigated with two definitions: one is the time elapsed in one cycle of serrations, the other is the average elapsed time within a strain limit.Elapsed time of individual serration appears independent on stress drops during serrated flow. It primarily distributes within the limits of short elapsed time in peak aged condition compared with underaged and overaged conditions, corresponding to low level of the average elapsed time that appears indifferent to increasing strain. It seems that shearing behaviour of δ' particles could be responsible for the variations in elapsed time of serrations.     

6061铝合金板材锯齿形屈服行为的研究

对6061铝合金板材锯齿形屈服行为中应力跌幅、跌落时间等多个特征物理量随应变率的变化规律进行了系统的研究,探讨了锯齿形行为对材料力学性能的影响。结果表明,应力跌幅个数,跌落时间及其个数,再加载时间及其个数均随着应变率的增大而逐渐减少;当应变率为1.4×10-3s-1时,6061铝合金板材的锯齿形屈服行为最弱,板材的力学性能最好。