Intermediate Strain Rate Tests Research Articles

Experimental and analytical study on the compressive behavior of PMI foam with different densities and cell sizes under intermediate strain rates

Polymethacrylimide (PMI) foam materials have great potential for applications in the field of protective energy absorption owing to their superior compressive properties. Existing studies on the mechanical behavior of PMI foams are limited, particularly for loading at intermediate strain rates. This paper presents a comprehensive experimental study of PMI foam with four different densities under quasi-static and intermediate strain rate compression (0.001 s−1 to 100 s−1). Each density included three different cell sizes to determine their effects on the compressive performance. Loads parallel and perpendicular to the foam rise direction were considered to investigate the anisotropic behavior. Intermediate strain rate tests were conducted using a high-speed hydraulic servo testing machine, which achieved a stable strain rate while ensuring consistent specimen sizes in both quasi-static and dynamic tests. In all the experiments, the compression process was captured using a high-speed camera and the macroscopic deformation mode and microscopic deformation mechanism were analyzed by combining Digital Image Correlation (DIC) and Scanning Electron Microscopy (SEM). The PMI foam with finer cell sizes exhibited an enhanced compression performance. As the strain rate increased, the strain rate effect became more evident in the high-density specimens and an increase in cell size diminished this effect. A modified analytical model incorporating the cell-size correction term was developed based on Gibson and Ashby's model. The modified model exhibited an average error of 4.9 % in the predicted plateau stress of PMI foam with different cell sizes at the same density.

A physics-informed impact model refined by multi-fidelity transfer learning

Impact performance is a key consideration when designing objects to be encountered in everyday life. Unfortunately, how a structure absorbs energy during an impact event is difficult to predict using traditional methods, such as finite element analysis, because of the complex interactions during high strain-rate compression. Here, we employ a physics-based model to predict impact performance of structures using a single quasistatic experiment and refine that model using intermediate strain rate and impact testing to account for strain-rate dependent strengthening. This model is trained and evaluated using experiments on additively manufactured generalized cylindrical shells. Using transfer learning, the trained model can predict the performance of a new design using data from a single quasistatic test. To validate the transfer learning model, we extrapolate to new impactor masses, new designs, and a new material. The accuracy of this model allows researchers to quickly screen new designs or leverage pre-existing databases of quasistatic test data. Furthermore, when impact tests are necessary to validate design selection, fewer impact tests are necessary to identify optimal performance.

Tensile behavior of CoCrFeMnNi high-entropy alloy with intermediate strain rate included

High-entropy alloys (HEAs) have garnered considerable attention for their exceptional mechanical properties, positioning them as promising candidates for diverse industrial applications. This study investigates the mechanical properties of CoCrFeMnNi HEAs over a wide range of strain rates. Based on a novel electromagnetic loading device equipped with high-speed photography, intermediate strain rate tests of the HEAs are conducted. The intermediate strain rate test results show the effectiveness of the experiments. Experimental results exhibit a remarkable strain rate sensitivity of the HEA during tension tests. Microstructural analysis reveals the collaborative interplay between deformation twins and dislocations, enhancing strength-plasticity relationships under tension loading. Finally, a constitutive model (M-JCK) integrated by Johnson-cook model and KHL model is proposed to describe the mechanical behavior of HEAs. The results demonstrate that the M-JCK model outperforms traditional models, providing enhanced accuracy in capturing the complex responses of HEAs across varying strain rates.

Experimental Characterization and Numerical Modelling of the Impact Behavior of PVC Foams

BackgroundPolyvinyl chloride (PVC) foams are widely used in crashworthiness and energy absorption applications due to their low density and the capability of crushing up to large deformations with limited loads. This property is due to their particular constitutive behavior: the stress-strain curve is characterized, after an initial yield or peak stress, by a relevant plateau region followed by a steep increase due to foam densification. Furthermore, the mechanical response of PVC foam is strongly strain rate dependent.ObjectiveThis work aims to characterize the mechanical behavior of PVC foams and to develop a complete constitutive model for impact and energy absorption applications.MethodsCompressive tests are carried out at different speeds on PVC foam samples having different relative densities. Quasi-static and intermediate strain rate tests are performed by a pneumatic machine, while high strain rate tests are conducted by means of a Split Hopkinson Pressure Bar. The uniaxial stress-strain curves are used to calibrate the visco-elastic and visco-plastic constitutive model. In particular, the material behavior is divided into two parallel branches: the former describes the elasto-plastic behavior, while the latter accounts for the visco-elastic one; the plastic branch also includes a multiplicative term accounting for the strain rate sensitivity of the base material.ResultsThe tests highlight a strong compressibility of the foam with negligible lateral expansion. The energy absorption efficiency, as well as the densification strain, is evaluated. The material model is also implemented in Finite Element (FE) simulations of puncture impact tests, validating the results of the calibration procedure.ConclusionsThe calibration of the visco-elasto-plastic material model offers a physically consistent identification of the constitutive response of the PVC foams, showing an effective characterization of the impact behavior of the material.

