Dynamic Fracture of Natural Rubber3

2007 ◽  
Vol 35 (4) ◽  
pp. 252-275 ◽  
Author(s):  
Ali A. Al-Quraishi ◽  
Michelle S. Hoo Fatt
Keyword(s):  
Finite Element ◽  
Carbon Black ◽  
Natural Rubber ◽  
Strain Rate ◽  
Fracture Energy ◽  
Dynamic Fracture ◽  
High Strain ◽  
Field Strain ◽  
Far Field ◽  
Strain Rates

Abstract This paper illustrates how the fracture energy of a tensile strip made of unfilled and 25 phr carbon black-filled natural rubber varies with far-field strain rate in the range 0.01–71 s−1. Quasistatic and dynamic fracture tests were performed at room temperature with an electromechanical INSTRON machine, a servo-hydraulic MTS machine, and Charpy tensile apparatus, respectively. It was found that the fracture energy of the unfilled natural rubber did not vary significantly over the range of sample strain rate, but there was significant variation in the fracture energy of the 25 phr carbon black-filled natural rubber from 0.01 to 71 s−1 sample strain rate. The fracture energy of the 25 phr carbon black-filled natural rubber at a sample strain rate of 0.1 s−1 was about three times greater than it was at the 10 s−1 sample strain rate. While the carbon black fillers increased the fracture energy of natural rubber by about 200% at quasistatic sample strain rates (0.01–0.1 s−1) and at 71 s−1, the carbon black fillers did nothing to improve the fracture energy of natural rubber at sample strain rates between 5 and 29 s−1. In this strain rate range, the fracture energy of 25 phr carbon black-filled natural rubber was almost the same as that in the unfilled natural rubber. The variation in the fracture energy with far-field strain rate was due to changes in the material behavior of natural rubber at high strain rates. Finite element analysis using a high-strain-rate constitutive equation for the 25 phr carbon black rubber specimen was used to calculate the fracture energy of the specimen at a sample strain rate of 55 s−1, and good agreement was found between the test and finite element results.

scholarly journals Dynamic constitutive relation of 5083P-O aluminium alloy and its influence on energy-absorbing structure

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880733
Author(s):  
Yue Feng ◽  
Shoune Xiao ◽  
Bing Yang ◽  
Tao Zhu ◽  
Guangwu Yang ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Aluminium Alloy ◽  
Constitutive Relation ◽  
High Strain ◽  
Deformation Mode ◽  
Strain Rates ◽  
Strengthening Effect ◽  
Element Simulation ◽  
Energy Absorbing

Dynamic and quasi-static tensile tests of 5083P-O aluminium alloy were carried out using RPL100 electronic creep/fatigue testing machine and the split Hopkinson tension bar, respectively. The dynamic constitutive relation of the material at high strain rates was studied, and the constitutive model in accordance with Cowper–Symonds form was established. At the same time, a method to describe the constitutive relation of material using the strain rate interpolation method which is included in LS-DYNA software was proposed. The advantages and accuracy of this method were verified by comparing the results of the finite element simulation with the fitting results of the Cowper-Symonds model. The influence of material strain rate effect on squeezing force, energy absorption and deformation mode of the squeezing energy-absorbing structure based on the constitutive models of 5083P-O were studied by means of finite element simulation. The results show that when the strain rate of the structure deformation is low, the material strain rate strengthening effect has little influence on the structure. However, with the increase of the strain rate, the strengthening effect of the material will improve the squeezing force and the energy absorption of the structure, and will also influence the deformation mode, that is, the decrease of the deformation with high strain rates while the increase of the deformation with low strain rates.

scholarly journals FE Analysis of Critical Testing Parameters in Kolsky Bar Experiments for Elastomers at High Strain Rate

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 3817
Author(s):  
Chaudhry ◽  
Czekanski
Keyword(s):  
Finite Element ◽  
High Strain Rate ◽  
Strain Rate ◽  
Pulse Shaping ◽  
High Strain ◽  
Kolsky Bar ◽  
Specimen Geometry ◽  
Strain Rates ◽  
Butadiene Rubber ◽  
Testing Apparatus

