Submodeling Technique Research Articles

Stress Impact of the Annealing Procedure of Cu-Filled TSV Packaging on the Performance of Nano-Scaled MOSFETs Evaluated by an Analytical Solution and FEA-Based Submodeling Technique.

Stress-induced performance change in electron packaging architecture is a major concern when the keep-out zone (KOZ) and corresponding integration density of interconnect systems and transistor devices are considered. In this study, a finite element analysis (FEA)-based submodeling approach is demonstrated to analyze the stress-affected zone of through-silicon via (TSV) and its influences on a planar metal oxide semiconductor field transistor (MOSFET) device. The feasibility of the widely adopted analytical solution for TSV stress-affected zone estimation, Lamé radial stress solution, is investigated and compared with the FEA-based submodeling approach. Analytic results reveal that the Lamé stress solution overestimates the TSV-induced stress in the concerned device by over 50%, and the difference in the estimated results of device performance between Lamé stress solution and FEA simulation can reach 22%. Moreover, a silicon–germanium-based lattice mismatch stressor is designed in a silicon p-type MOSFET, and its effects are analyzed and compared with those of TSV residual stress. The S/D stressor dominates the stress status of the device channel. The demonstrated FEA-based submodeling approach is effective in analyzing the stress impact from packaging and device-level components and estimating the KOZ issue in advanced electronic packaging.

Reliability Analysis of Solder Joints on Rigid-Flexible Printed Circuit Board for MEMS Pressure Sensors Under Combined Temperature Cycle and Vibration Loads With Continuously Monitored Electrical Signals

Abstract The reliability of lead-free solder joints on flexible printed circuit board (PCB) has created significant new challenges in the industry, especially in automotive electronics, and possibly for future wearable electronics. In the automotive industry, thermal cycling test and random vibration test need to be conducted to certify every electronic product to be used in harsh automotive environments. In order to accelerate the testing time, we may need to subject the electronic components, in particular, sensors to both loadings such as thermal cycling and vibration. During all the experiments, the electrical signals of each specimen were continuously monitored by using an event detector. One advantage of this method is that any individual soldering interconnect failure will result in the diagnostic signal of the circuit, which could be detected in real-time. A simulation was used to confirm the possibility of the stress concentration location caused by the vibration and thermal cycling loads. The influence of vibration frequency and acceleration on the vibration fatigue life of solid joints was investigated. In this paper, the submodeling technique was used to construct the finite element model of the rigid-flexible printed circuit board (rigid-flexible PCB) coupled with a MEMS pressure sensor subjected to temperature cycle and random vibration loadings. The research results are helpful to effectively characterize the performance of the MEMS sensors under both thermal cycling test and vibration test. Two kinds of land shapes and two kinds of PCB assemblies were selected. In order to investigate the crack growth in the solder joint, the solder joint is sliced and the crack on the cross section of the solder joint was observed. Results of finite element modeling analysis were consistent with the experimental results. Two design parameters have been identified in our research as being important to soldering usage in automotive environments: pad type (teardrop versus nonteardrop) and pad size (big versus small, matching size for Cu-wire and pad). Experimental results also showed that the solder joint with a big land shape presented a relatively good thermal fatigue resistance.

Submodeling in wear predictive finite element models with multipoint contacts

AbstractThe application of the submodeling technique to finite element (FE) wear analyses has been recently proposed as an efficient solution to reduce the computational cost of the simulations and provide accurate numerical results. However, the method was validated only on single point contact cases. The present study proposes a generalization of the wear submodeling procedure that can be used to speed up FE wear simulations with multipoint contacts. The modified global–local procedure is applied and evaluated on a double contact pin on plate wear test using three‐dimensional models developed in Ansys® mechanical APDL. Three different model geometries with different curvature radii at the contact regions were considered in order to replicate possible critical scenarios. Results suggest that an additional wear simulation step where the global model is used to simulate the first wear cycles is needed to correctly transfer the boundary conditions to the local models. The new proposed strategy demonstrates the possibility to extend the method to more general FE wear simulations by significantly reducing their computational cost.

