Luders Band Research Articles

Acoustic emission during the development of a Lüders band in a low-carbon steel

The acoustic emission (AE) during the plastic deformation of a low-carbon steel is experimentally studied. The data obtained on the time localization of AE signals in a sample allow the motion of a Luders band to be traced. The main informative AE parameters at various stages of plastic flow are analyzed. The results are compared with speckle video filming data and are supported by them. The possibilities of determining plastic deformation stages and Luders band characteristics using acoustic emission are discussed.

Modeling Stress Strain Curves for Nonlinear Analysis

Methods of modeling stress strain curves for nonlinear stress analysis are discussed in order to obtain comparable results between different finite element analysts and between different versions of designs. The most common method for modeling stress strain curves is to use Ramberg- Osgood equation. For materials with significant discontinuous yielding, Ramburg-Osgood approximation leads to some problems near discontinuous yielding point. Discontinuous yielding occurs when sudden onset of plastic deformation associated Luders band takes place in a uniform test sample. For engineering structures and machine components, the propagation of Luders band may not occur in deformation process because of non-uniform stress distribution caused by stress concentration, complicated loading condition etc. A modified Ramberg-Osgood method for modeling stress strain curve is proposed.

Magneto-optical setup for in situ strain and transport measurements on superconductors

A recently developed magneto-optical (MO) imaging setup for investigations on superconductors is reported. The main originality of our setup is its ability to combine both strain and transport measurements in the temperature range of 6-300 K with magneto-optical observations. We give here some theoretical considerations on the cryostat conception, which is a key point of our setup. In particular, the thermal and mechanical aspects are discussed. A detailed description of the MO setup and of the associated strain apparatus is given. Additionally, an example of MO strain and transport study on DyBCO coated conductors is given. Evidence of Luders Bands formation under strain in the Hastelloy is revealed by the field penetration inside cracks in the DyBCO and MgO layers. A correlation between the damaging morphology and the critical current at 70 K versus strain has been established.

Effects of alloy compositions on the bendability of pre-stretched Al–Mg–Si alloy sheets

Recently, the reduction of exhausted carbon-dioxide has been seriously required to avoid global warming. Naturally, this is an issue of great interest in the automobile industry. To achieve a sufficient reduction, lightening the autobody by converting the conventional steel sheets to aluminum alloy sheets is regarded as an effective and feasible method. Some Al–Mg–Si alloys have already been applied to a part of autobodies because these alloys have hardenability during paint baking and do not cause a stretcher strain pattern. However, their bendability is significantly poor compared to that of steels. In this study, the bendability has been assessed in terms of the macroscopic and microscopic appearance of the tension-side surface and measured surface roughness, as a function of the alloy composition, i.e., amount of Mg2Si, amount of excess Si and addition of Cu and Cr. Specimens were solutionized, air-cooled or water-quenched and then naturally aged for 7 d. Before the bending test the specimens were stretched by 10%, since such straining is frequently carried out in the actual autobody sheets prior to the bending process. The results obtained were compared with those obtained in the previous report where stretching prior to bending had not been performed. The effects of the amounts of Mg2Si and excess Si and of the Cu addition were similar to those in the specimen series without prior stretching, that is, bendability was decreased when the amounts of Mg2Si and excess Si were increased, while it was slightly improved by the Cu addition of 0.34%. The effect of Cr addition of 0.21% did not coincide with that in the previous report, that is, Cr addition deteriorated surface roughness and tended to cause cracking despite an improvement in the bendability in terms of macroscopic appearance assessment in the present study, while it totally improved the bendability in the previous study.

弾塑性有限要素法による薄鋼板の調質圧延における応力とひずみ解析

The temper rolling is applied to eliminate the stretcher strain, to improve the flatness and to control the surface roughness of rolled-sheet as the finishing process in cold rolling. However, there are some problems remain in analysis of the temper rolling. The classical rolling theory based on the rigid plastic theory, can not deal with non-uniform elastic–plastic deformation in the thickness direction, because the deformation is partly concentrated on the surface layer of the sheet. This paper presents an elastic–plastic finite element analysis of stress and strain behaviors in plane strain temper rolling for as-annealed mild steel sheet. In the analysis, the upper yield stress, the lower yield stress and yield point elongation are taken into account for the stress–strain relation of material rolled. For the contact boundary between roll and deforming material, both slipping and sticking are considered, and the Coulomb friction law is employed to represent the slipping friction. Furthermore, calculated rolling force by the EP-FEM is compared with that by the classical rolling theory as Karman's equation and that obtained by a laboratory scale rolling experiment with bright rolls or dull rolls. As the results, in the case of small friction between roll and deforming material, the rolling force obtained by Karman's equation coincide with that by EP-FEM and that by experiment.

