Exploration of Saint-Venant’s Principle in inertial high strain rate testing of materials

Current high strain rate testing procedures of materials are limited by poor instrumentation which leads to the requirement for stringent assumptions to enable data processing and constitutive model identification. This is the case for instance for the well known Split Hopkinson Pressure Bar (SHPB) apparatus which relies on strain gauge measurements away from the deforming sample. This paper is a step forward in the exploration of novel tests based on time and space resolved kinematic measurements obtained through ultra-high speed imaging. The underpinning idea is to use acceleration fields obtained from temporal differentiation of the full-field deformation maps measured through techniques like Digital Image Correlation (DIC) or the grid method. This information is then used for inverse identification with the Virtual Fields Method. The feasibility of this new methodology has been verified in the recent past on a few examples. The present paper is a new contribution towards the advancement of this idea. Here, inertial impact tests are considered. They consist of firing a small steel ball impactor at rectangular free standing quasi-isotropic composite specimens. One of the main contributions of the work is to investigate the issue of through thickness heterogeneity of the kinematic fields through both numerical simulations (3D finite element model) and actual tests. The results show that the parasitic effects arising from non uniform through-the-thickness loading can successfully be mitigated by the use of longer specimens, making use of Saint-Venant's principle in dynamics

Beyond Hopkinson's bar

In order to perform experimental identification of high strain rate material models, engineers have only a very limited toolbox based on test procedures developed decades ago. The best example is the so-called split Hopkinson pressure bar based on the bar concept introduced 100 years ago by Bertram Hopkinson to measure blast pulses. The recent advent of full-field deformation measurements using imaging techniques has allowed novel approaches to be developed and exciting new testing procedures to be imagined for the first time. One can use this full-field information in conjunction with efficient numerical inverse identification tools such as the virtual fields method (VFM) to identify material parameters at high rates. The underpinning novelty is to exploit the inertial effects developed in high strain rate loading. This paper presents results from a new inertial impact test to obtain stress–strain curves at high strain rates (here, up to 3000 s−1). A quasi-isotropic composite specimen is equipped with a grid and images are recorded with the new HPV-X camera from Shimadzu at 5 Mfps and the SIMX16 camera from Specialised Imaging at 1 Mfps. Deformation, strain and acceleration fields are then input into the VFM to identify the stiffness parameters with unprecedented quality

A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials

We present an inverse method to identify the spatially varying stiffness distributions in 3 dimensions. The method is an extension of the classical Virtual Fields Method—a numerical technique that exploits information from full-field deformation measurements to deduce unknown material properties—in the spatial frequency domain, which we name the Fourier-series-based virtual fields method (F-VFM). Three-dimensional stiffness distributions, parameterised by a Fourier series expansion, are recovered after a single matrix inversion. A numerically efficient version of the technique is developed, based on the Fast Fourier Transform. The proposed F-VFM is also adapted to deal with the challenging situation of limited or even non-existent knowledge of boundary conditions. The three-dimensional F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast magnetic resonance imaging experiment containing material with Poisson's ratio close to 0.5; such a case requires a slightly different interpretation of the F-VFM equations, to enable the application of the technique to incompressible materials

Identification of nonlinear kinematic hardening constitutive model parameters using the virtual fields method for advanced high strength steels

In this work, the nonlinear kinematic hardening combined with Voce isotropic hardening was selected to characterize the material behavior of advanced high strength steel sheet samples subjected to a few reverse loading cycles. Multi-components of backstress were considered for the combined nonlinear kinematical hardening model, namely, one, two, and three backstress components. To calibrate the model, an inverse problem solution tool, so-called virtual fields method, which takes full advantage of full-field deformation measurement, was applied to identify the material constitutive parameters. First, finite element simulations of forward-reverse simple shear were performed to validate the proposed identification method. The influence of strain noise on the identification accuracy was also evaluated. Then, the proposed method was applied to three kinds of sheet metals (DP600, TRIP780 and TWIP980) tested under two cycles of forward-reverse simple shear for parameter identification. The identification results obtained with different number of backstress components were critically discussed. (C) 2016 Elsevier Ltd. All rights reserved.1132Ysciescopu