Thermal elastohydrodynamic lubrication simulation model for the tooth guidance contact of a single tooth gearbox under mixed friction conditions

This article presents a simulation model for thermal elastohydrodynamic lubrication of the tooth guidance (piston/cylinder) contact of a single tooth gearbox. A finite-element analysis provides the boundary conditions for the thermal elastohydrodynamic lubrication simulation. The finite-element analysis under dry conditions allows calculating the macroscopic deformed contact surfaces for the elastohydrodynamic simulation model. The Hertzian deformation should be calculated in the presence of a lubricant and not with a dry finite-element analysis. A recently presented method, based on the finite-element submodeling technique, is extended to remove the Hertzian deformation of the macroscopic deformed lubrication gap from the dry finite-element analysis. A mixed friction with measured rough surfaces using the averaged flow model and mass conserving cavitation is implemented as well. An example shows how optimization of the gearbox by application of the simulation model is possible.

Numerical analysis of the mechanical behaviour of intact and implanted lumbar functional spinal units: Effects of loading and boundary conditions.

The objective of this study was to develop an improved finite element (FE) model of a lumbar functional spinal unit (FSU) and to subsequently analyse the deviations in load transfer owing to implantation. The effects of loading and boundary conditions on load transfer in intact and implanted FSUs and its relationship with the potential risk of vertebral fracture were investigated. The FE models of L1-L5 and L3-L4 FSUs, intact and implanted, were developed using patient-specific CT-scan dataset and segmentation of cortical and cancellous bone regions. The effect of submodelling technique, as compared to artificial boundary conditions, on the elastic behaviour of lumbar spine was examined. Applied forces and moments, corresponding to physiologic movements, were used as loading conditions. Results indicated that the loading and boundary conditions considerably affect stress-strain distributions within a FSU. This study, based on an improved FE model of a vertebra, highlights the importance of using the submodelling technique to adequately evaluate the mechanical behaviour of a FSU. In the intact FSU, strains of 200-400 µε were observed in the cancellous bone of vertebral body and pedicles. High equivalent stresses of 10-25 MPa and 1-5 MPa were generated around the pars interarticularis for cortical and cancellous regions, respectively. Implantation caused reductions of 85%-92% in the range of motion for all movements. Insertion of the intervertebral cage resulted in major deviations in load transfer across a FSU for all movements. The cancellous bone around cage experienced pronounced increase in stresses of 10-15 MPa, which indicated potential risk of failure initiation in the vertebra.

Fatigue Evaluation of API 12F Shop-Welded Tanks With a New Roof-to-Shell Junction Detail

Abstract The American Petroleum Institute (API) provides a series of standards and specifications on storage tanks, in which the API 12F specification provides 12 tank designs that can be fabricated in the shop and transported to the field. The nominal capacity of the 12 API 12F tank designs ranges from 90 bbl (14.3 m3) to 1000 bbl (158.99 m3). The minimum required thickness and operational pressure levels that each tank case can sustain are given in Table 1 of the current 13th edition of API 12F (API, 2019, “API 12F Specification for Shop-Welded Tanks for Storage of Production Liquids,” 13th ed., API Publishing Services, Washington, DC, Standard No. API 12F). The objective of this study is to estimate the fatigue life of API 12F tanks under normal operation pressure cycles following the procedure presented in ASME VIII-2. The stored liquid product specific gravity is assumed to be 1.2 when the liquid height is half of the tank height, while the specific gravity is assumed to be 0.7 when the stored liquid height is 18 in. (460 mm). Meanwhile, a new roof–shell attachment detail is proposed in this study, the new rectangular cleanout junction detail presented in the 13th edition of API 12F is modeled, and various component thickness combinations are considered to investigate the effect of component thickness on fatigue life. The roof–shell joint (top junction) and shell–bottom plate (bottom junction) are studied by axisymmetric models under axisymmetric idealization as they are away from the cleanout junction, while the cleanout junction is studied by applying a submodeling technique. Stress classification is performed at each location of interest to obtain the stress components to calculate the stress range within each loading cycle that is needed to perform fatigue evaluation. The results and discussion about fatigue evaluation of API 12F tanks are presented in this report.

