Some Implications of a Nonlinear Viscoelastic Constitutive Theory Regarding Interrelationships Between Creep and Strength Behavior of Ice at Failure

1989 ◽  
Vol 111 (2) ◽  
pp. 144-148 ◽  
Author(s):  
B. D. Harper
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Nonlinear Viscoelastic ◽  
Uniaxial Creep ◽  
Strength Behavior ◽  
Minimum Strain Rate ◽  
Strength Constant ◽  
Viscoelastic Constitutive Model ◽  
Stress And Strain Rate ◽  
Special Case

This study explores several possibilities for a correspondence in the behavior of ice at failure during uniaxial creep (constant stress) and strength (constant strain rate) experiments. The usual notion of failure in ice is employed (i.e., the occurrence of a minimum strain rate during a creep test and a peak or maximum stress during a strength test), and the behavior at failure is discussed in terms of a recently proposed nonlinear viscoelastic constitutive model for ice. It is demonstrated that no correspondence between creep and strength data can be expected in general; however, several approximate interrelationships do occur for the experimentally motivated special case of a constant (independent of stress and strain rate) failure strain.

A Uniaxial Nonlinear Viscoelastic Constitutive Relation for Ice

1986 ◽  
Vol 108 (2) ◽  
pp. 156-160 ◽  
Author(s):  
B. D. Harper
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Constitutive Theory ◽  
Uniaxial Deformation ◽  
Explicit Dependence ◽  
Deformation And Failure ◽  
Nonlinear Viscoelastic ◽  
Defect Growth ◽  
Special Cases ◽  
Strength Constant

The present paper concerns the description of uniaxial deformation and failure of ice in uniaxial compression in terms of a nonlinear viscoelastic constitutive theory. The constitutive model incorporates explicit dependence upon micro-structural defect growth and assumes the form of a so-called modified superposition integral contaiing a linear kernel which depends only upon time. This last feature will greatly simplify the task of experimentally characterizing the various material properties which appear in the theory. The existence of correspondence principles for the model will also facilitate the solution of practical boundary value problems. Predictions based upon this model will be shown to agree qualitatively with experimental results for creep (constant stress) and strength (constant strain-rate) tests on ice. In addition, specific empirically deduced relationships between stress, strain, strain-rate and time at certain critical points in these standard tests will be shown to result directly from the constitutive theory as special cases.

scholarly journals A Modified Fractional Maxwell Numerical Model for Constitutive Equation of Mn-Cu Damping Alloy

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2020
Author(s):  
Baoquan Mao ◽  
Rui Zhu ◽  
Zhiqian Wang ◽  
Yuying Yang ◽  
Xiaoping Han ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Maxwell Model ◽  
Nonlinear Viscoelastic ◽  
Fractional Maxwell Model ◽  
Hysteretic Characteristics ◽  
Nonlinear Elastic

To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

scholarly journals A nonlinear viscoelastic iceberg material model and its numerical validation

2016 ◽  
Vol 231 (2) ◽  
pp. 675-689 ◽  
Author(s):  
Chu Shi ◽  
Zhiqiang Hu ◽  
Jonas Ringsberg ◽  
Yu Luo
Keyword(s):  
Strain Rate ◽  
Contact Force ◽  
Steel Plate ◽  
Constant Strain Rate ◽  
Ductile Failure ◽  
Material Model ◽  
Damage Function ◽  
Triaxial Strength ◽  
Nonlinear Viscoelastic ◽  
Stress Dependent

This article proposes a nonlinear viscoelastic iceberg material model. A nonlinear Burgers’ model in which Kelvin and Maxwell units are strain rate- and stress-dependent is adopted for the iceberg material. The strain rate effect is considered in this model based on the experimental results. The stress of the iceberg model grows linearly (in log form) with increasing strain rate before reaching the transition strain rate, after which the stress remains rather constant. A damage function that reflects the microstructure changes and severe fractures in ice is adopted as the failure criterion. The iceberg model is implemented using implicit integration Crank–Nicolson method and is incorporated in the commercial software LS-DYNA by a user-defined material. Laboratory-scale experiments, creep experiments and constant strain rate experiments, and reality-scale experiment, iceberg–rigid steel plate collisions, are simulated to validate the proposed iceberg material model. Simulated time–strain curves are compared with the results of creep experiments. In the constant strain rate experiments, the strain–stress curves for brittle and ductile failure and ultimate triaxial strength of the ice model are analysed. Area–pressure curves and contact force–displacement relations are investigated for different impact speeds in iceberg–steel plate collisions. The contact force is also studied in view of the kinetic energy of icebergs. The numerical results show that the proposed iceberg material model yields reasonably good results.

Impact of a Nonlinear Viscoplastic Rod on a Rigid Wall

1966 ◽  
Vol 33 (3) ◽  
pp. 505-513 ◽  
Author(s):  
T. C. E. Ting
Keyword(s):  
Strain Rate ◽  
Power Law ◽  
Rigid Wall ◽  
The Other ◽  
Stress And Strain ◽  
Rigid Plastic ◽  
Residual Strains ◽  
Stress And Strain Rate ◽  
The Impact ◽  
Special Case

Barenblatt and Ishlinskii [5] considered the impact of a viscoplastic rod on a rigid wall in which the relation between stress and strain rate is linear. In this paper, their analysis is generalized to a power-law relation between stress and strain rate so that their results may be reduced as a special case. Some strikingly different behaviors are observed between linear viscoplastic materials and nonlinear viscoplastic materials. Comparisons are also made between the viscoplastic solution obtained here with the rate-independent, rigid-plastic solution by Lee and Tapper [2]. It is shown that the curves which represent the residual strains versus the axial length along the rod are concave upward for all viscoplastic rods. For the rate-independent, rigid-plastic rods, on the other hand, they are concave downward.

An Experimental Study on the Effect of Prior Plastic Straining on Creep Behavior of 304 Stainless Steel

1993 ◽  
Vol 115 (2) ◽  
pp. 200-203 ◽  
Author(s):  
Z. Xia ◽  
F. Ellyin
Keyword(s):  
Stainless Steel ◽  
Plastic Strain ◽  
Strain Rate ◽  
Creep Behavior ◽  
Test Procedure ◽  
Constant Strain Rate ◽  
304 Stainless Steel ◽  
Creep Model ◽  
Plastic Strain Rate ◽  
Creep Tests

Constant strain-rate plastic straining followed by creep tests were conducted to investigate the effect of prior plastic straining on the subsequent creep behavior of 304 stainless steel at room temperature. The effects of plastic strain and plastic strain-rate were delineated by a specially designed test procedure, and it is found that both factors have a strong influence on the subsequent creep deformation. A creep model combining the two factors is then developed. The predictions of the model are in good agreement with the test results.

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