Mathematical Modeling of the Influence Parameters During Formation and Propagation of the Lüders Bands

Abstract

In this study, an analysis of the influence parameters measured by the static tensile test, thermography and digital image correlation was performed during formation and propagation of the Lüders bands. A new approach to the prediction of stresses, maximum temperature changes and strains during the Lüders band formation and propagation is proposed in this paper. Application of the obtained mathematical models of influence parameters gives a clear insight into the behavior of niobium microalloyed steel at the beginning of the plastic flow, which can improve product quality and reduce costs during the forming of microalloyed steels with the appearance of the Lüders bands. The obtained models of influential parameters during formation and propagation of the Lüders bands have been developed by the regression analysis method. The proposed mathematical models showed low deviations of calculated results ranging from 1.34% to 12.37%.The local stress amounts, important in the forming of microalloyed steels since indicating surface roughness and plastic flow possibilities during the Lüders band propagation, are obtained by the mathematical model. It was found that stress amounts increase during the Lüders band propagation in the area behind the Lüders band front. The difference in stress amount between the start of the Lüders band propagation and advanced Lüders band propagation is 25.53 MPa.

Stress distribution at different deformation degrees in low carbon steel during cold deformation

“…The test points 3, Rm, 4 and 5 were selected for stress calculation in order to observe stress changes with a significant increase in the deformation degree. Mathematical model from the research [12], obtained at the start of plastic flow on low carbon steel with the addition of 0.048% of the microalloying element niobium, is presented in form of an Equation (1):…”

“…where σ is calculated stress, ΔTmax is maximum temperature change and ɛmax is maximum strain. Equation 1 from research [12] is applied for stress calculation in test points 3, Rm, 4 and 5. Figure 5 shows calculation results of stresses in selected points.…”

Mesoscale Deformation-Induced Surface Phenomena in Loaded Polycrystals

“…The stress necessary to start off the movement of existing dislocations or to nucleate new defects is assumed to be higher than the stress required to keeping propagation of the dislocations already involved in motion. A similar "stick-slip" mode of plastic deformation is typical for, e.g., Lüders band propagation [24][25][26] or PLC effect [23] where an extra stress is necessary to detach dislocations from interstitial atoms. An analogy can be drawn with friction [1], where the static friction force must be overcome by certain applied forces to disrupt the surface bonds between contacting bodies, whereupon their subsequent relative motion may occur at a lower force.…”

Line Analysis of Changes in the Deformation Zone During Lüders Band Propagation

“…Lüders bands appear at the beginning of plastic flow, and Portevin -Le Chatelier effect (PLC) occurs continuously from the beginning of plastic flow up to the breaking point of test material. Lüders band, as one of the mentioned phenomena, is usually researched by applying thermography and digital image correlation (DIC) [10]. Under certain conditions, with these methods it can be determined distribution and values of temperature changes (associated with stress changes in deformed metal [10]) and deformation during the plastic flow both of steel and other metal materials [11,12].…”

“…Lüders band, as one of the mentioned phenomena, is usually researched by applying thermography and digital image correlation (DIC) [10]. Under certain conditions, with these methods it can be determined distribution and values of temperature changes (associated with stress changes in deformed metal [10]) and deformation during the plastic flow both of steel and other metal materials [11,12]. Thermography and DIC results can be presented by line and point analysis, thus analysis of a certain zone of interest that shows appearance and propagation of the Lüders band, but also other phenomena happening during the plastic deformation of steel [13][14][15][16].…”