An Inverse Procedure for Estimating the Anand Viscoplastic Constitutive Model Parameters for Copper Free-Air Ball

2015 ◽  
Author(s):  
Sai Sudharsanan Paranjothy ◽  
Ganesh Subbarayan ◽  
Dae Young Jung ◽  
Bahgat G. Sammakia
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Low Cost ◽  
Constitutive Models ◽  
Model Parameters ◽  
Element Analysis ◽  
Pad Cratering ◽  
Free Air ◽  
Inverse Finite Element Analysis ◽  
Force Displacement

Due to its superior mechanical and electrical properties, as well as low cost, Cu is gradually replacing Au as wire bonding material. However, since copper is a stiffer material, it requires greater bonding force, which in turn increases risk of bond pad cratering and inter-layer dielectric (ILD) fracture. A critical challenge to numerically modeling the pad cratering or ILD fracture is the availability of appropriate constitutive models for the Cu free-air balls (FAB). In this work we first present rate and temperature dependent force-displacement response of micron-sized Cu FAB characterized using a custom-built high-precision microtester. From the experimental force-displacement data, Anand viscoplastic constitutive model parameters are obtained using an inverse finite element analysis procedure, where the material parameters are iterated through an automated procedure until the finite element and experimental force-displacement responses match. The constitutive model parameters to describe the FAB behavior at low and intermediate strain rates and at high temperatures are obtained and reported in this paper.

Thermomechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part 1—Theory and Formulation

1998 ◽  
Vol 120 (1) ◽  
pp. 41-47 ◽  
Author(s):  
C. Basaran ◽  
C. S. Desai ◽  
T. Kundu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Electronic Packaging ◽  
Constitutive Models ◽  
Cyclic Behavior ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Finite Element Procedure ◽  
Reliable Design ◽  
Number Of Cycles

Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In order to understand and predict the behavior of such interfaces there is a need for improved and unified constitutive models that can include elastic, inelastic, viscous, and temperature dependent microstructural behavior. Furthermore, such unified material models should be implemented in finite element procedures so as to yield accurate and reliable predictions of stresses, strains, deformations, microcracking, damage, and number of cycles to failure due to thermomechanical loading. The main objective of this paper is to present implementation of such an unified constitutive model in a finite element procedure and its application to typical problems in electronic packaging; details of the constitutive model are given by Desai et al. (1995). Details of the theoretical formulation is presented in this Part 1, while its applications and validations are presented in Part 2, Basaran et al. (1998).

Dynamic Constitutive Model Application and Validation for Offshore Structures Under Dropped Object Impact Loads

2018 ◽  
Author(s):  
Maryam Mortazavi ◽  
YeongAe Heo
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Constitutive Model ◽  
High Sensitivity ◽  
Offshore Structures ◽  
Model Parameters ◽  
Impact Loads ◽  
Structural Level ◽  
Analysis Model ◽  
Element Analysis

It is critical to incorporate an appropriate constitutive model into a finite element analysis model to evaluate the nonlinear and dynamic effects on offshore structures subjected to dropped object impact loads. This paper demonstrates the high sensitivity of a dynamic constitutive model to mechanical properties of a specific offshore structural steel and its effect on nonlinear transient finite element analysis results for a steel plate system subjected to dropped object impact loads. Available stress-strain data obtained from dynamic tensile tests are used to validate the numerical results. The dynamic constitutive model recommended by Det Norske Veritas (DNV) was examined at both constitutive level and structural level. This paper proposes constitutive model parameters to improve the DNV’s recommendation.

Analytical Formulae for the Lateral Buckling Behaviour of Pipelines Installed With Residual Curvature

2020 ◽  
Author(s):  
Martin Teigen ◽  
Malik Ibrahim
Keyword(s):  
Finite Element ◽  
Structural Reliability ◽  
High Reliability ◽  
Low Cost ◽  
Model Parameters ◽  
Lateral Buckling ◽  
Element Analysis ◽  
Suggested Approach ◽  
Residual Curvature ◽  
Analytical Approaches

