Effective Thermal-Mechanical Modeling of Solder Joints

An effective, two-staged global/local finite element (FE) modeling technique is proposed for characterizing the thermal-mechanical behaviors of solder joints in area array type packages under the temperature cycling. It consists of two essential features: the employment of a compact global FE model in the global analysis, and a two-staged, hybrid constitutive modeling strategy for solder materials, which is to apply the elastoplasticity constitutive law for solder joints in the global analysis during the first temperature rise while utilize the viscoelasticity in the rest of periods. To substantiate the proposed modeling technique, a large-scaled, 3-D FE model with a very fine mesh is constructed as a baseline model. The result derived from the proposed approach is then accordingly compared with those of the baseline solution. From these comparing results, it turns out that the proposed 3-D global/local FE modeling technique is an effective mean for simulating the thermal-mechanical behaviors of solder joints.

Download Full-text

Reliability Design of Multirow Quad Flat Nonlead Packages Based on Numerical Design of Experiment Method

Journal of Electronic Packaging ◽

10.1115/1.4025597 ◽

2013 ◽

Vol 135 (4) ◽

Cited By ~ 4

Author(s):

Guofeng Xia ◽

Fei Qin ◽

Cha Gao ◽

Tong An ◽

Wenhui Zhu

Keyword(s):

Fatigue Life ◽

Thermal Fatigue ◽

Design Of Experiment ◽

Solder Joints ◽

Temperature Cycling ◽

Circuit Board ◽

Fe Model ◽

Fatigue Reliability ◽

Original Design ◽

Factor Combination

A design of experiment (DOE) methodology based on numerical simulation is presented to improve thermal fatigue reliability of multirow quad flat nonlead (QFN) packages. In this method, the influences of material properties, structural geometries, and temperature cycling profiles on thermal fatigue reliability are evaluated, a L27(38) orthogonal array is built based on Taguchi method to figure out optimized factor combination design for promoting thermal fatigue reliability. Analysis of variance (ANOVA) is carried out to examine the influence of factors on the thermal fatigue reliability and to find the significant factors. Anand constitutive model is adopted to describe the viscoplastic behavior of lead-free solder Sn3.0Ag0.5Cu. The stress and strain in solder joints under temperature cycling are studied by 3D finite element (FE) model. The modified Coffin–Manson model is employed to predict the fatigue life of solder joints. Results indicate that the coefficients of thermal expansion (CTE) of printed circuit board (PCB), the height of solder joint, and CTE of epoxy molding compound (EMC) have critical influence on thermal fatigue life of solder joints. The fatigue life of multirow QFN package with original design is 767 cycles, which can be substantially improved by 5.43 times to 4165 cycles after the optimized factor combination design based on the presented method.

Download Full-text

Evolution of knowledge on meniscal biomechanics: a 40 year perspective

BMC Musculoskeletal Disorders ◽

10.1186/s12891-021-04492-2 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Amin Mohamadi ◽

Kaveh Momenzadeh ◽

Aidin Masoudi ◽

Kempland C. Walley ◽

Kenny Ierardi ◽

...

Keyword(s):

Future Research ◽

Fe Model ◽

Cruciate Ligaments ◽

Fe Modeling ◽

Meniscal Tears ◽

Medical Subject Headings ◽

Model Studies ◽

The Past ◽

Mesh Terms ◽

Kinematic Studies

Abstract Background Knowledge regarding the biomechanics of the meniscus has grown exponentially throughout the last four decades. Numerous studies have helped develop this knowledge, but these studies have varied widely in their approach to analyzing the meniscus. As one of the subcategories of mechanical phenomena Medical Subject Headings (MeSH) terms, mechanical stress was introduced in 1973. This study aims to provide an up-to-date chronological overview and highlights the evolutionary comprehension and understanding of meniscus biomechanics over the past forty years. Methods A literature review was conducted in April 2021 through PubMed. As a result, fifty-seven papers were chosen for this narrative review and divided into categories; Cadaveric, Finite element (FE) modeling, and Kinematic studies. Results Investigations in the 1970s and 1980s focused primarily on cadaveric biomechanics. These studies have generated the fundamental knowledge basis for the emergence of FE model studies in the 1990s. As FE model studies started to show comparable results to the gold standard cadaveric models in the 2000s, the need for understanding changes in tissue stress during various movements triggered the start of cadaveric and FE model studies on kinematics. Conclusion This study focuses on a chronological examination of studies on meniscus biomechanics in order to introduce concepts, theories, methods, and developments achieved over the past 40 years and also to identify the likely direction for future research. The biomechanics of intact meniscus and various types of meniscal tears has been broadly studied. Nevertheless, the biomechanics of meniscal tears, meniscectomy, or repairs in the knee with other concurrent problems such as torn cruciate ligaments or genu-valgum or genu-varum have not been extensively studied.

