scholarly journals Visualization of the damage evolution for Ti–3Al–2Mo–2Zr alloy during a uniaxial tensile process using a microvoids proliferation damage model

2021 ◽  
Vol 40 (1) ◽  
pp. 310-324
Author(s):  
Ying Tong ◽  
Jiang Zhao ◽  
Guo-zheng Quan
Keyword(s):  
Plastic Deformation ◽  
Damage Evolution ◽  
Volume Fraction ◽  
Tensile Deformation ◽  
Damage Model ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Stress Strain ◽  
Gtn Damage Model

Abstract Understanding the damage evolution of alloys during a plastic deformation process is significant to the structural design of components and accident prevention. In order to visualize the damage evolution in the plastic deformation of Ti–3Al–2Mo–2Zr alloy, a series of uniaxial tensile experiments for this alloy were carried out under the strain rates of 0.1–10 s−1 at room temperature, and the stress–strain curves were achieved. On the other hand, the finite element (FE) models of these uniaxial tensile processes were established. A microvoids proliferation model, Gurson–Tvergaard–Needleman (GTN) damage model, was implanted into the uniaxial tensile models, and the simulated stress–strain curves corresponding to different GTN parameter combinations were obtained. Based on the simulated and experimental stress–strain curves, the GTN parameters of this alloy were solved by response surface methodology (RSM). The solved GTN parameters suggest that higher strain rate can enhance the proliferation and coalescence of microvoids. Furthermore, the uniaxial tensile tests over different strain rates were simulated using the solved GTN parameters. Then, the damage processes were visualized and evaluated. The result shows that the degradation speed of this alloy is slow at the initial stage of the tensile deformation and then accelerates once the voids volume fraction reaches a critical value.

scholarly journals A Strain Rate-Dependent Damage Evolution Model for Concrete Based on Experimental Results

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Bin Xu ◽  
Xiaoyan Lei ◽  
P. Wang ◽  
Hui Song
Keyword(s):  
Strain Rate ◽  
Uniaxial Compression ◽  
Damage Evolution ◽  
Damage Model ◽  
Evolution Model ◽  
Experimental Results ◽  
Strain Rates ◽  
Compression Tests ◽  
Stress Strain ◽  
Actual Damage

There are various definitions of damage variables from the existing damage models. The calculated damage value by the current methods still could not well correspond to the actual damage value. Therefore, it is necessary to establish a damage evolution model corresponding to the actual damage evolution. In this paper, a strain rate-sensitive isotropic damage model for plain concrete is proposed to describe its nonlinear behavior. Cyclic uniaxial compression tests were conducted on concrete samples at three strain rates of 10−3s−1, 10−4s−1, and 10−5s−1, respectively, and ultrasonic wave measurements were made at specified strain values during the loading progress. A damage variable was defined using the secant and initial moduli, and concrete damage evolution was then studied using the experimental results of the cyclic uniaxial compression tests conducted at the different strain rates. A viscoelastic stress-strain relationship, which considered the proposed damage evolution model, was presented according to the principles of irreversible thermodynamics. The model results agreed well with the experiment and indicated that the proposed damage evolution model can accurately characterize the development of macroscopic mechanical weakening of concrete. A damage-coupled viscoelastic constitutive relationship of concrete was recommended. It was concluded that the model could not only characterize the stress-strain response of materials under one-dimensional compressive load but also truly reflect the degradation law of the macromechanical properties of materials. The proposed damage model will advance the understanding of the failure process of concrete materials.

Stress-Strain Equations for Some Near-Eutectic Tin-Lead Solders

1991 ◽  
Vol 113 (4) ◽  
pp. 475-484 ◽  
Author(s):  
K. P. Jen ◽  
J. N. Majerus
Keyword(s):  
Strain Rate ◽  
Printed Circuit Boards ◽  
Volume Fraction ◽  
Total Error ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Strain Rates ◽  
Stress Strain ◽  
Engineering Strain

