The contribution of kinematic hardening to the overall strain hardening of a high entropy alloy (HEA) was investigated for the first time ever. It was assessed for a single-phase equiatomic ...CoCrFeMnNi alloy based on a study of the Bauschinger effect. The observed occurrence of high back stresses signifies substantial kinematic hardening. We attribute it to the low probability of cross-slip in this HEA which, however, rises in the process of straining. A model that captures the mentioned effects was proposed and validated.
Comparison between experiment and modelling for the flow stress (colour lines) Display omitted
The major scientific and technological advances and breakthroughs of advanced high strength steels (AHSS) were achieved due to the strong demands of automotive industry. The development of AHSS began ...in the early 1980s with the aim of improving passenger safety and weight‐saving. The present paper presents the driving forces and logic of development of various AHSS for automotive applications since 1980s. The importance of crash performance, weight‐saving, formability, and rigidity are critically reviewed for the development of new steel grades for automotive applications. The logical sequences of the development of dual phase (DP) steel, transformation induced plasticity (TRIP) steels, tempered DP steels, complex phases (CP) steels, Ferrite‐Bainite steels, hot‐stamping technology, twinning induced plasticity (TWIP) steels, Quench and Partitioning (Q&P) steels, Medium Mn steels, and steels–polymer composites are presented.
The development of Advanced High Strength Steels (AHSS) began with the aim of improving passenger safety and weight‐saving. The image shows the automative parts (in red) that are made of AHSS.
The Adaptive Ridge Algorithm is an iterative algorithm designed for variable selection. It is also known under the denomination of Iteratively Reweighted Least-Squares Algorithm in the communities of ...Compressed Sensing and Sparse Signals Recovery. Besides, it can also be interpreted as an optimization algorithm dedicated to the minimization of possibly nonconvex
ℓ
q
penalized energies (with
0
<
q
<
2
). In the literature, this algorithm can be derived using various mathematical approaches, namely Half Quadratic Minimization, Majorization-Minimization, Alternating Minimization or Local Approximations. In this work, we will show how the Adaptive Ridge Algorithm can be simply derived and analyzed from a single equation, corresponding to a variational reformulation of the
ℓ
q
penalty. We will describe in detail how the Adaptive Ridge Algorithm can be numerically implemented and we will perform a thorough experimental study of its parameters. We will also show how the variational formulation of the
ℓ
q
penalty combined with modern duality principles can be used to design an interesting variant of the Adaptive Ridge Algorithm dedicated to the minimization of quadratic functions over (nonconvex)
ℓ
q
balls.
In this article, we present our take on modeling the Bauschinger effect. The main goal is to correlate the microstructure-based modeling developed for uniaxial tension/compression deformation and the ...tensorial modeling approach of the continuum mechanics. After a brief historial review, we present a microstructure-related model that was proven to provide an adequate description of the Bauschinger effect in terms of kinematic and isotropic strain hardening. Its generalization to the case of multiaxial loading is then formulated in terms of a continuum mechanics model. The full tensorial model developed is now being offered to the solid mechanics and physical metallurgy communities as an advanced modeling tool.
Graphic Abstract
In this article, we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time-to-event variables. The survival responses need to be ...ordered according to a numerical covariate. Our estimation method will aim at detecting heterogeneity that could arise through the ordering covariate. We formally introduce our model as a constrained Hidden Markov Model, where the hidden states are the unknown segmentation (breakpoint locations) and the observed states are the survival responses. We derive an efficient Expectation-Maximization framework for maximizing the likelihood of this model for a wide range of baseline hazard forms (parametrics or nonparametric). The posterior distribution of the breakpoints is also derived, and the selection of the number of segments using penalized likelihood criterion is discussed. The performance of our survival breakpoint model is finally illustrated on a diabetes dataset where the observed survival times are ordered according to the calendar time of disease onset.
Most advanced high-strength steel products contain complex phases, including ferrite, bainite and martensite, which form successively during elaboration. It is essential to understand the effect of ...prior ferrite transformation on the subsequent bainite and martensite transformation kinetics to achieve precise control of the final microstructure. Nevertheless, the effect of the interface between the prior formed ferrite and the residual austenite (α/γ), together with the related chemical heterogeneity at the interface, on the subsequent phase transformations has been studied only rarely, and remains unclear. This study pays particular attention to the effect of the α/γ interface and its related concentration gradients on bainite and martensite transformation. It is shown that the interface and its related concentration gradients can play a very significant role on the subsequent bainite or martensite transformation kinetics: it retards bainite transformation whereas it accelerates martensite transformation. It is revealed from microprobe wavelength-dispersive spectrometry analysis and model calculations that there are both manganese and carbon gradients in front of the α/γ interface at the end of the ferrite transformation holding. The subsequent bainite transformation kinetics is controlled by the competition between the acceleration effect of the interface boundary itself and the retardation effect of the higher alloying concentration near the interface. Martensite transformation should initiate at the pre-existing dislocations in the center of the residual austenite grains, where the C and Mn contents are the lowest. A simple martensite transformation kinetics model taking into account C heterogeneity is proposed that can describe well the martensite transformation kinetics following the prior ferrite transformation.