Research on TBM Cutterhead Crack Damage and Fatigue Reliability

The cutterhead of a tunnel-boring machine (TBM) is the main weighted part in the process of tunneling and bears loadings in different directions. A fatigue failure of a cutterhead would severely affect the construction progress and safety. Therefore, it is of great importance to study the fatigue reliability of its cracks. In this study, the area of the cutterhead with a higher stress was found using static strength analysis and we analyzed the dynamic stress characteristics. In addition, the stress intensity factor of a cutterhead crack was calculated using the submodeling technique, and the crack propagation mechanism and damage characteristics of a cutterhead crack were also analyzed. Then, combined with crack fatigue theory, we proposed a fatigue reliability evaluation method based on the Joint Committee on Structure Safety method (known as the JC method), and the effects of different factors on the reliability were discussed for different geological conditions. The results show that the crack propagation was of the open and tear types in the deepest part of the crack tip, but there are three kinds of propagation modes at both ends. As the initial crack depth increased, the fatigue reliability of the cutterhead decreased significantly. The reliability was positively correlated with the crack shape ratio. However, there were no significant relationships between the reliability and the depth of the critical crack.

The Effect of Fiber Waviness on the Residual Stress State and Its Prediction by the Hole Drilling Method in Fiber Metal Laminates: A Global-Local Finite Element Analysis

In this paper, fiber waviness, as one of the most frequently occurring defects in fiber reinforced composites, is numerically investigated with regard to the formation of residual stresses in fiber metal laminates. Furthermore, the prediction of the residual stress state in the thickness direction by means of the simulated hole drilling method is studied. To this regard, a global-local finite element analysis based on the submodel technique is presented. The submodel technique essentially consists of two governing steps: In the first step, a global model is first utilized to calculate and analyze the residual stress distribution and deformation in the intrinsically joined hybrid structure. Effective cure-dependent thermo–elastic properties predicted by a numerical homogenization procedure were used to simulate the curing-process and analyze the residual stresses state. However, the dimension of the intrinsically manufactured hybrid plate is large compared to the diameter of the drilled hole (2 mm), so that a local model is necessary, which provides only a geometric partial portion of the global model. The local model takes the global stress state into account and is subsequently used to simulate the incremental hole drilling method with a refined mesh discretization. The production-related fiber waviness is modeled by an element-wise orientation approximating a sinus function. In order to validate the global-local modeling approach, a comparison between numerical results and experimental data from literature is presented. The comparison between global residual stress state (global model) and the simulated hole drilling method (local model) is used to assess the applicability and reliability of the hole drilling method in case of fiber waviness. It is found that an in-plane fiber waviness leads to a rather low variance of residual stresses over thickness. In case of an out-of-plane fiber waviness, oscillating residual stress fields occur over the entire thickness along the fiber direction. Moreover, the current limits of the incremental hole drilling method could be pointed out by the presented investigations. It is seen that the simulated results of the incremental hole drilling method are sensitive to waviness, even if the amplitude-wavelength-ratio is small. Without further adjustment of the calibration coefficients the oscillating stress and strain fields lead, in particular fiber waviness in thickness direction, to unreliable predictions. For the experimental application it can be concluded that the specimens have to be carefully examined with regard to fiber waviness.

Submodeling method to study the residual stress of TBCs near the interfacial asperity on a vane

Modeling the residual stress of TBCs near the interfacial asperity on turbine component tends to encounter numerical cumbersomeness ordinarily due to huge computational scale and complex mechanical behavior. This paper proposed a numerical method named submodeling method to simulate the local stress near the asperity by a partition model (named submodel) of a coated vane, based on the submodeling technique of ABAQUS code. First a global mechanical analysis about the coated vane was carried lasting three thermal cycles without considering interface asperities. Then a submodel was established with asperity and divided into three unique zones with proper mesh density according to their functions. Finally the local mechanical analysis was separately processed by submodeling method, based on interpolation of the solution from the global analysis onto the outer zone of the submodel. The results show that the stress level of TC near the asperity is relatively low after 3 thermal cycles. The normal stress and the shear stress of BC near the asperity are concentrated in the peak and nearby the trough, respectively. These stress concentrations may lead to TGO/BC interfacial crack. The stress values and distribution feature of BC near the asperity is quite agreement with former results. These may prove that submodeling method can be applicable for local stress modeling and failure prediction.