This paper presents the evaluation of the stress-strain behavior, as a function of strain-rate, for three tin-lead solders at room temperature. This behavior is critically needed for reliability analysis of printed circuit boards (PCB) since handbooks list minimal mechanical properties for the eutectic solder used in PCBs. Furthermore, most handbook data are for stable eutectic microstructure whereas PCB solder has a metastable microstructure. All three materials were purchased as “eutectics.” However, chemical analysis, volume fraction determination, and microhardness tests show some major variations between the three materials. Two of the materials have a eutectic composition, and one does not. The true stress-strain equations of one eutectic and the one noneutectic material are determined from compressive tests at engineering strain-rates between 0.0002/s and 0.2/s. The second eutectic material is evaluated using tensile tests with strain-rates between 0.00017/s and 0.042/s. The materials appear to exhibit linear elastic behavior only at extremely small strains, i.e., less than 0.0005. However, this “elastic” behavior showed considerable variation, and depended upon the strain rate. In both tension and compression the eutectic alloy exhibits nonlinear plastic behavior, i.e., strain-softening followed by strain-hardening, which depends upon the strain rate. A quadratic equation σy = σy(ε˚/ε˚0) + A(ε˚/ε˚0)ε + B(ε˚/ε˚0)ε2 fit to the data gives correlation coefficients R2 > 0.91. The coefficients σy(ε˚/ε˚0), A(ε˚/ε˚0), B(ε˚/ε˚0) are fitted functions of the normalized engineering strain rate ε˚/ε˚0. Replicated experiments are used at each strain-rate so that a measure of the statistical variation could be estimated. Measures of error associated with the regression analysis are also obtained so that an estimate of the total error in the stress-strain relations can be made.

Anisotropic Damage Evolution for Perforated Sheet under Tensile Deformation

2016 ◽  
Vol 725 ◽  
pp. 489-494
Author(s):  
Shigeru Nagaki ◽  
Daigo Saboi ◽  
Kenta Muroi ◽  
Makoto Iizuka ◽  
Kenichi Oshita
Keyword(s):  
Plastic Deformation ◽  
Void Growth ◽  
Damage Evolution ◽  
Tensile Deformation ◽  
Yield Function ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Thermodynamic Consideration ◽  
Perforated Sheets ◽  
Growth Of Voids

It is important to formulate a constitutive equation which represents the growth of voids during plastic deformation in order to predict ductile fracture of metallic materials. For this purpose, we proposed an anisotropic Gurson’s yield function with the damage tensor, which represents the anisotropy due to the void distribution and the damage evolution was assumed isotropic for simplicity. Then we also proposed an anisotropic void growth law derived from the anisotropic Gurson’s yield function based on thermodynamic consideration. In this study we carried out the uniaxial tensile test of perforated sheets of stainless steel and aluminum alloy as the ideal two dimensional model of the damaged material and investigate the damage growth during plastic deformation. As a result, we obtained a good agreement between the experimental and the calculated void growth for both materials and it is also found that material parameters for damage evolutions are almost the same for both materials and are hardly affected by the work-hardening exponent.

Influence of Geometrical Features of Meso-Defects on Damage Evolution of Metal Structure

2015 ◽  
Vol 723 ◽  
pp. 21-25
Author(s):  
Chao Fan Zhao ◽  
Zhao Xia Li
Keyword(s):  
Aspect Ratio ◽  
Damage Evolution ◽  
Structural Damage ◽  
Volume Fraction ◽  
Failure Process ◽  
Damage Model ◽  
Metal Structure ◽  
Geometrical Features ◽  
Gtn Damage Model ◽  
Defect Volume

To study the failure process of metal structure with meso-defects, RVE (representative volume element) with various initial meso-defects were analyzed by using ABAQUS software, the parameter f (void volume fraction) of GTN damage model was regarded as the criterion of structural damage. The result shows that f increased more obvious with volume of defects for spherical defects with the same shape but different size. When the radius of defects is less than 0.15mm, the influence of defects’ volume on increases of f is clear enough. When the radius is greater than 0.15mm, the effects is diminishing. For ellipsoidal defects with the same volume but different aspect ratio, when the long axis perpendicular to the direction of load, the increased trend of f according to plastic deformation more obvious along with aspect ratio of defects. Apparently, as aspect ratio approaches infinity, f would have the fastest growth. Consequently, the bigger defect volume and aspect ratio, the more conducive for damage evolution of the metal structure.

