Strain Rate Dependent Constitutive Model of Multiaxial Ratchetting of 63Sn–37Pb Solder

2006 ◽  
Vol 129 (3) ◽  
pp. 278-286 ◽  
Author(s):  
Gang Chen ◽  
Xu Chen ◽  
Kwang Soo Kim ◽  
Mohammad Abdel-Karim ◽  
Masao Sakane
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Shear Strain ◽  
Kinematic Hardening ◽  
Axial Stress ◽  
Strain Range ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Viscous Term ◽  
Ratcheting Strain

A series of multiaxial ratcheting tests were conducted on 63Sn–37Pb solder. A unified viscoplastic constitutive model was developed on the basis of the Ohno–Wang kinematic hardening model, and the rate dependence of the material was taken into consideration by introducing a viscous term. The stress-strain hysteresis loop of 63Sn–37Pb under different strain rates can be simulated reasonably well by the model. However, since the axial ratcheting strain rate of 63Sn–37Pb solder is strongly dependent on the applied shear strain rates in axial/torsional ratcheting, the original constitutive model fails to describe the effect of shear strain rate on the ratcheting strain. To improve the rate sensitivity of the model, the material parameter μi was correlated to the strain rate. Comparisons of the experimental and simulated results verify that the modified constitutive model is able to predict the complicated deformation of 63Sn–37Pb. The effects of axial stress, shear strain range, loading history, and strain rate on ratcheting behavior can be reflected fairly well.

Biaxial ratcheting deformation of type 304 stainless steel: Effect of memorization of back stress

2004 ◽  
Vol 218 (9) ◽  
pp. 901-908 ◽  
Author(s):  
T Mayama ◽  
K Sasaki ◽  
H Ishikawa
Keyword(s):  
Stainless Steel ◽  
Constitutive Model ◽  
Shear Strain ◽  
Axial Stress ◽  
304 Stainless Steel ◽  
Shear Strain Rate ◽  
Cyclic Shear ◽  
Ratcheting Strain ◽  
Type 304 ◽  
Type 304 Stainless Steel

This paper treats both experiments and simulations of biaxial ratcheting. The experiments are conducted using a tubular specimen of type 304 stainless steel at room temperature. The specimen was subjected to cyclic shear straining under the axial superposed stress. The experiments show that the biaxial ratcheting strain was affected by the cyclic shear strain amplitude, the shear strain rate and the superposed stress level. Larger biaxial ratcheting strain occurred in the case of tensile superposed stress compared with that in the case of the compressive superposed stress. Moreover, even under the zero superposed stress, biaxial ratcheting strain occurred in the axial direction due to the cyclic shearing straining. Finally, the biaxial ratcheting behaviours were simulated by the unified constitutive model proposed by the authors. The characteristic features of the biaxial ratcheting behaviour, especially the axial strain due to the cyclic shear straining superposed on the zero axial stress, are well simulated by the constitutive model.

scholarly journals Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

1974 ◽  
Vol 13 (67) ◽  
pp. 27-35 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Shear Strain ◽  
Longitudinal Strain ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Mcmurdo Sound ◽  
Glacier Tongue ◽  
The Past ◽  
Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

scholarly journals Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy

1996 ◽  
Vol 23 ◽  
pp. 247-252 ◽  
Author(s):  
Li Jun ◽  
T.H Jacka ◽  
W.F. Budd
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Stress State ◽  
Strain Rate ◽  
Shear Strain ◽  
Uniaxial Compression ◽  
Simple Shear ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
State Dependent

Laboratory-prepared fine-grained, initially isotropic polycrystalline ice samples were deformed under conditions of simple shear with simultaneous uniaxial compression at a constant temperature of −2.0°C. The aim was to investigate the effects of stress configuration on the flow rate of initially isotropic ice and on ice with subsequent stress and strain-induced anisotropy. Experiments were carried out for various combinations of shear and compression with shear stress ranging from 0 to 0.49 MPa and compressive stress ranging from 0 to 0.98 MPa, but such that for every experiment the octahedral shear stress was 0.4 MPa.The strain curves resulting from the experiments clearly exhibit minimum strain rates while the ice is still isotropic, and steady-state tertiary strain rates along with the development of steady-state anisotropic fabric patterns. With constant octahedral stress (root-mean-square of the principal stress deviators), the minimum octahedral shear-strain rate has no dependence on stress configuration. This result supports the hypothesis that the flow of isotropic ice is dependent only on the second invariant of the stress tensor. This fundamental assumption has been used to provide a general description of ice-flow behaviour independent of the stress configuration (e.g. Nye, 1953; Glen, 1958; Budd, 1969).For the tertiary flow of anisotropic ice, the octahedral strain rate is stress-state dependent as a consequence of the developed crystal-orientation fabric, which is also stress-state dependent, and which develops with strain and rotation. The present tests indicate that the enhancement factor for steady-state tertiary octahedral shear-strain rate depends on the shear or compression fraction and varies from about 10 for simple shear (with zero compression) to about 3 for uniaxial compression (with zero shear).

