A Revised Anand Constitutive Model for Lead Free Solder That Includes Aging Effects

2013 ◽  
Author(s):  
Mohammad Motalab ◽  
Munshi Basit ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Constitutive Equations ◽  
Mechanical Tests ◽  
The Other ◽  
Lead Free ◽  
Model Parameters ◽  
Aging Effects ◽  
Stress Strain ◽  
Profile Matching

Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle model) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In this study, we have developed a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stress-strain tests on SAC305 samples that were aged for various durations (0–6 months) at temperature of 100 C. The stress-strain data were measured at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). The mechanical tests have been performed using both water quenched (WQ) and reflowed (RF) samples (two unique specimen microstructures). In the case of the water quenched samples, there is rapid microstructural transitioning during the brief time that occurs between placing molten solder into the glass tubes and immersing the tubes in water bath. On the other hand, the reflowed samples are first cooled by water quenching, and then sent through a reflow oven to re-melt the solder in the tubes and subject them to a desired temperature profile matching that used in PCB assembly. As expected, the observed mechanical properties of water quenched samples were better (higher in magnitude) than the corresponding mechanical properties of the reflowed samples. Although the differences in elastic modulus between the water quenched and reflowed samples are small, significant differences are present for the yield and ultimate tensile stresses (for each aging condition). For both the water quenched and reflowed specimens, significant degradation of the mechanical properties has been observed with aging. Using the measured stress-strain and creep data, mathematical expressions have been developed for the evolution of the Anand model parameter with aging time. Our results show that 2 of the 9 constants remain essentially constant during aging, while the other 7 show large changes (30–70%) with up to 6 months of aging. The revised Anand constitutive equations for solder with aging effects have also been incorporated into commercial finite element codes (ANSYS and ABAQUS).

Viscoplastic Constitutive Model for Lead-Free Solder Including Effects of Silver Content, Solidification Profile, and Severe Aging

2015 ◽  
Author(s):  
Munshi Basit ◽  
Mohammad Motalab ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Silver Content ◽  
Material Behavior ◽  
Lead Free ◽  
Model Parameters ◽  
Strain Rates ◽  
Lead Free Solder ◽  
Stress Strain ◽  
Free Solder

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 viscoplastic 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 this work, an investigation on the Anand constitutive model and its application to SAC solders of various Ag contents (i.e. SACN05, with N = 1, 2, 3, 4) has been performed. For each alloy, both water quenched (WQ) and reflowed (RF) solidification profiles were utilized to establish two unique specimen microstructures, and the same reflow profile was used for all four of the SAC alloys so that the results could be compared and the effects of Ag content could be studied systematically. In addition, we have performed tensile testing on reflowed specimens subjected to 6 months of aging at 100 C. After this level of aging, any further changes in the mechanical response and properties will be rather small. Thus, the results for these tests can be regarded as approaching the highest level of mechanical behavior degradation possible for a “severely aged” lead free solder material. The nine Anand parameters were determined for each unique solder alloy and microstructure from a set of stress strain 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. As expected, the mechanical properties (modulus and strength) increase with the percentage of Ag content, and these changes strongly affect the Anand parameters. The sensitivity of the mechanical properties and Anand parameters to silver content is higher at lower silver percentages (1–2%). Also, the observed mechanical properties of water quenched samples were better (higher in magnitude) than the corresponding mechanical properties of the reflowed samples. Although the differences in elastic modulus between the water quenched and reflowed samples are relatively small, significant differences are present for the yield and ultimate tensile stresses of all four SAC alloys. The changes in the Anand model parameters after severe aging (6 months at 100 °C) were significant. The measured experimental results have been used to illustrate the range of values possible for Anand parameters for the SACN05 alloys. The upper extreme was the water quenched limit, where the materials have extremely fine microstructures and high mechanical properties. The lower extreme was the severely aged limit, where the materials have extremely coarsened microstructures and highly degraded mechanical properties. While further degradations are certainly possible with even further aging, the limiting values found for a severely aged SAC alloy can be used by designers as a conservative set of constitutive parameters representing the lower end of the material properties for that alloy. After deriving the Anand parameters for each alloy and microstructure, 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 Simulation of thermal cycle aging process on fiber-reinforced polymers by extended finite element method

2017 ◽  
Vol 52 (14) ◽  
pp. 1947-1958 ◽  
Author(s):  
Sergio González ◽  
Gianluca Laera ◽  
Sotiris Koussios ◽  
Jaime Domínguez ◽  
Fernando A Lasagni
Keyword(s):  
Finite Element ◽  
Degradation Process ◽  
Damage Mechanism ◽  
Fiber Reinforced Polymers ◽  
Model Parameters ◽  
Suitable Model ◽  
Fiber Reinforced ◽  
Aging Effects ◽  
Extended Finite Element ◽  
Element Analysis

The simulation of long life behavior and environmental aging effects on composite materials are subjects of investigation for future aerospace applications (i.e. supersonic commercial aircrafts). Temperature variation in addition to matrix oxidation involves material degradation and loss of mechanical properties. Crack initiation and growth is the main damage mechanism. In this paper, an extended finite element analysis is proposed to simulate damage on carbon fiber reinforced polymer as a consequence of thermal fatigue between −50℃ and 150℃ under atmospheres with different oxygen content. The interphase effect on the degradation process is analyzed at a microscale level. Finally, results are correlated with the experimental data in terms of material stiffness and, hence, the most suitable model parameters are selected.

Analysis of the Deformation Characteristics of Loess Based on Thermal–Mechanical Coupling under an Energy Internet

2021 ◽  
Author(s):  
Zengle Li ◽  
Bin Zhi ◽  
Enlong Liu
Keyword(s):  
Mechanical Properties ◽  
Temperature Change ◽  
Clean Energy ◽  
Model Parameters ◽  
Stress Strain ◽  
Energy Internet ◽  
Influence Of Temperature ◽  
Medium Model ◽  
Strain Relationship ◽  
Natural Loess

In response to the major challenges faced by China’s transition to green low-carbon energy under the dual-carbon goal, the use of energy Internet cross-boundary thinking will help to develop research on the integration of renewable clean energy and buildings. Energy piles are a new building-energy-saving technology that uses geothermal energy in the shallow soil of the Earth’s surface as a source of cold (heat) to achieve heating in winter and cooling in summer. It is a complex thermomechanical working process that changes the temperature of the rock and soil around the pile, and the temperature change significantly influences the mechanical properties of natural loess. Although the soil temperature can be easily and quickly obtained by using sensors connected to the Internet of Things, the mechanical properties of natural loess will change greatly under the influence of temperature. To explore the influence of temperature on the stress–strain relationship of structural loess, the undrained triaxial consolidation tests were carried out under different temperatures (5, 20, 50 and 70∘C) and different confining pressures (50, 100, 200 and 400[Formula: see text]kPa), and a binary-medium model was introduced to simulate the stress–strain relationship. By introducing the damage rate under temperature change conditions, a binary-medium model of structural loess under variable temperature conditions was established, and the calculation method of the model parameters was proposed. Finally, the calculated results were compared with the test results. The calculation results showed that the established model has good applicability.

scholarly journals Influence of the Mechanical Properties of Elastoplastic Materials on the Nanoindentation Loading Response

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4842
Author(s):  
Huanping Yang ◽  
Wei Zhuang ◽  
Wenbin Yan ◽  
Yaomian Wang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
The Other ◽  
Equivalent Model ◽  
Strain Hardening Exponent ◽  
Mechanical Parameters ◽  
The Finite Element Method ◽  
Fem Simulations ◽  
Elastoplastic Materials

The nanoindentation loading response of elastoplastic materials was simulated by the finite element method (FEM). The influence of the Young’s modulus E, yield stress σy, strain hardening exponent n and Poisson’s ratio ν on the loading response was investigated. Based on an equivalent model, an equation with physical meaning was proposed to quantitatively describe the influence. The calculations agree well with the FEM simulations and experimental results in literature. Comparisons with the predictions using equations in the literature also show the reliability of the proposed equation. The investigations show that the loading curvature C increases with increasing E, σy, n and ν. The increase rates of C with E, σy, n and ν are different for their different influences on the flow stress after yielding. It is also found that the influence of one of the four mechanical parameters on C can be affected by the other mechanical parameters.

FEA Based Reliability Predictions for PBGA Packages Subjected to Isothermal Aging Prior to Thermal Cycling

2015 ◽  
Author(s):  
Munshi Basit ◽  
Mohammad Motalab ◽  
Jeffrey C. Suhling ◽  
John L. Evans ◽  
Pradeep Lall
Keyword(s):  
Finite Element ◽  
Solder Joint ◽  
Thermal Cycling ◽  
Isothermal Aging ◽  
Material Behavior ◽  
Lead Free ◽  
Stress Strain ◽  
Solder Material ◽  
Free Solder ◽  
Temperature Aging

The microstructure, mechanical response, and failure behavior of lead free solder joints in electronic assemblies are constantly evolving when exposed to isothermal aging and/or thermal cycling environments. In our prior work on aging effects, we have demonstrated that the observed material behavior degradations of Sn-Ag-Cu (SAC) lead free solders during room temperature aging (25 C) and elevated temperature aging (50, 75, 100, 125, and 150 C) were unexpectedly large. The measured stress-strain data demonstrated large reductions in stiffness, yield stress, ultimate strength, and strain to failure (up to 50%) during the first 6 months after reflow solidification. In this study, we have used both accelerated life testing and finite element modeling to explore how prior isothermal aging affects the overall reliability of PBGA packages subjected to thermal cycling. In the experimental work, an extensive test matrix of thermal cycling reliability testing has been performed using a test vehicle incorporating several sizes (5, 10, 15, 19 mm) of BGA daisy chain components with 0.4 and 0.8 mm solder joint pitches (SAC305). PCB test boards with 3 different surface finishes (ImAg, ENIG and ENEPIG) were utilized. In this paper, we concentrate on the reporting the results for a PBGA component with 15 mm body size. Before thermal cycling began, the assembled test boards were divided up into test groups that were subjected to several sets of aging conditions (preconditioning) including 0, 6, and 12 months aging at T = 125 °C. After aging, the assemblies were subjected to thermal cycling (−40 to +125 °C) until failure occurred. The Weibull data failure plots have demonstrated that the thermal cycling reliabilities of pre-aged assemblies were significantly less than those of non-aged assemblies. A three-dimensional finite element model of the tested 15 mm PBGA packages was also developed. The cross-sectional details of the solder ball and the internal structure of the BGA were examined by scanning electron microscopy (SEM) to capture the real geometry of the package. Simulations of thermal cycling from −40 to 125 C were performed. To include the effects of aging in the calculations, we have used a revised set of Anand viscoplastic stress-strain relations for the SAC305 Pb-free solder material that includes material parameters that evolve with the thermal history of the solder material. The accumulated plastic work (energy density dissipation) was used is the failure variable; and the Darveaux approach to predict crack initiation and crack growth was applied with aging dependent parameters to estimate the fatigue lives of the studied packages. We have obtained good correlation between our new reliability modeling procedure that includes aging and the measured solder joint reliability data. As expected from our prior studies on degradation of SAC material properties with aging, the reliability reductions were more severe for higher aging temperature and longer aging times.

scholarly journals Flexural Capacity of Steel-Concrete Composite Beams under Hogging Moment

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Liu ◽  
Fa-xing Ding ◽  
Xue-mei Liu ◽  
Zhi-wu Yu ◽  
Zhe Tan ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Flexural Strength ◽  
Composite Beams ◽  
The Other ◽  
Transverse Reinforcement ◽  
Beam Length ◽  
Simply Supported ◽  
Shear Connection ◽  
Abaqus Software

This study investigates the flexural strength of simply supported steel-concrete composite beams under hogging moment. A total of 24 composite beams are included in the experiments, and ABAQUS software is used to establish finite element (FE) models that can simulate the mechanical properties of composite beams. In a parametric study, the influences of several major parameters, such as shear connection degree, stud arrangement and diameter, longitudinal and transverse reinforcement ratios, loading manner, and beam length, on flexural strength were investigated. Thereafter, three standards, namely, GB 50017, Eurocode 4, and BS 5950, were used to estimate the flexural strength of the composite beams. These codes were also compared with experimental and numerical results. Results indicate that GB 50017 may provide better estimations than the other two codes.

