Portevin-Le Chatelier Bands Research Articles

On the PLC Effect in a Particle Reinforced AA2017 Alloy

The Portevin–Le Châtelier (PLC) effect often results in serrated plastic flow during tensile testing of aluminum alloys. Its magnitude and characteristics are often sensitive to a material’s heat treatment condition and to the applied strain rate and deformation temperature. In this study, we analyze the plastic deformation behavior of an age-hardenable Al-Cu alloy (AA2017) and of a particle reinforced AA2017 alloy (10 vol. % SiC) in two different conditions: solid solution annealed (W) and naturally aged (T4). For the W-condition of both materials, pronounced serrated flow is observed, while both T4-conditions do not show distinct serrations. It is also found that a reduction of the testing temperature (−60 °C, −196 °C) shifts the onset of serrations to larger plastic strains and additionally reduces their amplitude. Furthermore, compressive jump tests (with alternating strain rates) at room temperature confirm a negative strain rate sensitivity for the W-condition. The occurring PLC effect, as well as the propagation of the corresponding PLC bands in the W-condition, is finally characterized by digital image correlation (DIC) and by acoustic emission measurements during tensile testing. The formation of PLC bands in the reinforced material is accompanied by distinct stress drops as well as by perceptible acoustic emission, and the experimental results clearly show that only type A PLC bands occur during testing at room temperature (RT).

Tsallis q-triplet, intermittent turbulence and Portevin–Le Chatelier effect

In this paper, we extend a previous study concerning Portevin–LeChatelier (PLC) effect and Tsallis statistics (Iliopoulos et al., 2015). In particular, we estimate Tsallis’ q-triplet, namely {qstat, qsens, qrel} for two sets of stress serration time series concerning the deformation of Cu-15%Al alloy corresponding to different deformation temperatures and thus types (A and B) of PLC bands. The results concerning the stress serrations analysis reveal that Tsallis q- triplet attains values different from unity ({qstat, qsens, qrel} ≠ {1,1,1}). In particular, PLC type A bands’ serrations were found to follow Tsallis super-q-Gaussian, non-extensive, sub-additive, multifractal statistics indicating that the underlying dynamics are at the edge of chaos, characterized by global long range correlations and power law scaling. For PLC type B bands’ serrations, the results revealed a Tsallis sub-q-Gaussian, non-extensive, super-additive, multifractal statistical profile. In addition, our results reveal also significant differences in statistical and dynamical features, indicating important variations of the stress field dynamics in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. We also estimate parameters commonly used for characterizing fully developed turbulence, such as structure functions and flatness coefficient (F), in order to provide further information about jerky flow underlying dynamics. Finally, we use two multifractal models developed to describe turbulence, namely Arimitsu and Arimitsu (A&A) [2000, 2001] theoretical model which is based on Tsallis statistics and p-model to estimate theoretical multifractal spectrums f(a). Furthermore, we estimate flatness coefficient (F) using a theoretical formula based on Tsallis statistics. The theoretical results are compared with the experimental ones showing a remarkable agreement between modeling and experiment. Finally, the results of this study verify, as well as, extend previous studies which stated that type B and type A PLC bands underlying dynamics are connected with distinct dynamical behavior, namely chaotic behavior for the first and self-organized critical (SOC) behavior for the latter, while they shed new light concerning the turbulent character of the PLC jerky flow.

Modeling the complexity of acoustic emission during intermittent plastic deformation: Power laws and multifractal spectra.

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.

Temperature-dependent micromechanical behavior of medium-Mn transformation-induced-plasticity steel studied by in situ synchrotron X-ray diffraction

The temperature-dependent micromechanical behavior of medium-Mn transformation-induced-plasticity (TRIP) steel with a nominal chemical composition of Fe-0.1C-10Mn-2Al (mass%) fabricated by intercritical annealing 650 °C for 1 h after cold-rolling, was investigated using in situ high-energy X-ray diffraction (HE-XRD) with uniaxial tensile tests at temperatures of 100, 25 and −50 °C. We find that as the deformation temperature decreases, the Lüders strain decreases and more austenite transforms to martensite during Lüders band propagation. The Lüders bands are associated with sudden changes of lattice strain in austenite. At 100 °C, austenite is too stable to transform to martensite, resulting in limited work-hardening capability and a relatively low strain to failure. At 25 °C, the austenite is found to transform in bursts during applied loading. These transformations correlate with stepwise peak broadening in the austenite phase and are attributed to Portevin-Le Châtelier (PLC) band propagation. At −50 °C, we observe a more intense TRIP effect which suppresses PLC band formation and leads to a high ultimate tensile strength. In addition to the TRIP effect, we find that work hardening in the deformation-induced martensite phase plays an important role in the plastic stability at low temperature, by accommodating stress compatibility between grains and phases. Our studies provide the first direct experimental evidence for the existence of large stress concentrations in the austenite phase near the Lüders band propagation front. These observations help to deepen understanding of the complex temperature-dependent micromechanical behaviors of advanced medium-Mn TRIP steels.