Numerical modeling of the thermomechanical behavior of steels with allowance for the propagation of Luders bands

A thermomechanical model based on physical representations of the motion of dislocation continuum and a model for the initiation and propagation of plastic shear are proposed to describe slow flows of the type of Luders bands. Two-dimensional calculations of Luders band propagation are performed for HSLA-65 steel samples under compression at various strain rates and temperatures. The calculation results are in good agreement with experimental data.

Prediction of the Lüders band in fine grained steel strips under uniaxial tension

Abstract The Luders band and the other regions outside the Luders band in fine grained steel strips are treated as two phases in equilibrium in the present paper. The discontinuities of stress and deformation gradient across interfaces between the Luders band and the other regions are considered, and the continuities of traction and displacements across interfaces and the Maxwell relation are imposed. The governing equations for two-phase piecewise-homogeneous deformations are obtained. The analysis is reduced to finding the minimum value of the loading at which governing equations have a unique, real, physically acceptable solution. As an illustration, the trilinear stress–strain response under uniaxial tension for fine grained steel used by other authors is applied to calibrate the three-dimensional elastoplastic model, the Maxwell stress, the inclined angle of the Luders band, the kinking angle of the strip and the strain and stress in the Luders band are predicted numerically. The predictions are in reasonable agreement with experimental measurements. The analysis also explains why the Luders band can spread along the length of the displacement-controlled specimen under the constant Maxwell stress plateau as observed in experiments.

Analysis and elimination of the stretcher strains on TH415 tinplate rings in the stamping process

Deep drawing process, although deceptively simple, involves a complex interplay between material properties, die geometry and process variables. The process optimisation is at the same time often affected by visual and design demands of a final product. The annealed low carbon steels used for tinplate rings, often undergo the strain hardening with extended yield point (yield point elongation) that results in surface defects of the formed part—the so-called stretcher strains (connected with Lueders’ bands phenomenon). This paper presents the finite element analysis of tinplate rings with ABAQUS program in order to analyse the phenomenon of the stretcher strains on an industrial case study. Numerical results were compared with the measured deformation of the stamped part. Finally the geometrical part optimisation was implemented in order to reduce the area with stretcher strains to a technologically attainable minimum.

Correlation between Luder strain and retained austenite in TRIP-assisted cold rolled steel sheets

In developed multiphase high strength, high formability TRIP-aided steel, Luders bands are observed similar to conventional low carbon steels. Retained austenite as the most effective constituent in TRIP steels, is responsible for Luders band formation as well as other properties such as formability, physical and mechanical properties. In the present study, a correlation between the Luders strain and the retained austenite characterization is proposed and verified by experimental evidences of the work carried out on two types of TRIP steel sheets. Intercritical annealing of cold rolled TRIP steels at different temperatures change the volume fraction of the retained austenite as well as the carbon concentration of samples which in turn leads to different Luders strain values. The experimental results show that the Luders strain is limited when the volume fraction and carbon concentration of the retained austenite increase in the TRIP steels.

Detection of Crack Initiation by Observations of Free Surface Condition

Abstract A simple method to detect crack initiation is presented. By polishing the surface of carbon steel structure properly and using the Lüders bands and orange peel as indicators for damage, it is possible to predict crack initiation with the naked eye. The initiation of the Lüders bands is the yellow light of the crack initiation, for instance, in the traffic signal, and orange peel is the red light. The relationship between the observed surface condition and the cyclic stress-strain characteristics is discussed.

Influence of Lüders band formation on the cyclic creep behaviour of a low-carbon steel for piping applications

Abstract The paper presents a study on the influence of formation of Luders band on the cyclic creep or ratcheting behaviour in low carbon steel bound for pipeline applications. The Luders band formation has been characterized by carrying out stress-controlled monotonic tensile tests in terms of the stress required for it to propagate and the amount of strain accumulated during its propagation. Low-cycle fatigue at different strain ranges and cyclic stress-controlled tests at different stress ratios and stress rate combinations have been carried out. It has been observed that the hysteresis behaviour in conditions favouring Luders band formation leads to a significant enhancement in ratcheting and cyclic softening in the low-cycle fatigue tests. The evolution of the hysteresis loop behaviour has been characterized by the Bauschinger energy parameter. The accelerated strain softening has been attributed faster proliferation of dislocation sources and to greater dislocation annihilation rates as a consequen...

