On the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings

In this work a stability analysis on flow localization in the dynamic expansion of ductile rings is con ducted. Within a 1 D theoretical framework, the boundary value problem of a radially expanding thin ring is posed. Based on a previous work, the equations governing the stretching process of the expanding ring are derived and solved using a linear perturbation method. Then, three different perfectly plastic material constitutive behaviours are analysed: the rate independent material, the rate dependent mate rial showing constant logarithmic rate sensitivity and the rate dependent material showing non constant and non monotonic logarithmic rate sensitivity. The latter allows to investigate the interaction between inertia and strain rate sensitivity on necking formation. The main feature of this work is rationally dem onstrate that under certain loading conditions and material behaviours: (1) decreasing rate sensitivity may not lead to more unstable material, (2) increasing loading rate may not lead to more stable material. This finding reveals that the relation between rate sensitivity and loading rate controls the unstable flow growth. Additionally a finite element model of the ring expansion problem is built in ABAQUS/Explicit. The stability analysis properly reflects the results obtained from the numerical simulations. Both proce dures, perturbation analysis and numerical simulations, allow for emphasizing the interplay between rate sensitivity and inertia on strain localization.The financial support of the Comunidad Autónoma de Madrid (Project CCG10 UC3M/DPI 5596) and of the Ministerio de Ciencia e Innovación de España (Project DPI/2008 06408) is kindly acknowledged.Publicad

Molecular recognition through divalent interactions with a self-assembled fibrillar network of a supramolecular organogel

The interaction of phenol derivatives with the self-assembled fibrillar network of two different supramolecular gels has been studied. NMR relaxometry reveals the selective interaction of resorcinol over other related molecules with a gel formed by the gelator 2 which contains terminal pyridine units. No selectivity is observed for a related gelator that contains phenyl instead of pyridine moieties. The selectivity observed by NMR experiments permits the selective suppression of the 1H NMR signals of resorcinol. This behaviour is translated to macroscopic properties such as the thermal stability of the gels. The observed selectivity together with X-ray diffraction data and molecular modelling suggest that the gels formed by 2 present arrays of pyridine H-bond acceptor groups capable of selective multivalent interaction with phenolic substrate

The role of constitutive relation in the stability of hyper-elastic spherical membranes subjected to dynamic inflation

In this work the mechanical response of hyper-elastic spherical membranes subjected to dynamic inflation is revisited. Specifically, a comprehensive analysis on the role that the constitutive behaviour of the material has on the mechanical stability of the membrane has been developed. Six different strain-energy functions, frequently used to approximate the constitutive behaviour of elastomeric solids, have been considered: three of the Mooney-Rivlin class and three of the Ogden class. For all the constitutive models used, the material parameters have been obtained from Bucchi and Hearn (2013a, 2013b), where the same set of experimental results was used to calibrate the models. We show that essential features of the dynamic response of the spherical shell are closely related to the strain-energy function selected to describe the constitutive behaviour of the membrane. As reported by Bucchi and Hearn (2013a, 2013b), this issue is frequently overlooked within the literature since too often only one strain-energy function is used to address this type of dynamic problems. (C) 2015 Elsevier Ltd. All rights reserved

Identification of the critical wavelength responsible for the fragmentation of ductile rings expanding at very high strain rates

This work examines the mechanisms governing the fragmentation of ductile ringsexpanding at very high strain rates. Based on previous works three different methodologies have been addressed, namely: fully 3D finite element computationsof the radial expansion of ductile rings, numerical simulations of unitary axisymmetric cells with sinusoidal spatial imperfections subjected to tensile loading and a linear perturbation technique derived within a quasi-1D theoretical framework. The results derived from these three different approaches allow for identification of a critical wavelength which dictates the fragmentation of ductile rings expanding at very high strain rates. This critical wavelength is revealed quite independent of the material properties but closely related to the ratio (L0/Ø0) critical ≈1:5 where L0 is the fragment size and Ø0 is the diameter of the circular section of the ring. This work highlights the fundamental role played by material inertia in the fragmentation at very high strain rates, setting aside the mechanisms associated to the classical statistical theories.Comunidad Autónoma de Madrid (Project CCG10-UC3M/DPI-5596) and to the Ministerio de Ciencia e Innovación de España (Project DPI/2011-24068) for the financial support received which allowed conducting part of this work.Publicad

Collective behaviour and spacing of necks in ductile plates subjected to dynamic biaxial loading

Diffuse or localized dynamic necking of a sheet metal is a major issue in high speed forming processes, leading to unacceptable thinning and even failure if fully developed, and in the dynamic behaviour of metallic structural elements of small thickness used for energy absorption purposes. This process is frequently related to the collective development of localization bands resulting in a necking pattern which depends on the sheet properties and on the loading conditions. This work investigates the spacing between necking bands in sheets made of a thermoviscoplastic metal and submitted to dynamic biaxial loading. For that task a linear perturbation technique, derived within a 2D framework which specifically accounts for stress triaxiality effects upon strain localization, has been developed. Using this methodology, a dominant instability mode can be identified, whose wavelength is related to the necking-band spacing. Likewise, fully 3D finite element simulations have been performed in order to verify and complement the outcomes of the aforementioned theoretical approach. The effects of loading conditions (loading path and loading rate), and thermal coupling on the stability of the deformation process and on the distance between necking bands are examined. We have shown that the neck spacing increases with the ratio of strains and decreases with the loading rate and the temperature rise.JFS, RZ, GV and JARM are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191) for the financial support which permitted to conduct this work. AM and JARM acknowledge the support by the French State through the program Investment in the future operated by the National Research Agency (ANR) and referenced by ANR-11-LABX-0008-01 (LabEx DAMAS). AM acknowledges the support by the University Carlos III de Madrid through the Cátedra de Excelencia funded by Banco Santander.Publicad

Dynamic necking in materials with strain induced martensitic transformation

This work investigates the interplay between inertia and strain induced martensitic transformation (SIMT) on necking inception and energy absorption in dynamically stretched cylindrical rods. For that task a linear stability technique, derived within a quasi-1D framework and specifically accounting for SIMT, has been developed. Likewise, finite element simulations have been performed, using a specific constitutive equation to consider SIMT. Stability analysis and numerical simulations demonstrate that, at high strain rates, inertia may take the dominant role in stabilizing the material, on top of the transformation hardening effects. Furthermore, under certain loading conditions the martensitic transformation may penalize either ductility or energy absorption capacity.Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191)Publicad

On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings

In this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished.The authors are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011 24068 and DPI/ 2011 23191) for the financial support

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 sem inal 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 austen itic steels submitted to impact conditions. Regarding most of the works reported in the lit erature 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.Publicad

An analysis of microstructural and thermal softening effects in dynamic necking

The competition between material and thermal induced destabilizing effects in dynamic shear loading has been previously addressed in detail using a fully numerical approach in Osovski et al. (2013). This paper presents an analytical solution to the related problem of dynamic tensile instability in a material that undergoes both twinning and dynamic recrystallization. A special prescription of the initial and loading conditions precludes wave propagation in the specimen which retains nevertheless its inertia. This allows for a clear separation of material versus structural effects on the investigated localization. The outcome of this analysis confirms the dominant role of microstructural softening in the lower strain-rate regime (of the order of 10(3) s(-1)), irrespective of the extent of prescribed thermal softening. By contrast, the high strain-rate regime is found to be dominated by inertia as a stabilizing factor, irrespective of the material's thermo-physical conditions, a result that goes along the predictions of Rodriguez-Martinez et al. (2013a) regarding dynamically expanding rings.The authors are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191) for the financial support. D. Rittel acknowledges the support of University Carlos III of Madrid with a Cátedra de Excelencia funded by Banco Santander during academic year 2011-2012

Dynamic recrystallization and adiabatic shear localization

It has recently been reported that, in alloys exhibiting early dynamic recrystallization (DRX), the onset of adiabatic shear bands (ASB) is primarily related to microstructural transformations, instead of the commonly assumed thermal softening mechanism as shown by Rittel et al. (2006, 2008) and Osovski et al. (2012b). Further, the dominant role of microstructural softening in the necking process of dynamically stretching rods showing DRX has been verified using linear stability analysis and finite element simulations by Rodriguez-Martinez et al. (2014). With the aim of extending this coupled methodology to shear conditions, this paper presents an analytical solution to the related problem of ASB in a material that undergoes both twinning and dynamic recrystallization. A special prescription of the initial and loading conditions precludes wave propagation in the specimen which retains nevertheless its inertia, allowing for a clear separation of material versus structural effects on the localization process. A parametric study, performed on the constants of the constitutive model, permits the identification of their relative role in the onset of the dynamic instability. The main outcome of the analysis confirms the strong destabilizing effect played by the development of DRX, consistently with the former statement regarding ASB, and contributes to rationalize the observations of other authors.The authors are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191) for the financial support.Publicad