Coincidence of strain-induced TRIP and propagative PLC bands in Medium Mn steels

An Fe-0.2C-5Mn-2.5Al medium manganese steel is studied for three different intercritical annealing temperatures TIA to observe the effects of variations of retained austenite stability on the mechanical work hardening in uniaxial tension. Digital image correlation (DIC) showed that both Lüders bands and type A Portevin-le-Châtelier (PLC) bands occurred in samples with a lower TIA, but both disappeared when TIA was increased. In-situ measurements of sample magnetization with a correction for stress effects on the magnetic properties of the sample allowed for continuous measurement of the retained austenite volume fraction. This method provided a complete characterization of the kinetics of transformation-induced plasticity (TRIP) in the sample over the course of tensile testing. It is shown that the martensite transformation was purely strain-induced and coincided with the passage of both Lüders and PLC bands. An Olson-Cohen model was applied to magnetic data to attempt to explain the differences in TRIP kinetics with varying TIA.

Tensile Fracture Modes in Fe-22Mn-0.6C and Fe-30Mn-3Si-3Al Twinning-Induced Plasticity (TWIP) Steels

Tensile tests were carried out to investigate the differences in fracture mechanisms between Fe-22Mn-0.6C and Fe-30Mn-3Si-3Al (wt pct) twinning-induced plasticity steels. Although both steels possess a strong twinning capability during tensile deformation, they display different tensile fracture modes of shear and necking. The Portevin–le Chatelier band is proposed as the key factor influencing the different fracture mechanisms.

Experimental study of Portevin–Le Châtelier bands on tensile and plane strain tensile tests

The aim of this article is to show that it is possible to create an experimental database to better model Portevin–Le Châtelier (PLC) phenomenon with two kinds of solicitation. Indeed, two kinds of specimen are tested: conventional tensile specimens and specimens designed for plane strain tensile test. In order to better understand this phenomenon and above all to put away any geometry effect, two materials are tested: one without PLC bands (AU4G) that is used as reference and AlMg3 which is well known for its PLC bands. The image correlation tool is used to analyse the creation and the spread of PLC bands. Characteristic parameters of the bands are then measured: width, angle, transported strain, strain rate, and velocity.The originality of this paper is first to show that PLC bands are present during plane strain tensile test and then to characterize the bands thanks to image correlation. These experimental databases could be very useful for those who develop models on PLC phenomenon.

Effect of microstructure on continuous propagation of the Portevin–Le Chatelier deformation bands

Influence of severe plastic deformation (SPD) on plastic instability associated with the Portevin-Le Chatelier (PLC) effect was investigated in an AlMg alloy in a high strain-rate range corresponding to the well-known phenomenon of continuous propagation of PLC bands. Comparison with the model coarse-grained alloy reveals numerous unusual features of spatiotemporal behavior observed after different kinds of SPD processing that gives rise to an extreme grain refinement and an increase in the lattice dislocation density. Whereas SPD strongly alters the deformation curves, leading to either suppression of stress serrations or occurrence of serration types usually associated with static deformation bands, the band propagation persists in all material states. Surprisingly, smooth plastic deformation of the mostly work-hardened alloy neither corresponds to a uniform plastic flow but is related to propagation of a deformation band. The effect of the microstructure parameters on jerky flow can be explained through their influence on the propagation velocity and degree of localization of plastic deformation in the PLC bands. In particular, the loss of the PLC band mobility is discussed in relation with the conditions for the onset of necking and the formation of the localized shear band leading to fracture.

