Effect of strain hardening and speed effect on the strain distribution in rods under impact

1967 ◽  
Vol 2 (4) ◽  
pp. 257-264
Author(s):  
E A Davis
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Strain Distribution ◽  
Stress Strain ◽  
Strain And Strain Rate ◽  
Long Rod ◽  
Speed Effect

The distribution of the stress, strain, and strain rate in a long rod, one end of which has been given a fixed velocity, is analysed. Computer programmes have been written for three different classes of materials: purely rate-sensitive materials, purely strain-hardening materials, and materials exhibiting both strain hardening and speed effect. Where possible the results have been checked against known solutions.

scholarly journals Evolution of specimen strain rate in split Hopkinson bar test

2019 ◽  
Vol 233 (13) ◽  
pp. 4667-4687 ◽  
Author(s):  
Hyunho Shin ◽  
Jong-Bong Kim
Keyword(s):  
Strain Rate ◽  
Rate Equation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Hopkinson Bar ◽  
Stress Strain ◽  
Split Hopkinson Bar ◽  
Specimen Diameter ◽  
Strain And Strain Rate ◽  
Split Hopkinson

The specimen strain rate in the split Hopkinson bar (SHB) test has been formulated based on a one-dimensional assumption. The strain rate is found to be controlled by the stress and strain of the deforming specimen, geometry (the length and diameter) of specimen, impedance of bar, and impact velocity. The specimen strain rate evolves as a result of the competition between the rate-increasing and rate-decreasing factors. Unless the two factors are balanced, the specimen strain rate generally varies (decreases or increases) with strain (specimen deformation), which is the physical origin of the varying nature of the specimen strain rate in the SHB test. According to the formulated strain rate equation, the curves of stress–strain and strain rate–strain are mutually correlated. Based on the correlation of these curves, the strain rate equation is verified through a numerical simulation and experiment. The formulated equation can be used as a tool for verifying the measured strain rate–strain curve simultaneously with the measured stress–strain curve. A practical method for predicting the specimen strain rate before carrying out the SHB test has also been presented. The method simultaneously solves the formulated strain rate equation and a reasonably estimated constitutive equation of specimen to generate the anticipated curves of strain rate–strain and stress–strain in the SHB test. An Excel® program to solve the two equations is provided. The strain rate equation also indicates that the increase in specimen stress during deformation (e.g., work hardening) plays a role in decreasing the slope of the strain rate–strain curve in the plastic regime. However, according to the strain rate equation, the slope of the strain rate–strain curve in the plastic deformation regime can be tailored by controlling the specimen diameter. Two practical methods for determining the specimen diameter to achieve a nearly constant strain rate are presented.

scholarly journals Estimation of Stress-Strain behavior of polyethylene terephthalate (PET) at different strain rates by Artificial Neural Network under simultaneous stretch scenario

2021 ◽  
Author(s):  
Fei Teng ◽  
Gary Menary ◽  
Savko Malinov ◽  
Shiyong Yan
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Strain Rate ◽  
Strain Rates ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain And Strain Rate ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
High Degree

In this paper, an Artificial Neural Network (ANN) is used to predict the stress-strain behavior of PET at conditions relevant to Stretch Blow Moulding i.e. Large equibiaxial deformation at elevated temperature and high strain rate. The input vectors considered are temperature, strain, and strain rate with a corresponding output parameter of stress. In the present work, a feed-forward back backpropagation algorithm was used to train the ANN. The ANN is able to approximate the relationship between stress and strain at various strain rates & temperatures to a high degree of accuracy for all conditions tested.

Stress, strain and strain-rate cemented carbide properties determined with a fem-supported evaluation of impact test imprints

2021 ◽  
Vol 94 ◽  
pp. 105384
Author(s):  
Antonios Bouzakis ◽  
Georgios Skordaris ◽  
Konstantinos-Dionysios Bouzakis ◽  
Mehmet-Gökhan Gökcen ◽  
Apostolos Boumpakis ◽  
...  
Keyword(s):  
Strain Rate ◽  
Impact Test ◽  
Cemented Carbide ◽  
Stress Strain ◽  
Strain And Strain Rate

An Empirical Creep Law From a Single Test

1962 ◽  
Vol 84 (2) ◽  
pp. 236-238
Author(s):  
Iain Finnie
Keyword(s):  
Strain Rate ◽  
Creep Test ◽  
Constant Load ◽  
Constant Stress ◽  
Single Test ◽  
Creep Tests ◽  
Stress Strain ◽  
Strain And Strain Rate ◽  
Single Constant

A method is described by which an empirical creep law, relating stress, strain, and strain rate, may be obtained from a single constant-load creep test. An example to illustrate the method is given, and the empirical creep law is compared with the results of several constant stress creep tests.

