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.

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 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 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.

Elasto-viscoplastic constitutive equations for the description of glassy polymers behavior at constant strain rate

2006 ◽  
Vol 129 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Fahmi Zaïri ◽  
Moussa Naït-Abdelaziz ◽  
Krzysztof Woznica ◽  
Jean-Michel Gloaguen
Keyword(s):  
Constitutive Equations ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Glassy Polymers ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Strain Rates ◽  
State Variable ◽  
Rubber Toughened ◽  
Compressive Tests

In this study, a modelization of the viscoplastic behavior of amorphous polymers is proposed, from an approach originally developed for metal behavior at high temperature, in which state variable constitutive equations have been modified. A procedure for the identification of model parameters is developed through the use of experimental data from both uniaxial compressive tests extracted from the literature and uniaxial tensile tests performed in this study across a variety of strain rates. The numerical algorithm shows that the predictions of this model well describe qualitatively and quantitatively the intrinsic softening immediately after yielding and the subsequent progressive orientational hardening corresponding to the response of two polymers, amorphous polyethylene terephthalate and rubber toughened polymethyl methacrylate.

Tensile Stress-Strain Curves Modeling of Four Kinds of Solders with Temperature and Rate Dependence

2005 ◽  
Vol 297-300 ◽  
pp. 905-911 ◽  
Author(s):  
Xu Chen ◽  
Li Zhang ◽  
Masao Sakane ◽  
Haruo Nose
Keyword(s):  
Tensile Stress ◽  
Constitutive Model ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Strain Rate Range ◽  
Rate Dependence ◽  
Strain Rates ◽  
Stress Strain ◽  
Rate Range

A series of tensile tests at constant strain rate were conducted on tin-lead based solders with different Sn content under wide ranges of temperatures and strain rates. It was shown that the stress-strain relationships had strong temperature- and strain rate- dependence. The parameters of Anand model for four solders were determined. The four solders were 60Sn-40Pb, 40Sn-60Pb, 10Sn-90Pb and 5Sn-95Pb. Anand constitutive model was employed to simulate the stress-strain behaviors of the solders for the temperature range from 313K to 398K and the strain rate range from 0.001%sP -1 P to 2%sP -1 P. The results showed that Anand model can adequately predict the rate- and temperature- related constitutive behaviors at all test temperatures and strain rates.

A Mathematical Description for the Stress-Strain Behavior of Annealed 2 1/4 Cr-1 Mo Steel

1976 ◽  
Vol 98 (2) ◽  
pp. 118-125 ◽  
Author(s):  
R. L. Klueh ◽  
T. L. Hebble
Keyword(s):  
Mathematical Description ◽  
Flow Behavior ◽  
True Strain ◽  
Empirical Relationship ◽  
Tensile Tests ◽  
Strain Rates ◽  
Strain Behavior ◽  
Test Conditions ◽  
Wide Range ◽  
Strain Data

We have conducted a detailed series of tensile tests on one heat of annealed 2 1/4 Cr-1 Mo steel over the range 25 to 593°C (75 to 1100°F) and at nominal strain rates of 0.4, 0.04, 0.004, and 0.0004/min. To determine an empirical relationship to represent the flow behavior, we fitted the true-stress true-strain data from these tests to several proposed models. The models fit were those proposed by Hollomon, Ludwik, Ludwigson, and Voce. From a comparison of the standard error of estimate, the Voce equation was concluded to be the best mathematical description of the data under most test conditions and the best single representation over the wide range of test conditions.

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.

scholarly journals Strain Rate-Dependent Constitutive and Low Stress Triaxiality Fracture Behavior Investigation of 6005 Al Alloy

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yong Peng ◽  
Xuanzhen Chen ◽  
Shan Peng ◽  
Chao Chen ◽  
Jiahao Li ◽  
...  
Keyword(s):  
Flow Stress ◽  
Plastic Strain ◽  
Strain Rate ◽  
Fracture Behavior ◽  
Equivalent Plastic Strain ◽  
Stress Triaxiality ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Stress States