Download Full-text

Modeling Method of Constitutive Law of Rubber Hyperelasticity Based on Finite Element Simulations

Rubber Chemistry and Technology ◽

10.5254/1.3547739 ◽

2003 ◽

Vol 76 (1) ◽

pp. 271-285 ◽

Cited By ~ 21

Author(s):

Li-Rong Wang ◽

Zhen-Hua Lu

Keyword(s):

Finite Element ◽

Finite Element Simulations ◽

Constitutive Law ◽

Modeling Technique ◽

Characteristic Analysis ◽

Rubber Material ◽

Element Simulation ◽

Tension And Compression ◽

Nonlinear Elastic ◽

Elastic Characteristics

Abstract This paper is to present a method and procedure for modeling the constitutive law of anti-vibration rubber hyperelasticity based on finite element simulations. The hyperelasticity of rubber-like material is briefly summarized first. Then a method and procedure for determining an accurate constitutive law of rubber hyperelasticity from uniaxial tension and compression experiment data is presented and implemented. Due to nonlinear elastic properties of rubber and application limitations of various forms of constitutive law, results of finite element simulation to rubber material experiments show that different forms of constitutive law have to be adopted in different ranges of strain. The proposed procedure to obtain an appropriate constitutive law of rubber hyperelasticity of vibration isolator provides engineers with an effective modeling technique for design and analysis of anti-vibration rubber components. Finally, models of three kinds of rubber materials of a hydraulically damped rubber mount (HDM) are determined by tests and finite element simulations and applied to static and dynamic characteristic analysis of the HDM. The predicted elastic characteristics of the HDM and its major rubber components agree well with experimental data, which demonstrates the practicability and effectiveness of the presented modeling technique to modeling engineering rubber materials in dynamic systems.

Download Full-text

Multidirection Validation of a Finite Element 50th Percentile Male Hybrid III Anthropomorphic Test Device for Spaceflight Applications

Journal of Biomechanical Engineering ◽

10.1115/1.4041906 ◽

2019 ◽

Vol 141 (3) ◽

Cited By ~ 1

Author(s):

Derek A. Jones ◽

James P. Gaewsky ◽

Mona Saffarzadeh ◽

Jacob B. Putnam ◽

Ashley A. Weaver ◽

...

Keyword(s):

Finite Element ◽

Injury Risk ◽

Fe Model ◽

Fe Modeling ◽

Test Device ◽

Qualitative And Quantitative ◽

Hybrid Iii ◽

Physical Tests ◽

Quantitative Results ◽

Male Hybrid

The use of anthropomorphic test devices (ATDs) for calculating injury risk of occupants in spaceflight scenarios is crucial for ensuring the safety of crewmembers. Finite element (FE) modeling of ATDs reduces cost and time in the design process. The objective of this study was to validate a Hybrid III ATD FE model using a multidirection test matrix for future spaceflight configurations. Twenty-five Hybrid III physical tests were simulated using a 50th percentile male Hybrid III FE model. The sled acceleration pulses were approximately half-sine shaped, and can be described as a combination of peak acceleration and time to reach peak (rise time). The range of peak accelerations was 10–20 G, and the rise times were 30–110 ms. Test directions were frontal (−GX), rear (GX), vertical (GZ), and lateral (GY). Simulation responses were compared to physical tests using the correlation and analysis (CORA) method. Correlations were very good to excellent and the order of best average response by direction was −GX (0.916±0.054), GZ (0.841±0.117), GX (0.792±0.145), and finally GY (0.775±0.078). Qualitative and quantitative results demonstrated the model replicated the physical ATD well and can be used for future spaceflight configuration modeling and simulation.