Effects of Thermal Cycling on the Mechanical and Microstructural Evolution of SAC305 Lead-Free Solder

2019 ◽  
Author(s):  
S. M. Kamrul Hasan ◽  
Abdullah Fahim ◽  
Jeffrey C. Suhling ◽  
Sa’d Hamasha ◽  
Pradeep Lall
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
High Temperature ◽  
Thermal Cycling ◽  
Microstructural Evolution ◽  
Lead Free ◽  
Lead Free Solder ◽  
Temperature Extreme ◽  
Aging Effects ◽  
Free Solder

Abstract Lead free electronic assemblies are often subjected to thermal cycling during qualification testing or during actual use. The dwell periods at the high temperature extreme during thermal cycling cause thermal aging phenomena in the solder material, including microstructural evolution and material property degradation. In addition, lead free solders can also experience aging effects during the ramp periods between the low and high temperature extremes of the cycling. In this study, the mechanical behavior evolution occurring in SAC305 lead free solder subjected to various thermal cycling exposures has been investigated. Uniaxial test specimens were prepared by reflowing solder in rectangular cross-section glass tubes with a controlled temperature profile. After reflow solidification, the samples were placed into the environmental chamber and thermally cycled from −40 C to +125 C under a stress-free condition (no load). Several thermal cycling profiles were examined including: (1) 90 minute cycles with 15 minutes ramps and 30 minutes dwells, (2) air-to-air thermal shock exposures with 30 minutes dwells and near instantaneous ramps, (3) 30 minute cycles with 15 minutes ramps and no dwells (saw tooth profile), (4) 150 minute cycles with 45 minutes ramps and 30 minutes dwells, and (5) no cycling (simple aging at the high temperature extreme). For each profile, 10–15 samples were cycled for various durations of cycling (e.g. 48, 96, and 240 cycles), which were equivalent to various aging times at the high temperature extreme of T = 125 C. After cycling, the stress-strain curves and mechanical properties including effective elastic modulus and Ultimate Tensile Strength (UTS) of all the cycled samples were measured. For each cycling profile, the evolutions of the mechanical properties were characterized as a function of the cycling duration, as well as the net aging time at the high temperature extreme. Comparison of the results of various thermal cycling profiles showed that the detrimental effects of aging are accelerated in a thermal cycling environment. Furthermore, microstructure evolution during thermal cycling has also been investigated to validate the observed mechanical properties degradation. The test results revealed that the mechanical properties degradation of SAC305 are higher in thermal cycling compared to simple equivalent aging. For example, the elastic modulus and UTS of SAC305 reduced by 41%, and 38%, respectively after 5 days aging whereas these properties reduced by 69%, and 51%, respectively after 5 days equivalent aging using thermal cycling profile #4 (240 cycles).

Mechanical Properties of Ion-Irradiated Stainless Steel Determined by Nanoindentation Tests and Finite Element Analyses

2020 ◽  
Author(s):  
Jae Min Sim ◽  
Yoon-Suk Chang ◽  
Byeong Seo Kong ◽  
Changheui Jang
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Test Data ◽  
Radiation Effects ◽  
Ion Irradiation ◽  
Nanoindentation Test ◽  
Finite Element Analyses ◽  
Stress Strain ◽  
Term Operation ◽  
Constitutive Parameters