Discontinuous strain-induced martensite transformation related to the Portevin-Le Chatelier effect in a medium manganese steel

The correlation between the strain-induced martensite transformation (SIMT) and the Portevin-Le Chatelier (PLC) effect during tensile testing of a ferrite-austenite duplex medium manganese (Mn) steel was investigated in this study. A discontinuous SIMT phenomenon (D-SIMT) was observed in the steel by in situ magnetic induction measurements complemented with ex situ X-ray diffraction analysis. This unique behavior was due to the localized martensite formation in the PLC bands forming and propagating continuously during tensile straining. The PLC bands were characterized by the digital image correlation technique and their origin is further discussed.

Mechanical Properties Identification of Sheet Metals by 2D-Digital Image Correlation Method

Digital Image Correlation (DIC) method is a powerful technique for measuring material deformation field. By comparison of digital images of the undeformed and deformed configuration, DIC provides full-field displacements to sub-pixel accuracy and full-field strains in recorded images. Recently, the DIC method has been developed and used increasingly in various researches because of its advantages. However, a commercial 2D-DIC system requires a high initial investment. In this study, an in-house 2D-DIC system is developed to measure Young's modulus, Poisson's ratio, anisotropic plastic ratio parameters and flow curve under uniaxial tension of AL5052-O and high strength steel (DP980) sheets in rolling direction. The measured 2D-DIC results were compared with those of standard test method using strain-gauge type extensometer. The good agreement between the two measurement methods verifies the accuracy of the established 2D-DIC system. Furthermore, this method has been utilized in order to observe Portevin-Le Chatelier (PLC) band behaviour, Lüders band behaviour and shear band behaviour during tensile deformation of materials. The results of DIC method revealed reasonable results in measuring strain and local strain to capture ductile fracture behaviour of materials.

Calorimetric analysis of Portevin-Le Chatelier bands under equibiaxial loading conditions in Al–Mg alloys: Kinematics and mechanical dissipation

This paper investigates the thermomechanical behavior of Al–Mg alloys submitted to equibiaxial loading until failure. More particularly, the study aims to characterize calorimetric signature accompanying the formation and propagation of Portevin-Le Chatelier (PLC) bands induced by such a loading condition. Digital Image Correlation (DIC) and infrared thermography (IRT) on both sides of a cruciform shaped specimen were performed in order to characterize full kinematic and thermal fields on the specimen surface. Heat source field was reconstructed from the temperature field and the heat diffusion equation. The heat source map enables us to visualize spatio-temporal gradients in the calorimetric response of the material and to investigate the kinematics of PLC bands induced by equibiaxial tensile loading. At the specimen center, the heat source exhibits jumps that fit with jumps of temperature and equivalent deformation rate. Until a 30% equivalent strain rate is reached, these jumps are due to repeatable PLC band propagation in the two perpendicular loading directions. In certain cases, heat source maps may be seen as mechanical dissipation maps.

The Portevin-Le Chatelier Effect and Kinematics of Deformation Bands in an Al-Mg-Sc Alloy: Effect of Grain Size

Stress serration patterns and kinematics of deformation bands associated with the Portevin-Le Chatelier (PLC) effect were examined for an Al–6%Mg–0.35%Mn–0.2%Sc–0.08%Zr–0.07%Cr (in wt.%) alloy with two grain sizes: 22 μm and 0.7 μm. The fine-grained structure of the alloy was obtained using equal-channel angular pressing (ECAP) at 320°C up to a total strain of ~12. Tensile tests were carried out at room temperature and strain rate ranging from 10-5 s-1 to 10-2 s-1. In addition, high-frequency local extensometry technique was applied to monitor the evolution of the axial strain distribution during deformation. Depending on the strain rate, conventional A, B, C, or mixed types of serrations were observed on the stress-strain curves. These types of behavior usually correspond to different kinematics of the PLC bands, including band propagation and localization. However, the propagation regime was found to dominate in the investigated alloy in the entire strain-rate range. This unusual behavior of deformation bands and their features depending on the grain size are discussed.

Kinematic and thermal characteristics of Lüders and Portevin-Le Châtelier bands in a medium Mn transformation-induced plasticity steel

This paper focuses on experimental investigations on the kinematic and thermal aspects of the propagative plastic instabilities, namely Lüders band and Portevin–Le Châtelier (PLC) band, observed in a medium Mn transformation-induced plasticity (TRIP) steel. The full-field strain and heat source measurements are used concurrently to investigate in-situ the propagative bands. The kinematic analysis provides the real-time strain field evolution allowing the observation and quantification of the band nucleation and propagation. The local Lüders strain is demonstrated both space and time independent, and its magnitude is equivalent to the macroscopic Lüders strain. The spatio-temporal independent characteristic is also verified on the local strain in the PLC bands. Concerning the thermal field analysis, the heat sources are estimated and used to obtain the geometrical and dynamic parameters of the propagating bands, including the band width, orientation, propagation velocity, and appearance moment. Then the estimated heat sources are applied to establish an experimental energy balance during the plastic deformation. The quantitative energy analysis reveals that the strain-induced martensitic transformation takes place in the Lüders band but barely in the PLC bands. The ex-situ X-ray diffraction measurement on the phase content and surface hardness testing of the material confirm well this determination.

