Image-Based Inertial Impact Research Articles

Image‐based inertial impact test for viscoelastic constitutive identification: A digital replica for error quantification

AbstractPolymers find widespread use in applications where they are subjected to impact loading. Therefore, understanding the time dependence of their mechanical response is critical to the design of structures subjected to these high strain rate environments. However, characterising these materials on microsecond time scales has proven challenging. Traditional experimental techniques rely on satisfying a number of limiting assumptions and typically do not provide direct measurements of the material parameters. Here, we propose a novel implementation of the image‐based inertial impact (IBII) test to extract viscoelastic constitutive parameters on these microsecond time scales using the stress gauge implementation of the virtual fields method. We validate the experiment using a digital replica approach in which the constitutive parameters are first extracted on a finite element model of an IBII test on a viscoelastic material. The finite element data are then used to synthetically deform computer‐generated grid images, which are then polluted with grey‐level noise to simulate the images that would be captured in a real‐life experiment. These images are processed identically to a physical experiment, and the identification is repeated using the full‐field displacements extracted from the computer‐generated images to determine the ideal processing parameters. Parameter identification was found to strongly depend on the processing parameters used to extract the kinematic fields from full‐field images, emphasising the need for computational validation before attempting a physical experiment to extract constitutive parameters. The IBII experimental method was found to be capable of simultaneously identifying the bulk modulus and the shear modulus along with their associated time constant.

High strain rate elasto‐plasticity identification using the image‐based inertial impact (IBII) test part 1: Error quantification

AbstractCurrent high strain rate testing procedures generally rely on the split Hopkinson bar (SHB). In order to gain accurate material data with this technique, it is necessary to assume the test sample is in a state of quasi‐static equilibrium so that inertial effects can be neglected. During the early portion of an SHB test, it is difficult to satisfy this assumption making it challenging to investigate the elastic–plastic transition for metals. With the development of ultra‐high speed imaging technology, the image‐based inertial impact (IBII) test has emerged as an alternative to the SHB. This technique uses full‐field measurements coupled with the virtual fields method to identify material properties without requiring the assumption of quasi‐static equilibrium.The purpose of this work is to develop the IBII method for the identification of elasto‐plasticity in metals. In this paper (part 1), the focus is on using synthetic image deformation simulations to analyse identification errors for two plasticity models, a simple linear hardening model and a modified Voce model. Additionally, two types of virtual fields are investigated, a simple rigid body virtual field and the recently developed sensitivity‐based virtual fields. The results of these simulations are then used to select optimal processing parameters for the experimental data analysed in part 2.

High strain rate elasto‐plasticity identification using the image‐based inertial impact (IBII) test part 2: Experimental validation

AbstractCurrent high strain rate testing techniques typically rely on the split‐Hopkinson bar (SHB). The early response in an SHB test is corrupted by inertia making it difficult to accurately characterise the transition from elasticity to plasticity for metals. Therefore, a new test method is required. This article is the second in a two‐part series which aims at developing a new high strain rate test for elasto‐plasticity identification using the image‐based inertial impact (IBII) method. The goal of this article is to validate the new method experimentally using IBII tests on aluminium 6082‐T6 (minimal rate sensitivity) and stainless steel 316L (rate sensitive). Comparison of the quasi‐static and dynamic stress–strain curves for the aluminium case showed minimal difference providing experimental validation of the method. The same comparison for the steel showed that the method was able to detect rate sensitivity.

The Off-Axis IBII Test for Composites

Composite components regularly experience dynamic loads in service. Despite this, it is still difficult to obtain accurate mechanical properties of composite materials under high strain rate conditions. In this study, a new application of the Image-Based Inertial Impact (IBII) test methodology was developed, to generate an accurate in-plane transverse and shear moduli dataset from unidirectional (UD) off-axis composite specimens. The obtained dataset was consistent across different sample configurations, where results from the UD45^{circ } off-axis specimens agreed well with the UD90^{circ } values. Validation of the shear modulus identification was also undertaken by comparing the results from the UD90^{circ } and UD45^{circ } specimens with a multi-directional (MD) configuration. Here, it was found that MD±45^{circ } specimen shear modulus values where marginally lower than that from the UD specimens, in accordance with the lower fibre volume fraction of the MD laminate. Low strain rate sensitivities in the 0.5-2times10^{3} hbox {s}^{-1} regime evidenced in this work suggest previously published data (often from split-Hopkinson bar tests) may include both a material and system i.e. testing apparatus response.

