Reliability Estimation of Solder Joint Utilizing Thermal Fatigue Models

2005 ◽  
Vol 297-300 ◽  
pp. 1816-1821
Author(s):  
Ouk Sub Lee ◽  
No Hoon Myoung ◽  
Dong Hyeok Kim
Keyword(s):  
Solder Joint ◽  
Thermal Fatigue ◽  
Failure Probability ◽  
Coefficient Of Thermal Expansion ◽  
Probability Model ◽  
Limit State ◽  
Reliability Estimation ◽  
State Function ◽  
First Order ◽  
Reliability Method

The differences of coefficient of thermal expansion (CTE) of component and FR-4 board connected by solder joint generally cause the dissimilarity in shear strain and failure in solder joint when they are heated. The first order Taylor series expansion of the limit state function (LSF) incorporating with thermal fatigue models is used in order to estimate the failure probability of solder joints under heated condition. Various thermal fatigue models, classified into five categories: categories four such as plastic strain-based, creep strain-based, energy-based, and damage-based except stress-based, are utilized in this study. The effects of random variables such as CTE, distance of the solder joint from neutral point (DNP), temperature variation and height of solder on the failure probability of the solder joint are systematically investigated by using a failure probability model with the first order reliability method (FORM) and thermal fatigue models.

Reliability Evaluation of BGA Solder Joints by Using Thermal Fatigue Models

2005 ◽  
Author(s):  
Ouk Sub Lee ◽  
No Hoon Myoung ◽  
Dong Hyeok Kim
Keyword(s):  
Solder Joint ◽  
Thermal Cycling ◽  
Thermal Fatigue ◽  
Failure Probability ◽  
Solder Joints ◽  
State Function ◽  
Mechanical Loads ◽  
First Order ◽  
Reliability Method ◽  
Fatigue Model

The use of Ball Grid Array (BGA) interconnects utilizing the BGA solder joint has grown rapidly because of its small volume and diversity of its application. Therefore, the continuous quantification and refinement of BGA solder joint in terms of its reliability are required. The creep and cyclically applied mechanical loads generally cause metal fatigue on the BGA solder joint which inevitably leads to an electrical discontinuity. In the field application, the BGA solder joints are known to experience mechanical loads during temperature changes caused by power up/down events as the result of the Coefficient of Thermal Expansion (CTE) mismatch between the substrate and the Si die. In this paper, extremely small resistance changes in the lead free joints corresponding to the through-cracks generated by the thermal fatigue were measured and the failure was defined in terms of anomalous changes in the joint resistance. Furthermore, the reliability of BGA solder joints under thermal cycling was evaluated by using a criterion that may define and distinguish a failure in the solder joint. Any changes in circuit resistance according to the accumulated damage induced by the thermal cycling in the joint were recorded and evaluated by the First Order Reliability Method (FORM) procedure in order to quantify the reliability of solder joint. The first order Taylor series expansion of the limit state function incorporating with thermal fatigue models is used in order to estimate the failure probability of solder joints under heated condition. Various thermal fatigue models are utilized in this study. Models based on various plastic-strain rates such as Coffin-Manson fatigue model, total strain fatigue model and Solomon fatigue model are utilized in this study. The effects of random variables such as the CTE, the pitch of solder joint, the diameter of solder joint, and the CTE difference solder joints on the failure probability of the solder joint are systematically investigated by using a failure probability model with the FORM.

Reliability Estimation of Solder Joint by Using the Failure Probability Models

2006 ◽  
Vol 326-328 ◽  
pp. 621-624 ◽  
Author(s):  
Ouk Sub Lee ◽  
Man Jae Hur ◽  
Jai Sug Hawong ◽  
No Hoon Myoung ◽  
Dong Hyeok Kim
Keyword(s):  
Solder Joint ◽  
Boundary Conditions ◽  
Failure Probability ◽  
Coefficient Of Thermal Expansion ◽  
Bending Moment ◽  
Fatigue Loading ◽  
Reliability Estimation ◽  
Probability Models ◽  
Reliability Method ◽  
The Difference

