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Characterization of local deformation in Pb-free solder joints using three dimensional (3D) X-ray microtomography

Description

Pb-free solder joints are commonly used as interconnects in semiconductor packaging. One of the major defects affecting the mechanical performance of solder joints are reflow pores that form during processing.

Pb-free solder joints are commonly used as interconnects in semiconductor packaging. One of the major defects affecting the mechanical performance of solder joints are reflow pores that form during processing. These pores exhibit significant variability in size and distribution, and understanding the effects of pore geometry on failure is an important reliability concern. In this thesis, the pore microstructures of solder joint samples and the localized plastic deformation around individual pores was characterized in 3D using lab scale X-ray Microtomography. To observe the deformation of a solder joint in 3D, a solder joint was imaged with Microtomography after reflow and then deformed in shear in several loading steps with additional tomography data taken between each. The 3D tomography datasets were then segmented using the 3D Livewire technique into regions corresponding to solder and pores, and used to generate 3D models of the joint at each strain value using Mimics software. The extent of deformation of individual pores in the joint as a function of strain was quantified using sphericity measurements, and correlated with the observed cracking in the joint. In addition, the error inherent in the data acquisition and 3D modeling process was also quantified. The progression of damage observed with X-ray Microtomography was then used to validate the deformation and failure predicted by a Finite Element (FE) simulation. The FE model was based on the as-reflowed tomography data, and incorporated a ductile damage failure model to simulate fracture. Using the measured sphericity change and cracking information obtained from the tomography data, the FE model is shown to correctly capture the broad plastic deformation and strain localization seen in the actual joint, as well as the crack propagation. Lastly, Digital Image Correlation was investigated as a method of obtaining improved local strain measurements in 3D. This technique measures the displacement of the inherent microstructural features of the joint, and can give localized strain measurements that can be directly comparable to that predicted by modeling. The technique is demonstrated in 2D on Pb-Sn solder, and example 3D data is presented for future analysis.

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Created

Date Created
  • 2012

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Experimental investigations and modeling of the strain sensing response of matrices containing metallic inclusions

Description

This study explores the possibility of two matrices containing metallic particulates to act as smart materials by sensing of strain due to the presence of the conducting particles in the

This study explores the possibility of two matrices containing metallic particulates to act as smart materials by sensing of strain due to the presence of the conducting particles in the matrix. The first matrix is a regular Portland cement-based one while the second is a novel iron-based, carbonated binder developed at ASU. Four different iron replacement percentages by volume (10%, 20%, 30% and 40%) in a Portland cement matrix were selected, whereas the best performing iron carbonate matrix developed was used. Electrical impedance spectroscopy was used to obtain the characteristic Nyquist plot before and after application of flexural load. Electrical circuit models were used to extract the changes in electrical properties under application of load. Strain sensing behavior was evaluated with respect to application of different stress levels and varying replacement levels of the inclusion. A similar approach was used to study the strain sensing capabilities of novel iron carbonate binder. It was observed that the strain sensing efficiency increased with increasing iron percentage and the resistivity increased with increase in load (or applied stress) for both the matrices. It is also found that the iron carbonate binder is more efficient in strain sensing as it had a higher gage factor when compared to the OPC matrix containing metallic inclusions.

Analytical equations (Maxwell) were used to extract frequency dependent electrical conductivity and permittivity of the cement paste (or the host matrix), interface, inclusion (iron) and voids to develop a generic electro-mechanical coupling model to for the strain sensing behavior. COMSOL Multiphysics 5.2a was used as finite element analysis software to develop the model. A MATLAB formulation was used to generate the microstructure with different volume fractions of inclusions. Material properties were assigned (the frequency dependent electrical parameters) and the coupled structural and electrical physics interface in COMSOL was used to model the strain sensing response. The experimental change in resistance matched well with the simulated values, indicating the applicability of the model to predict the strain sensing response of particulate composite systems.

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Agent

Created

Date Created
  • 2017

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Finite element based microstructural modeling of cementitious composites

Description

This study employs a finite element method based modeling of cementitious composite microstructure to study the effect of presence of inclusions on the stress distribution and the constitutive response of

This study employs a finite element method based modeling of cementitious composite microstructure to study the effect of presence of inclusions on the stress distribution and the constitutive response of the composite. A randomized periodic microstructure combined with periodic boundary conditions forms the base of the finite element models. Inclusion properties of quartz and light weight aggregates of size 600μm obtained from literature were made use of to study the effect of their material (including inclusion stiffness, stiffness of interfacial transition zone and matrix stiffening) and geometric properties (volume fraction of inclusion, particle size distribution of inclusion and thickness of the interfacial transition zone) on the composite. Traction-separation relationship was used to incorporate the effect of debonding at the interface of the matrix and the inclusion to study the effect on stress distribution in the microstructure. The stress distributions observed upon conducting a finite element analysis are caused due to the stiffness mismatch in both the quartz and the light weight aggregates as expected. The constitutive response of the composite microstructure is found to be in good conformance with semi-analytical models as well as experimental values. The effect of debonding throws up certain important observations on the stress distributions in the microstructure based on the stress concentrations and relaxations caused by the stiffness of the individual components of the microstructure. The study presented discusses the different micromechanical models employed, their applicability and suitability to correctly predict the composite constitutive response.

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Created

Date Created
  • 2016

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Finite element analysis of micro-cantilever beam experiments in UO2

Description

Uranium Dioxide (UO2) is a significant nuclear fission fuel, which is widely used

in nuclear reactors. Understanding the influence of microstructure on thermo-mechanical behavior of UO2 is extremely important to predict

Uranium Dioxide (UO2) is a significant nuclear fission fuel, which is widely used

in nuclear reactors. Understanding the influence of microstructure on thermo-mechanical behavior of UO2 is extremely important to predict its performance. In particular, evaluating mechanical properties, such as elasticity, plasticity and creep at sub-grain length scales is key to developing this understanding as well as building multi-scale models of fuel behavior with predicting capabilities. In this work, modeling techniques were developed to study effects of microstructure on Young’s modulus, which was selected as a key representative property that affects overall mechanical behavior, using experimental data obtained from micro-cantilever bending testing as benchmarks. Beam theory was firstly introduced to calculate Young's modulus of UO2 from the experimental data and then three-dimensional finite element models of the micro-cantilever beams were constructed to simulate bending tests in UO2 at room temperature. The influence of the pore distribution was studied to explain the discrepancy between predicted values and experimental results. Results indicate that results of tests are significantly affected by porosity given that both pore size and spacing in the samples are of the order of the micro-beam dimensions. Microstructure reconstruction was conducted with images collected from three-dimensional serial sectioning using focused ion beam (FIB) and electron backscattering diffraction (EBSD) and pore clusters were placed at different locations along the length of the beam. Results indicate that the presence of pore clusters close to the substrate, i.e., the clamp of the micro-cantilever beam, has the strongest effect on load-deflection behavior, leading to a reduction of stiffness that is the largest for any location of the pore cluster. Furthermore, it was also found from both numerical and i

analytical models that pore clusters located towards the middle of the span and close to the end of the beam only have a very small effect on the load-deflection behavior, and it is concluded that better estimates of Young's modulus can be obtained from micro- cantilever experiments by using microstructurally explicit models that account for porosity in about one half of the beam length close to the clamp. This, in turn, provides an avenue to simplify micro-scale experiments and their analysis.

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Agent

Created

Date Created
  • 2015