Characterization of Doped SAC Solder Materials and Determination of Anand Parameters

2015 ◽  
Author(s):  
Sudan Ahmed ◽  
Munshi Basit ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
High Reliability ◽  
Low Cost ◽  
Tensile Tests ◽  
Material Behavior ◽  
Lead Free ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Stress Strain ◽  
Free Solder ◽  
Viscoelastic Constitutive Model

In the electronic packaging industry, it is important to be able to make accurate predictions of board level solder joint reliability during thermal cycling exposures. The Anand viscoelastic constitutive model is often used to represent the material behavior of the solder in finite element simulations. This model is defined using nine material parameters, and the reliability prediction results are often highly sensitive to the Anand parameters. In present work, three new doped lead free solder materials recommended for high reliability applications have been chemically analyzed and then mechanically tested in order to determine the nine Anand parameters. The alloys are referred to as Ecolloy (SAC_R), CYCLOMAX (SAC_Q), and Innolot by their vendors. The first two doped alloys (SAC_R and SAC_Q) were found to be composed of Sn, Ag, Cu, and a single X-element dopant. Such solders are commonly referred to as SAC-X in the literature. For the third material (Innolot), three different dopants are present along with Sn, Ag and Cu. The EDX method was used to determine the approximate chemical composition of the materials, and Bismuth (Bi) was found to be the X-additive for both SAC_R and SAC_Q. In addition, the SAC_R material was found to have no silver (Ag), which is the reason it is marketed as a low cost (economy) material. The nine Anand parameters were determined for each unique solder alloy from a set of uniaxial tensile tests performed at several strain rates and temperatures. Testing conditions included strain rates of 0.001, 0.0001, and 0.00001 (sec−1), and temperatures of 25, 50, 75, 100, and 125 C. The Anand parameters were calculated from each set of stress-strain data using an established procedure that is described in detail in the paper. The mechanical properties and the values of Anand parameters for these new doped alloys were compared with those for standard SAC105 and SAC405 lead free alloys. Although the SAC_R material does not have any silver, it was shown to have better mechanical behavior than SAC105 due to the presence of Bismuth (Bi) along with a little higher percentage of Copper (Cu). The SAC_Q and Innolot materials were shown to have significantly higher strength than SAC405. After deriving the Anand parameters for each alloy, the stress-strain curves have been calculated for various conditions, and excellent agreement was found between the predicted results and experimental stress-strain curves.

scholarly journals Experimental Study on the Mechanical Behavior of EN08 Steel at Different Temperatures and Strain Rates

Metals ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 736 ◽  
Author(s):  
Farid Abed ◽  
Akrum Abdul-Latif ◽  
Ayatollah Yehia
Keyword(s):  
Strain Rate ◽  
Mechanical Response ◽  
Dynamic Compression ◽  
Damage Model ◽  
Tensile Tests ◽  
Dynamic Strain ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Compression Tests ◽  
Sem Images

The objective of this paper is to investigate the mechanical response of EN08 steel at quasi-static and dynamic strain rates. Uniaxial tensile tests under quasi-static regime (from 0.0015 s−1 to 0.15 s−1) are conducted on EN08 steel at a range of temperatures between 298 K and 923 K. Dynamic compression tests are also performed by using a drop hammer and by considering different masses and heights to study the material response at strain rates up to 800 s−1. Through the stress-strain responses of EN08 steel, a strong dependency of the yield stress as well as the ultimate strength on the strain rate and temperature is recognized. Furthermore, the strain hardening is highly affected by the increase of temperature at all levels of strain rate. The microstructure of the steel is also examined at a fracture by using SEM images to quantify the density of microdefects and define the damage evolution by using an energy-based damage model.

scholarly journals Study of Alloy Hot Flow and Hardening Behavior Using a New Correction Method for Hot Uniaxial Tests

Metals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 42
Author(s):  
Shuguang Qu ◽  
Heli Peng ◽  
Zhubin He ◽  
Kailun Zheng ◽  
Jinghua Zheng
Keyword(s):  
Titanium Alloys ◽  
Flow Behavior ◽  
Tensile Tests ◽  
Correction Method ◽  
Hot Forming ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Uniform Temperature ◽  
Stress Strain ◽  
Hardening Behavior

The precise characterisation of hot flow behavior of titanium alloys is of vital importance for practical hot forming processes. To precisely determine the hot flow behavior of titanium alloys under the forming conditions, Gleeble hot tensile tests are usually performed to simulate the forming processes by accurately controlling the deformation temperatures and strain rates under designed conditions. However, there exists a non-uniform temperature distribution during the Gleeble tests, which leads to inaccuracies in the determined hot flow behavior. To overcome such an issue, this paper proposed a new strain-based correction method for Gleeble hot tensile tests, enabling the mitigation of the non-uniform temperature-induced stress-strain curve inaccuracies. The non-uniform temperature zones have been successfully excluded in the calculation of the true strain levels. A series of hot uniaxial tensile tests of TA32 at temperatures, ranging from 750 °C to 900 °C, and strain rates, 0.01/s~1/s, were carried out. The obtained stress-strain correlations for a large gauge zone were characterized using the new correction method, which was further used to evaluate the hardening behavior of titanium alloys. The results have shown that the ductility, strain hardening component (i.e., n), strain rate hardening component (i.e., m) and uniform strain value (i.e., ) are over-estimated, compared to conventional method. Higher strain rates and lower temperature leads to enhanced hardening behavior. This research provides an alternative correction method and may achieve more accurate stress-strain curves for better guidance of the hot forming process for titanium alloys.