It is almost commonplace to say that physics-based constitutive models developed to characterize the mechanical behavior of materials are to be preferred over phenomenological models. However, the ...constitutive relations offered by physics-based approaches are oftentimes too involved to be handled in finite element (FE) simulations for practical applications. There is a demand for physics-based, yet robust and user-friendly models, and one such model will be highlighted in this article. A simple constitutive model developed recently by Bouaziz to extend the classical physics-based Kocks-Mecking model provides a viable tool for modelling a broad range of materials – beyond the single-phase coarse-grained materials it was initially devised for. The efficacy of the model was put to the test by investigating its applicability for different materials. A broad interval of the true stress vs. true strain curve was studied by the measurement-in-neck-section method in the uniaxial tensile mode for six types of metallic materials, and simulations using the finite element method emulating the experimental conditions were developed. In this way, the engineering stress-strain curves were obtained corresponding to the true stress-strain curves for these materials. A comparison of the numerical simulations of the tensile behaviour of all six materials with the experimental results for a broad range of strains showed that among the models trialled, the Bouaziz model was the best-performing one. The proposed model can be recommended for use in FE simulations of the mechanical behaviour of engineering structures as a viable alternative to complex physics-based or simplistic phenomenological constitutive models.
Model dual-phase microstructures were developed to decouple the effect of martensite volume fraction and martensite hardness on the plastic behavior of dual-phase steels. The martensite volume ...fraction ranges from 11% to 37%, involving two levels of martensite hardness. The yield strength and tensile strength increase with increasing martensite volume fraction, while the uniform elongation decreases. The martensite hardness has a weak impact on the initial yield strength, but it significantly affects the flow behavior for sufficiently large martensite volume fraction. Increasing the hardness of the martensite leads to higher tensile strength combined with only a limited impact on uniform elongation, resulting in an improved strength/ductility balance. The experimental results are successfully captured using finite element based micromechanical analysis. Among others, periodic cell calculations show very good predictive capabilities of the overall plastic response when the stage-IV hardening of the ferrite is taken into account. Our numerical analysis reveals that an accurate description of the elasto-plastic behavior of the martensite is a key element to rationalize the mechanical behavior of DP steels. This modeling approach provides a framework for designing dual-phase steels with optimized plastic flow properties.
•Effects of martensite volume fraction and hardness are decoupled experimentally.•Higher martensite hardness increases tensile strength without decreasing ductility.•Periodic cell model shows good predictive capabilities of the plastic response.•The stage-IV hardening of ferrite should be considered to improve the prediction.•We show the importance to accurately describe the deformation state of martensite.
Under some circumstances, composites with a corrugated reinforcement geometry show larger necking strains compared to traditional straight reinforced composites. In this work, finite element modeling ...studies were performed for linearly hardening materials, examining the effect of material parameters on the stress–strain response of both corrugation and straight-reinforced composites. These studies showed that improvements in necking strain depend on the ability of the corrugation to unbend and to provide a boost in work hardening at the right time. It was found that there is a range of matrix yield strengths and hardening rates for which a corrugated geometry will improve the necking strain and also a lower threshold of reinforcement yield strength below which no improvement in necking strain is possible. In addition, benefit maps and surfaces were generated that show which regions of property space benefit through corrugation and the corresponding improvement in necking strain that can be achieved.
The kinematic and isotropic hardening behavior was investigated for high and medium entropy alloys with a single-phase face-centered cubic (FCC) structure. The cross-slip associated with screw ...dislocations in FCC structures is strongly influenced by local fluctuations in the spatial distribution of different atom species. The local atomic arrangements inhibit the movement of Shockley partial dislocations during plastic deformation, thereby lowering the probability of cross-slip and generating a higher back-stress. This study used a solid-solution induced back-stress model, which combines nonlinear kinematic and isotropic hardening, to investigate the effects of dislocation forest stress and back-stress in a non-equiatomic Cr12Fe42Mn24Ni22 medium entropy alloy. Based on the experimental results, numerical simulations by the finite element method were performed to validate this modeling approach.
PDF
