The Effects of Strain Rate and Thickness on the Response of Thin Layers of Solder Loaded in Pure Shear

1997 ◽  
Vol 119 (2) ◽  
pp. 81-84 ◽  
Author(s):  
A. Gilat ◽  
K. Krishna
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Strain Rate ◽  
Mechanical Response ◽  
Pure Shear ◽  
Strain Curve ◽  
Thin Layers ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Stress And Deformation

A new configuration for testing thin layers of solder is introduced and employed to study the effects of strain rate and thickness on the mechanical response of eutectic Sn-Pb solder. The solder in the test is loaded under a well defined state of pure shear stress. The stress and deformation in the solder are measured very accurately to produce a reliable stress-strain curve. The results show that both the stress needed for plastic deformation and ductility increase with increasing strain rate.

Molecular dynamics simulations of the effect of temperature and strain rate on the plastic deformation of body centred cubic iron nanowires

2021 ◽  
pp. 1-19
Author(s):  
Qian Wu ◽  
Yong Wang ◽  
Tao Han ◽  
Hongtao Wang ◽  
Laihui Han ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Plastic Deformation ◽  
Strain Rate ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Strain Curve ◽  
Dislocation Slip ◽  
Stress Strain Curve ◽  
Stress Strain

Abstract The tensile tests of BCC Fe nanowires were simulated through molecular dynamics methods. The temperature and strain rate effects on the mechanical properties as well as the orientation-dependent plastic deformation mechanism were analyzed. For [001]-oriented BCC Fe nanowires, as the temperature increased, the yield stress and Young's modulus decreased. While the yield stress and Young's modulus increased as the strain rate increased. With the increase of temperature, when the temperature was less than 400 K, the twin propagation stress decreased dramatically, and then tended to reach a saturation value at higher temperatures. Under different temperatures and strain rates, the [001]-oriented Fe nanowires all deformed by twinning. The oscillation stage in the stress-strain curve corresponds to the process from the nucleation of the twin to the reorientation of the nanowire. For [110]-oriented Fe nanowires, the plastic deformation is dominated by dislocation slip. The independent events such as the nucleation, slip, and annihilation of dislocations are the causes of the unsteady fluctuations in the stress-strain curve. The Fe nanowires eventually undergo shear damage along the dominant slip surface.

Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach

2007 ◽  
Vol 558-559 ◽  
pp. 441-448 ◽  
Author(s):  
Jong K. Lee
Keyword(s):  
Differential Equation ◽  
Strain Rate ◽  
Critical Strain ◽  
Strain Curve ◽  
Single Peak ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Delay Differential

During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.

Some Properties of a Mechanical Model of Plasticity

1948 ◽  
Vol 15 (3) ◽  
pp. 222-225
Author(s):  
H. F. Bohnenblust ◽  
Pol Duwez
Keyword(s):  
Plastic Deformation ◽  
Potential Energy ◽  
Work Hardening ◽  
Mechanical Model ◽  
Strain Curve ◽  
Hysteresis Curve ◽  
Plastic Range ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Mechanical Models

Abstract Various mechanical models explaining the plastic deformation of metals have been proposed. One of the present authors has shown that in some cases an analytical expression for the stress-strain curve and the hysteresis curve of a metal in the plastic range can be deduced from such a model. The present investigation is a further analysis of the model leading to the computation of the change in potential energy of the metal due to work-hardening.

Influence of strain rate on the stress-strain curve in the range of Lüders strain

1996 ◽  
Vol 67 (11) ◽  
pp. 495-500 ◽  
Author(s):  
Essam El-Magd ◽  
Herbert Scholles ◽  
Herbert Weisshaupt
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain

High Strain Rate Test of a Steel Plate under Blast Loading from High Explosive

2013 ◽  
Vol 767 ◽  
pp. 144-149 ◽  
Author(s):  
Tei Saburi ◽  
Shiro Kubota ◽  
Yuji Wada ◽  
Tatsuya Kumaki ◽  
Masatake Yoshida
Keyword(s):  
Strain Rate ◽  
Dynamic Stress ◽  
Steel Plate ◽  
High Strain ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Time Deformation ◽  
Rate Test ◽  
High Strain Rate Test

In this study, a high strain rate test method of a steel plate under blast loading from high explosive was designed and was conducted by a combined experimental/numerical approach to facilitate the estimation process for the dynamic stress-strain curve under practical strain rate conditions. The steel plate was subjected to a blast load, which was generated by Composition C4 explosive and the dynamic deformation of the plate was observed with a high-speed video camera. Time-deformation relations were acquired by image analysis. A numerical simulation for the dynamic behaviors of the plate identical to the experimental condition was conducted using a coupling analysis of finite element method (FEM) and discrete particle method (DPM). Explosives were modeled by discrete particles and the steel plate and other materials were modeled by finite element. The blast load on the plate was described fluid-structure interaction (FSI) between DPM and FEM. As inverse analysis scheme to estimate dynamic stress-strain curve, an evaluation using a quasistatic data was conducted. In addition, two types of approximations for stress-strain curve were assumed and optimized by least square method. One is a 2-piece approximation, and was optimized by least squares method using a yield stress and a tangent modulus as parameters. The other is a continuous piecewise linear approximation, in which a stress-strain curve was divided into some segments based on experimental time-deformation relation, and was sequentially optimized using youngs modulus or yield stress as parameter. The results showed that the piecewise approximation can gives reasonably agreement with SS curve obtained from the experiment.