The main aim of this research is to present complete methodological guidelines for dynamic characterization of elastomers when subjected to strain rates of 100/s–10,000/s. We consider the following three aspects: (i) the design of high strain rate testing apparatus, (ii) finite element analysis for the optimization of the experimental setup, and (iii) experimental parameters and validation for the response of an elastomeric specimen. To test low impedance soft materials, design of a modified Kolsky bar is discussed. Based on this design, the testing apparatus was constructed, validated, and optimized numerically using finite element methods. Furthermore, investigations on traditional pulse shaping techniques and a new design for pulse shaper are described. The effect of specimen geometry on the homogeneous deformation has been thoroughly accounted for. Using the optimized specimen geometry and pulse shaping technique, nitrile butadiene rubber was tested at different strain rates, and the experimental findings were compared to numerical predictions.

SIF Evaluation Using XFEM and Line Spring Models Under High Strain Rate Environment for Leadfree Alloys

2011 ◽  
Author(s):  
Pradeep Lall ◽  
Mandar Kulkarni ◽  
Sandeep Shantaram ◽  
Jeff Suhling
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Speed ◽  
High Strain ◽  
Strain Rates ◽  
Fracture Properties

In this paper, fracture properties of Sn3Ag0.5Cu leadfree high strain-rate solder-copper interface have been evaluated and validated with those from experimental methods. Bi-material Copper-Solder specimen have been tested at strain rates typical of shock and vibration with impact-hammer tensile testing machine. Models for crack initiation and propagation have been developed using Line spring method and extended finite element method (XFEM). Critical stress intensity factor for Sn3Ag0.5Cu solder-copper interface have been extracted from line spring models. Displacements and derivatives of displacements have been measured at crack tip and near interface of bi-material specimen using high speed imaging in conjunction with digital image correlation. Specimens have been tested at strain rates of 20s−1 and 55s−1 and the event is monitored using high speed data acquisition system as well as high speed cameras with frame rates in the neighborhood of 300,000 fps. Previously the authors have applied the technique of XFEM and DIC for predicting failure location and to develop constitutive models in leaded and few leadfree solder alloys [Lall 2010a]. The measured fracture properties have been applied to prediction of failure in ball-grid arrays subjected to high-g shock loading in the neighborhood of 12500g in JEDEC configuration. Prediction of fracture in board assemblies using explicit finite element full-field models of board assemblies under transient-shock is new. Stress intensity factor at Copper pad and bulk solder interface is also evaluated in ball grid array packages.

Stress Softening in Carbon Black Reinforced Vulcanizates. Strain Rate and Temperature Effects

1966 ◽  
Vol 39 (5) ◽  
pp. 1530-1543 ◽  
Author(s):  
G. Kraus ◽  
C. W. Childers ◽  
K. W. Rollmann
Keyword(s):  
Carbon Black ◽  
Strain Rate ◽  
Low Temperatures ◽  
High Strain ◽  
Failure Behavior ◽  
Strain Rates ◽  
High Strain Rates ◽  
Temperature Function ◽  
Network Chain ◽  
Stress Softening

Abstract Stress softening of carbon black reinforced butadiene styrene rubber was studied as a function of the rate and temperature of the original tensile deformation. To a good approximation, stress softening depends on the product of the extension rate and a temperature function which is analytically well represented by the familiar Williams-Landel-Ferry relationship. When the elongation of the original deformation is also varied, a good correlation is obtained between stress softening and the maximum stress attained in the original extension, irrespective of the particular combination of strain, strain rate, and temperature used to achieve this stress. Variables which tend to increase the stiffness of the vulcanizate, such as increased degree of crosslinking or carbon black chain structure, also increase stress softening; dilution by plasticizers decreases it. Prestressing at high strain rates and low temperatures affects the stress—strain curve of the softened vulcanizates beyond the elongation of the original extension. Connections are established between stress softening and viscoelastic and failure behavior. The evidence presented favors the contribution of several mechanisms to the general phenomenon of stress softening. These are thixotropy of transient filler structures, network chain rupture, and breakage of “permanent” filler structure. The latter appears to be most important at high strain rates, low temperatures, and with highly reticulated “structure” blacks.

