A Rate-Dependent Stress-Strain Relationship for Sea Ice

1983 ◽  
Vol 105 (1) ◽  
pp. 2-5 ◽  
Author(s):  
Y. S. Wang
Keyword(s):  
Sea Ice ◽  
Strain Rate ◽  
Nonlinear Models ◽  
Constant Strain Rate ◽  
Relative Difference ◽  
Constant Stress ◽  
Stress Rate ◽  
Loading Conditions ◽  
Stress Strain ◽  
Strain Relationship

A one-dimensional rate-sensitive stress-strain relationship is developed to describe the uniaxial mechanical behavior in compression for sea ice. It is a one-term, nonlinear model and is simpler in form than the nonlinear models proposed by other investigators. It contains four independent constants that are determined by experimental data. This model can describe the behavior of sea ice very well under constant strain rate loading, constant stress rate loading and creep loading conditions. In particular, it describes the following features of sea behavior: 1 the increase in ice strength with strain rate and with stress rate; 2 the increase in strain-softening effects with strain rate; 3 the relative difference between the strengths obtained by constant stress rate and constant strain rate tests; 4 the rate dependence of ice stiffness; 5 primary, secondary, and tertiary creep, where the duration and rate depend on the applied stress level. This paper presents the proposed rate-sensitive stress-strain relationship and discusses its behavior under various loading conditions. A set of coefficients has been selected to compare with test results under constant strain rates. Agreement between predicted and observed stress-strain behaviors is very good. Predicted behavior under constant stress rate and creep are also presented.

An Investigation of Transient Creep by Means of Endochronic Viscoplasticity and Experiment

1995 ◽  
Vol 117 (3) ◽  
pp. 260-268 ◽  
Author(s):  
Han C. Wu ◽  
Chin C. Ho
Keyword(s):  
Stainless Steel ◽  
Strain Rate ◽  
Creep Strain ◽  
Constant Strain Rate ◽  
Transient Creep ◽  
Constant Stress ◽  
Stress Rate ◽  
304 Stainless Steel ◽  
Unified Approach ◽  
Creep Tests

Creep of metals has been investigated by means of the endochronic constitutive equation. This is a unified approach. Transient creep tests have been conducted on 304 stainless-steel specimens with carefully monitored precreep loading stage, either loaded at a prescribed constant strain-rate or at a constant stress-rate. It has been found that, for the same hold stress, the creep strain is larger for test with a constant stress-rate preloading than that for a constant strain-rate preloading. This is an effect of plasticity-creep interaction. In all cases, the initial creep strain rate is a continuation of the preloading strain rate. The theory satisfactorily describes the experimental results.

Stress-Strain Relationship for Steel under Uniaxial Cyclic Loadings

2002 ◽  
Vol 5 (3) ◽  
pp. 143-151 ◽  
Author(s):  
Luís Calado ◽  
António Brito
Keyword(s):  
Complex Loading ◽  
Steel Structures ◽  
General Purpose ◽  
Loading Conditions ◽  
Stress Strain ◽  
Strain Relationship ◽  
Complete Failure ◽  
Loading Tests ◽  
Cyclic Loading Tests ◽  
Mathematical Relationships

The mechanical properties of steel in the inelastic range can generally be described by mathematical relationships. Many such constitutive relationships have been validated by static or uniaxial cyclic loading tests. Very few models have been substantiated by test results under complex loading conditions. For that reason, the implementation of such models in general purpose structural analysis programs for steel structures under seismic actions, is in some cases complex and in others impossible. This paper is concerned with a uniaxial non-linear model for structural steel under complex loading condition and with damage accumulation. The Giuffré, Menegoto and Pinto model was taken as a basis for the development of this model. The accuracy of the proposed numerical model was drawn with uniaxial cyclic experiments. Some numerical simulations are presented in order to illustrate the capabilities of the model for use as a stress-strain relationship for steel under uniaxial complex loading conditions up to the complete failure of the material.

Tensile Stress-Strain Curves Modeling of Four Kinds of Solders with Temperature and Rate Dependence

2005 ◽  
Vol 297-300 ◽  
pp. 905-911 ◽  
Author(s):  
Xu Chen ◽  
Li Zhang ◽  
Masao Sakane ◽  
Haruo Nose
Keyword(s):  
Tensile Stress ◽  
Constitutive Model ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Strain Rate Range ◽  
Rate Dependence ◽  
Strain Rates ◽  
Stress Strain ◽  
Rate Range

A series of tensile tests at constant strain rate were conducted on tin-lead based solders with different Sn content under wide ranges of temperatures and strain rates. It was shown that the stress-strain relationships had strong temperature- and strain rate- dependence. The parameters of Anand model for four solders were determined. The four solders were 60Sn-40Pb, 40Sn-60Pb, 10Sn-90Pb and 5Sn-95Pb. Anand constitutive model was employed to simulate the stress-strain behaviors of the solders for the temperature range from 313K to 398K and the strain rate range from 0.001%sP -1 P to 2%sP -1 P. The results showed that Anand model can adequately predict the rate- and temperature- related constitutive behaviors at all test temperatures and strain rates.