scholarly journals Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

1974 ◽  
Vol 13 (67) ◽  
pp. 27-35 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Shear Strain ◽  
Longitudinal Strain ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Mcmurdo Sound ◽  
Glacier Tongue ◽  
The Past ◽  
Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

scholarly journals Bubble Coalescence in Ice as a Tool for the Study of its Deformation History

1968 ◽  
Vol 7 (50) ◽  
pp. 155-159 ◽  
Author(s):  
J. Weertman
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Ice Sheets ◽  
Temperature Gradients ◽  
Bubble Coalescence ◽  
Bottom Surface ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Deformation History ◽  
Ice Shelves

An analysis is made of the rate of bubble coalescence in an ice mass that is deforming. A total strain of at least 8 is required before appreciable coalescence occurs. The analysis has been applied to deforming ice shelves and ice sheets. No appreciable coalescence is expected in ice shelves but coalescence should occur in ice sheets (or glaciers) if the shear strain-rate at the bottom surface is of the order of 0·075/year or larger. Measurements of bubble concentration are capable of setting limits on paleo-strain-rates of the present ice sheets. Bubble migration down temperature gradients presents complications to the study of bubble coalescence.

scholarly journals Velocity and strain rates derived from InSAR analysis over the Amery Ice Shelf, East Antarctica

2002 ◽  
Vol 34 ◽  
pp. 228-234 ◽  
Author(s):  
N. W. Young ◽  
G. Hyland
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Transverse Shear ◽  
Transverse Shear Strain ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Ice Shelf ◽  
Local Flow ◽  
Synthetic Aperture Radar Data ◽  
Amery Ice Shelf

AbstractWe use displacements derived from matching complex synthetic aperture radar data using maximum coherence to generate a dense network of velocity estimates over the Amery Ice Shelf. From these velocities we generate the horizontal strain-rate components and resolve them with respect to the local flow direction. We present the spatial distributions of velocity and transverse shear strain rate and use them to investigate features of the flow regime for the shelf. From the southern end of the shelf, velocity decreases from a high of about 800ma–1 to around 300 ma–1, and then increases to a maximum of about 1350ma–1 at the centre of the front. Strain rates vary systematically across and along the shelf. The pattern of the transverse shear strain rate clearly identifies the shear margins, where values exceed 0.1 a–1 in the southern section of the shelf. The pattern also shows longitudinal bands of enhanced shear strain rate containing ice with a strong preferred crystal fabric that was advected from shear margins upstream. In the northern section of the shelf, significant values of longitudinal and traverse stresses lead to enhanced shear deformation through their effect on the octahedral shear stress term.

scholarly journals Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy

1996 ◽  
Vol 23 ◽  
pp. 247-252 ◽  
Author(s):  
Li Jun ◽  
T.H Jacka ◽  
W.F. Budd
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Stress State ◽  
Strain Rate ◽  
Shear Strain ◽  
Uniaxial Compression ◽  
Simple Shear ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
State Dependent

