Pre-Yield Strain Hardening in Thermoplastics

1986 ◽  
Vol 79 ◽  
Author(s):  
David C. Martin
Keyword(s):  
Flow Stress ◽  
Stress Relaxation ◽  
Strain Hardening ◽  
Small Strain ◽  
Rate Of Change ◽  
Yield Strain ◽  
Deformation Region ◽  
Nucleation Of Defects ◽  
Change State ◽  
Kinetics Of

AbstractSuccessive stress relaxation testing was used to investigate the strain hardening of polypropylene and polystyrene in the stage of deformation before yielding. By combining this information with that of a stress relaxation test it was possible to measure the change in flow stress with plastic strain or “workhardening” parameter K. K has been associated with the nucleation of “defects” of some sort which slow down the kinetics of the deformation process.Both polymers were found to strain harden in this deformation region. In polystyrene, the amount of time need to relax through a fixed stress increment reached a plateau at a point corresponding with visible crazing in the gage section of the sample. The workhardening parameter K was determined and found to decrease with stress. By plotting the rate of change of flow stress with total strain plots were obtained which avoided the use of strain, an ill-defined parameter in materials which change state during deformation. From these plots it was seen that polystyrene exhibits a well-defined linear region at small strain whereas polypropylene deviates from linearity immediately. Hardening of polystyrene was observed even in the linear response regime.

scholarly journals Constitutive Modelling of Polylactic Acid at Large Deformation Using Multiaxial Strains

Polymers ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2967
Author(s):  
John Sweeney ◽  
Paul Spencer ◽  
Glen Thompson ◽  
David Barker ◽  
Phil Coates
Keyword(s):  
Steady State ◽  
Stress Relaxation ◽  
Strain Hardening ◽  
Small Strain ◽  
Limited Range ◽  
Constitutive Modelling ◽  
True Stress ◽  
Final Strain ◽  
Transverse Stresses

Sheet specimens of a PLLA-based polymer have been extended at a temperature near to the glass transition in both uniaxial and planar tension, with stress relaxation observed for some time after reaching the final strain. Both axial and transverse stresses were recorded in the planar experiments. In all cases during loading, yielding at small strain was followed by a drop in true stress and then strain hardening. This was followed by stress relaxation at constant strain, during which stress dropped to reach an effectively constant level. Stresses were modelled as steady state and transient components. Steady-state components were identified with the long-term stress in stress relaxation and associated with an elastic component of the model. Transient stresses were modelled using Eyring mechanisms. The greater part of the stress during strain hardening was associated with dissipative Eyring processes. The model was successful in predicting stresses in both uniaxial and planar extension over a limited range of strain rate.

High-Temperature Deformation Constitutive Law for Dissimilar Weld Residual Stress Modeling: Effect of Thermal Load on Strain Hardening

2015 ◽  
Author(s):  
Xinghua Yu ◽  
Paul Crooker ◽  
Yanli Wang ◽  
Zhili Feng
Keyword(s):  
Residual Stress ◽  
Flow Stress ◽  
Constitutive Model ◽  
Strain Hardening ◽  
Time Dependent ◽  
Dynamic Strain ◽  
Weld Residual Stress ◽  
Stress Prediction ◽  
Residual Stress Modeling ◽  
Kinetics Of

Weld residual stress is one of the primary driving forces for primary water stress corrosion cracking in dissimilar metal welds (DMWs). To mitigate tensile residual stress in DMWs, it is critical to understand residual stress distribution by modeling techniques. Recent studies have shown that weld residual stress prediction using today’s DMW residual stress models strongly depends on the strain-hardening constitutive model chosen. The commonly used strain-hardening models (isotropic, kinematic, and mixed) are all time-independent and inadequate to account for the time-dependent (viscous) plastic deformation at the elevated temperatures experienced during welding. For materials with profound strain-hardening, such as stainless steels and nickel-based alloys that are widely used in nuclear reactor and piping systems, the equivalent plastic strain — the determinate factor of the flow stress — can be highly dependent on the recovery and recrystallization processes. These processes are in turn a strong function of temperature, time, and deformation rate. Recently, the authors proposed a new temperature- and time-dependent strain-hardening constitutive model: the dynamic strain-hardening constitutive model. The application of such a model has resulted in improved weld residual stress prediction compared to the residual stress measurement results from the contour and deep-hole drilling methods. In this study, the dynamic strain-hardening behavior of Type 304 stainless steel and Alloy 82 used in pressure vessel nozzle DMWs is experimentally determined. The kinetics of the recovery and recrystallization of flow stress are derived from experiments, resulting in a semi-empirical equation as a function of pre-strain, time, and temperature that can be used for weld residual stress modeling. The method used in this work also provides an approach to study the kinetics of recovery and recrystallization of other materials with significant strain-hardening.

Derivatives of isatin in aqueous solution. I. Kinetics of ring opening of Isatin-5-sulfonate

1981 ◽  
Vol 34 (2) ◽  
pp. 365 ◽  
Author(s):  
H Stunzi
Keyword(s):  
Ring Opening ◽  
Rate Of Change ◽  
Spectroscopic Methods ◽  
Ph Values ◽  
Buffer Region ◽  
Pka Value ◽  
Back Titration ◽  
Kinetics Of ◽  
Derivatives Of ◽  
Sulfonate Anion

The reactions of isatin-5-sulfonate anion (si-) which cause a hysteresis in pH titrations were studied by pH-metric and n.m.r, spectroscopic methods. Rapid alkalimetric titrations [I 0.15 M (KNO3),37�] gave the pKa value corresponding to the addition of OH- to si- [pKa(ring) 9.55]. The slow ring opening to the sulfonatoisatate dianion (sia2-) led to a drift of the pH values towards an equilibrium buffer region. Its pKa, value [pKa(eq) 3.44] corresponds to the reaction si-+H2O ↔ sia 2-+H+ Rapid back-titration gave the pKa value of the ring-opened species Hsia- [pKa(open) c. 1.3]. The rate law for the ring opening d[sia]/dt=k2 [siOH](OH)+k1*[si] was obtained from the rate of change of pH. N-Methylisatin-5-sulfonate behaves analogously.

Study on Dynamic Mechanical Response of TC21 Alloy

2011 ◽  
Vol 88-89 ◽  
pp. 674-678
Author(s):  
Shuang Zan Zhao ◽  
Xing Wang Cheng ◽  
Fu Chi Wang
Keyword(s):  
Flow Stress ◽  
High Strain Rate ◽  
Strain Rate ◽  
Strain Hardening ◽  
High Strain ◽  
Dynamic Flow ◽  
Dynamic Mechanical ◽  
Hardening Effect ◽  
High Strain Rate Deformation ◽  
Binary Morphology

Some results of an experimental study on high strain rate deformation of TC21 alloy are discussed in this paper. Cylindrical specimens of the TC21 alloys both in binary morphology and solution and aging morphology were subjected to high strain rate deformation by direct impact using a Split Hopkinson Pressure Bar. The deformation process is dominated by both thermal softening effect and strain hardening effect under high strain rate loading. Thus the flow stress doesn’t increase with strain rate at the strain hardening stage, while the increase is obvious under qusi-static compression. Under high strain rate, the dynamic flow stress is higher than that under quasi-static and dynamic flow stress increase with the increase of the strain rate, which indicates the strain rate hardening effect is great in TC21 alloy. The microstructure affects the dynamic mechanical properties of TC21 titanium alloy obviously. Under high strain rate, the solution and aging morphology has higher dynamic flow stress while the binary morphology has better plasticity and less prone to be instability under high strain rate condition. Shear bands were found both in the solution and aging morphology and the binary morphology.

Extrusion of stiffening ribs on body parts with local heating

2021 ◽  
pp. 72-74
Author(s):  
Keyword(s):  
Velocity Field ◽  
Stress Relaxation ◽  
Local Heating ◽  
Hot Extrusion ◽  
Body Parts ◽  
Calculation Results ◽  
Energy Equilibrium ◽  
Stiffening Ribs ◽  
Analytical Expressions ◽  
Kinetics Of