Stress-Strain Behavior of an Aluminum Alloy Under Transient Strain-Rates

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Y. W. Kwon ◽  
Y. Esmaeili ◽  
C. M. Park
Keyword(s):  
Aluminum Alloy ◽  
Strain Rate ◽  
Fracture Strain ◽  
Strain Curve ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Single Strain ◽  
Transient Strain ◽  
Strain Rate Loading

Because most structures are subjected to transient strain-rate loading, an experimental study was conducted to investigate the stress-strain behaviors of an aluminum alloy undergoing varying strain-rate loading. To this end, uniaxial tensile loading was applied to coupons of dog-bone shape such that each coupon underwent two or three different strain-rates, i.e., one rate after another. As a basis, a series of single-strain-rate tests was also conducted with strain-rates of 0.1–10.0 s−1. When the material experienced multistrain-rate loading, the stress-strain curves were significantly different from any single-strain-rate stress-strain curve. The strain-rate history affected the stress-strain curves under multistrain-rate loading. As a result, some simple averaging of single-strain-rate curves did not predict the actual multistrain-rate stress-strain curve properly. Furthermore, the fracture strain under multistrain-rate loading was significantly different from that under any single-strain-rate case. Depending on the applied strain-rates and their sequences, the former was much greater or less than the latter. A technique was proposed based on the residual plastic strain and plastic energy density in order to predict the fracture strain under multistrain-rate loading. The predicted fracture strains generally agreed well with the experimental data. Another observation that was made was that the unloading stress-strain curve was not affected by the previous strain-rate history.

Model for predicting the variation of shear stress in unsaturated soils during strain-softening

2020 ◽  
Author(s):  
Xiuhan Yang ◽  
Sai Vanapalli
Keyword(s):  
Shear Stress ◽  
Large Deformation ◽  
Unsaturated Soils ◽  
Strain Softening ◽  
Strain Curve ◽  
Published Data ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Relationship ◽  
State Stress

Several of the geotechnical structures constructed with unsaturated soils undergo a large deformation prior to reaching failure conditions (e.g. progressive failure of a soil slope). During this process, the shear stress in soils typically increases initially and then reduces with an increase in the shear strain. The prediction of the stress-strain relationship is critical for reasonable interpretation of the mechanical behavior of those geo-structures that undergo large deformation. This paper introduces a model based on the disturbed state concept (DSC) to predict the variation of shear stress in unsaturated soils during strain-softening process under consolidated drained triaxial compression condition. In this model, the apparent stress-strain relationship is formulated as a weighted average of a hyperbolic hardening response extending the pre-peak state stress-strain curve and a linear response extending the critical state stress-strain curve with an assumed disturbance function as the weight. The prediction procedure is described in detail and the proposed model is validated using several sets of published data on unsaturated soils varying from coarse- to fine-grained soils. Finally, a comprehensive error analysis is undertaken based on an index of agreement approach.

scholarly journals High Strain Rate Behavior of Ultrafine Grained AA2519 Processed via Multi Axial Cryogenic Forging

Metals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 115 ◽  
Author(s):  
Amin Azimi ◽  
Gbadebo Moses Owolabi ◽  
Hamid Fallahdoost ◽  
Nikhil Kumar ◽  
Grant Warner
Keyword(s):  
Plastic Deformation ◽  
Flow Stress ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Strain Curve ◽  
Thermal Softening ◽  
Stress Strain Curve ◽  
Ultrafine Grained ◽  
Cryogenic Forging

The present work deals with studies on the dynamic behavior of ultrafine grained AA2519 alloy synthesized via cryogenic forging (CF) and room temperature forging (RTF) techniques. A split-Hopkinson pressure bar was used to perform high strain rate tests on the processed samples and the microstructures of the samples were characterized before and after impact tests. Electron backscatter diffraction (EBSD) maps demonstrated a significant grain size refinement from ~740 nm to ~250 nm as a result of cryogenic plastic deformation showing higher dislocation densities and stored strains in the CF sample when compared to the RTF sample. This microstructure modification caused the increase of dynamic flow stress in this alloy. In addition, the aluminum matrix of the CF alloy is more densely populated with fragmented particles than the RTF alloy due to the heavier plastic deformation applied to the cryogenically forged alloy. The results obtained from the stress–strain curve for the RTF sample showed intense thermomechanical instabilities in the RTF sample which led to a severe thermal softening and the subsequent sharp drop in the flow stress. However, no significant decrease was observed in the stress–strain curve of the CF alloys with ultrafine grains which means that thermal softening would probably not be the most effective failure mechanism. Furthermore, higher level of sensitivity of CF alloys to strain rates was observed which is ascribed to transition of rate-controlling plastic deformation mechanisms. In the post-mortem microstructure investigation, deformed and transformed adiabatic shear bands (ASBs) were identified on the RTF alloy when the strain rate is over 4000 s−1 at which it had experienced a significant thermal softening. On the other hand, circular path and aligned split arcs are the various shapes of the deformed ASB seen at no earlier than 4500 s−1 in the CF alloys. This is associated with the crack failure caused by grain boundary sliding.

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