Constitutive relations describing creep deformation for multi-axial time-dependent stress states

1981 ◽  
Vol 29 (1) ◽  
pp. 13-33 ◽  
Author(s):  
L.N. McCartney
Keyword(s):  
Creep Deformation ◽  
Constitutive Relations ◽  
Time Dependent ◽  
Stress States

Evaluation of Creep Deformation Property of Grade 91 Steels

2015 ◽  
Author(s):  
Kazuhiro Kimura ◽  
Kota Sawada ◽  
Hideaki Kushima
Keyword(s):  
Creep Rate ◽  
Creep Deformation ◽  
Minimum Creep Rate ◽  
Deformation Property ◽  
Time Dependent ◽  
Tertiary Creep ◽  
Total Strain ◽  
Dominant Factor ◽  
Creep Equation ◽  
Time To Rupture

Creep deformation property of Grade T91 steels over a range of temperatures from 550 to 625°C was analyzed by means of the empirical creep equation reported in the previous study [1]. The creep equation consists of four time dependent terms and one constant and time to rupture is estimated as a time to total strain of 10%. Accuracy of the creep equation to represent creep curve and to predict time to rupture and minimum creep rate was indicated. Times to minimum creep rate, total strain of 1%, initiation of tertiary creep and rupture were evaluated by the creep equation. Stress dependence of strains at minimum creep rate and the initiation of tertiary creep were analyzed. Contribution of four time dependent terms to the strains at minimum creep rate, total strain of 1% and initiation of tertiary creep was investigated. Three parameters to determine a temperature and time-dependent stress intensity limit, St, were compared and a dominant factor of St was examined. Heat-to-heat variation of the creep deformation property was investigated on two heats of T91 steels contain low and high nickel concentrations.

Modeling of Stiffness Reduction of Vibration Conveyor Springs Subjected to Ultra High Cyclic Loading under High Humidity

2011 ◽  
Vol 471-472 ◽  
pp. 975-980
Author(s):  
Takahiko Yoshi ◽  
Kazuya Okubo ◽  
Toru Fujii
Keyword(s):  
Crack Propagation ◽  
Creep Deformation ◽  
Crack Tip ◽  
Time Dependent ◽  
High Humidity ◽  
Humidity Condition ◽  
Stiffness Reduction ◽  
Carbon Fiber Cloth ◽  
Plate Spring ◽  
High Humidity Condition

Significant stiffness reduction of the plate spring due to delaminations around the interwoven cloths could be prevented by using CFRTP (carbon fiber cloth and Polyethylene Terephthalate (PET)) rather than that by using CFRP (carbon fiber cloth and epoxy), when ultra high cyclic loading was applied to the plate spring under high humidity condition. To explain the result, the prediction model of stiffness reduction was introduced considering time-dependent crack propagation accompanying with creep deformation around the crack tip. Stiffness reduction of CFRP under high humidity condition was not only determined by cyclic crack propagation but also by time-dependent crack propagation accompanying with creep deformation around the crack tip. It was found that CFRTP was effective material of the plate springs on vibration conveyer for the uses under high humidity condition to prevent significant stiffness reduction, where the crack propagation accompanying with creep deformation should be prevented around the crack tip.

scholarly journals A Computational Model of Viscoelastic Composite Materials for Ligament or Tendon Prostheses

2000 ◽  
Vol 9 (3) ◽  
pp. 096369350000900
Author(s):  
P. Vena
Keyword(s):  
Composite Materials ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Time Dependent ◽  
Element Formulation ◽  
Viscoelastic Composite ◽  
Uniaxial Test ◽  
The Matrix ◽  
Tissue Reconstruction ◽  
Constitutive Formulation

A constitutive model and a finite element formulation for viscoelastic anisotropic materials subject to finite strains is expounded in this paper. The composite material is conceived as a matrix reinforced with stiff fibres. The constitutive relations are obtained by defining a strain energy function and a relaxation function for each constituent. By means of this approach, the viscoelastic properties of the material constituents can be taken into account and therefore different time dependent behaviour can be assigned to the matrix and to the reinforcing fibres. The response provided by this kind of constitutive formulation allows for the description of mechanical behaviour for either natural anisotropic tissues (such as tendons and ligaments) and for the composite materials which are currently adopted for tissue reconstruction. The main features of those mechanical properties observed in an ideal uniaxial test are: a non linear stress-strain response and a time dependent response which is observed in relaxation of stresses for a prescribed constant stretch and in a moderate strain rate dependence of the measured response.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