A scheme is proposed and analytical expressions are obtained for calculating the kinematics, pressure and damageability of the material during hot extrusion of ribs on body parts. The equations of states during creep, energy equilibrium, kinetics of material discontinuity are used. The calculation results are presented. Keywords: extrusion, local heating, stiffening rib, viscosity, plasticity, stress relaxation, pressure, velocity field [email protected], [email protected]

scholarly journals On Computational Modelling Of Strain-Hardening Material Dynamics

2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski
Keyword(s):  
Relaxation Time ◽  
Stress Relaxation ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Computational Modelling ◽  
Constitutive Models ◽  
Successful Implementation ◽  
Hardening Material ◽  
Dislocation Mechanics

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

Studies on Softening Kinetics of Niobium Microalloyed Steel Using Stress Relaxation Technique

2012 ◽  
Vol 715-716 ◽  
pp. 794-799 ◽  
Author(s):  
Cheng Liang Miao ◽  
Cheng Jia Shang ◽  
Guo Dong Zhang ◽  
Guo Hui Zhu ◽  
Hatem S. Zurob ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Microalloyed Steels ◽  
Distinct Advantage ◽  
Low Carbon ◽  
Shape Processing ◽  
Physically Based ◽  
Near Net Shape ◽  
Niobium Microalloyed Steel ◽  
Relaxation Curves ◽  
Kinetics Of

Stress relaxation was studied in a series of low carbon, high Mn microalloyed steels containing 0.012, 0.06 and 0.1 wt% Nb. The stress-relaxation curves were modeled using a physically-based model that takes into account the time evolution of precipitation, recovery and recrystallization as well as their interactions. The results confirm that high Mn-high Nb design can offer distinct advantage over the low-Mn design for the application of near net shape processing.

Analysis of Hot Anisotropic Tensile Flow Stress and Strain Hardening Behavior for Inconel 625 Alloy

2019 ◽  
Vol 28 (12) ◽  
pp. 7537-7553 ◽  
Author(s):  
C. Anand Badrish ◽  
Nitin Kotkunde ◽  
Gauri Mahalle ◽  
Swadesh Kumar Singh ◽  
K. Mahesh
Keyword(s):  
Flow Stress ◽  
Strain Hardening ◽  
Inconel 625 ◽  
Stress And Strain ◽  
Hardening Behavior ◽  
Inconel 625 Alloy ◽  
Strain Hardening Behavior

Relaxation Processes in the Deformation of Unloaded Rubbers and the Influence of the Degree of Vulcanization

1951 ◽  
Vol 24 (4) ◽  
pp. 810-819
Author(s):  
B. A. Dogadkin ◽  
M. M. Reznikovskii˘
Keyword(s):  
Stress Relaxation ◽  
Natural Rubber ◽  
Elastic Deformation ◽  
Relaxation Processes ◽  
Spatial Network ◽  
Relaxation Properties ◽  
Constant Rate ◽  
Different Temperatures ◽  
Kinetics Of

Abstract 1. It is shown that the process of stress relaxation at different initial elongations as well as the process of deformation at constant rate for unloaded rubbers at different temperatures (20–70° C) can be represented quantitatively by equations suggested in earlier works. Likewise the possibility of expanding the theories proposed for the kinetics of high-elastic deformation of spatial polymers is substantiated. 2. It is shown that the relaxation properties of soft unloaded vulcanizates of natural rubber and many synthetic rubbers do not undergo essential changes during vulcanization. 3. The conjecture is expressed that the invariability of the relaxation properties during vulcanization continues until the bonds of the spatial network are distributed sufficiently widely not to influence the activity or heat movement of the chain segments between them.

A New Force-Displacement Model for Continuous Indentation of Bilayer Materials

2001 ◽  
Vol 695 ◽  
Author(s):  
A. Nayebi ◽  
R. El Abdi ◽  
G. Mauvoisin ◽  
O. Bartier
Keyword(s):  
Flow Stress ◽  
Strain Hardening ◽  
Indentation Load ◽  
Numerical Results ◽  
Stress And Strain ◽  
Proposed Model ◽  
Displacement Model ◽  
Force Displacement ◽  
Continuous Indentation

ABSTRACTA new relationship between indentation load and depth in relation to flow stress and strain hardening exponents of film and substrate of bilayers is given. The comparison between the numerical results and those experimentally obtained from known materials, confirms the interest of the proposed model for film characterization of these materials.

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