Download Full-text

Studies on the Dynamic Behavior of a Printed Circuit Board

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8126 ◽

1999 ◽

Author(s):

Hongfang Wang ◽

Mei Zhao

Keyword(s):

Natural Frequency ◽

Dynamic Behavior ◽

Fundamental Frequency ◽

Strong Influence ◽

Printed Circuit Board ◽

External Environment ◽

Circuit Board ◽

Fe Modeling ◽

Printed Circuit ◽

Modeling Strategy

Abstract The dynamic behavior of printed circuit (PC) boards exercises strong influence on the reliability of electronic equipment. In this paper, the dynamic behavior of a PC board is studied by means of computation and verified by experiment with results compared favorably. This shows that FE modeling strategy used is sound. In general, excitement frequencies induced by external environment are in the range from several Hz to several hundred Hz. In order to avoid product failures due to resonance, it is desirable to make the fundamental natural frequency of PC boards as high as possible. Two structural modified design methods to raise the fundamental frequency are given with a numerical example.

Download Full-text

Length-Scale-Dependent Micromechanical Modeling for Precipitate Hardening in Inconel 718 Superalloy

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.315.84 ◽

2021 ◽

Vol 315 ◽

pp. 84-89

Author(s):

Chang Feng Wan ◽

Dong Feng Li ◽

Hai Long Qin ◽

Ji Zhang ◽

Zhong Nan Bi

Keyword(s):

Dislocation Density ◽

Strain Gradient ◽

Inconel 718 ◽

Micromechanical Modeling ◽

Fe Model ◽

Gradient Effect ◽

Fine Mesh ◽

Geometrically Necessary Dislocation ◽

In718 Superalloy ◽

Inconel 718 Superalloy

In this paper, a micromechanical finite element (FE) model has been proposed to investigate the effect of the nanoscale precipitates on the development of microplasticity for Inconel 718 (IN718) superalloy. A strain gradient crystal plasticity formulation has been developed with the considerations of the evolution of statistically stored dislocation density and geometrically necessary dislocation density. The mesh convergence has been examined, showing that sufficiently fine mesh is required in the FE model. The results show that the model with strain gradient effect incorporated shows less peak plastic strain and higher value of dislocation density than the model with no strain gradient effect. The present study indicates that the strain hardening process at the scale of strengthening precipitate is mainly governed by the evolution of geometrically necessary dislocation densities.

Download Full-text

Rapid Temperature Cycling (RTC) Methodology for Reliability Assessment of Solder Interconnection in Tape Ball Grid Array (TBGA) Assembly

Journal of Electronic Packaging ◽

10.1115/1.2056574 ◽

2005 ◽

Vol 127 (4) ◽

pp. 466-473 ◽

Cited By ~ 4

Author(s):

B. L. Chen ◽

X. Q. Shi ◽

G. Y. Li ◽

K. H. Ang ◽

Jason P. Pickering

Keyword(s):

Solder Joints ◽

Reliability Assessment ◽

Ball Grid Array ◽

Temperature Cycling ◽

Rapid Temperature ◽

Reliability Of Solder Joints ◽

Solder Joint Fatigue ◽

Time Required ◽

Failure Location

In this study, a thermoelectric cooler-based rapid temperature cycling (RTC) testing method was established and applied to assess the long term reliability of solder joints in tape ball grid array (TBGA) assembly. This RTC testing methodology can significantly reduce the time required to determine the reliability of electronic packaging components. A three-parameter Weibull analysis characterized with a parameter of failure free time was used for assembly reliability assessment. It was found that the RTC not only speedily assesses the long-term reliability of solder joints within days, but also has the similar failure location and failure mode observed in accelerated temperature cycling (ATC) test. Based on the RTC and ATC reliability experiments and the modified Coffin-Manson equation, the solder joint fatigue predictive life can be obtained. The simulation results were found to be in good agreement with the test results from the RTC. As a result, a new reliability assessment methodology was established as an alternative to ATC for the evaluation of long-term reliability of electronic packages.