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 Constant Strain-Rate Tensile Testing of Natural Snow

1980 ◽  
Vol 26 (94) ◽  
pp. 519 ◽  
Author(s):  
H. Singh ◽  
F.W. Smith
Keyword(s):  
Strain Rate ◽  
Strain Gage ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Strain Rates ◽  
Strain Gages ◽  
Compression Tests ◽  
Snow Sample ◽  
Stress Strain ◽  
Natural Snow

Abstract In conducting tension and compression tests on snow samples, strains and strain-rates are usually determined from the displacements of the ends of the samples. In this work, a strain-gage which mounts directly onto the snow sample during testing, was developed and was found to give accurate and direct measurements of strain and strain-rates. A commercially available 0-28 pF variable capacitor was modified to perform the required strain measurements. It is a polished metallic plunger sliding inside a metal-coated glass tube. The plunger and tube were each soldered to the end of a spring-steel wire arm. To the other end of these arms were soldered to 10 mm square pads made of thin brass shim stock. The whole device weighs 2.5 g and the low coefficient of friction in the capacitor resulted in a very low actuation force. To mount the strain gage, the pads are wetted and frozen onto the snow sample. A high degree of sensitivity was achieved through the use of “phase-lock-loop” electronic circuitry. The capacitance change caused by the strain in the sample, changes the frequency of output signal from an oscillator and thus causes the change in output from the system. In the locked state, to which the system is constantly driven by a feed-back loop, the system output is almost ripple free. The strain gages were calibrated in the field in order to take into account the effects of very low field temperatures. The calibration curves were almost linear over the travel of 15 mm, the maximum limit. The sensitivity of the system is 4 mV per strain unit, but this could be increased by an order of magnitude by minor adjustments in the circuit. Constant strain-rate tensile tests were performed on natural snow at Berthoud Pass, Colorado, U.S.A., in the density range of 140-290 kg m-3. Four strain gages were mounted onto the samples to sense any non-uniform deformation which otherwise would have gone unnoticed or caused scatter in the data. The average indication of these gages was used to construct stress—strain curves for various types of snow at different strain-rates. The effect of strain-rate on the behavior of snow was studied. “Ratcheting” in the stress-strain curve in the region where the snow becomes plastic was observed first by Kinosita in his compression tests. A similar phenomenon was observed in these tension tests. It was found that directly measured strain is quite different from that which would be calculated from sample end movement. Strain softening was not observed in these tests up to total strains of 8%. The strain-rate effects found were comparable to the results of other investigators.

The Simulation and Role of Discontinuous Yield Behaviors of Material

2010 ◽  
Vol 163-167 ◽  
pp. 4590-4594
Author(s):  
Shao Wei Hu
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Stress Rate ◽  
Instability Criterion ◽  
Stress Strain ◽  
Dynamic Behaviors ◽  
Jerky Flow ◽  
Thermal Origin

Discontinuous yield of material as Jerky flow was explained. Then, the strain rate sensitivity (SRS) and instability criterion was given out. Some tests were carried out at constant stress rate, so Jerky flow is manifested as a discontinuity in the stress-strain curves in form of strain bursts. Finally, the dynamic behaviors of specimens during instability of thermal origin were simulated with COLSYS software, whose results are good with test ones.

scholarly journals Primary, secondary and tertiary creep of ice modelled as a viscoelastic fluid

2009 ◽  
Vol 55 (189) ◽  
pp. 170-178 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Strain Rate ◽  
Viscoelastic Fluid ◽  
Ice Sheet ◽  
Constant Strain Rate ◽  
Constant Stress ◽  
Constitutive Law ◽  
Asymptotic Limit ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Viscous Behaviour

AbstractAs an ice sheet evolves, there are ice elements near the surface only recently subjected to stress following deposition, and others that have been subjected to stress over many ranges of time. The constant stress and constant strain-rate responses of ice in uniaxial compressive stress exhibit non-viscous behaviour, that is, the strain rate is not fixed by the stress (and conversely) but both vary with time. At constant stress the initial primary strain rate decreases with time to a minimum, described as secondary creep. It then increases and approaches an asymptotic limit, described as tertiary creep. Analogously, at constant strain rate the initial stress increases to a maximum then decreases to an asymptotic limit. These responses are used to construct a simple viscoelastic fluid constitutive law of differential type. Such a time-dependent law, with timescales changing widely with temperature, can be expected to yield a flow field in an ice sheet that is very different from that obtained from the viscous law. Only comparison solutions for both constitutive laws can determine the differences and significance of the non-viscous behaviour, and the simple law constructed would be a candidate for such comparisons.

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