Loading measurement for intermediate strain rate material test based on dynamic oscillation

Loading measurement is one of the critical components of mechanical tests. Different technologies are applied for loading measurement at different spans of time and space. In the past century, the quasi-static hypothesis has been widely applied for low-speed loading conditions (strain rate < 1/s), and the stress wave theory has been applied for high-speed loading conditions (strain rate > 1000/s). However, so far, the feasibility of the quasi-static and stress wave approaches for loading measurement is questionable under intermediate strain rate loading conditions (1 000/s > strain rate > 1/s).For quasi-static approach, the signal ringing (caused by dynamic oscillation) is the main problem that hinders the accuracy of the loading measurement with the increment of strain rate. In this present study, in order to tackle the ringing signal obtained from the intermediate strain rate material test, a signal recognition algorithm was introduced, named the semi-period perturbation algorithm (SPPA). As SPPA is based on the first-order spring-mass oscillatory model, the corresponding test method for intermediate strain rate test was called single-mode method (SMM). To satisfy the basic hypothesis of SPPA, the corresponding load cell and material specimen was designed. Through modal analysis and dynamic simulations, SPPA and the load cell-specimen assembly were proved effective in restoring the loading signal from the ringing signal. Based on the high-speed tests of 6061 aluminum alloy and Q235 steel, and compared with the preponderant material test approach based on SEP 1230/ISO 26,203–2 sample, the SMM was proved effective in the loading measurement of intermediate strain rate tests. What's more, based on the accessibility of the test design and the simplicity of the data processing procedure of SMM, this method exhibited great application potential for similar mechanical scenarios of impact tests.

Design and Validation of New Torsion Test Bench for Intermediate Strain Rate Testing

Design and Validation of New Torsion Test Bench for Intermediate Strain Rate Testing

A Laboratory-Scale Instrumented Forging Hammer as an Intermediate Strain Rate Testing Device

Mechanical characterisation of metallic materials at intermediate strain rates is essential to calibrate and validate computational models for industrial applications such as high-speed forming processes i.e. hammer forging, blanking, forming, etc. The most common devices that perform medium to high loading rate experiments are the servo-hydraulic universal testing machines and Split Hopkinson bar systems. Here we analyse the possibility of employing an in-house designed and constructed DirectImpact Drop Hammer (DIDH) for material mechanical characterisation at medium strain rates, ranging from 100 to 300 s-1. To show the suitability of the DIDH for mechanical characterisation, uniaxial compression experiments on S235JR structural steel are conducted and compared with finite element (FE) simulations performed with an elasticthermoviscoplastic material model previously calibrated with Split Hopkinson Pressure Bar (SHPB) tests.

Electromagnetic Hopkinson bar: A powerful scientific instrument to study mechanical behavior of materials at high strain rates.

The split Hopkinson bar (SHB) has been widely used for testing the dynamic mechanical behavior of materials. However, it is hard to involve complex stress conditions in traditional SHB due to its intrinsic characteristics. The Electromagnetic Hopkinson bar (E-Hopkinson bar) has been recently proposed as a solution. Different from the traditional SHB, the stress pulse of the E-Hopkinson bar is generated directly by the electromagnetic force. Therefore, the stress pulse that loads the specimen can be accurately controlled. With this advantage, some experiments that cannot be done with traditional SHB can be conducted by the E-Hopkinson bar technique. In this review, we introduced briefly the basic principles of the E-Hopkinson bar. Some lasted tests, such as symmetrically dynamic compression/tension of materials, interlaminar fracture of composites, dynamic Bauschinger effect of metals, intermediate strain rate tests, and dynamic multi-axial tests were also introduced. This new technique will be helpful for those researchers in the field of solid mechanics, especially when the strain rate and complex stress condition are involved.