The differences in the coefficient of thermal expansion (CTE) between the chip and the FR-4 board generate the shear strains and the bending moment in the solder joint. It seems to be a main cause of failure in the solder joint when the chip and the FR-4 board are heated repeatedly. Thus, the fatigue loading induced by thermal cycling is a major concern in the reliability of the solder joint. The magnitude of shear strain and the final failure are known to be influenced by varying boundary conditions such as the difference of CTE, the height of solder, the distance of the solder joint from the neutral point (DNP) and the temperature variation. In this paper, the effects of boundary conditions on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Monte Carlo Simulation (MCS). Furthermore, the stiffness of the solder joint is considered to investigate the influence at the failure probability.

Effect of Boundary Conditions of Failure Pressure Models on Reliability Estimation of Buried Pipelines

2004 ◽  
Vol 261-263 ◽  
pp. 803-808
Author(s):  
Ouk Sub Lee ◽  
Jang Sik Pyun ◽  
Si Won Hwang ◽  
Kyoo Sung Cho
Keyword(s):  
Boundary Conditions ◽  
Failure Probability ◽  
Probability Model ◽  
Limit State ◽  
Fluid Pressure ◽  
Taylor Series Expansion ◽  
Reliability Estimation ◽  
State Function ◽  
Buried Pipelines ◽  
Failure Pressure

This paper presents the effect of boundary conditions of various failure pressure models published for the estimation of failure pressure. Furthermore, this approach is extended to the failure prediction with the help of a failure probability model. The first order Taylor series expansion of the limit state function is used in order to estimate the probability of failure associated with each corrosion defect in buried pipelines for long exposure periods with unit of years. The effects of random variables such as defect depth, pipe diameter, defect length, fluid pressure, corrosion rate, material yield stress, material ultimate tensile strength and pipe thickness on the failure probability of the buried pipelines are systematically investigated for the corrosion pipeline by using an adapted failure probability model and varying failure pressure model.

Effects of Various Types of Distribution on Probabilistic Method and FAD

2007 ◽  
Vol 353-358 ◽  
pp. 2561-2564
Author(s):  
Ouk Sub Lee ◽  
Dong Hyeok Kim
Keyword(s):  
Failure Probability ◽  
Probabilistic Method ◽  
Limit State ◽  
Random Variables ◽  
Reliability Estimation ◽  
Probabilistic Methods ◽  
State Function ◽  
Operating Pressure ◽  
Lognormal Distributions ◽  
Reliability Method

The reliability estimation of pipeline is performed in accordance with the probabilistic methods such as the FORM (first order reliability method) and the SORM (second order reliability method). A limit state function has been formulated with help of the FAD (failure assessment diagram). Various types of distribution of random variables are assumed to investigate its effect on the failure probability. It is noted that the failure probability increases with the increase of the dent depth, the operating pressure and the outside radius, and the decrease of the wall thickness. Furthermore it is found that the failure probability for the random variables having the Weibull distribution is larger than those of the normal and the lognormal distributions.

Effect of Boundary Conditions of Failure Pressure Models on Reliability Estimation of Buried Pipelines

2003 ◽  
Author(s):  
Ouk Sub Lee ◽  
Jang Sik Pyun ◽  
Dong Hyeok Kim
Keyword(s):  
Boundary Conditions ◽  
Failure Probability ◽  
Probability Model ◽  
Limit State ◽  
Fluid Pressure ◽  
Random Variables ◽  
Reliability Estimation ◽  
State Function ◽  
Buried Pipelines ◽  
Failure Pressure

This paper presents the effect of boundary conditions of various failure pressure models published for the estimation of failure pressure. Furthermore, this approach is extended to the failure prediction with the help of a failure probability model. The first order Taylor series expansion of the limit state function is used in order to estimate the probability of failure associated with each corrosion defect in buried pipelines for long exposure period with unit of years. A failure probability model based on the von-Mises failure criterion is adapted. The log-normal and standard normal probability functions for varying random variables are adapted. The effects of random variables such as defect depth, pipe diameter, defect length, fluid pressure, corrosion rate, material yield stress, material ultimate tensile strength and pipe thickness on the failure probability of the buried pipelines are systematically investigated for the corrosion pipeline by using an adapted failure probability model and varying failure pressure model.

