Constitutive Relationships for the Time-Dependent Deformation of Metals

1976 ◽  
Vol 98 (1) ◽  
pp. 47-51 ◽  
Author(s):  
A. R. S. Ponter ◽  
F. A. Leckie
Keyword(s):  
High Temperature ◽  
Strain Hardening ◽  
Potential Function ◽  
Inelastic Deformation ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Thermal Softening ◽  
Time Dependent ◽  
Polycrystalline Metal ◽  
State Potential

The paper discusses the constitutive relations for the inelastic deformation of a polycrystalline metal at high temperature. Commencing from a description of a dislocation structure in terms of strain hardening and thermal softening, the general form of the constitutive relation is developed in terms of a potential function. The existence of a stationary state potential is established and generalizations of isotropic and kinematic hardening are described.

From Instability and Time Dependence on the Microscale to Stability and Time Independence on the Macroscale

1995 ◽  
Vol 117 (4) ◽  
pp. 368-372 ◽  
Author(s):  
Daniel C. Drucker
Keyword(s):  
Time Dependence ◽  
Inelastic Deformation ◽  
Factor Of Safety ◽  
Constitutive Relations ◽  
Plasticity Theory ◽  
Time Dependent ◽  
Dynamic Activity ◽  
Micro Scale ◽  
Simplifying Assumptions ◽  
Structural Metals

The quasistatic inelastic deformation of ductile structural metals observed on the macroscale reflects a diversity of dynamic inelastic effects on the microscale. The generation, motion, and immobilization of dislocations are primary among them, but a host of other activities such as the opening and growth of cracks and voids, also may contribute. Dynamic activity on the microscale is strongly time-dependent on the time scales of importance to the microscopic processes. Also, the atomic configurations of single dislocations and groups of dislocations are highly unstable over a significant portion of each path of rapid motion. Nevertheless, engineers continue to design structures and machines with a reasonable factor of safety against failure on the basis of conventional plasticity theory with its assumption of both time-independence and stability (normality and convexity). This discussion of the validity of these simplifying assumptions for macroscopic constitutive relations despite instability and time-dependence on the atomic- and micro-scale expands upon a recent paper with Ming Li.

Nonproportional Loading Steps in Multiaxial Creep of 2618 Aluminum

1985 ◽  
Vol 52 (3) ◽  
pp. 621-628 ◽  
Author(s):  
J. L. Ding ◽  
W. N. Findley
Keyword(s):  
Experimental Data ◽  
Strain Hardening ◽  
Kinematic Hardening ◽  
Superposition Principle ◽  
High Stress ◽  
Material Behavior ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Strain Component ◽  
Dependent Strain

Experimental data on the creep behavior of 2618-T61 aluminum alloy under nonproportional loadings are presented. Among the important findings are the anisotropy induced by creep strain, synergistic effects during creep recovery, and strongly nonlinear material behavior at high stress levels. Data were compared with two theoretical models, a viscous-viscoelastic (VV) model and a viscoplastic (VP) model. In the VV model the time-dependent strain was decomposed into recoverable (viscoelastic) and nonrecoverable components. The VP model differs from the VV model in that all the time-dependent strain is assumed nonrecoverable. In each model, three viscoplastic flow rules based on different hardening natures, namely, isotropic strain hardening, kinematic hardening, and independent strain hardening were derived to describe the time-dependent nonrecoverable strain component, and compared with experiments. The viscoelastic component in the VV model was represented by the third-order multiple integral representation combined with the modified superposition principle. Predictions for all theories used material constants obtained from creep and recovery data only. Possible causes for the discrepancies between theories and experimental data were discussed. Further experimental and theoretical work necessary for the study of the time-dependent material behavior at high temperature were also suggested.

Implicit Stress Integration for High-Temperature Inelastic Constitutive Models Using Linearization

2007 ◽  
Vol 340-341 ◽  
pp. 907-912
Author(s):  
Masafumi Akamatsu ◽  
Kazuhiko Nakane ◽  
Nobutada Ohno
Keyword(s):  
High Temperature ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Inelastic Strain ◽  
Euler Method ◽  
Joint Analysis ◽  
Integration Scheme ◽  
Implicit Integration ◽  
Backward Euler

In this study, a linearization approach is used to develop an implicit integration scheme for high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments.

An Inelastic Constitutive Equation of Fiber Reinforced Plastic Laminates

1998 ◽  
Vol 120 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Y. Kanagawa ◽  
S. Murakami ◽  
T. Mizobe
Keyword(s):  
Inelastic Deformation ◽  
Evolution Equations ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Equivalent Strain ◽  
Time Dependent ◽  
Inelastic Behavior ◽  
Fiber Reinforced ◽  
Reinforced Plastics ◽  
Reinforced Plastic

A Constitutive model for describing the time dependent inelastic deformation of unidirectional and symmetric angle-ply CFRP (Carbon Fiber Reinforced Plastics) laminates is developed. The kinematic hardening creep law of Malinin and Khadjinsky and the evolution equation of Armstrong and Frederick are extended to describe the creep deformation of initially anisotropic materials. In particular, the evolution equations of the back stresses of the anisotropic material were formulated by introducing a transformed strain tensor, by which the expression of the equivalent strain rate of the an isotropic material has the identical form as that of the isotropic materials. The resulting model is applied to analyze the time dependent inelastic deformation of symmetric angle ply laminates. Comparison between the predictions and the experimental observations shows that the present model can describe well the time dependent inelastic behavior under different loadings.