Theoretical estimation of systematic errors in local deformation measurements using digital image correlation

The measurement accuracy using the digital image correlation (DIC) method in local deformations such as the Portevin–Le Chatelier bands, the deformations near the gap, and the crack tips has raised a major concern. The measured displacement and strain results are heavily affected by the calculation parameters (such as the subset size, the grid step, and the strain window size) due to under-matched shape functions (for displacement measurement) and surface fitting functions (for strain calculation). To evaluate the systematic errors in local deformations, theoretical estimations and approximations of displacement and strain systematic errors have been deduced when the first-order shape functions and quadric surface fitting functions are employed. The following results come out: (1) the approximate displacement systematic errors are proportional to the second-order displacement gradients and the ratio is only determined by the subset size; (2) the approximate strain systematic errors are functions of the third-order displacement gradients and the coefficients are dependent on the subset size, the grid step and the strain window size. Simulated experiments have been carried out to verify the reliability. Besides, a convenient way by comparing displacement results measured by the DIC method with different subset sizes is proposed to approximately evaluate the displacement systematic errors.

Crystal plasticity simulation of strain aging phenomena in α-titanium at room temperature

Strain aging phenomena are shown to affect the viscoplastic behavior of commercially pure α-titanium at room temperature. A yield stress anomaly corresponding to static strain aging was experimentally observed when the material was loaded in the transverse direction. At low strain rates small serrations on the stress-strain curves, typical for the Portevin-Le Chatelier effect are observed for the material loaded in the transverse and rolling directions at room temperature. The presence of a stress peak is attributed to the interaction between activated <c+a> slip systems with the atoms of interstitial oxygen. The Portevin-Le Chatelier effect is presumably due to the non-planar core of screw-type dislocations. A phenomenological strain aging model is combined with a comprehensive description of slip systems active in HCP crystals in order to take into account the role of crystal plasticity in static as well as dynamic strain aging. Finite element simulations are performed on polycrystalline aggregates with various numbers of grains accounting for the elastic and plastic anisotropy of α-titanium. The simulations of static strain aging do not show formation and propagation of macroscopic shear bands. Instead, a complex strain localization phenomenon is taking place within some grains and specific associations of grains, which leads to the formation of meso-Lüders bands. The results of dynamic strain aging simulations predict the initiation and propagation of macroscopic Portevin-Le Chatelier bands even in the presence of positive apparent strain rate sensitivity.

Investigation of Portevin–Le Chatelier Band Strain and Elastic Shrinkage in Al-Based Alloys Associated with Mg Contents

The Portevin–Le Chatelier (PLC) effect in Al–2.30wt%Mg, Al–4.57wt%Mg and Al–6.91wt%Mg alloys has been investigated at various applied strain rates at room temperature in this study. Three-dimensional digital image correlation (3D-DIC) technique was applied to obtaining the further insight into the spatiotemporal characteristics, in particular the influence of Mg content on deformation behaviors. Mg content has a pronounced effect on serration characteristics, including the serration type and amplitude; Mg content tends to weaken the spatial correlation of the propagative bands. Additionally, the serration amplitude linearly increases with the maximum PLC band strain; high Mg content generates a higher PLC band strain at a given serration amplitude compared with low Mg content. Mg content is found to be effective to enhance the serration amplitude, the maximum PLC band strain and also the amount of elastic shrinkage outside PLC bands.