Intergranular strain and texture in steel Luders bands

Neutron diffraction was used to examine residual strains and deformation texture related to Luders bands phenomenon in uniaxially deformed mild steel samples. Samples of two different thickness, 1.5 mm (thin) and 3.0 mm (thick), were uniaxially deformed to between 0.5% and 20% engineering strain, followed by unloading. The shape and texture of the Luders bands depended on the sample thickness. Neutron diffraction texture measurements indicated that there was little texture within the Luders bands in the thicker samples. There was, however, significant texture in the Luders bands of the thinner samples, and this same texture intensified once the Luders bands covered the entire sample and up to 20% deformation. The residual strains in the Luders bands were similar for both sample thicknesses. In the bands the {2 0 0} planes exhibited the largest intergranular strain; even at only 1% deformation, the {2 0 0} strain in the Luders band was very high (400 με). These high {2 0 0} strains were present only in the transverse and normal directions, with essentially no {2 0 0} strain in the rolling (applied stress) direction. Intergranular strains in the {2 2 0} and {2 1 1} were much lower and displayed much less variation with sample direction. In all samples the intergranular strains were essentially constant in the bands until the bands had propagated fully across the sample (∼5%) after this there was a small but progressive increase in the intergranular strains up to 20% deformation.

Intergranular strain correlation with magnetic behavior in steel

The correlation between the magnetic behavior and intergranular residual strain was investigated on several mild steel samples which were plastically deformed in the range 0.5%–20% engineering strain followed by unloading. At low deformation levels (0.5%–∼2%) the samples exhibited Luders banding, but after 2% strain the samples appeared uniformly deformed. Magnetic Barkhausen noise (MBN) measurements were used to characterize magnetic behavior and neutron diffraction measurements were used to determine the inter-granular strain. MBN results indicated a high MBN value in the direction transverse to the applied stress. This corresponded to a high strain in the (100) crystallographic direction (the easy magnetization direction), as observed using neutron diffraction. Little correlation was obtained between the MBN result and the (112) strain, which is generally assumed to reflect the macroscopic residual stress. Angular MBN and neutron diffraction results further confirmed the strong correlation between the (100) strain and the MBN result.

Deformation behavior of bimodal nanostructured 5083 Al alloys

Cryomilled 5083 Al alloys blended with volume fractions of 15, 30, and 50 pct unmilled 5083 Al were produced by consolidation of a mixture of cryomilled 5083 Al and unmilled 5083 Al powders. A bimodal grain size was achieved in the as-extruded alloys in which nanostructured regions had a grain size of 200 nm and coarse-grained regions had a grain size of 1 µm. Compression loading in the longitudinal direction resulted in elastic-perfectly plastic deformation behavior. An enhanced tensile elongation associated with the occurrence of a Luders band was observed in the bimodal alloys. As the volume fraction of coarse grains was increased, tensile ductility increased and strength decreased. Enhanced tensile ductility was attributed to the occurrence of crack bridging as well as delamination between nanostructured and coarse-grained regions during plastic deformation.

Dynamic impact behavior and ferrite variation of special stainless steels

Abstract The duplex stainless steel and super-austenitic stainless steel were impacted at two strain rates of 8.5 × 102 s−1 and 5 × 103 s−1. Two duplex stainless steels show strain softening and shear band was revealed at the surface. Austenitic stainless steel 254 SMO exhibits strain hardening completely and the diffuse Luders bands appear at the surface.

Influence of pre-straining on mechanical properties of HSLA steel by using ball indentation technique

Abstract Ball indentation technique has been employed to explore the possibilities for revealing the effect of pre-strain on mechanical properties of two groups of high-strength low-alloy steels. These steels were pre-strained up to 5%. Results are presented here for 1, 3, 4, and 5% of pre-strain effect on these steels. The dependence of yield strength, ultimate tensile strength, strength coefficient, strain-hardening component and true stress–strain curves on pre-straining effect are available from the ball indentation test, and they are validated with the standard mechanical test results. It is found that the increment of the pre-straining effect results in an increment of the yield strength and ultimate tensile strength values, while strength coefficient and strain-hardening component values are decreased. The existence of Luders bands in the conventional stress–strain curves is also revealed in ball indentation test by the presence of the Luders strain surrounding the indentation profile. In the conve...

Multiscale structure and properties of cast and deformation processed polycrystalline NiTi shape-memory alloys

The objective of this study is to examine fundamental processing-structure-property relationships in polycrystalline NiTi bars. Three different polycrystalline Ti-50.9 at. pct Ni (Ti-55.7 wt pct Ni) materials were examined: (1) cast, (2) cast then hot rolled, and (3) cast, hot rolled, then cold drawn. The structure of the materials was investigated at various scales ranging from nanometers to micrometers. The cast materials contained random crystallographic textures along the loading axis of the extracted samples. The hot-rolled and cold-drawn materials contained a strong 〈111〉 texture parallel to the deformation-processing direction. The high-temperature hot-rolling process facilitated recrystallization and recovery, and curtailed precipitate formation, leaving the hot-rolled and cold-drawn materials in near solutionized states. The cold-drawn material contained a high density of dislocations and martensite. After a mild aging treatment, all three materials contained distributed coherent Ti3Ni4 precipitates on the order of 10 nm in size. The cast material was capable of full shape-memory transformation strain recovery up to approximately 5 pct strain at room temperature under both tension and compression. The hot-rolled and cold-drawn materials demonstrated significant tension-compression stress-strain asymmetry owing to their strong crystallographic texture. Under compression, the deformation-processed materials were only capable of 3 pct transformation strain recovery while under tension they were capable of nearly 7 pct transformation strain recovery. Based on the present results, the presence of small coherent Ti3Ni4 precipitates is determined to be the driving force for the favorable strain transformation strain recovery properties in all three materials, despite drastically different grain sizes and crystallographic textures. The unique dependence of elastic modulus on stress-state, temperature, and structure is also presented and discussed for the deformation-processed materials. In addition, we demonstrate that the appearance of a Luders band transformation under tensile loading can be controlled by material structure. Specifically, the presence of significant martensite and dislocations in the cold-drawn materials was shown to mitigate the Luders band propagation and result in a more gradual transformation.

Ａｌ−Ｍｇ系合金板材のリューダース帯形成に及ぼす２軸引張荷重比の影響

It is well known that Luders bands form in Al–Mg alloy sheets by tensile deformation. The Luders bands are classified in two types; type-A and type-B. In this study, the influence of stress ratio of biaxial tensile test on the type-B Luders band formation in an Al–5.5mass%Mg–0.3mass%Cu alloy sheet was investigated. The type-B Luders bands were observed at the stress ratio (R.D. : T.D.) from 8 : 0 to 8 : 6, and they were not observed at 8 : 7 and 8 : 8. The mechanism of Luders bands formation was considered as below. In the case of uniaxial tensile deformation, the slip planes were limited easily because of pinning of dislocations by magnesium atoms. The deformation did not occur uniformly, then the type-B Luders bands occurred. On the other hand, multiple slip occurred easily in the case of balanced biaxial tensile deformation. Then, the sessile dislocations formed easily and the deformation occurred uniformly. Moreover, the type-B Luders bands formed at an angle of 57 degrees to the applied load in the case of uniaxial tension, while 90 degrees in the case of plane strain tension. It was considered that the change of the Luders bands direction occurred because of the difference of the activated slip system.

Effects of temperature on yield locus for 5083 aluminum alloy sheet

Warm press forming of aluminum alloy sheets is quite attractive, since undesirable stretcher strain marks, which often appear on the surface of the sheets during cold press forming, will disappear at high temperature, and furthermore, some aluminum alloys exhibit high-temperature superplasticity at a certain forming speed. In order to determine the optimum condition of press forming for an aluminum alloy sheet, the effect of forming temperature on the yield locus was experimentally investigated. The yield locus for a fine-grain Al–Mg alloy (5083-O) sheet was obtained by performing biaxial tensile tests, using cruciform specimens, at temperatures of 30, 100, 170, 250 and 300°C at strain rate of 10s−1. The size of yield locus drastically decreased with increasing temperature. Neither von Mises’ criterion or Hill’s can well predict the shape of the yield locus of this sheet metal. Instead of these quadratic yield functions, the yield criterion of Logan–Hosford or Barlat is a better choice for the accurate description of biaxial stress–strain responses at a high temperature.

Untersuchungen zur Anrisslebensdauervorhersage gekerbter Proben mit dem örtlichen Konzept am Beispiel des Stahls Cm15

Abstract A prerequisite for an exact prediction with the local strain approach is the same evolution of damage during cyclic fatigue both in smooth and notched specimens. Examinations on a low-carbon steel SAE 1017 in fine and coarse grain condition indicate the influence of fatigue Luders bands on the accuracy of such a prediction. As a consequence of cyclic loading, the surface of smooth polished specimens becomes rough while this effect is much less pronounced in the notch root. The reduction of Luders strain in coarse-grained material leads to an improved congruence between predicted and measured lifetime.