Download Full-text

Nonlinear poroplastic model of ventricular dilation in hydrocephalus

Journal of Neurosurgery ◽

10.3171/jns/2008/109/7/0100 ◽

2008 ◽

Vol 109 (1) ◽

pp. 100-107 ◽

Cited By ~ 15

Author(s):

Shahan Momjian ◽

Denis Bichsel

Keyword(s):

Brain Tissue ◽

Normal Pressure ◽

Porous Matrix ◽

Brain Parenchyma ◽

Plastic Behavior ◽

Fe Model ◽

Mechanical Behaviors ◽

Ventricular Dilation ◽

Numerical Finite Element ◽

The Brain

Object The mechanism of ventricular dilation in normal-pressure hydrocephalus remains unclear. Numerical finite-element (FE) models of hydrocephalus have been developed to investigate the biomechanics of ventricular enlargement. However, previous linear poroelastic models have failed to reproduce the relatively larger dilation of the horns of the lateral ventricles. In this paper the authors instead elaborated on a nonlinear poroplastic FE model of the brain parenchyma and studied the influence of the introduction of these potentially more realistic mechanical behaviors on the prediction of the ventricular shape. Methods In the proposed model the elasticity modulus varies as a function of the distension of the porous matrix, and the internal mechanical stresses are relaxed after each iteration, thereby simulating the probable plastic behavior of the brain tissue. The initial geometry used to build the model was extracted from CT scans of patients developing hydrocephalus, and the results of the simulations using this model were compared with the real evolution of the ventricular size and shape in the patients. Results The authors' model predicted correctly the magnitude and shape of the ventricular dilation in real cases of acute and chronic hydrocephalus. In particular, the dilation of the frontal and occipital horns was much more realistic. Conclusions This finding suggests that the nonlinear and plastic mechanical behaviors implemented in the present numerical model probably occur in reality. Moreover, the availability of such a valid FE model, whose mechanical parameters approach real mechanical properties of the brain tissue, might be useful in the further modeling of ventricular dilation at a normal pressure.

Download Full-text

Numerical Modelling of FRCM Materials Using Augmented-FEM

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.817.23 ◽

2019 ◽

Vol 817 ◽

pp. 23-29

Author(s):

Santi Urso ◽

Houman A. Hadad ◽

Chiara Borsellino ◽

Antonino Recupero ◽

Qing Da Yang ◽

...

Keyword(s):

Mechanical Properties ◽

Tensile Test ◽

Failure Modes ◽

Elevated Temperatures ◽

The United States ◽

Design Guidelines ◽

Constitutive Law ◽

Analytical Models ◽

Fiber Reinforced Polymers ◽

Fe Model

The use of externally-bonded composite materials for strengthening and rehabilitation of existing structures is among the most popular reinforcement techniques. Technologies, such as Fabric Reinforced Cementitious Matrix (FRCM) have been recently developed to address some of the issues of Fiber Reinforced Polymers (FRP), such as sensitivity to elevated temperatures and UV, impermeability, restricted application in presence of moisture or uneven substrate. For a detailed strengthening design with FRCM composites, the mechanical properties of the materials are required. Analytical models in literature discuss the interaction between the FRCM matrix and fabric using a fracture mechanics approach. These analytical laws were simplified using a trilinear curve in which a constant branch correlated to the friction is added. In the United States, “Acceptance Criteria AC434” includes the test methods to evaluate the mechanical properties of the FRCM through a direct tensile test which uses clevis grips. The material characterization per AC434 is in harmony with ACI 549.4R design guidelines. This study deals with the analysis of FRCM materials using 2D Augmented-Finite Element Method (A-FEM) approach. Constitutive material behaviors were used to implement on A-FE model, which can predict the failure modes of the composite material. The damage of the mortar was described by a trilinear curve, and the number and position of the cracks were fixed preliminarily. The fabric was modelled as a continuum layer attached to the mortar with no-thickness cohesive elements. The cohesive law between fabric and mortar was taken from the literature. The tensile test on the FRCM coupon with one layer of fabric was numerically modeled and compared to the experimental stress-strain curves. Results show that the numerical curves matched the experimental ones and capture the three branches of the FRCM constitutive law as well as the failure mode. This modelling tool will allow researchers to predict the constitutive law of an FRCM mater

Download Full-text