Review of Intermediate Strain Rate Testing Devices

Materials undergo various loading conditions during different manufacturing processes, including varying strain rates and temperatures. Research has shown that the deformation of metals and alloys during manufacturing processes such as metal forming, machining, and friction stir welding (FSW), can reach a strain rate ranging from 10−1 to 106 s−1. Hence, studying the flow behavior of materials at different strain rates is important to understanding the material response during manufacturing processes. Experimental data for a low strain rate of &lt;101 s−1 and a high strain rate of &gt;103 s−1 are readily available by using traditional testing devices such as a servo-hydraulic testing machine and the split Hopkinson pressure bar method, respectively. However, for the intermediate strain rate (101 to 103 s−1), very few testing devices are available. Testing the intermediate strain rate requires a demanding test regime, in which researchers have expanded the use of special instruments. This review paper describes the development and evolution of the existing intermediate strain rate testing devices. They are divided based on the loading mechanism; it includes the high-speed servo-hydraulic testing machines, hybrid testing apparatus, the drop tower, and the flywheel machine. A general description of the testing device is systematically reviewed; which includes the working principles, some critical theories, technological innovation in load measurement techniques, components of the device, basic technical assumption, and measuring techniques. In addition, some research direction on future implementation and development of an intermediate strain rate apparatus is also discussed in detail.

An Apparatus for Tensile Characterization of Materials within the Upper Intermediate Strain Rate Regime

A new “Drop-Hopkinson bar” apparatus has been successfully developed for material tensile property characterization at intermediate strain rates. This new apparatus design combines a drop table, which generates a relatively long and stable low-speed impact to the specimen, with a Hopkinson bar, which provides the load history while accounting for inertia effect in the system. The inertia effect in the specimen was minimized through pulse shaping. The pulse shaping technique was also used to facilitate constant strain rate in the specimen. The newly developed apparatus for intermediate-strain-rate tests was experimentally verified by comparing the tensile stress-strain responses of two materials, 6061-T6 aluminum and 304L stainless steel, obtained from the new apparatus and the conventional Kolsky tension bar, respectively, at the same strain rate of ~600 s−1. The results showed that the new apparatus apparatus is reliable and repeatable for intermediate strain-rate testing as well as comparable to Kolsky bar measurements. The 6061-T6 aluminum and 304L stainless steel were also characterized at low, intermediate, and high strain rates with MTS, the new apparatus, and Kolsky tension bar, respectively, to determine the effect of strain rate on tensile stress-strain response for both materials.

Microcrack Evolution and Associated Deformation and Strength Properties of Sandstone Samples Subjected to Various Strain Rates

The evolution of micro-cracks in rocks under different strain rates is of great importance for a better understanding of the mechanical properties of rocks under complex stress states. In the present study, a series of tests were carried out under various strain rates, ranging from creep tests to intermediate strain rate tests, so as to observe the evolution of micro-cracks in rock and to investigate the influence of the strain rate on the deformation and strength properties of rocks. Thin sections from rock samples at pre- and post-failure were compared and analyzed at the microscale using an optical microscope. The results demonstrate that the main crack propagation in the rock is intergranular at a creep strain rate and transgranular at a higher strain rate. However, intergranular cracks appear mainly around the quartz and most of the punctured grains are quartz. Furthermore, the intergranular and transgranular cracks exhibit large differences in the different loading directions. In addition, uniaxial compressive tests were conducted on the unbroken rock samples in the creep tests. A comparison of the stress–strain curves of the creep tests and the intermediate strain rate tests indicate that Young’s modulus and the peak strength increase with the strain rate. In addition, more deformation energy is released by the generation of the transgranular cracks than the generation of the intergranular cracks. This study illustrates that the conspicuous crack evolution under different strain rates helps to understand the crack development on a microscale, and explains the relationship between the micro- and macro-behaviors of rock before the collapse under different strain rates.

High Strain-Rate Compressive Properties of Carbon/Epoxy Laminated Composites – Effects of loading direction and temperature

The high strain-rate compressive characteristics of a cross-ply carbon/epoxy laminated composite in the three principal material directions or fibre (1-), in-plane transverse (2-) and throughthickness (3-) directions are investigated on the conventional split Hopkinson pressure bar (SHPB) over a range of temperatures between 20 and 80 °C. A nearly 10 mm thick cross-ply carbon/epoxy composite laminate fabricated using vacuum assisted resin transfer molding (VaRTM) was tested. Cylindrical specimens with a slenderness ratio (= length/diameter) of 0.5 are used in high strain-rate tests, and those with the slenderness ratios of 1.0 and 1.5 are used in low and intermediate strain-rate tests. The uniaxial compressive stress-strain curves up to failure at quasi-static and intermediate strain rates are measured on an Instron testing machine at elevated temperatures. A pair of steel rings is attached to both ends of the cylindrical specimens to prevent premature end crushing in the 1-and 2-direction tests on the Instron testing machine. It is shown that the ultimate compressive strength (or failure stress) exhibits positive strainrate effects and negative temperature ones over a strain-rate range of 10–3 to 103/s and a temperature range of 20 to 80 °C in the three principal material directions.