Finite Element Modelling of a Modified Kolsky Bar Developed for High Strain Rate Testing of Elastomers

2015 ◽  
Author(s):  
M. S. Chaudhry ◽  
R. Carrick ◽  
A. Czekanski
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
High Strain ◽  
Soft Materials ◽  
Kolsky Bar ◽  
Strain Rates ◽  
Pulse Shaper ◽  
Hyperelastic Materials ◽  
High Strain Rate Testing ◽  
Split Hopkinson

Elastomers are finding a wide variety of dynamic applications in aerospace, automobile and biomedical industries. The response of these complex material is based on the loading conditions and the strain rate at which the loading is applied. To suit the designer’s requirement, there is an ever increasing need to characterize this application specific, dynamic behavior under high strain rates. The Kolsky bar apparatus, also known as the Split Hopkinson Bar, is the most common apparatus used to test engineering materials at strain rates between 100/s and 10000/s. In this paper a modified Kolsky bar to characterize soft material is numerically modeled using Finite Element Method. The focus of the study is to numerically analyze the modifications made to a conventional Kolsky bar to specifically test nonlinear hyperelastic, soft materials. The challenge for testing low strength materials is the impedance mismatch between the bar and specimen interfaces, which results in a very weak distorted signal. One of the solution is to use a hollow transmission bar instead of solid one. With the use of FEM it can be numerically verified that using a hollow bar increases the amplitude of the transmitted signal up to several times. It is known that the rise time of the elastic wave can be increased by using a copper pulse shaper. Different dimensions of pulse shaper are modeled and the effect on the incident pulse is analyzed. The main aim of this study is to provide a detailed numerical analysis on the testing parameters, and to model one way wave propagation in Kolsky bar experiment for hyperelastic materials. The constitutive equations used to model the parts of the apparatus are also discussed.

Strain rate effects of tensile behaviors of 3-D orthogonal woven fabric: Experimental and finite element analyses

2012 ◽  
Vol 83 (4) ◽  
pp. 337-354 ◽  
Author(s):  
Yangqing Hou ◽  
Lili Jiang ◽  
Baozhong Sun ◽  
Bohong Gu
Keyword(s):  
Finite Element ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Woven Fabric ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Two Phase ◽  
Tensile Stiffness

The tensile behaviors of 3-D woven fabric under high strain-rate states, i.e. tensile impact behaviors, are important for the design of the fabrics and the reinforced composites under impulsive loading. This paper reports the testing and the numerical simulation of the impact tension behaviors of 3-D woven fabric under high strain rates compared with those under quasi-static tension. The tensile behaviors of 3-D orthogonal woven fabric (3DOWF) were investigated using a MTS 810.23 material testing system and a self-designed split Hopkinson tension bar apparatus, under a wide range of strain rates (0.003–2308/s). The tensile stress–strain curves obtained from the quasi-static and high strain rates were used to analyze the rate-sensitivity of 3DOWF tensile behaviors. It was found that both the tensile strength and the failure strain increased with increases in the strain rate. The two-phase tensile stiffness phenomenon of 3DOWF under high strain rates has been observed experimentally. A microstructure model combined with finite element analysis was established to explain the tensile failure mechanisms of 3DOWF under high strain rates. It was found that the fabric architecture influences the stress wave propagation, thus leading to the two-phase tensile stiffness phenomenon in the stress–strain curve under high strain-rate tensions.