Abstract While austenitic stainless steels (ASSs) have been widely adopted for reactor vessel internals because of their excellent material properties, diverse ageing-related degradation may occur due to high temperature, corrosive and neutron radiation environments during operation. In particular, since the change of mechanical properties is a major concern in long-term operation but it is difficult to prepare and handle standard specimens influenced by neutrons, most of experimental researches for enhanced understanding of the radiation effects have been focused on high-energetic ion-irradiation and tests of small specimens. In this study, systematic finite element analyses were carried out to quantify changing mechanical properties based on both virgin and ion-irradiated nanoindentation test data of typical ASS material. First of all, numerical analysis was carried out to obtain unirradiated material constitutive parameters by using trial set along the miniature specimen and comparing test data, and then indentation stress-strain (ISS) curve was derived. Subsequently, ISS was converted into uniaxial stress-strain response taking into account simple correlation. Finally, with regard to the irradiated material, similar analytical procedures were established. 304 SS was irradiated with 2 MeV proton and radioactivity is being measured. Comparison between analysis result and experimental one will be carried out, of which details and key findings will be discussed.

Determining Stress-Strain Behavior of Zr60Cu10Al15Ni15 Bulk Metallic Glass Using Object Oriented Finite Element Analysis

2017 ◽  
Vol 29 ◽  
pp. 1-8 ◽  
Author(s):  
Ketul Arvindbhai Patel ◽  
Ganesh R. Karthikeyan ◽  
S. Vincent
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Metallic Glass ◽  
Strain Analysis ◽  
Indentation Test ◽  
Object Oriented ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior

Determining mechanical properties of Bulk Metallic Glasses (BMGs) requires synthesizing of the alloys in bulk form. However obtaining metallic glass in bulk form is quite challenging due to its tendency towards crystallization. In such circumstances it is beneficial to determine the mechanical properties of materials using finite elemental analysis of microstructures. Thus, in the present investigation, using Object Oriented Finite Element Analysis (OOF2) software package, Stress-Strain analysis has been carried out on Zr60Cu10Al15Ni15 BMG to determine such mechanical properties. Specimen of Zr60Cu10Al15Ni15 BMG exhibiting three microstructurally distinct regions amorphous, partial crystalline and crystalline regions was used for this analysis. The Stress-Strain relationship have been estimated for each of the three distinct phases and the results are validated by determining the Modulus of Elasticity for all the phases and comparing it with the available experimental results from Nano-indentation test.

A finite element study of the pressuremeter test in sand using a nonlinear elastic plastic model

1993 ◽  
Vol 30 (2) ◽  
pp. 348-362 ◽  
Author(s):  
Martin Fahey ◽  
John P. Carter
Keyword(s):  
Finite Element ◽  
Shear Modulus ◽  
Hyperbolic Model ◽  
Type Model ◽  
Model Parameters ◽  
Nonlinear Behaviour ◽  
Stress Strain ◽  
Pressuremeter Test ◽  
Strain Behaviour ◽  
Highly Nonlinear

The stress–strain behaviour of sands is highly nonlinear, even at stresses well below the peak strength of the sand. The hyperbolic model is a reasonable conceptual model for representing the stress–strain behaviour of sand, but some empirical curve fitting is required to obtain a more realistic model for calculation purposes. This can readily be performed for reconstituted samples of sand using laboratory tests. Recent evidence shows that the stiffness of natural sands is often much greater than that of the same sand when reconstituted at the same density and stress state in the laboratory, and it is therefore necessary to use in situ testing methods to determine the stress–strain behaviour of such sands. In this paper, the finite element method is used to simulate pressuremeter tests in a soil modelled using a hyperbolic-type model. It concentrates on the behaviour in unload-reload loops, which are often included in pressuremeter tests to measure shear modulus. The effect on the whole unload-reload loop of varying some of the model parameters is examined. The results are compared with a high-quality pressuremeter test in sand. It is concluded that, though the results to date are encouraging, some further experimental work is required to verify some of the features of the model. Key words : pressuremeter test, hyperbolic model, nonlinear behaviour, initial shear modulus, sand behaviour.

Sign in / Sign up

Export Citation Format

Share Document