Development of “Dropkinson” Bar for Intermediate Strain-rate Testing

A new apparatus – “Dropkinson Bar” – has been successfully developed for material property characterization at intermediate strain rates. This Dropkinson bar combines a drop table and a Hopkinson bar. The drop table is used to generate a relatively long and stable low-speed impact to the tensile specimen, whereas the Hopkinson bar principle is applied to measure the load history with accounting for inertia effects in the system. In addition, pulse shaping techniques were applied to the Dropkinson bar to facilitate uniform stress and strain as well as constant strain rate in the specimen. The Dropkinson bar was used to characterize 304L stainless steel and 6061-T6 aluminum at a strain rate of ~600 s−1. The experimental data obtained from the Dropkinson bar tests were compared with the data obtained from conventional Kolsky tensile bar tests of the same material at similar strain rates. Both sets of experimental results were consistent, showing the newly developed Dropkinson bar apparatus is reliable and repeatable.

State-of-the-art: intermediate and high strain rate testing of solid wood

The following state-of-the-art report summarizes important work done in wood science concerning intermediate and high strain rate testing. Intermediate testing may be done with hydraulic machines, which are generally classified as rapid loading. Intermediate testing may also be done using a transverse impact of a beam specimen with a pendulum, drop mass, or toughness tester, whereas high strain rate testing is generally done with the Kolsky bar. The article analyzes the different experimental testing apparatuses, the conclusions past researchers have made about them, and the toughness and strength measurements which were usually done. The transverse impact test is examined in detail because of its adjustability for specimen sizes. The value of this research is it delves into certain impact mechanics principles which are missing from the analysis of impact testing in wood science, which must be included to validate previously held assumptions. The physical response of wood to a dynamic load is not any different from other materials such as metals or rigid foams and is governed by the same principles. Nevertheless, over the years the application of impact mechanics principles to wood testing has been scarce and “black box” experimental, where empirical approaches such as the duration-of-load were often preferred. An example of these principles is the influence of higher modes of vibration plays a greater role on the stress state in testing than its influence on deflections. This principle has been thoroughly investigated for small strain rate vibrations, however, not applied to impact testing. Presently, there is no consensus on a constitutive strain rate model for wood under intermediate and high strain rates. This article provides direction for obtaining dynamic Young’s modulus and yield strength, which can be normally expected in the design of structures subjected to dynamical loadings, for the future creation of applicable constitutive strain rate models.

Investigating LES Turbulence Model in Modeling the Velocity Distribution Around the Hydraulic Structure Using ANSYS

Dynamic rock mechanics investigates the mechanical behavior of rock under dynamic loading conditions and change in mechanical properties of the rock. Loading techniques were almost used for both intermediate and high strain rate tests. In this work, dynamic tests and dynamic mechanical behavior of rock materials were studied. Dynamic tests were discussed to predict the stress-strain behavior. Different dynamic mechanical properties of rock materials including uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness were summarized. The effect of pressure, temperature and water saturation as well as microstructure, size and shape of rock on the mechanical properties of rock materials was considered.

Dynamic Mechanical Behavior of Rock Materials

Dynamic rock mechanics investigates the mechanical behavior of rock under dynamic loading conditions and change in mechanical properties of the rock. Loading techniques were almost used for both intermediate and high strain rate tests. In this work, dynamic tests and dynamic mechanical behavior of rock materials were studied. Dynamic tests were discussed to predict the stress-strain behavior. Different dynamic mechanical properties of rock materials including uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness were summarized. The effect of pressure, temperature and water saturation as well as microstructure, size and shape of rock on the mechanical properties of rock materials was considered.

A novel intermediate strain rate testing device: The serpentine transmitted bar

A material's stress–strain behavior at intermediate strain rates (between 5 s−1 to 500 s−1) is essential for characterization of important events such as a car crash or a metal forming process. In addition, a material's stress–strain behavior can be strongly strain rate dependent, such that calibrating and validating the constitutive model at the actual strain rate of interest are important if finite element analyses are used for components that experience these strain rates. Testing of materials below 5 s−1 is easily accomplished with conventional electro-mechanical or servo-hydraulic load frames. Rates above 500 s−1 are typically performed with the split Kolsky/Hopkinson pressure bar (SHPB) and other devices depending upon the strain rate. However, the intermediate strain rate regime is a demanding test regime in which researchers have extended the use of specially instrumented servo-hydraulic load frames or very long Hopkinson bars. We describe a novel design of a serpentine Hopkinson transmitted bar that allows for accurate and robust load acquisition at intermediate strain rates in a compact form. Our new design produces repeatable stress–strain results without stress oscillations typical of a specially instrumented servo-hydraulic load frame and produces data for a longer loading time than a conventional Kolsky/Hopkinson bar of the same length. We demonstrate the intermediate bar's stress–strain response on a 6061-T6 Al alloy in which low rate and high rate data from the literature bounded the intermediate bar's response.

Uniaxial Compressive Response and Constitutive Modeling of Selected Polymers Over a Wide Range of Strain Rates

The present work deals with constitutive modeling of the compressive stress–strain response of selected polymers at strain rates from 10−3 to nearly 103 s−1. Six different commercially available extruded polymers—ABS, HDPE, PC, POM, PP and PVC—are tested at room temperature. Cylindrical specimens with a slenderness ratio (=length/diameter) of 0.5 are used in high strain-rate tests, and those with the slenderness ratios of 1.0 and 2.0 are used in low and intermediate strain-rate tests. High strain-rate compressive stress–strain loops up to a strain of nearly 0.08 are obtained on a standard split Hopkinson pressure bar. Low and intermediate strain-rate compressive ones are measured on an Instron testing machine. By fitting experimental loading stress–strain data to a modified Ramberg–Osgood equation, material parameters are uniquely determined using a linear least-squares procedure. Experimental results indicate that all polymers tested exhibit intrinsic dynamic viscoelastic–plastic characteristics and a higher elastic after-effect following complete unloading. It is shown that the modified Ramberg–Osgood constitutive model is appropriate for describing the monotonic loading compressive stress–strain relations of the three semi-crystalline polymers over a wide range of strain rates. The advantages and limitations of the constitutive model are also discussed.

Characterization and modeling of polymeric matrix under multi-axial static and dynamic loading

A polymeric foam commonly used in composite sandwich structures was characterized under multi-axial loading at strain rates varying from quasi-static to dynamic. Tests were conducted under uniaxial compression, tension, pure shear and combinations of normal and shear stresses. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson pressure bar (Kolsky bar) system made of polycarbonate bars having an impedance compatible to that of the foam material. The typical compressive stress-strain behavior of the polymeric foam exhibits a linear elastic region up to a yield point, a nonlinear elastic-plastic region up to an initial peak or “critical stress” corresponding to collapse initiation of the cells, followed by strain softening up to a local minimum (plateau or saddle point stress) and finally, a strain hardening region up to densification of the foam. The characteristic stresses of the stress-strain behavior vary linearly with the logarithm of strain rate. A general three-dimensional elastic-viscoplastic model, formulated in strain space, was proposed. The model expresses the multi-axial state of stress in terms of an effective stress, incorporates strain rate effects and includes the large deformation region. Stress-strain curves obtained under multi-axial loading at different strain rates were used to develop and validate the elastic-viscoplastic constitutive model. Excellent agreement was shown between model predictions and experimental results.

Hopkinson bar techniques for the intermediate strain rate testing of bovine cortical bone

Detailed knowledge of the dynamic viscoelastic properties of bone is required to understand the mechanisms of macroscopic bone fracture in humans, and other terrestrial mammals, during impact loading events (e.g. falls, vehicle accidents, etc.). While the dynamic response of bone has been studied for several decades, high-quality data remain limited, and it is only within the last decade that techniques for conducting dynamic compression tests on bone at near-constant strain rates have been developed. Furthermore, there appears to be a lack of published bone data in the intermediate strain rate (ISR) range (i.e. 1-100 s(-1)), which represents a regime in which many dynamic bone fractures occur. In this paper, preliminary results for the dynamic compression of bovine cortical bone in the ISR regime are presented. The results are obtained using two Hopkinson-bar-related techniques, namely the conventional split Hopkinson bar arrangement incorporating a novel cone-in-tube striker design, and the recently developed wedge bar apparatus. The experimental results show a rapid transition in the strain rate sensitive behaviour of bovine cortical bone in the ISR range. Finally, a new viscoelastic model is proposed that captures the observed transition behaviour.