Investigation of the 2D assumption in the image‐based inertial impact test

AbstractThe image‐based inertial impact (IBII) test has shown promise for measuring properties of composites at strain rates where existing test methods become unreliable due to inertial effects (> 102 s−1). Typically, the IBII tests are performed with a single camera, and therefore, to use surface measurements for material property identification, it is necessary to assume that the test is two‐dimensional. In this work, synchronised ultra‐high‐speed cameras are used to quantify the relevance of this assumption when nonuniform, through‐the‐thickness loading is applied to interlaminar samples. Initial experiments revealed that an angular misalignment of approximately 1° between the impact faces of the waveguide and projectile created a bending wave that propagated along the sample behind the axial pulse. Even under these conditions, consistent measurements of stiffness were made by assuming a linear distribution of the behaviour through‐the‐thickness. When the misalignment was reduced to 0.2°, the effects on single‐sided measurements were significantly reduced. The two alignment cases were compared to show that three‐dimensional loading had a small effect on stiffness identification (approximately 5% bias) relative to failure stress (approximately 30% bias). This study highlights the importance of impact alignment for reliable characterisation of the interlaminar failure stress and was used to establish guidelines for diagnosing loading issues from single‐sided measurements.

Image-Based Inertial Impact (IBII) Tests for Measuring the Interlaminar Shear Moduli of Composites

The image-based inertial impact test has previously shown that inertial effects generated with high-strain-rate loading can be used to measure the dynamic constitutive properties of composites at strain rates on the order of 1600,{rm s}^{-1}. This work represents an important next step in exploring the potential of this concept with two tests presented where loading heterogeneity is exploited to measure the interlaminar shear modulus and stress–strain behaviour at high strain rates. The first test configuration used a short-beam with asymmetric loading to activate the shear behaviour. The virtual fields method was used to directly identify the interlaminar shear modulus from heterogeneous full-field maps of strain and acceleration. Simulated experiments were used to optimise the test configuration, select optimal smoothing parameters, and quantify uncertainty from grid rotation on the shear modulus identifications. The test was validated experimentally with three different virtual fields identifying an average shear modulus ranging from 5.7 to 5.9 GPa measured at 1600,{rm s}^{-1}, representing a 16–19% increase compared to quasi-static measurements. The shear modulus could also be identified from shear introduced into specimens tested in the standard, end-on interlaminar IBII configuration from slight in-plane misalignments of the impactor. The identified value of 5.6 GPa validates measurements from the first configuration and also demonstrates the capability to identify multiple interlaminar stiffness parameters from a single test.

Image-Based Inertial Impact Test for Characterisation of Strain Rate Dependency of Ti6Al4V Titanium Alloy

In the present work Image-Based Inertial Impact (IBII) tests are performed on Ti6Al4V material. The IBII test uses an impact on the edge of the specimen to generate a short pulse that loads the specimen. Three specimen geometries have been tested: a classic rectangular specimen, and two specimen geometries with stress concentrating geometries (i.e. a hole and notches) to enhance high levels of plastic strain. Full-field measurement of the acceleration and strain are successfully used in combination with the Virtual Fields Method (VFM) to identify the strain rate sensitivity parameter of the Johnson-Cook model. The strain/strain rate spectra covered by each specimen are analysed. Finally, the influence of the virtual field used in the identification process is discussed as well as the simultaneous identification of the Johnson-Cook model strain rate sensitivity parameter and the strain rate threshold parameter.

A computational approach to design new tests for viscoplasticity characterization at high strain-rates

Rate-dependent behaviour characterization of metals at high strain rate remains challenging mainly because of the strong hypotheses when tests are processed with statically determinate approaches. As a non-standard methodology, Image-Based Inertial Impact (IBII) test has been proposed to take advantage of the dynamic Virtual Fields Method (VFM) which enables the identification of constitutive parameters with strain and acceleration fields. However, most of the test parameters (e.g. projectile velocity, specimen geometry) are not constrained. Therefore, an FE-based approach is addressed to optimize the identification over a wide range of strain and strain-rate, according to two design criteria: (1) the characterized viscoplastic spectra, (2) the identifiability of the parameters. Whereas the first criterion is assessed by processing the FEA simulations, the second is rated extracting material parameters using synthetic images to input the VFM. Finally, uncertainties regarding the identification of material constants are quantified for each IBII test configuration and different camera performances.

Generalized Stress\u2013Strain Curves for IBII Tests on Isotropic and Orthotropic Materials

This article presents a particular use of the Virtual Fields Method to exploit the results of Image-Based Inertial Impact (IBII) tests. This test consists on an edge-on impact of a free-standing thin flat rectangular coupon. The specimen response is recorded using an ultra-high speed camera filming the deformation of a grid pattern printed at its surface. From these images, displacement fields are derived, from which strain and acceleration can be obtained. The Virtual Fields Method makes use of the acceleration fields to derive stress information. Until now, a very simple ‘stress-gauge’ approach was used that could only provide relevant stress-strain information if the test was predominantly uniaxial. The alternative was to use the full inverse approach with the Virtual Fields Method but this would not allow the same degree of data understanding as the ‘stress-gauge’ approach. This article proposes an extension to this ‘stress-gauge’ approach for fully multiaxial tests. The equations are first derived and then validated using simulated and experimental IBII test data on isotropic and orthotropic materials.