Brittle fracture assessment of API 12F shop-welded tanks with a new roof-to-shell junction detail

Temporary production storage is largely needed in the oil and gas industry, thus, storage tanks that have the capability to sustain the normal operation condition are needed. The American Petroleum Institute (API) specification 12F provides twelve shop-welded tank designs that can accommodate storage and operational pressure needs of the facility requires temporary production storage. The nominal capacity of these twelve designs ranges from 90 bbl. (14.3 m3) to 1000 bbl. (158.99 m3). These API 12F tanks are typically fabricated in shop and transported to facilities of needs, they are relatively smaller than tank designs provided in API 12D, which is the specification of field-welded storage tanks for production liquids. The brittle fracture assessment is conducted following FAD technique adopted by API 579, with updated operational pressure in the API 12F standard published in 2019. The specific gravity of the stored liquid is assumed to be 1.2 and more component thickness combinations are under consideration in this study, thus, effects of internal pressure, hydrostatic pressure, and component thickness to brittle fracture behavior are investigated. The stresses at roof-shell joint (top junction), shell-bottom plate (bottom junction), and cleanout junction are obtained using finite element analysis approach. The top junction and bottom junction are studied under axisymmetric idealization; thus, the axisymmetric models are generated. The cleanout junction is studied by using sub-modeling technique. Stress classification is performed after performing elastic stress analysis, the results are then used to evaluate brittle fracture behavior with assuming operating at a location with one-day mean temperature of −55 °F (−48.3 °C). The report presents the results and discussion obtained from the brittle fracture assessment of the twelve API 12F tank designs.

Computationally-efficient thermal simulations of large Li-ion battery packs using submodeling technique

Accurate and rapid prediction of temperature distribution in a large Li-ion battery pack comprising thousands of cells is critical for ensuring safety and performance of battery packs for electric vehicles. Due to the multiscale geometry and the large number of individual cells in an automotive battery pack, full-scale thermal simulations typically take a long time to complete. Approaches for rapidly computing the temperature field in a large battery pack without significant loss of accuracy is, therefore, a key technological need. This paper presents thermal simulations of a large, air-cooled Li-ion battery pack containing thousands of individual cells using the submodeling technique. A coarse model that neglects fine geometrical details is first solved, and the results are used to solve a more detailed sub-model. It is shown that this approach results in 7X reduction in computation time while preserving the accuracy of the predicted temperature field. Trade-offs between computation time and accuracy are examined. The submodeling technique is used to investigate the thermal design of a large Li-ion battery pack, including the effect of discharge rate and coolant flowrate on temperature field, and the thermal response to a pulsed spike in discharge rate. Limitations of the submodeling technique are discussed. The technique discussed here is a general one, and may help significantly reduce computation time for thermal design and optimization of large, realistic Li-ion battery packs.

A numerical study on the effect of the fixation methods on the vibration fatigue of electronic packages

This paper presents a comprehensive finite element analysis study on the effect of the support and fixation schemes on the dynamic characteristics and fatigue life of electronic assemblies under vibration. In this study, high accuracy finite element (FE) model was created and thoroughly validated with modal analysis experiments in terms of natural frequencies and mode shape. Accordingly, the finite element model was adopted to run the analysis and to investigate the influence of point support configurations on the out-of-plane deformations of the electronic structure and solder area array stress distributions. Additionally, submodeling technique was implemented to thoroughly analyze the most-critical solder interconnect stresses. The simulations results showed that the support type and locations could significantly affect solder stresses and hence the vibration fatigue performance. Finally, this paper suggest an optimum point support design that provides improved electronic assemblies fatigue life and it also provides another support system that could be considered in the accelerated vibration reliability experiments.

Adaptive local-global multiscale approach for thermal simulation of the selective laser melting process

Numerical simulation is a powerful tool for understanding the complex physics of metal additive manufacturing (MAM) processes and to provide guidelines for optimization of the process conditions. The fast kinetics and highly localized nature of the involved phenomena demand high levels of time and space discretization for MAM simulations which significantly increases the computational costs. The existing simplified simulation approaches apply gross approximations to overcome the numerical cost barrier. This study proposes a multiscale approach which breaks down the problem into two scales of local and global simulations. The method argues that a high level of discretization is only required for capturing the physics of fast-kinetics phenomena occurring in the vicinity of the melt-pool, while a much coarser discretization is applicable for the rest of the simulation domain. As a particular type of adaptive submodeling technique, the results of fine-mesh local simulations around the moving melt-pool are combined with the outcome of a coarse-mesh global solution to provide reliable predictions at a significantly reduced computational cost. The efficiency and reliability of the proposed idea has been evaluated for 2D thermal simulation of the selective laser melting process. The outcome of the exercise demonstrates that the methodology can reduce the computational cost of the simulations by an order of magnitude with minimal loss of accuracy.

Experimental and submodeling technique to investigate the wear of silicon nitride against Ti6Al4V alloy with bio-lubricants for various gait activities

The present work focused on analyzing the wear and friction coefficients of Si3N4 against titanium alloy grade 5 material using ball-on-disc tribometer for a sliding distance of 20 km with five different bio-lubricants. Later using finite element submodeling technique, post implantation wear is predicted for 2 years considering four different gait activities which includes normal walking, stairs down 25 kg, carrying 25 kg and lifting 40 kg. The friction coefficient value is found to be least for sesame oil. The increase in percentage difference in friction coefficients for phosphate buffer saline (PBS), distilled water, Ringer's solution and saline solution are 77.27%, 81.81%, 84.09% and 86.36% when compared with sesame oil. The percentage difference in reduction in wear coefficients for sesame oil, saline solution, Ringer's solution and PBS are 36.49%, 48.81%, 56.11% and 84.36%. The linear and volumetric wear is found to be quite low for all gait activities for PBS bio-lubricant. Overall the least linear and volumetric wear are obtained for normal walking gait activity followed by Stair down 25 kg, Carrying 25 kg and Lifting 40 kg gait activity.

Procedures of Fatigue Analysis by Supporting Direct Load Application on Midship Sections

Fatigue evaluation of ship structures using direct calculation methods to calculate fatigue loads are standard practice today. There are several numerical codes available for use in analyses of these fatigue loads. In addition to the varying degrees of computational complexity associated with fatigue prediction methods, the inherent uncertainties of these procedures are also large. This paper introduces the procedure for stochastic fatigue analysis of typical midship models with direct load transfer applied, where an oil tanker is considered. It also covers a comparison of the results with the component-based approach included in the DNVGL Class Note 30.7: “Fatigue Assessment of Ship Structures”. The "real" case analysis includes both internal pressure loads from tank fluids as well as external pressure adjusted for wet and dry surfaces in the waterline area, according to DNVGL Class Note 30.7. Local fine mesh models of fatigue details have been analysed using the sub-modelling technique. The procedure performs well on a typical midship model apart from the file sizes of the generated load transfer files. With 25 wave periods and 12 different headings, the analysed 3-cargo-hold model (1/2 + 1 + 1/2) in the midship area had to be split into four super elements in order to get the analysis through finite element analyses. The procedure is suitable for vessels where warping (torsion) is of less importance. The described procedures are supported by a developed tool to be used in the analysis procedures. Three details of local fine mesh models such as deck erection butt weld, longitudinal stiffener through web-frame, and bottom erection butt weld have been analysed. The results have been compared with the component-based approach. For some of the details there are comparable results, but for others the results vary significantly. The typical trend is that the details heavily influenced by the external pressure (side longitudinal) give less comparable results than e.g. a detail in the main deck mainly influenced by global loads. A comparison of the effect of reducing versus not reducing the pressure amplitude in the waterline on the fatigue life has also been performed and discussed.

Elemental Crack Advance assessment and verification for its use in LBB analysis

The leak before break (LBB) concept is today widely employed at the nuclear industry to preclude catastrophic rupture, mainly on pipes. This paper presents two complimentary procedures. Both of them are applied via the Finite Element Method, for demonstrating LBB on austenitic stainless steel vessels. Those procedures are submodeling and the Elemental Crack Advance method. One procedure verifies the results obtained using the other, making them robust and trustworthy. Those practices are illustrated on the ALFRED reactor using the software ANSYS. They are applicable to geometrical shapes for which simplified expressions of the J-integral are not available. This illustration, proves as well, that by means of small design modifications such as thickening the bottom head, LBB can be demonstrated in the ALFRED reactor. The submodeling technique stands as the main vehicle in the LBB demonstration exposed at this work. The Elemental Crack Advance method lies as a tool for verifying a wide variety of Fracture Mechanics assessment, including non-LBB related ones.

