Correlation between band propagation property and the nature of serrations in the Portevin–Le Chatelier effect

Sarmah, Ritupan; Ananthakrishna, G.

doi:10.1016/j.actamat.2015.03.027

Cited by 41 publications

(39 citation statements)

References 37 publications

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“…This is a general result in dynamical systems that has been well illustrated in the case of the PLC effect (see Ref. [30,33] and in particular Figure 2.1a of Ref. [42]).…”

Section: General Conclusion On the Dynamical Approach To Nanoindentamentioning

confidence: 90%

“…As discussed in a number of earlier publications, two distinct types of short range interactions can be identified that act as the source for the growth of the forest density ρ f . These act as loss terms to the mobile density ρ m [28,30,33,34,42,49]. When two dislocations moving in nearby glide planes approach a minimum distance (typically a few nanometers), they can form dipoles.…”

Section: General Form Of Time Evolution Equations For Dislocation Denmentioning

confidence: 99%

“…Following our earlier publications [28][29][30][32][33][34]41,46], we develop the time evolution equations for the mobile ρ m and forest ρ f densities based on relevant dislocation mechanisms contributing to the plastic flow. Dislocation mechanisms can be broadly categorized into dislocation production and transformation mechanisms.…”

Section: General Form Of Time Evolution Equations For Dislocation Denmentioning

confidence: 99%

“…Thus, the more complex the phenomenon, the more the number of dislocation mechanisms and the more the number of parameters. For instance, the AK model [30,32,33,46,50] for the complex spatio-temporal PLC instability has ten parameters. Even in simple models such as the storage recovery model [40] and the model for plastic deformation of micro-pillars [43], there are three and six respectively.…”

Section: Estimation Of Parametersmentioning

confidence: 99%

“…The purpose of this paper is to review the recently introduced dynamical approach and the models that predict the results for the DC and LC mode nanoindentation experiments [28,29]. The approach is based on our previous experience in modeling a significantly more complex spatio-temporal instability, namely, the Portevin-Le Chatelier (PLC) effect seen in bulk samples of dilute alloys under constant strain rate conditions [30][31][32][33][34]. The approach is applicable to ideal single crystals without any kind of defects.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Novel Approach to Modelling Nanoindentation Instabilities

Ananthakrishna

Krishnamoorthy

2018

Crystals

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Abstract:We review the recently developed models for load fluctuations in the displacement controlled mode and displacement jumps in the load controlled mode of indentation. To do this, we devise a method for calculating plastic contribution to load drops and displacement jumps by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities by including relevant dislocation mechanisms. These equations are then coupled to the equation defining constant displacement rate or load rate. The model for the displacement controlled mode using a spherical indenter predicts all the generic features of nanoindentation such as the elastic branch followed by several force drops of decreasing magnitudes and residual indentation depth after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted numbers for all the quantities match experiments on single crystals of Au using a spherical indenter. We extend the approach to model the load controlled nanoindentation experiments that employ a Berkovich indenter. We first identify the dislocation mechanisms contributing to different regions of the F − z curve as a first step for obtaining a good fit to a given experimental F − z curve. This is done by studying the influence of the parameters associated with various dislocation mechanisms on the model F − z curves. The study also demonstrates that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes and residual plasticity after unloading for a range of model parameter values. Furthermore, an optimized set of parameter values can be easily determined that give a good fit to the experimental load-displacement curves for Al single crystals of (110) and (133) orientations. Our model also predicts the indentation size effect in a region where the displacement jumps disappear. The good agreement of the results of the models with experiments supports our view that the present approach can be used as an alternate method to simulations. The approach also provides insights into several open questions.

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“…This is a general result in dynamical systems that has been well illustrated in the case of the PLC effect (see Ref. [30,33] and in particular Figure 2.1a of Ref. [42]).…”

Section: General Conclusion On the Dynamical Approach To Nanoindentamentioning

confidence: 90%

Section: General Form Of Time Evolution Equations For Dislocation Denmentioning

confidence: 99%

Section: General Form Of Time Evolution Equations For Dislocation Denmentioning

confidence: 99%

Section: Estimation Of Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Novel Approach to Modelling Nanoindentation Instabilities

Ananthakrishna

Krishnamoorthy

2018

Crystals

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Influence of Temperature and Grain Size on Austenite Stability in Medium Manganese Steels

Zhang

Wang²,

Findley

et al. 2017

Metall Mater Trans A

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Temperature-Dependent Macroscopic Mechanical Behaviors and Their Microscopic Explanations in a Medium Mn Steel

Liu

et al. 2020

Metall Mater Trans A

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Plastic instability (e.g., Lü ders band and PLC band) is a phenomenon frequently observed in cold-rolled medium Mn steels. In this study, through a number of quasi-static uniaxial tensile tests with digital image correlation (DIC) measurement of the strain rate field, we found the medium Mn steel (Fe-0.14C-7.14Mn-0.23Si wt. pct with approximately 33 vol pct of retained austenite and 67 vol pct of ferrite) exhibited distinct competition/coordination between the Lu¨ders band and the PLC band at different deformation temperatures: (1) at 25°C and 55°C, a Lu¨ders band was followed by several PLC bands; (2) at 100°C, fracture occurred right after the Lu¨ders band formation, without the presence of a PLC band; (3) at 250°C, only PLC bands were observed. We propose that these macroscopic behaviors can be explained by the temperature-dependent conditions for the formation/appearance and propagation of Lu¨ders bands and PLC bands. The propagation of Lu¨ders bands becomes difficult when the temperature increases as less hardening is provided by martensitic transformation. In contrast, the appearance and propagation of PLC bands become easier when the temperature increases and/or the plastic strain becomes large (16.5 and 18.9 pct in this material at the deformation temperatures of 25°C and 55°C, respectively), as the difference in the average velocities of solute atom diffusion and dislocation gliding is reduced. Either condition for Lu¨ders bands or for PLC bands will be satisfied at different deformation temperatures or plastic strains, thus leading to the competition/coordination between them.

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Correlation between band propagation property and the nature of serrations in the Portevin–Le Chatelier effect

Cited by 41 publications

References 37 publications

A Novel Approach to Modelling Nanoindentation Instabilities

A Novel Approach to Modelling Nanoindentation Instabilities

Influence of Temperature and Grain Size on Austenite Stability in Medium Manganese Steels

Temperature-Dependent Macroscopic Mechanical Behaviors and Their Microscopic Explanations in a Medium Mn Steel

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