scholarly journals Microstructural Characterization and Mechanical Properties of Ti-6Al-4V Alloy Subjected to Dynamic Plastic Deformation Achieved by Multipass Hammer Forging with Different Forging Temperatures

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Xiurong Fang ◽  
Jiang Wu ◽  
Xue Ou ◽  
Fuqiang Yang
Keyword(s):  
Mechanical Properties ◽  
Plastic Deformation ◽  
Volume Fraction ◽  
Microstructural Characterization ◽  
Optical Microscope ◽  
Strain Rates ◽  
Materials Properties ◽  
Forging Process ◽  
Hammer Forging ◽  
Dynamic Plastic Deformation

Dynamic plastic deformation (DPD) achieved by multipass hammer forging is one of the most important metal forming operations to create the excellent materials properties. By using the integrated approaches of optical microscope and scanning electron microscope, the forging temperature effects on the multipass hammer forging process and the forged properties of Ti-6Al-4V alloy were evaluated and the forging samples were controlled with a total height reduction of 50% by multipass strikes from 925°C to 1025°C. The results indicate that the forging temperature has a significant effect on morphology and the volume fraction of primary α phase, and the microstructural homogeneity is enhanced after multipass hammer forging. The alloy slip possibility and strain rates could be improved by multipass strikes, but the marginal efficiency decreases with the increased forging temperature. Besides, a forging process with an initial forging temperature a bit above β transformation and finishing the forging a little below the β transformation is suggested to balance the forging deformation resistance and forged mechanical properties.

scholarly journals A Flow Stress Model of 300M Steel for Isothermal Tension

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 252
Author(s):  
Rongchuang Chen ◽  
Shiyang Zhang ◽  
Xianlong Liu ◽  
Fei Feng
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Tensile Deformation ◽  
Flow Behavior ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Average Deviation ◽  
Cross Sectional ◽  
300M Steel

To investigate the effect of hot working parameters on the flow behavior of 300M steel under tension, hot uniaxial tensile tests were implemented under different temperatures (950 °C, 1000 °C, 1050 °C, 1100 °C, 1150 °C) and strain rates (0.01 s−1, 0.1 s−1, 1 s−1, 10 s−1). Compared with uniaxial compression, the tensile flow stress was 29.1% higher because dynamic recrystallization softening was less sufficient in the tensile stress state. The ultimate elongation of 300M steel increased with the decrease of temperature and the increase of strain rate. To eliminate the influence of sample necking on stress-strain relationship, both the stress and the strain were calibrated using the cross-sectional area of the neck zone. A constitutive model for tensile deformation was established based on the modified Arrhenius model, in which the model parameters (n, α, Q, ln(A)) were described as a function of strain. The average deviation was 6.81 MPa (6.23%), showing good accuracy of the constitutive model.

Influence of Severe Plastic Deformation on the PLC Effect and Mechanical Properties in Al 5XXX Alloy

2006 ◽  
Vol 114 ◽  
pp. 171-176 ◽  
Author(s):  
Joanna Zdunek ◽  
Pawel Widlicki ◽  
Halina Garbacz ◽  
Jaroslaw Mizera ◽  
Krzysztof Jan Kurzydlowski
Keyword(s):  
Mechanical Properties ◽  
Plastic Deformation ◽  
Grain Size ◽  
Severe Plastic Deformation ◽  
True Strain ◽  
Tensile Tests ◽  
Size Reduction ◽  
Hydrostatic Extrusion ◽  
Stress Strain ◽  
Chatelier Effect

In this work, Al-Mg-Mn-Si alloy (5483) in the as-received and severe plastically deformed states was used. Plastic deformation was carried out by hydrostatic extrusion, and three different true strain values were applied 1.4, 2.8 and 3.8. All specimens were subjected to tensile tests and microhardness measurements. The investigated material revealed an instability during plastic deformation in the form of serration on the stress-strain curves, the so called Portevin-Le Chatelier effect It was shown that grain size reduction effected the character of the instability.

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