Abstract Residual curvature installation of subsea pipelines has become a popular method for lateral buckling management because of its low-cost implementation and high reliability. The method is foreseen to remain attractive due to the positive operational feedback made available to the public domain. On the design methods, previous research has predicted the behaviour of pipelines installed with residual curvature mainly via finite element analysis (FEA). These analyses include lateral buckling, installation, reeling etc. Further to this, Teigen and Ibrahim have put an effort into quantifying design uncertainties using structural reliability analysis (SRA). Analytical approaches have also been explored, such as pipeline rolling, and other effects during pipeline installation. However, there is little published work on analytical approaches for the lateral buckling behaviour. Therefore, this paper suggests analytical formulations for the lateral buckling behaviour of pipelines installed with residual curvature. For predicting the critical buckling force, the Palmer formulation was used as a basis. For predicting the pipeline integrity post buckling while accounting for non-linear effects and residual plasticity in the system, the formulation is derived using a combination of dimensional analysis, regression analysis and a modified Hobbs formulation. The resulting analytical formulation is calibrated to a database of finite element solutions. The suggested approach is assessed for a configuration that applies model parameters based on the Skuld pipeline. A validation has been performed and the errors have been assessed to verify the suitability of the proposed analytical approach.

On the Development and Computational Implementation of Complex Constitutive Models and Parameters’ Identification Procedures

2013 ◽  
Vol 554-557 ◽  
pp. 936-948 ◽  
Author(s):  
Tiago Jordão Grilo ◽  
Nelson Souto ◽  
Robertt Angelo Fontes Valente ◽  
António Andrade-Campos ◽  
Sandrine Thuillier ◽  
...  
Keyword(s):  
Finite Element ◽  
Aluminum Alloys ◽  
Constitutive Model ◽  
Constitutive Models ◽  
High Strength ◽  
Model Parameters ◽  
Finite Element Code ◽  
Mapping Procedure ◽  
Computational Implementation ◽  
Constitutive Parameters

Nowadays, the automotive industry has focused its attention to weight reduction of the vehicles to overcome environmental restrictions. For this purpose, new materials, namely, advanced high strength steels and aluminum alloys have emerged. These materials combine good formability and ductility, with a high tensile strength due to a multi-phase structure (for the steel alloys) and reduced weight (for the aluminum alloys). As a consequence of their advanced performances, complex constitutive models are required in order to describe the various mechanical features involved. In this work, the anisotropic plastic behavior of dual-phase steels and high strength aluminum alloys is described by the non-quadratic Yld2004-18p yield criterion, combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex anisotropy and Bauschinger effects of the materials, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations. To this end, an efficient computational implementation is needed, altogether with an inverse methodology to properly identify the constitutive parameters to be used as numerical simulation input. The constitutive model is implemented in the commercial finite element code ABAQUS as a user-defined material subroutine (UMAT). A multi-stage return mapping procedure, which utilizes the control of the potential residual, is implemented to integrate the constitutive equations at any instant of time (pseudo-time), during a deformation process. Additionally, an inverse methodology is developed to identify the constitutive model parameters of the studied alloys. The identification framework is based on an interface program that links an optimization software and the commercial finite element code. This methodology compares experimental data with the respective results numerically obtained. The implemented optimization process aims to minimize an objective function, which defines the difference between experimental and numerical results using the Levenberg-Marquardt gradient-based optimization method. The proposed integrated approach is validated in a number of benchmarks in sheet metal forming, including monotonic and cyclic loading, with the goal to infer about the modelling of anisotropic effects.

Progressive failure analysis of scarf-repaired composite laminate based on damage constitutive model

2016 ◽  
Vol 233 (2) ◽  
pp. 180-188 ◽  
Author(s):  
Qiuyi Shen ◽  
Zhenghao Zhu ◽  
Yi Liu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Composite Laminate ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Load Capacity ◽  
Three Dimensional ◽  
Zone Model ◽  
State Variables ◽  
Element Analysis

A three-dimensional finite element model for scarf-repaired composite laminate was established on continuum damage model to predict the load capacity under tensile loading. The mixed-mode cohesive zone model was adopted to the debonding behavior analysis of adhesive. Damage condition and failure of laminates and adhesive were subsequently addressed. A three-dimensional bilinear constitutive model was developed for composite materials based on damage mechanics and applied to damage evolution and loading capacity analyses by quantifying damage level through damage state variables. The numerical analyses were implemented with ABAQUS finite element analysis by coding the constitutive model into material subroutine VUMAT. Good agreement between the numerical and experimental results shows the accuracy and adaptability of the model.

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.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

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