scholarly journals A constitutive law for snow taking into account the compressibility

2004 ◽  
Vol 38 ◽  
pp. 145-149 ◽  
Author(s):  
Aloke Mishra ◽  
Puneet Mahajan
Keyword(s):  
Constitutive Equation ◽  
Iterative Scheme ◽  
Constant Strain Rate ◽  
Primary Creep ◽  
Constitutive Law ◽  
Density Range ◽  
Stress Range ◽  
Total Deformation ◽  
Hereditary Integral ◽  
Linear Spring

AbstractA constitutive law for snow derived from a complementary power potential is proposed. The total deformation of snow is divided into elastic and creep parts. A hereditary integral using Norton’s power law is employed to describe primary creep. The concept of effective stress, which takes compressibility of snow into account, is used to calculate creep deformation. The hereditary integral is approximated by a non-linear spring–dashpot model. Results from uniaxial compression experiments (stress range 15– 45 kPa) on sieved snow of density range 180–470 kgm-3 were used to determine the constants appearing in the constitutive equation. The response of snow to constant strain rate (7.4×10-6 s-1 to 2.2×10-5 s-1) under bilaterally confined conditions was found with an iterative scheme employing the proposed constitutive law. The simulated results agree well with the measured axial stresses and volumetric changes.

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 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.

A Combined Model for Hardening, Softening, and Damage Processes in Advanced Heat Resistant Steels at Elevated Temperature

2010 ◽  
Vol 20 (4) ◽  
pp. 578-597 ◽  
Author(s):  
Konstantin Naumenko ◽  
Holm Altenbach ◽  
Andreas Kutschke
Keyword(s):  
Elevated Temperature ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Rupture Strength ◽  
Axial Stress ◽  
Constant Strain Rate ◽  
Primary Creep ◽  
Tertiary Creep ◽  
Inelastic Behavior ◽  
Damage Processes

Phenomenological constitutive equations that describe inelastic behavior of advanced steels at elevated temperature are developed. To characterize hardening, recovery, and softening processes, a composite model with creep-hard and creep-soft constituents is applied. The volume fraction of the creep-hard constituent is assumed to decrease toward a saturation value. This approach reproduces well the primary creep as a result of stress redistribution between constituents and tertiary creep as a result of softening. To describe the whole tertiary creep stage, a damage variable in the sense of continuum damage mechanics is introduced. The material parameters and the response functions in the model are calibrated against experimental creep curves for X20CrMoV12-1 steel. For the verification, simulations of the inelastic response are performed and the results compared with experimental data including creep under stress change conditions and stress-strain response under constant strain rate. Furthermore, the lifetime predictions are analyzed and compared with the published creep rupture strength data. The results show that the consideration of both softening and damage processes is necessary to characterize the long-term strength in a wide stress range. Finally, the model is generalized to the multi-axial stress state.

A Physically Based Flow Rule for the Simulation of Ti-6Al-4V Forging in the α - β Range

2007 ◽  
Vol 539-543 ◽  
pp. 3661-3666 ◽  
Author(s):  
A. Colin ◽  
Christophe Desrayaud ◽  
Marie Mineur ◽  
Frank Montheillet
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Thermomechanical Processing ◽  
Deformation Behaviour ◽  
True Strain ◽  
Hot Forging ◽  
Constitutive Law ◽  
Flow Rule ◽  
Plastic Energy

The aim of this work is to study the flow instabilities occurring during hot forging of titanium alloy blades. In this view, the viscoplastic deformation behaviour of Ti-6Al-4V alloy is investigated by means of torsion tests under isothermal hot working conditions at temperatures ranging from 800 to 1020 °C and strain rates of 0.01, 0.1 and 1s−1. The thermomechanical processing is performed up to a true strain of 10. The flow stress data are analysed in terms of strain rate and temperature sensitivities. A constitutive equation that relates not only the dependence of the flow stress on strain, strain rate and temperature, but also for the fraction of each phase α and β is proposed. Two mechanical models are compared : the uniform strain rate model (Taylor) and the uniform plastic energy model (IsoW). The usual strain rate sensitivity and activation energy values of Ti-6Al-4V alloy are obtained by fitting the experimental data. Furthermore, specific values of strain rate sensitivities and activation energies are calculated for the α and β phases providing thus a constitutive law based on the physics of the α / β phase diagram. The flow stress is then related to strain by an empirical equation taking into account the flow softening observed after a true strain of 0.5 and the steady state flow reached after a true strain of 4. Comparison of the calculated and measured flow stresses shows that the constitutive equation predicts the experimental results with a reasonable accuracy. The above constitutive equation is then used for simulating forging processes by the finite element method. The calculations exhibit the localisation of deformation produced by shearing effects in the form of the classical X shape.

Viscoplastic Analysis of Adhesive Joints

1996 ◽  
Vol 63 (1) ◽  
pp. 21-26 ◽  
Author(s):  
G. K. Hu ◽  
F. Schmit ◽  
D. Baptiste ◽  
D. Franc¸ois
Keyword(s):  
Hydrostatic Stress ◽  
Three Dimensional ◽  
Constant Strain Rate ◽  
Adhesive Layer ◽  
Butt Joint ◽  
Lap Joints ◽  
Experimental Results ◽  
Constitutive Law ◽  
Tensile Creep ◽  
Account Due

The uniaxial constitutive law for an adhesive is studied by constant strain rate tensile, creep and relaxation tests. The S-D effect of the adhesive is taken into account by using the Raghava yielding criterion in a three dimensional constitutive formulation. The obtained constitutive law is then used to analyze a single lap joint and a butt joint by a finite element method. Constant cross head speed tensile and creep loading cases are examined. For a butt joint, the results show that the viscous effect and the influence of the hydrostatic stress must be taken into account due to the variation of the hydrostatic stress and of the loading rate in the adhesive layer as function of its thickness. A comparison with experimental results is also given. A good agreement between viscoplastic calculations and experimental results is obtained for single-lap joints. A reasonable result is obtained for butt joints and the discrepancy is attributed to interfacial debonding.