A Novel Image-Based Inertial Impact Test (IBII) for the Transverse Properties of Composites at High Strain Rates

Current methods for testing the high strain rate properties of composites require multiple assumptions that limit achievable strain rates. Therefore, this study presents a new method for testing the transverse properties of composites at high strain rates using ultra-high speed imaging. The image-based inertial impact test developed here uses the reflection of a compressive stress wave to generate tensile stress in the specimen. Throughout the test, full-field displacement measurements are taken. The acceleration and strain fields are then derived from the displacement fields. The acceleration is then used to calculate the average stress in the specimen. This paper describes the optimisation of the experimental configuration using simulations and the experimental validation of the technique. The elastic modulus and tensile strength were identified at strain rates of ∼ 2000 s−1. The results showed an increase of 8% in elastic modulus and an increase of 57% in strength compared to quasi-static values.

Image-Based Inertial Impact Test for Composite Interlaminar Tensile Properties

In this work an image-based inertial impact test is proposed to measure the interlaminar tensile stiffness and strength of fibre-reinforced polymer composite materials at high strain rates. The principle is to combine ultra-high-speed imaging and full-field measurements to capture the dynamic kinematic fields and exploit the inertial effects generated under high strain rate loading. The kinematic fields are processed using the virtual fields method to reconstruct stress averages from maps of acceleration. In this way, the specimen acts like a dynamic load cell, with no gripping or external force measurement required. Stress averages are combined with strain measurements to construct stress–strain curves and identify the interlaminar stiffness and tensile strength. Special optimised virtual fields are also implemented to identify interlaminar stiffness parameters from complete maps of strain and acceleration. Interlaminar stiffness and tensile strength are successfully identified at average, peak strain rates on the order 3500 s^{-1} and 5000 s^{-1}, respectively. Results show an increase in stiffness between 30 and 35%, and an increase in strength of 125% compared to quasi-static values.

An Image-Based Inertial Impact (IBII) Test for Tungsten Carbide Cermets

Testing tungsten carbide cermets at high strain rates is difficult due to their high stiffness and brittle failure mode. Therefore, the aim of this study is to apply the image-based inertial impact (IBII) test methodology to analyse the high strain rate properties of tungsten carbide cermets. The IBII test uses an edge on impact test configuration with a narrow stress pulse. The narrow input pulse travels through the specimen in compression and reflects in tension causing failure. Full-field measurements of acceleration and strain are then coupled with the virtual fields method to identify the stiffness components and tensile strength of a test sample at high strain rates. Image deformation simulations were used to select optimal test processing parameters and predict the associated experimental errors. The elastic modulus and tensile strength of the tested tungsten carbide cermet samples were successfully identified using the IBII test at strain rates on the order of 1000~text{s}^{-1}. No significant strain rate dependence was detected for either the stiffness or tensile strength.

An Image-Based Impact Test for the High Strain Rate Tensile Properties of Brittle Materials

Testing ceramics at high strain rates presents many experimental diffsiculties due to the brittle nature of the material being tested. When using a split Hopkinson pressure bar (SHPB) for high strain rate testing, adequate time is required for stress wave effects to dampen out. For brittle materials, with small strains to failure, it is difficult to satisfy this constraint. Because of this limitation, there are minimal data (if any) available on the stiffness and tensile strength of ceramics at high strain rates. Recently, a new image-based inertial impact (IBII) test method has shown promise for analysing the high strain rate behaviour of brittle materials. This test method uses a reflected compressive stress wave to generate tensile stress and failure in an impacted specimen. Throughout the propagation of the stress wave, full-field displacement measurements are taken, from which strain and acceleration fields are derived. The acceleration fields are then used to reconstruct stress information and identify the material properties. The aim of this study is to apply the IBII test methodology to analyse the stiffness and strength of ceramics at high strain rates. The results show that it is possible to identify the elastic modulus and tensile strength of tungsten carbide at strain rates on the order of 1000 s-1. For a tungsten carbide with 13% cobalt binder the elastic modulus was identified as 516 GPa and the strength was 1400 MPa. Future applications concern boron carbide and sapphire, for which limited data exist in high rate tension.

Combined shear/tension testing of fibre composites at high strain rates using an image-based inertial impact test

Testing fibre composites off-axis has been used extensively to explore shear/tension coupling effects. However, off-axis testing at strain rates above 500 s-1 is challenging with a split Hopkinson bar apparatus. This is primarily due to the effects of inertia, which violate the assumption of stress equilibrium necessary to infer stress and strain from point measurements taken on the bars. Therefore, there is a need to develop new high strain rate test methods that do not rely on the assumptions of split Hopkinson bar analysis. Recently, a new image-based inertial impact test has been used to successfully identify the transverse modulus and tensile strength of a unidirectional composite at strain rates on the order of 2000 -1. The image-based inertial impact test method uses a reflected compressive stress wave to generate tensile stress and failure in an impacted specimen. Thus, the purpose of this study is to modify the image-based inertial impact test method to investigate the high strain rate properties of fibre composites using an off-axis configuration. For an off-axis specimen, a combined shear/tension or shear/compression stress state will be obtained. Throughout the propagation of the stress wave, full-field displacement measurements are taken. Strain and acceleration fields are then derived from the displacement fields. The kinematic fields are then processed with the virtual fields method (VFM) to reconstruct stress averages and identify the in-plane stiffness components G12 and E22.