Experimental Study on Three-Dimensional Deformation Field of Portevin–Le Chatelier Effect Using Digital Image Correlation

In view of its high precision and high efficiency, three-dimensional digital image correlation (3D-DIC) is widely used to accurately measure full-field deformation. A spatiotemporal experimental study using 3D-DIC to explore the Portevin–Le Chatelier (PLC) deformational behavior, provides a new insight into the whole 3D deformation field, including the out-of-plane displacement, and in particular the relationship between the serrations and the strain field in the deformation bands corresponding to individual serrations. Specimens 1, 2 and 3 mm thick of 5456 Al-based alloy were tested in uniaxial tension at room temperature at strain rates from 1.8 × 10−4 to 9.1 × 10−3 s −1. The spatial and temporal characteristics of the strain localization were quantitatively analyzed. The out-of-plane displacement increment field (w) of the localized bands was observed by 3D-DIC, and found to be related to the specimen thickness and the in-plane strain increment. The largest displacement increments were respectively 15, 10 and 5 μm for 3, 2 and 1 mm specimens at maximum strain increment of about 12000 μ e. The elastic shrinkage outside the deformation bands was found to be an essential characteristic of the PLC effect. The width of the PLC band (w b a n d ) increased with increasing thickness; the angle of the PLC band (𝜃 b a n d ) was not affected by either specimen thickness or serration amplitude. Temporally, the serrations in the plots both of in-plane strain and out-of-plane displacement vs. time coincided throughout the entire loading procedure. When PLC banding occurred, the serration amplitude within the bands was found to be proportional to the maximum strain increment in the direction of the applied tensile force (𝜖 m a x ).

Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems

The spatio-temporal characteristics associated with the Portevin–Le Chatelier (PLC) effect in a 5456 Al-based alloy were investigated by employing two orthogonal digital image correlation systems. This investigation yielded the first-ever experimental observations of the strain localization in the thickness direction, which was measured to be homogenous along the thickness of the specimen. In fact, this localization was more severe in the thickness plane than in the widthwise plane. This confirmed that the assumption of a plane-stress state is invalid for specimens, which are susceptible to the PLC effect. With respect to the deformation mode of the PLC bands, the localized region in the thickness and widthwise planes were actually in an unequal biaxial stress state and a state of simple shear, respectively. The deformation continuity of the boundary corresponding to the widthwise and thickness planes was discussed on the basis of the experimental data. Moreover, two different fracture modes, i.e., the shearing-to-opening mode and the pure shearing mode, were proposed. The aforementioned observations can provide new insights into the deformation behaviors of the plastic instabilities, especially as it relates to the numerical modeling of the morphology and propagation of the PLC band.

Experimental studies of Portevin-Le Chatelier plastic instabilities in carbon-manganese steels by infrared pyrometry

The dynamic strain aging (DSA) phenomenon that occurs in some materials under certain temperature and strain rate conditions can cause plastic strain localization in the form of Portevin-Le Chatelier (PLC) bands. Carbon-manganese steels are used commonly and frequently in construction because of their ductility, low cost and ability to form mechanically. In these steels, the DSA phenomenon occurs for common quasi-static strain rates from 150 to 300°C, which makes band observation complicated. PLC bands on a carbon-manganese steel that was sensitive to DSA were studied using an infrared camera. Specimen heating was achieved using an induction furnace (with an adapted coil inductor), which allows for temperature recording during tensile tests. Thermography with an infrared camera was used to estimate the band characteristics and increments in band plastic strain, which is an important parameter for material behavior identification necessary for DSA phenomenon modeling. This technique had been developed only for PLC phenomenon observation at ambient temperature on aluminum alloys. Band characteristics on the carbon-manganese steels have been compared with results obtained previously on aluminum alloys.

Calorimetric signature of the Portevin–Le Châtelier effect in an aluminum alloy from infrared thermography measurements and heat source reconstruction

This study is an experimental investigation of the Portevin–Le Châtelier (PLC) effect in 5052 aluminum alloy specimens. Infrared thermography and heat source reconstruction are used for this purpose. Uniaxial tensile tests at ambient temperature are first performed using macroscopic strain rates which induce type-A PLC bands. Temperature changes are measured on the specimen surface during the tests. The heat sources produced by the material are then deduced using the heat diffusion equation and a suitable filtering procedure. In addition to the calorimetric response related to thermoelastic coupling and homogeneous plasticity, mobile bands of high-intensity heat sources are revealed. The calorimetric signature of the PLC effect is analyzed with respect to the macroscopic strain rate applied to the specimen. Various microstructures are experimentally evidenced: single or multiple bands, as well as cohorts of bands forming complex X-shaped, Y-shaped and V-shaped patterns. Then, by reducing the strain rate, we focus on the heat source evolution accompanying stress serration associated with type-B bands. Heat sources related to band propagation and thermoelastic coupling during the stress drops are evidenced. Several videos illustrate the main results of this study.