Time-resolved full-field imaging of ultrasonic Lamb waves using deflectometry

This pioneering experimental work is a proof of concept in which ultrasonic flexural waves have been imaged in a spatially and temporally resolved manner. Thin vibrating plates made of mirror glass and carbon/epoxy composite have been used in the experiments. Results obtained via a standard approach (scanning laser Doppler vibrometry) and the novel methodology based on deflectometry have been compared with a multi-physics finite element simulation. There is a very good correlation between the two experimental techniques. The numerical model provides insight into the experiments, but differs in its detailed structure due to uncertainties over material properties. The extreme slope resolution of deflectometry allows the measurement of peak-to-peak deflections of a few tens of nanometres in one shot. The use of an ultra-high speed camera allows for both space and time resolved measurements of Lamb waves which, to the best knowledge of the authors, has never been reported before. The limitations of the technique arise from the need for a flat specularly reflective surface. However, coating is possible for non-reflective materials and extension to moderately curved surfaces is possible in the future

Microstructural Assessment of 316L Stainless Steel Using Infrared Thermography Based Measurement of Energy Dissipation Arising from Cyclic Loading

A procedure is developed that evaluates the energy dissipated from a material subject to cyclic loading and enables identification of the difference in material microstructure. It is demonstrated that the dissipated energy can be derived from specimens loaded in the elastic region using temperature measurements obtained by infrared thermography. To obtain accurate values of the small temperature changes resulting from the intrinsic dissipation below the yield point, a key part of the procedure is to eliminate the effect of external heat sources and sinks from the vicinity of the test specimen under investigation. To this end, a chamber was designed to minimise the external radiation whilst allowing the specimens to be cyclically loaded; the configuration of the chamber is described, alongside its integration into the procedure. A reference specimen was specifically introduced in the chamber to take into account the thermal exchanges between the specimen and the chamber environment. A data processing procedure, based on the thermomechanical heat diffusion equation, is applied to enable the dissipated energy to be derived from the temperature measurements. It is established that quantifying the amount of energy dissipation provides an opportunity to identify the material condition. The procedure is demonstrated on specimens made from 316L stainless steel containing a range of microstructures produced by different heat treatments. It is shown that the dissipative energy is dependent on the microstructure and that the dissipative source can be identified using the experimental procedure

Application of the Virtual Fields Method to determine dynamic properties at intermediate strain rates

Crash analysis simulation is now very important in automotive industry to assess automotive crashworthiness and safety. In order to acquire reliable crash simulation results, precise material behaviors at intermediate strain rates should be used as input data. To determine the stress-strain curves at various strain rates, the number of expensive and complicated experiments is large. The present study aims at determining the stress-strain curves of sheet metals at various strain rates from a single dynamic experiment. A new type of high speed tensile tester for sheet metal specimens was built and high speed tensile tests were carried out. Full-field heterogeneous strain fields were measured by a digital image correlation technique using a highspeed camera. The load data was acquired from strain gauges attached to the elastic deformation region on the specimen. Then, an inverse identification scheme with a rate dependent hardening law was applied to retrieve dynamic parameters. The stress-strain curves of advanced high strength steel at intermediate strain rates (100 /s - 300 /s) were successfully obtained from a single experiment.11Ysciescopu

Quantifying ultrasonic deformation of cell membranes with ultra-high-speed imaging

We present a new method for controllable loading of cell models in an ultrasonic (20 kHz) regime. The protocol is based on the inertial-based ultrasonic shaking test and allows to deform cells in the range of few mm/m to help understand potential consequences of repeated loading characteristic of ultrasonic cutting

Characterization of dynamic hardening behavior using acceleration information

Crash analysis simulation is very important in automotive industry to assess automotive crashworthiness and safety. In the FE simulation, accurate dynamic hardening behavior should be used as input data to provide reliable results. But, it is difficult to obtain precise hardening properties at intermediate or high strain rates due to inaccurate measurement of load caused by the inertial effect. In this study, a new methodology was applied to retrieve dynamic strain hardening properties of sheet metal specimens. The virtual fields method (VFM) was adopted as an inverse method to identify hardening parameters without load information. As an initial study, Swift model for a rate independent hardening law was selected for an elasto-plastic constitutive model. In order to validate the proposed methodology in the experiments, a new type of high speed tensile tester for sheet metal specimens was built and high speed tensile tests were performed. Digital image correlation technique using a high-speed camera was utilized to measure strain and acceleration fields so that the identification is carried out from the measured quantities. The validation of the proposed VFM identification procedure using the acceleration will be performed by comparing with the conventional procedure using a load-cell. (C) 2017 The Authors. Published by Elsevier Ltd.110Ysciescopu

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated