Finite element modelling of atomic force microscope cantilever beams with uncertainty in material and dimensional parameters

Copyright © 2014 by Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, PolandThe stiffness and the natural frequencies of a rectangular and a V-shaped micro-cantilever beams used in Atomic Force Microscope (AFM) were analysed using the Finite Element (FE) method. A determinate analysis in the material and dimensional parameters was first carried out to compare with published analytical and experimental results. Uncertainties in the beams’ parameters such as the material properties and dimensions due to the fabrication process were then modelled using a statistic FE analysis. It is found that for the rectangular micro-beam, a ±5% change in the value of the parameters could result in 3 to 8-folds (up to more than 45%) errors in the stiffness or the 1st natural frequency of the cantilever. Such big uncertainties need to be considered in the design and calibration of AFM to ensure the measurement accuracy at the micron and nano scales. In addition, a sensitivity analysis was carried out for the influence of the studied parameters. The finding provides useful guidelines on the design of micro-cantilevers used in the AFM technology.The research was supported by Sichuan International Research Collaboration Project (2014HH0022)

Effect of projectile nose shape on ballistic resistance of interstitial-free steel sheets

In this paper an experimental and numerical work is reported concerning the process of perforation of thin steel plates using different projectile nose shapes. The main goal is to analyze how the projectile shape may change the ballistic properties of materials. A wide range of impact velocities from 35 to 180 m/s has been covered during the tests. All the projectiles were 13 mm in diameter and the targets were 1 mm thick, as such the projectile can be regarded as rigid and the target sheets were of interstitial-free (IF) steel. The mass ratio (projectile mass/steel sheet mass) and the ratio between the span of the steel sheet and the diameter of the projectile were kept constant, equal to 0.38 and 3.85 respectively. To define the thermoviscoplastic behavior of the target material, the Rusinek-Klepaczko (RK) constitutive model [1] was used. The complete identification of the material constants was done based on a rigorous material characterization. Numerical simulations of some experimental tests were carried out using a non-linear finite element code ABAQUS/Explicit. It was found that the numerical models are able to describe the physical mechanisms in the perforation process with a good accuracy.The National Centre of Research and Development under the grant WND-DEM-1-203/00

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

Experimental survey on the behaviour of AISI 304 steel sheets subjected to perforation

This paper presents and analyzes the behaviour of AISI 304 steel sheets subjected to perforation under a wide range of impact velocities. The relevance of this steel resides in the potential transformation of austenite into martensite during mechanical loading. This process leads to an increase in strength and ductility of the material. It makes the AISI 304 attractive for many engineering applications, especially for building structural elements responsible for absorbing energy under fast loading. However, this transformation takes place only under determined loading conditions strongly dependent on initial temperature and deformation rate. In order to study the material behaviour under impact loading, perforation tests have been performed at room temperature using both, a drop weight tower and a pneumatic gas gun within the range of impact velocities 2.5 m/s≤V0≤85 m/s. The results are compared with those reported in [18] and [21] for ES steel and TRIP 1000 steel. The comparison highlights the good performance of the AISI 304 under high loading rates. Martensitic transformation taking place in this steel during perforation is identified responsible for such behaviour

Numerical simulations of impact behaviour of thin steel plates subjected to cylindrical, conical and hemispherical non-deformable projectiles

In this paper, a numerical study of normal perforation of thin steel plates impacted by different projectile shapes is reported. The numerical simulations of this problem have been performed using a finite element code, ABAQUS-Explicit with a fixed and an adaptive mesh for the plate. To define the thermoviscoplastic behaviour of the material constituting the plate, the Johnson-Cook model has been used. This homogeneous behaviour has been coupled with the Johnson-Cook fracture criterion to predict completely the perforation process. Three kinds of projectile shape (blunt, conical and hemispherical) have been simulated with a large range of impact velocities from 190 to 600 m/s. The analysis considers the influence of adiabatic shear bands, plastic work and the gradient of temperature generated in the plate. The numerical results predict correctly the behaviour projectile-plate in agreement with experimental data published by other authors.Publicad

A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper

In this paper a physical-based constitutive relation for defining the thermo-viscoplastic behaviour of FCC metals with dependence on strain on thermal activation processes is presented. The model, based on previous considerations reported by Rusinek and Klepaczko [Rusinek A, Klepaczko JR. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plasticity 2001;17:87-115], is founded on physical aspects of the material behaviour. The proposed constitutive relation is applied to define the behaviour of oxygen-free high conductivity (OFHC) copper using the experimental data reported in Nemat-Nasser and Li [Nemat-Nasser S, Li Y. Flow stress of FCC polycrystals with application to OFHC copper. Acta Mater 1998;46:565-77]. The description of the material behaviour provided by the model gets satisfactory agreement with the experiments. The analytical predictions of this constitutive description are compared with those obtained from the models due to Voyiadjis and Almasri [Voyiadjis GZ, Almasri AH. A physically based constitutive model for fcc metals with applications to dynamic hardness. Mech Mater 2008;40:549-63], and Nemat-Nasser and Li. This comparison reveals that the original formulation proposed in this paper is a suitable alternative to other physically based relations for modeling OFHC copper.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (ProjectCCG08UC3M/MAT4464) and to the Ministerio de Ciencia e Innovación de España (ProjectDPI/200806408)Publicad

Thermo-viscoplastic behaviour of 2024-T3 aluminium sheets subjected to low velocity perforation at different temperatures

This paper deals with the mechanical behaviour of the aluminium alloy 2024-T3. This alloy has particular relevance since it is widely used in the aeronautical industry for building aircraft structures. The deformation behaviour of this material has been characterised in tension under wide ranges of strain rate and temperature. Among the aluminium alloys, the AA 2024-T3 highlights due to its high flow stress and strain hardening. Moreover, the material temperature sensitivity has been found dependent on plastic strain. The Modified Rusinek-Klepaczko constitutive description [Rusinek A, Rodriguez-Martinez JA, Arias A. A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper. Int. J. Mech. Sci. 52 (2010) 120-135], which takes into account such dependence of the temperature sensitivity on plastic strain, has been applied for modelling the thermo-viscoplastic response of the material. Satisfactory agreement between experiments and analytical predictions provided by the Modified Rusinek-Klepaczko model has been found. In order to study the material behaviour under impact loading, low velocity perforation tests on AA 2024-T3 sheets have been performed at different initial temperatures using a drop weight tower. Plastic instabilities formation and progression are identified as the cause behind the target collapse for all the impact tests conducted. The results from these perforation tests are compared with those reported in [Rodriguez-Martinez JA, Pesci R, Rusinek A, Arias A, Zaera R, Pedroche DA. Thermo-mechanical behaviour of TRIP 1000 steel sheets subjected to low velocity perforation by conical projectiles at different temperatures. Int. J. Solids Struct. 47 (2010) 1268-1284.] for TRIP 1000 steel sheets. The comparison reveals that the amount of specific energy absorbed by the aluminium targets is much lower than that corresponding to the steel targets. The role played by inertia on delaying plastic instabilities formation is determined as potential responsible for such behaviour.Publicad