scholarly journals On the Plastic Strain Accumulation in Notched Bars During High-Temperature Creep Dwell

2020 ◽  
Vol 36 (2) ◽  
pp. 167-176 ◽  
Author(s):  
Daniele Barbera ◽  
Haofeng Chen
Keyword(s):  
High Temperature ◽  
Cyclic Loading ◽  
Plastic Strain ◽  
Kinematic Hardening ◽  
High Temperature Creep ◽  
Strain Accumulation ◽  
Material Models ◽  
Cyclic Loading Condition ◽  
Hardening Material ◽  
Temperature Creep

ABSTRACTStructural integrity plays an important role in any industrial activity, due to its capability of assessing complex systems against sudden and unpredicted failures. The work here presented investigates an unexpected new mechanism occurring in structures subjected to monotonic and cyclic loading at high temperature creep condition. An unexpected accumulation of plastic strain is observed to occur, within the high-temperature creep dwell. This phenomenon has been observed during several full inelastic finite element analyses. In order to understand which parameters make possible such behaviour, an extensive numerical study has been undertaken on two different notched bars. The notched bar has been selected due to its capability of representing a multiaxial stress state, which is a practical situation in real components. Two numerical examples consisting of an axisymmetric v-notch bar and a semi-circular notched bar are considered, in order to investigate different notches severity. Two material models have been considered for the plastic response, which is modelled by both Elastic-Perfectly Plastic and Armstrong-Frederick kinematic hardening material models. The high-temperature creep behaviour is introduced using the time hardening law. To study the problem several results are presented, as the effect of the material model on the plastic strain accumulation, the effect of the notch severity and the mesh element type and sensitivity. All the findings further confirm that the phenomenon observed is not an artefact but a real mechanism, which needs to be considered when assessing off-design condition. Moreover, it might be extremely dangerous if the cyclic loading condition occurs at such a high loading level.

The Microstructure and Mechanical Properties of Ni-Based Superalloy after Service Exposure in Gas Turbine

2010 ◽  
Vol 654-656 ◽  
pp. 2523-2526 ◽  
Author(s):  
Keun Bong Yoo ◽  
Han Sang Lee
Keyword(s):  
High Temperature ◽  
Gas Turbine ◽  
Mechanical Tests ◽  
Time Dependent ◽  
Second Stage ◽  
Degradation Analysis ◽  
Check Points ◽  
Tcp Phase ◽  
Service Exposure ◽  
High Temperature Tensile

Many investigations about superalloys and coatings have been done in the laboratory, but evaluating the degradation condition of hot section components during service is still important not only for repair and reuse but also for outage prevention. Time dependent degradation for second stage blades of gas turbine was investigated. The degradation analysis for used blades was divided into microstructure changes by position of the blade and mechanical tests of high temperature tensile test. In the microstructure analysis, the rafting and coarsening of γ', MC decomposition and TCP phase formation occurred and progressed with increasing service time, and especially the leading and trailing edge of top layer should be a check points for used blade. High temperature tensile results of 25,000 and 52,000 hrs used blades were also compared with serviced time and position in each blade.

Uniaxial time-dependent ratcheting behavior of bronze powder filled polytetrafluoroethylene at room and high temperature

2013 ◽  
Vol 54 (7) ◽  
pp. 1571-1578 ◽  
Author(s):  
Wenjuan Xu ◽  
Hong Gao ◽  
Lilan Gao ◽  
Jianhua Ma ◽  
Xu Chen
Keyword(s):  
High Temperature ◽  
Time Dependent ◽  
Bronze Powder

scholarly journals An Experimental Study of the Tension-Compression Asymmetry of Extruded Ti-6.5Al-2Zr-1Mo-1V under Quasi-Static Conditions at High Temperature

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1299
Author(s):  
Chen Zhang ◽  
Dongsheng Li ◽  
Xiaoqiang Li ◽  
Yong Li
Keyword(s):  
High Temperature ◽  
Strain Hardening ◽  
Yield Stress ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Uniaxial Tensile ◽  
Tensile Direction ◽  
Stress Asymmetry ◽  
Static Conditions ◽  
Tension Compression Asymmetry

The tension-compression asymmetry (TCA) behavior of an extruded titanium alloy at high temperatures has been investigated experimentally in this study. Uniaxial tensile and compressive tests were conducted from 923 to 1023 K with various strain rates under quasi-static conditions. The corresponding yield stress and asymmetric strain hardening behavior were obtained and analyzed. In addition, the microstructure at different temperatures and stress states indicates that the extruded TA15 profile exhibits a significant yield stress asymmetry at different testing temperatures. The flow stress and yield stress during tension are greater than compression. The yield stress asymmetry decreases with the increase in temperature. The alloy also exhibits TCA behavior on the strain hardening rate. Its mechanical response during compression is more sensitive than tension. A dynamic recrystallization phenomenon is observed instead of twin generated in tension and compression under high-temperature quasi-static conditions. The grains are elongated along the tensile direction and deformed by about 45° along the compressive load axis. Finally, the TCA of Ti-6.5Al-2Zr-1Mo-1V (TA15) alloy is due to slip displacement. The tensile deformation activates basal <a>, prismatic <a> and pyramidal <c + a> slip modes, while the compressive deformation activates only prismatic <a> and pyramidal <c + a> slip modes.

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