United void index for normalizing virgin compression of reconstituted clays

2020 ◽  
Vol 57 (10) ◽  
pp. 1497-1507
Author(s):  
Ling-Ling Zeng ◽  
Zhen-Shun Hong ◽  
Yu-Jun Cui
Keyword(s):  
Constitutive Equation ◽  
Yield Stress ◽  
Research Team ◽  
Physical Parameters ◽  
Scatter Problem ◽  
Independent Data ◽  
Stress Range ◽  
Empirical Correlations ◽  
Intrinsic Parameters ◽  
Compression Line

The intrinsic compression framework that uses the void index for normalizing the virgin compression of reconstituted clays has been widely applied for academic and practical purposes. Past studies have shown that the data of void index are scattered when the stress is out of the range from 100 to 1000 kPa. In this study, the key cause responsible for the scatter problem in the existing intrinsic compression framework is identified. A united void index is introduced for normalizing the compression curves of reconstituted clays over a wide stress range starting from the remoulded yield stress to 1000 kPa. The normalized unique line is termed the unified normalized compression line (UNCL). Its constitutive equation is established in terms of the united void index versus the effective vertical stress. The uniqueness of the UNCL is validated based on independent data from the literature and the data from the research team. It is suggested that the UNCL should be directly measured from the virgin compression. In the case without conducting consolidation tests, the correlations between the intrinsic parameters in the UNCL’s equation and two physical parameters are proposed for indirectly determining the UNCL. The accuracy of the empirical correlations is investigated via the comparisons between the calculated intrinsic parameters and the measurements.

A 3D Masonry-Like Model with Bounded Shear Stress

2017 ◽  
Vol 747 ◽  
pp. 20-27 ◽  
Author(s):  
Massimiliano Lucchesi ◽  
Barbara Pintucchi ◽  
Nicola Zani
Keyword(s):  
Shear Stress ◽  
Constitutive Equation ◽  
Convex Subset ◽  
Numerical Results ◽  
Stress Range ◽  
Symmetric Tensors ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Non Linear

This paper deals with non linear elastic materials for which not all the stresses are admis-sible but only those which belong to the stress range, i.e. a closed and convex subset of the spaceof all symmetric tensors. The constitutive equation that has been formulated and explicitly solved issufficiently general to include, besides the so-called masonry-like materials, many others whose stressrange is obtained experimentally or is theoretically defined. The model, implemented into the finiteelement code MADY, has been used to analyze a masonry panel under a bi-directional monotonicallyincremental load and the obtained numerical results have been discussed.

A numerical study of parameters controlling stress redistribution in circular notched specimens during creep

1993 ◽  
Vol 28 (1) ◽  
pp. 13-22 ◽  
Author(s):  
G Eggeler ◽  
C Wiesner
Keyword(s):  
Flat Plate ◽  
Numerical Study ◽  
Order Approximation ◽  
Creep Behaviour ◽  
Primary Creep ◽  
Constitutive Law ◽  
Ductile Material ◽  
Stress Distributions ◽  
Creep Life ◽  
Notched Specimens

In this study, numerical calculations of the creep behaviour of circular notched specimens have been performed with emphasis placed on the role of specimen geometry, material ductility, and the constitutive creep law used for the calculations. In a first order approximation, the calculations performed using primary, secondary, and tertiary-types of constitutive equations result in similar stress distributions for most of the creep life. Therefore, acceptable engineering creep calculations can be performed using a pure Norton-type of constitutive law. In the beginning of creep life, however, there are signifiant differences in calculated stress distributions obtained using primary, secondary, and teriary constitutive laws. Brittle material undergoing primary creep can redistribute stresses faster than a ductile material exhibiting tetriary dominated creep behaviour. Comparing flat plate and cylindrical circular notched specimens it is found that maximum axial stresses are higher for flat plate specimens than for cylindrical specimens. Implications of these results on possible failure mechanisms are discussed.

Effects of Primary and Secondary Creep Formulations on API 579-1 Residual Life Evaluation

2018 ◽  
Author(s):  
Lorenzo Scano ◽  
Luca Esposito
Keyword(s):  
Constitutive Equation ◽  
Residual Life ◽  
Creep Damage ◽  
Primary Creep ◽  
Secondary Creep ◽  
Time To Rupture ◽  
Life Evaluation ◽  
Omega Method ◽  
Material Constitutive Equation ◽  
Rate Formulation

A sound material constitutive equation is crucial for the residual life evaluation of pressure components operating in the creep range. In a previous work [1], the authors investigated how a secondary creep formulation encompassing both the dislocational and the diffusional range influences the assessment of damage according to API 579-1 [2] within the whole component stress range. In the present paper the work has been extended in order to include the effects of primary creep in the constitutive equation for the ASTM A335 P22 low-alloy steel used for the manufacturing of the HRSG header whose welded details were previously investigated. The creep damage was first calculated according to API 579-1 Section 10 via inelastic, time-dependent FEA and the Larson-Miller approach (LMP) with code-defined, minimum time-to-rupture data. This led to a first reckoning of the primary creep impact in terms of API 579-1 residual life for the components under evaluation. The API 579-1 time-to-rupture was then assessed with a detailed stress analysis implementing the Omega Method and its creep strain rate formulation. The obtained results were finally compared to those previously determined through the LMP procedure and the different creep correlations (secondary and primary+secondary).

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