Creep and Creep Recovery of 304 Stainless Steel Under Combined Stress With a Representation by a Viscous-Viscoelastic Model

1980 ◽  
Vol 47 (4) ◽  
pp. 755-761 ◽  
Author(s):  
U. W. Cho ◽  
W. N. Findley
Keyword(s):  
Stainless Steel ◽  
Viscoelastic Model ◽  
Multiple Integral ◽  
Time Dependent ◽  
304 Stainless Steel ◽  
Creep Recovery ◽  
Strain Component ◽  
Stress Dependence ◽  
Nonlinear Stress ◽  
Stress States

Creep and creep-recovery data of 304 stainless steel are reported for experiments under constant combined tension and torsion at 593°C (1100°F). The data were represented by a viscous-viscoelastic model in which the strain was resolved into five components—elastic, plastic (time-independent), viscoelastic (time-dependent recoverable), and viscous (time-dependent nonrecoverable) which has separate positive and negative components. The data are well represented by a power function of time for each time-dependent strain. By applying superposition to the creep-recovery data, the recoverable creep strain was separated from the nonrecoverable. The form of stress-dependence associated with a third-order multiple integral representation was employed for each strain component. The time-dependent recoverable and nonrecoverable strains had different nonlinear stress dependence; but, the time-independent plastic strain and time-dependent nonrecoverable strain had similar stress-dependence. A limiting stress below which creep was very small or negligible was found for both recoverable and nonrecoverable components as well as a yield limit. The limit for recoverable creep was substantially less than the limits for nonrecoverable creep and yielding. The results showed that the model and equations used in the analysis described quite well the creep and creep-recovery under the stress states tested.

The Time Dependent Behavior of Linear Viscoelastic Polymers

2011 ◽  
Vol 675-677 ◽  
pp. 435-438
Author(s):  
Wei Xiang Zhang ◽  
Xing Shao ◽  
Zhao Ran Xiao
Keyword(s):  
Mechanical Behavior ◽  
Mechanical Characteristics ◽  
Mechanical Response ◽  
Constitutive Relations ◽  
Time Dependent ◽  
Numerical Examples ◽  
General Methodology ◽  
Inverse Transform ◽  
Dependent Behavior ◽  
Linear Viscoelastic

Polymers have been proved to have attractive mechanical characteristics, which made it desirable to choose these materials over traditional materials for numerous types of applications. As the uses of polymers increase, a thorough understanding of the mechanical behavior of these materials becomes vital in order to perform innovative and economical designs of various components. The main objective of this paper is to develop an effective method with the use of the Laplace inverse transform to describe the time dependent mechanical response of viscoelastic polymers. This general methodology is based on differential constitutive relations for viscoelastic polymers, avoiding the use of relaxation integral functions. As its application, the creep and relaxation properties of the materials are exhibited in the numerical examples.

Correlation Between Creep and Uniaxial Ratchetting of Sn/37Pb and Sn/3Ag/0.5Cu Solder Alloys

2005 ◽  
Author(s):  
Katsuhiko Sasaki ◽  
Takuji Kobayashi ◽  
Ken-Ichi Ohguchi
Keyword(s):  
Creep Deformation ◽  
Time Dependent ◽  
Lead Free ◽  
Solder Alloys ◽  
Creep Tests ◽  
Cyclic Tension ◽  
Creep Curves ◽  
Safety And Reliability ◽  
Reliability Of Solder Joints ◽  
The Difference

Ratchetting deformations of solder alloys are significant deformations for the safety and reliability of solder joints of electronic packaging. This paper discusses a correlation between creep and uniaxial ratchetting deformations to clarify the difference in the time-dependent deformations between lead-free and lead-containing solder alloys. Uniaxial ratchetting tests are conducted by cyclic tension-compression and cyclic tension-unloading with the several ratios of maximum to minimum stresses. Additional creep tests are also conducted after the uniaxial ratchetting tests to clarify the effect of the uniaxial ratchetting on the creep deformation. A method to evaluate the uniaxial ratchetting deformation is discussed using the creep curves. The results show that the uniaxial ratchetting deformation correlates to the creep deformation and that the correlation is different between the lead-free and lead-containing solder alloys.

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