A New High Strain-Rate Biaxial Experiment to Validate Constitutive Models for Polymers

2016 ◽  
Author(s):  
Sean S. Teller ◽  
Eric C. Schmitt ◽  
Jörgen S. Bergström
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Constitutive Models ◽  
Finite Element Simulations ◽  
Strain Rates ◽  
Peak Strain ◽  
Impact Head

We have developed a new high strain rate experiment in biaxial tension that allows for constitutive model validation at engineering strain rates from 50/s to over 1000/s. In the experiment, a flat disk of the material is clamped at a fixed radial distance. A rail-guided impact sled with a hemispherical impact head is released from the desired height and impacts the disk at the center, potentially deforming the sample to failure. Drop height and impact mass can be varied to modify peak strain rate and impact energy, and the wide range of test conditions allow for testing to be performed on many classes of materials, including thermoplastics and elastomers. The stress and strain fields are calculated using finite element simulations with the proposed constitutive model, and the constitutive model is validated by matching the force versus displacement data of the impact head recorded during experiment to the simulation. In this paper, we discuss results from the experiment and finite element simulations of the experiment on PA (polyamide, nylon) and PEEK (polyether ether ketone). The new experiment allows for validation and refinement of constitutive models, including failure, at high strain rates and in a multiaxial stress state.

Dynamic Deformation Behavior of As-Extruded Mg-Gd-Y Magnesium Alloy and the Microstructural Evolution

2011 ◽  
Vol 284-286 ◽  
pp. 1579-1583
Author(s):  
Ping Li Mao ◽  
Zheng Liu ◽  
Chang Yi Wang ◽  
Feng Wang
Keyword(s):  
Magnesium Alloy ◽  
Strain Rate ◽  
Deformation Behavior ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Dynamic Deformation ◽  
Strain Rates ◽  
Compression Axis ◽  
Deformation Localization ◽  
Dynamic Deformation Behavior

The dynamic deformation behavior of an as-extruded Mg-Gd-Y magnesium alloy was studied by using Split Hopkinson Pressure Bar (SHPB) apparatus under high strain rates of 102 s-1 to 103s-1 in the present work, in the mean while the microstructure evolution after deformation were inspected by OM and SEM. The results demonstrated that the material is not sensitive to the strain rate and with increasing the strain rate the yield stress of as-extruded Mg-Gd-Y magnesium alloy has a tendency of increasing. The microstructure observation results shown that several deformation localization areas with the width of 10mm formed in the strain rates of 465s-1 and 2140s-1 along the compression axis respectively, and the grain boundaries within the deformation localization area are parallel with each other and are perpendicular to the compression axis. While increasing the strain rate to 3767s-1 the deformation seems become uniform and all the grains are compressed flat in somewhat. The deformation mechanism of as-extruded Mg-Gd-Y magnesium alloy under high strain rate at room temperature was also discussed.

scholarly journals Measurement of fracture energy of concrete at high strain rates

2018 ◽  
Vol 183 ◽  
pp. 02065
Author(s):  
V. Rey-de-Pedraza ◽  
F. Gálvez ◽  
D. Cendón Franco
Keyword(s):  
Tensile Strength ◽  
Fracture Energy ◽  
Dynamic Fracture ◽  
Dynamic Properties ◽  
Hopkinson Bar ◽  
Experimental Information ◽  
Tensile Fracture ◽  
Strain Rates ◽  
Dynamic Tensile Strength ◽  
Conventional Concrete

The Hopkinson Bar has been widely used by many researchers for the analysis of dynamic properties of different brittle materials and, due to its great interest, for the study of concrete. In concrete structures subjected to high velocity impacts, initial compression pulses travel through the material leading to tensile stresses when they reach a free surface. These tensile efforts are the main cause of concrete fracture due to its low tensile strength compared to the compressive one. This is the reason why dynamic tests in concrete are becoming of great interest and are mostly focused in obtaining tensile fracture properties. Apart form the dynamic tensile strength, which has been widely studied by many authors in the last decades, the dynamic fracture energy presents an increased difficulty and so not too much experimental information can be found in literature. Moreover, up to date there is not a clear methodology proposed in order to obtain this parameter in an accurate way. In this work a new methodology for measuring the dynamic fracture energy is proposed by using the Hopkinson Bar technique. Initial tests for a conventional concrete have been carried out and the results for the dynamic fracture energy of concrete at different strain rates are presented.

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