Finite element submodeling technique to analyze the contact pressure and wear of hard bearing couples in hip prosthesis

Finite element (FE) simulation plays a major role in computing stress and predicting the failure of biomedical components. Normally in past, researchers focused on developing a global computational model from the scanned data of patients to analyze the stresses and deformations. To compute the wear of the hip prosthesis, mostly the global model (GM) is used to predict the expected life for million cycles using nodal updating technique which leads to high computational effort and time. The proposed work utilizes a submodeling finite element technique to analyze the contact pressure and wear of biomaterials for three different combinations in hip prosthesis including metal, ceramic and polycrystalline diamond materials. Initially the global model boundary and loading conditions are transferred to the submodel. The mesh is refined further using finer mesh and then the results are computed which consumes lesser time. The contact stress as well as the linear wear of biomaterials is found to be quite high for the local model (LM) when compared with the global model. However, no changes in volumetric wear of these biomaterials are observed when compared with previous experimental results. The computational time as well as accuracy in estimating the contact stress and the wear of bearings is improved effectively. Among local model with different element sizes, 0.75 mm element size of local model showed improved results in estimating the contact stress and linear wear of bearing.

Validation and Application of Magnetic Sub-Model Techniques in Turbogenerator End Zones for Local Eddy Current Calculation in Roebel Bars

Applying a novel magnetic sub-modeling technique allows resolving local phenomena such as eddy currents in electric machine components while incorporating effects due to magnetic fields arising from larger machine parts. Employing this procedure to turbogenerators gives the opportunity to study effects of a rotor's magnetic field impinging upon and penetrating individual copper strands of stator Roebel bars at core ends. It should be noted that the magnetically relevant end region of examined non-salient pole synchronous machines extends to several meters, whereas the complex geometry of a Roebel bar is four to five orders of magnitude smaller. This article highlights the significance of step iron design for joule heating inside stator bars and describes the mathematical framework of the applied procedure. This cutting-edge method enables accurate calculation of resulting heat generation rates due to the described phenomenon with high resolution for different end zone designs.

Towards efficient design optimization of a miniaturized thermoelectric generator for electrically active implants via model order reduction and submodeling technique.

Thermoelectric generators (TEG) convert the thermal energy into electrical energy and are under investigation as a power supply for medical implants. To improve the performance of TEG, the design optimization process through finite element model simulation is preferred by biomedical engineers. This paper aims to provide an efficient method of speeding up the design optimization process of TEG. A three-dimensional realistic human torso model incorporating the TEG is investigated, where the internal heat transfer in human tissue is characterized by Pennes bioheat equation. In addition, convection, radiation, and evaporation effects at the skin surface are applied to identify the heat transfer effects between the human body and the environment. To speed up finite element simulation of the large-scale human torso model, projection-based model order reduction (MOR) is applied for generation of a compact but highly accurate model. Parametric MOR (pMOR) further enables generating a parameter-independent compact model. For an efficient design optimization of TEG, this compact human torso model is applied within a thermal submodeling approach. Its temperature distribution results are back-projected and used as boundary conditions for the TEG submodel. The achieved speed-up in simulation time, demonstrated in this work, clearly indicates that the design optimization process of TEG is more efficient with the combination of MOR and submodeling techniques.

Fracture Failure Analysis for MQXFA Magnet Aluminum Shells

The High-Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP) is approaching the production phase of the US-contributed Q1 and Q3 Interaction Region Quadrupoles (MQXFA). The structures for the MQXFA prototypes were designed and inspected by the US-LARP (LHC Accelerator Research Program), AUP developed criteria, which will be used for the pre-series structures. The first two full-length prototypes with 4.2 m magnetic length, MQXFAP1 and MQXFAP2, were designed and assembled at Lawrence Berkeley National Laboratory (LBNL), and tested at Brookhaven National Laboratory (BNL). The end aluminum short shell of MQXFAP2 was fractured along the shell length during the test, and tests were stopped. Analytical and Finite Element analysis were performed in light of the graded procedure defined in the Structural Design Criteria to investigate the fracture failure for MQXFAP2. In this paper, we report the fracture analysis of the current shell design, including the elasto-plastic simulations with sub-model technique, and calculations with Linear Elastic Fracture Mechanics (LEFM). Test material properties are also presented. The results of this analysis explain why the end shell of MQXFAP2 failed, and suggest fillets on the end shell notches to meet the margin specified in the Structural Design Criteria.