Laboratory-prepared fine-grained, initially isotropic polycrystalline ice samples were deformed under conditions of simple shear with simultaneous uniaxial compression at a constant temperature of −2.0°C. The aim was to investigate the effects of stress configuration on the flow rate of initially isotropic ice and on ice with subsequent stress and strain-induced anisotropy. Experiments were carried out for various combinations of shear and compression with shear stress ranging from 0 to 0.49 MPa and compressive stress ranging from 0 to 0.98 MPa, but such that for every experiment the octahedral shear stress was 0.4 MPa. The strain curves resulting from the experiments clearly exhibit minimum strain rates while the ice is still isotropic, and steady-state tertiary strain rates along with the development of steady-state anisotropic fabric patterns. With constant octahedral stress (root-mean-square of the principal stress deviators), the minimum octahedral shear-strain rate has no dependence on stress configuration. This result supports the hypothesis that the flow of isotropic ice is dependent only on the second invariant of the stress tensor. This fundamental assumption has been used to provide a general description of ice-flow behaviour independent of the stress configuration (e.g. Nye, 1953; Glen, 1958; Budd, 1969). For the tertiary flow of anisotropic ice, the octahedral strain rate is stress-state dependent as a consequence of the developed crystal-orientation fabric, which is also stress-state dependent, and which develops with strain and rotation. The present tests indicate that the enhancement factor for steady-state tertiary octahedral shear-strain rate depends on the shear or compression fraction and varies from about 10 for simple shear (with zero compression) to about 3 for uniaxial compression (with zero shear).

scholarly journals Bubble Coalescence in Ice as a Tool for the Study of its Deformation History

1968 ◽  
Vol 7 (50) ◽  
pp. 155-159
Author(s):  
J. Weertman
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Ice Sheets ◽  
Temperature Gradients ◽  
Bubble Coalescence ◽  
Bottom Surface ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Deformation History ◽  
Ice Shelves

An analysis is made of the rate of bubble coalescence in an ice mass that is deforming. A total strain of at least 8 is required before appreciable coalescence occurs. The analysis has been applied to deforming ice shelves and ice sheets. No appreciable coalescence is expected in ice shelves but coalescence should occur in ice sheets (or glaciers) if the shear strain-rate at the bottom surface is of the order of 0·075/year or larger. Measurements of bubble concentration are capable of setting limits on paleo-strain-rates of the present ice sheets. Bubble migration down temperature gradients presents complications to the study of bubble coalescence.

Constitutive Modeling for Elevated Temperature Flow Behavior of ZHMn34-2-2-1 Manganese Brass

2017 ◽  
Vol 872 ◽  
pp. 30-37
Author(s):  
Meng Han Wang ◽  
Kang Wei ◽  
Xiao Juan Li
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Flow Behavior ◽  
Peak Stress ◽  
Strain Rates ◽  
Hollomon Parameter ◽  
Prediction Ability ◽  
Absolute Relative Error ◽  
Deformation Behaviors ◽  
State Stress

The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures (923K-1073K) and strain rates (0.01s-1-10s-1). The true stress-strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. A revised constitutive model coupling flow stress with strain, strain rate and deformation temperature is established with the material constants expressed by polynomial fitting of strain. Moreover, better prediction ability of the constitutive model is achieved by implementation of a simple approach for modified the Zener-Hollomon parameter considering the compensation of strain rate and temperature increment. By comparing the predicted and experimented values, the correlation coefficient and mean absolute relative error are 0.997 and 2.363%, respectively. The quantitative statistical results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.

scholarly journals Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

2020 ◽  
Author(s):  
Chuang Liu ◽  
Dongzhi Sun ◽  
Xianfeng Zhang ◽  
Florence Andrieux ◽  
Tobias Gerster
Keyword(s):  
Cast Iron ◽  
Constitutive Model ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
Damage Model ◽  
Iron Alloys ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Damage Models ◽  
Rate Dependent

Abstract Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry. To study the mechanical behavior of a typical ductile cast iron (GJS-450) with nodular graphite, uni-axial quasi-static and dynamic tensile tests at strain rates of 10− 4, 1, 10, 100, and 250 s− 1 were carried out. In order to investigate the effects of stress state, specimens with various geometries were used in the experiments. Stress–strain curves and fracture strains of the GJS-450 alloy in the strain-rate range of 10− 4 to 250 s− 1 were obtained. A strain rate-dependent plastic flow law based on the Voce model is proposed to describe the mechanical behavior in the corresponding strain-rate range. The deformation behavior at various strain rates is observed and analyzed through simulations with the proposed strain rate-dependent constitutive model. The available damage model from Bai and Wierzbicki is extended to take the strain rate into account and calibrated based on the analysis of local fracture strains. The validity of the proposed constitutive model including the damage model was verified by the corresponding experimental results. The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys. The predictions with the proposed constitutive model and damage models at various strain rates agree well with the experimental results, which illustrates that the rate-dependent flow rule and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.

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