Reliability of Buried Pipeline Using a Theory of Probability of Failure

2006 ◽  
Vol 110 ◽  
pp. 221-230 ◽  
Author(s):  
Ouk Sub Lee ◽  
Dong Hyeok Kim ◽  
Seon Soon Choi
Keyword(s):  
Failure Probability ◽  
Probability Of Failure ◽  
Operating Conditions ◽  
Reliability Estimation ◽  
Design Parameters ◽  
Buried Pipeline ◽  
Safety Level ◽  
First Order ◽  
Reliability Method ◽  
Corrosion Defects

The reliability estimation of buried pipeline with corrosion defects is presented. The reliability of corroded pipeline has been estimated by using a theory of probability of failure. And the reliability has been analyzed in accordance with a target safety level. The probability of failure is calculated using the FORM (first order reliability method). The changes in probability of failure corresponding to three corrosion models and eight failure pressure models are systematically investigated in detail. It is highly suggested that the plant designer should select appropriate operating conditions and design parameters and analyze the reliability of buried pipeline with corrosion defects according to the probability of failure and a required target safety level. The normalized margin is defined and estimated accordingly. Furthermore, the normalized margin is used to predict the failure probability using the fitting lines between failure probability and normalized margin.

Vibration Fatigue Reliability of Lead and Lead-Free Solder Joint by FORM/SORM

2007 ◽  
Vol 345-346 ◽  
pp. 1393-1396
Author(s):  
Ouk Sub Lee ◽  
Man Jae Hur ◽  
Yeon Chang Park ◽  
Dong Hyeok Kim
Keyword(s):  
Solder Joint ◽  
Failure Probability ◽  
Lead Free ◽  
Lead Free Solder ◽  
Fatigue Reliability ◽  
Probability Models ◽  
First Order ◽  
Reliability Method ◽  
Vibration Fatigue ◽  
Free Solder

It is well-known that the vibration significantly affect the life of solder joint. In this paper, the effects of the vibration on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM). The accuracies of the results are estimated by a help of the Monte Carlo Simulation (MCS). The reliability of the lead and the lead-free solder joint was also evaluated. The reliability of lead-free solder joint is found to be higher than that of lead solder joint.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

Reliability Estimation for PVC Pipe Using Probability Theory and Stress Intensity Factor

2008 ◽  
Author(s):  
O. S. Lee ◽  
D. H. Kim ◽  
H. M. Kim ◽  
H. B. Choi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Wall Thickness ◽  
Failure Probability ◽  
Probabilistic Method ◽  
Reliability Estimation ◽  
State Function ◽  
Operating Pressure ◽  
Reliability Method

In this paper, the reliability estimation of Polyvinyl chloride (PVC) pipelines is performed by utilizing the probabilistic method, which accounts for the uncertainties in the load and resistance parameters in the limit state function (LSF). The LSF is formulated with the help of fracture control concept including the stress intensity factor (SIF) for the pipeline having crack or crack like defects. The common cracks found at pipeline can be assumed as semi-elliptical shape and the main load is hoop stress due to the internal pressure. The FORM (first order reliability method) and the SORM (second order reliability method) are carried out to estimate the failure probability of pipeline utilizing the SIF for semi-elliptical crack. The reliability is assessed using this failure probability. It is found that the failure probability increases with the operating pressure, and the decrease of the pipeline wall thickness, and the increase of the crack depth, the crack length, the outside diameter of pipeline. The failure probability increases when the initial crack approaches to a semi-circle shape of crack and the failure probability steeply increases at the ratios of larger than 0.5 of a/t and larger than 30 of D/t. Moreover, it is recognized that the effects of the fracture toughness and the pipe wall thickness on the failure probability are the significant one.

Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Author(s):  
Xiaoping Du ◽  
Junfu Zhang
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

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