Determination of Critical Stress for Dynamic Recrystallization of a High-Mn Austenitic TWIP Steel Micro-Alloyed with Vanadium

2016 ◽  
Vol 1812 ◽  
pp. 41-46
Author(s):  
Elvira García-Mora ◽  
Ignacio Mejía ◽  
Francisco Reyes-Calderón ◽  
José M. Cabrera
Keyword(s):  
Dynamic Recrystallization ◽  
Strain Rate ◽  
Strain Hardening ◽  
Critical Stress ◽  
Twip Steel ◽  
True Strain ◽  
Compression Tests ◽  
Hollomon Parameter ◽  
Strain And Strain Rate ◽  
Twip Steels

ABSTRACTWhen high strength and high ductility are required, the Twinning Induced Plasticity steels are an excellent choice. Their mechanical advantages are perfectly known in the automotive industry. Then, they are currently deeply studied. During the deformation at high temperature, TWIP steel experiences dynamic recrystallization. This mechanism results from dislocation interactions, and it depends of temperature, stress, strain, and strain rate. Experimental data give the maximum stress reached by the material, but the critical stress which determinates the DRX onset must be calculated from the strain hardening rate. Both stress and strain change simultaneously, and this variation gives the analytic data to determine σc, which is located at the inflection point of θ-σ plot. The main purpose of this paper was to study how the chemical composition and the experimental parameters (temperature and strain rate) affect the DRX, by the calculation and analysis of the σc values. Hot compression tests were applied to a pair of TWIP steels to compare the DRX onset and its relationship with the vanadium addition. The experimental variables were temperature and strain rate. The true stress–true strain plots were used to calculate σc by cutting data up to a previous point before the σp value, then, a polynomial fit and derivation were applied. The Zener-Hollomon parameter (Z) versus the stresses (peak and critical) plots show how the micro-alloying element vanadium improves the strain hardening in the analyzed TWIP steels.

Effects of Constitutive Parameters on Thickness of Phase Transformed Adiabatic Shear Band for Ductile Metal Based on Johnson-Cook and Gradient Plasticity Models

2006 ◽  
Vol 15-17 ◽  
pp. 609-614 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Phase Transformation ◽  
Strain Rate ◽  
Strain Hardening ◽  
Yield Stress ◽  
Thermal Softening ◽  
Flow Shear ◽  
Stress Strain ◽  
Static Yield ◽  
Flow Shear Stress ◽  
Static Yield Stress

Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) is introduced into Johnson-Cook model considering the effects of strain-hardening, thermal softening and strain rate sensitivity. Effects of initial static yield stress, strain-hardening coefficient and exponent, strain-rate and thermal-softening parameters on the occurrence of phase transformation and the thickness of phase transformed adiabatic shear band (ASB) in deformed ASB are numerically investigated. Higher initial static yield stress, strain-hardening coefficient, strain-rate parameter and lower strain-hardening exponent lead to earlier occurrence of phase transformation (lower plastic shear strain). Effect of thermal-softening parameter on plastic shear strain corresponding to the onset of phase transformation is not monotonous. Transformed ASB is located at the center of deformed ASB since the position has higher temperature exceeding the temperature of phase transformation. The thickness of transformed ASB increases with decreasing flow shear stress and the increasing tendency becomes slow. For the same flow shear stress, the thickness of transformed ASB is wider for higher initial static yield stress, strain-hardening coefficient and exponent, strain-rate and thermal-softening parameters. Compared with classical elastoplastic theory applicable to completely homogenous material, gradient-dependent plasticity considering the microstructural effect predicts that phase transformation occurs earlier and that the thickness of transformed ASB changes with flow shear stress.

Effects of Foot Strike and Step Frequency on Achilles Tendon Stress During Running

2016 ◽  
Vol 32 (4) ◽  
pp. 365-372 ◽  
Author(s):  
Michael Lyght ◽  
Matthew Nockerts ◽  
Thomas W. Kernozek ◽  
Robert Ragan
Keyword(s):  
Strain Rate ◽  
Achilles Tendon ◽  
Musculoskeletal Model ◽  
Stress And Strain ◽  
Step Frequency ◽  
Stress Strain ◽  
Strain And Strain Rate ◽  
Subject Specific ◽  
Foot Strike ◽  
Crosssectional Area

Achilles tendon (AT) injuries are common in runners. The AT withstands high magnitudes of stress during running which may contribute to injury. Our purpose was to examine the effects of foot strike pattern and step frequency on AT stress and strain during running utilizing muscle forces based on a musculoskeletal model and subject-specific ultrasound-derived AT crosssectional area. Nineteen female runners performed running trials under 6 conditions, including rearfoot strike and forefoot strike patterns at their preferred cadence, +5%, and –5% preferred cadence. Rearfoot strike patterns had less peak AT stress (P < .001), strain (P < .001), and strain rate (P < .001) compared with the forefoot strike pattern. A reduction in peak AT stress and strain were exhibited with a +5% preferred step frequency relative to the preferred condition using a rearfoot (P < .001) and forefoot (P=.005) strike pattern. Strain rate was not different (P > .05) between step frequencies within each foot strike condition. Our results suggest that a rearfoot pattern may reduce AT stress, strain, and strain rate. Increases in step frequency of 5% above preferred frequency, regardless of foot strike pattern, may also lower peak AT stress and strain.