In order to study the dynamic and fracture behavior of 6005 aluminum alloy at different strain rates and stress states, various tests (tensile tests at different strain rates and tensile shearing tests at five stress states) are conducted by Mechanical Testing and Simulation (MTS) and split-Hopkinson tension bar (SHTB). Numerical simulations based on the finite element method (FEM) are performed with ABAQUS/Standard to obtain the actual stress triaxialities and equivalent plastic strain to fracture. The results of tensile tests for 6005 Al show obvious rate dependence on strain rates. The results obtained from simulations indicate the feature of nonmonotonicity between the strain to fracture and stress triaxiality. The equivalent plastic strain reduces to a minimum value and then increases in the stress triaxiality range from 0.04 to 0.30. A simplified Johnson-Cook (JC) constitutive model is proposed to depict the relationship between the flow stress and strain rate. What is more, the strain-rate factor is modified using a quadratic polynomial regression model, in which it is considered to vary with the strain and strain rates. A fracture criterion is also proposed in a low stress triaxiality range from 0.04 to 0.369. Error analysis for the modified JC model indicates that the model exhibits higher accuracy than the original one in predicting the flow stress at different strain rates. The fractography analysis indicates that the material has a typical ductile fracture mechanism including the shear fracture under pure shear and the dimple fracture under uniaxial tensile.

Methods for the Experimental Evaluation of True Stress-Strain Curves After Necking of Conventional Tensile Specimens: Exploratory Investigation and Proposals

2012 ◽  
Author(s):  
Grace Kelly Q. Ganharul ◽  
Nick de Brangança Azevedo ◽  
Gustavo Henrique B. Donato
Keyword(s):  
Real Time ◽  
Weighted Average ◽  
Tensile Tests ◽  
Plastic Instability ◽  
True Stress ◽  
Experimental Results ◽  
Uniaxial Tensile ◽  
High Definition ◽  
Stress Strain

Numerical elastic-plastic simulations have undergone significant expansion during the last decades (e.g. refined fracture mechanics finite element models including ductile tearing). However, one limitation to increase the accuracy of such models is the reliable experimental characterization of true stress-strain curves from conventional uniaxial tensile tests after necking (plastic instability), which complicates the direct assessment of the true stress-strain curves until failure. As a step in this direction, this work presents four key activities: i) first, existing correction methods are presented, including Bridgman, power law, weighted average and others; ii) second, selected metals are tested to experimentally characterize loads and the geometric evolution of necking. High-definition images are used to obtain real-time measurements following a proposed methodology; iii) third, refined non-linear FEM models are developed to reproduce necking and assess stresses as a function of normalized neck geometry; iv) finally, existing correction methods are critically compared to experimental results and FEM predictions in terms of potential and accuracy. The experimental results evaluated using high-definition images presented an excellent geometrical characterization of instability. FEM models were able to describe stress-strain-displacement fields after necking, supporting the exploratory validations and proposals of this work. Classical methodologies could be adapted based on experiments to provide accurate stress-strain curves up to failure with less need for real-time measurements, thus giving further support to the determination of true material properties considering severe plasticity.

Validation of the Hardening Behaviors for Metallic Materials at High Strain Rate and Temperature by Using the Taylor Impact Test

2016 ◽  
Vol 715 ◽  
pp. 153-158
Author(s):  
Ming Jun Piao ◽  
Hoon Huh ◽  
Ik Jin Lee ◽  
Hyung Won Kim ◽  
Lee Ju Park
Keyword(s):  
Tensile Tests ◽  
Thermal Softening ◽  
Experimental Results ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Metallic Materials ◽  
Softening Effect ◽  
Impact Tests ◽  
Wide Range ◽  
Taylor Impact

This paper is concerned with the validation of the dynamic hardening behaviors of metallic materials by comparing numerical and experimental results of the Taylor impact tests. Several uniaxial tensile tests are performed at different strain rates and temperatures by using three kinds of materials: 4130 steel (BCC); OFHC copper (FCC); and Ti6Al4V alloy (HCP). Uniaxial material tests are performed at a wide range of strain rates from 10−3 s−1 to 103 s−1. Moreover, tensile tests are performed at temperature of 25 °C and 200 °C at strain rates of 10−3 s−1, 10−1 s−1, and 102 s−1, respectively. A modified Johnson–Cook type thermal softening model is utilized for the accurate application of the thermal softening effect at different strain rates. The hardening behaviors of the three materials are characterized by comparing the seven sequentially deformed shapes of the projectile from numerical and experimental results of Taylor impact tests.

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