A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

This study presents a constitutive model for steels exhibiting SIMT, based on previous seminal works, and the corresponding methodology to estimate their parameters. The model includes temperature effects in the phase transformation kinetics, and in the softening of each solid phase through the use of a homogenization technique. The model was validated with experimental results of dynamic tensile tests on AISI 304 sheet steel specimens, and their predictions correlate well with the experimental evidence in terms of macroscopic stress–strain curves and martensite volume fraction formed at high strain rates. The work shows the value of considering temperature effects in the modeling of metastable austenitic steels submitted to impact conditions. Regarding most of the works reported in the literature on SIMT, modeling of the martensitic transformation at high strain rates is the distinctive feature of the present paper.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (Project CCG10-UC3M/DPI-5596)) and to the Ministerio de Ciencia e Innovación de España (Project DPI/2008-06408) for the financial support received which allowed conducting part of this work. The authors express their thanks to Mr. Philippe and Mr. Tobisch from the company Zwick for the facilities provided to perform the tensile tests at high strain rates

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

This study presents a constitutive model for steels exhibiting SIMT, based on previous seminal works, and the corresponding methodology to estimate their parameters. The model includes temperature effects in the phase transformation kinetics, and in the softening of each solid phase through the use of a homogenization technique. The model was validated with experimental results of dynamic tensile tests on AISI 304 sheet steel specimens, and their predictions correlate well with the experimental evidence in terms of macroscopic stress–strain curves and martensite volume fraction formed at high strain rates. The work shows the value of considering temperature effects in the modeling of metastable austenitic steels submitted to impact conditions. Regarding most of the works reported in the literature on SIMT, modeling of the martensitic transformation at high strain rates is the distinctive feature of the present paper.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (Project CCG10-UC3M/DPI-5596)) and to the Ministerio de Ciencia e Innovación de España (Project DPI/2008-06408) for the financial support received which allowed conducting part of this work. The authors express their thanks to Mr. Philippe and Mr. Tobisch from the company Zwick for the facilities provided to perform the tensile tests at high strain rates

Bending of Euler-Bernoulli beams using Eringen's integral formulation: A paradox resolved

The Eringen nonlocal theory of elasticity formulated in differential form has been widely used to address problems in which size effect cannot be disregarded in micro- and nano-structured solids and nano-structures. However, this formulation shows some inconsistencies that are not completely understood. In this paper we formulate the problem of the static bending of Euler-Bernoulli beams using the Eringen integral constitutive equation. It is shown that, in general, the Eringen model in differential form is not equivalent to the Eringen model in integral form, and a general method to solve the problem rigorously in integral form is proposed. Beams with different boundary and load conditions are analyzed and the results are compared with those derived from the differential approach showing that they are different in general. With this integral formulation, the paradox that appears when solving the cantilever beam with the differential form of the Eringen model (increase in stiffness with the nonlocal parameter) is solved, which is one of the main contributions of the present work.This work was supported by the Ministerio de Economía y Competitividad de España (grants numbers DPI2011-23191 and DPI2014-57989-P). Prof. J.N. Reddy acknowledges the support of Universidad Carlos III de Madrid with a Cátedra de Excelencia funded by Banco Santander during academic year 2014–2015

Dynamic necking of notched tensile bars: an experimental study

The mechanics of necking inception in dynamically-stretched notched specimens have been investigated. For that task, a systematic experimental campaign of quasi-static and dynamic tensile tests on martensitic steel specimens has been conducted. Samples with and without notches have been considered. Unlike the quasi-static tests, the dynamically-tested notched samples revealed that, under certain loading conditions, flow localization may develop away from the groove. The experimental results presented in this investigation show that the presence of sharp geometrical imperfections in ductile materials subjected to dynamic loading does not necessarily dictate the necking and fracture locus.D. Rittel acknowledges the support of Carlos III University with a Cátedra de Excelencia funded by Banco Santander during academic year 2011-2012. The researchers of the University Carlos III of Madrid are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191) for the financial suppor

Numerical simulation of the effect of adiabatic temperature increase in martensitic transformation of austenitic steels

This work presents a constitutive model for metastable austenitic steels exhibiting Strain Induced Martensitic Transformation (SIMT). Based on the description of the kinetics of phase transformation proposed by Olson and Cohen [3], and later generalized to 3D by Stringfellow et al. [7] and Papatriantafillou et al. [4], this model includes the effect of temperature increase on the kinetics of SIMT and on the thermal softening of the phases. This allows capturing relevant phenomena exhibited by metastable austenitic steels when subjected to plastic deformation at high strain rates. A systematic procedure for the identification of the constitutive parameters has been proposed. The predictions of the constitutive description are compared with experiments for the austenitic steel AISI 304 provided by Rodríguez-Martínez et al. [6]. Good correlation between experiments and modelling are achieved in terms of macroscopic strain-stress curves and volume fraction of martensite formed during straining

Numerical simulation of the effect of adiabatic temperature increase in martensitic transformation of austenitic steels

This work presents a constitutive model for metastable austenitic steels exhibiting Strain Induced Martensitic Transformation (SIMT). Based on the description of the kinetics of phase transformation proposed by Olson and Cohen [3], and later generalized to 3D by Stringfellow et al. [7] and Papatriantafillou et al. [4], this model includes the effect of temperature increase on the kinetics of SIMT and on the thermal softening of the phases. This allows capturing relevant phenomena exhibited by metastable austenitic steels when subjected to plastic deformation at high strain rates. A systematic procedure for the identification of the constitutive parameters has been proposed. The predictions of the constitutive description are compared with experiments for the austenitic steel AISI 304 provided by Rodríguez-Martínez et al. [6]. Good correlation between experiments and modelling are achieved in terms of macroscopic strain-stress curves and volume fraction of martensite formed during straining

Numerical Simulation of the effect adiabatic temperature increase in martensitic transformation of austenitic steels

The predictions of the constitutive model agree with experimental results in terms of macroscopy stress-strain curves and volume fraction of martensite formed during loadin