Hardening by Crystallization During Superplastic Flow in a Powder-metallurgy-processed Zr65Al10Ni10Cu15 Glass Metallic Alloy

2005 ◽  
Vol 20 (6) ◽  
pp. 1447-1455 ◽  
Author(s):  
H.G. Jeong ◽  
W.J. Kim
Keyword(s):  
Powder Metallurgy ◽  
Strain Rate ◽  
Strain Hardening ◽  
Tensile Elongation ◽  
Metallic Alloy ◽  
Powder Metallurgy Method ◽  
Testing Time ◽  
Liquid Region ◽  
Strain Rates ◽  
Strain And Strain Rate

The superplastic behavior of the Zr65Al10Ni10Cu15 glass metallic alloy produced by the powder metallurgy method was examined in the supercooled liquid region. A tensile elongation as large as 750% was obtained at 6.3 × 10−3 s−1 at 697 K. Large strain hardening took place during the course of deformation and systematic trend was observed in the hardening behavior. Plots of stress versus strain and strain rate versus stress at 697 K showed that Newtonian viscous flow governed the plastic flow until the onset of strain hardening. Microstructure and differential scanning calorimetry analyses as well as flow stress versus testing time curves provided consistent evidence that the strain hardening was induced by crystallization. Crystallization was enhanced in the gauge region (deformed region) as compared to the grip region (undeformed region). Crystallization is expected to decrease tensile ductility by decreasing the strain-rate-sensitivity value and increasing the degree of brittleness. Hardening by crystallization, however, can contribute to neck stability if crystallization is enhanced in the neck region. The strain hardening and plastic stability parameters were measured as a function of strain for different strain rates at 696 K. The strain hardening parameter remained highly positive until failure. Because of this, the neck stability parameter (I) could be I < 0 in the entire hardening region. The contribution of hardening by crystallization to neck stability was found to be much more significant than that by grain growth in the superplastic metallic alloys. Reducing the specimen heating-and-holding time was suggested to promote superplasticity deformation without delaying initiation of crystallization. The largest tensile strain in the hardening region where crystallization may be obtained at the strain rates and temperatures where crystallization rate is controlled to be the lowest while maintaining I ≤ 0 throughout deformation.

Crystallization during Superplastic Deformation in a Zr65Al10Ni10Cu15 Glass Metallic Alloy

2005 ◽  
Vol 475-479 ◽  
pp. 2981-2986
Author(s):  
Woo Jin Kim ◽  
H.S. Kim ◽  
Ha Guk Jeong
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Superplastic Deformation ◽  
Large Strain ◽  
Supercooled Liquid ◽  
Supercooled Liquid Region ◽  
Metallic Alloy ◽  
Liquid Region ◽  
Superplastic Behavior ◽  
Stress Strain

Superplastic behavior of the Zr65Al10Ni10Cu15 glass metallic alloy produced by powdermetallurgy method was examined in the supercooled liquid region. Stress-strain and stress-strain rate relationships showed that Newtonian viscous flow governed the plastic flow until strain hardening took place. The large strain hardening was proved to a result of occurrence of crystallization during deformation.

The Biomechanical Determinants of Concussion: Finite Element Simulations to Investigate Tissue-Level Predictors of Injury During Sporting Impacts to the Unprotected Head

2015 ◽  
Vol 31 (4) ◽  
pp. 264-268 ◽  
Author(s):  
Declan A. Patton ◽  
Andrew S. McIntosh ◽  
Svein Kleiven
Keyword(s):  
Finite Element ◽  
Corpus Callosum ◽  
Strain Rate ◽  
Tissue Level ◽  
Von Mises Stress ◽  
Tolerance Limits ◽  
Stress Strain ◽  
Head Impacts ◽  
Strain And Strain Rate ◽  
Von Mises

Biomechanical studies of concussions have progressed from qualitative observations of head impacts to physical and numerical reconstructions, direct impact measurements, and finite element analyses. Supplementary to a previous study, which investigated maximum principal strain, the current study used a detailed finite element head model to simulate unhelmeted concussion and no-injury head impacts and evaluate the effectiveness of various tissue-level brain injury predictors: strain rate, product of strain and strain rate, cumulative strain damage measure, von Mises stress, and intracranial pressure. Von Mises stress was found to be the most effective predictor of concussion. It was also found that the thalamus and corpus callosum were brain regions with strong associations with concussion. Tentative tolerance limits for tissue-level predictors were proposed in an attempt to broaden the understanding of unhelmeted concussions. For the thalamus, tolerance limits were proposed for a 50% likelihood of concussion: 2.24 kPa, 24.0 s−1, and 2.49 s−1 for von Mises stress, strain rate, and the product of strain and strain rate, respectively. For the corpus callosum, tolerance limits were proposed for a 50% likelihood of concussion: 3.51 kPa, 25.1 s−1, and 2.76 s−1 for von Mises stress, strain rate, and the product of strain and strain rate, respectively.

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