The variations of residual stress distributions on solder balls under the cyclic thermal load and aging processes are investigated in this thesis. The solidification phenomena for different shapes and materials of the solder balls during the reflow process are predicted by using the Surface Evolver program. The distribution of residual stress in the solder ball is calculated by employing the MARC finite element package. The temperature dependent material properties of the solders, i.e. 63Sn/37Pb and 96.5Sn/3.5Ag, are used in the residual stresses calculations. The variation of the residual stresses distributions of different solder balls under the temperature cycling test ( between ¡V40¢J and 85¢J ) and the aging test ( at 85¢J ) are simulated and studied. The effects of the solder parameters, i.e. the solder height and the pad geometry shapes on the residual stresses distribution are also studied. Besides, the same simulation and analysis has also applied on the solder ball with an unleaded solder 96.5Sn/3.5Ag. A better understanding about the variation of the residual stress in a solder ball is expected from this analysis.

During the bending of flange plate used for dapped girders some highway bridge fabricators are experiencing cracking of the flange plate particularly when heat is used in assisting the bending process. Due to the extreme strains experienced during the fabrication process, investigating this problem requires the use of a finite element analysis. The fabrication process was broken down into two parts, first the heating of the plate through the use of either a furnace or an acetylene torch (thermal), and the second was the bending process (structural). The five different temperatures collected during the thermal analysis were a uniform temperature of 75oF, a 1100oF uniform temperature as a result of furnace heating, both five and ten minutes of air-cooling after the plate had reached a uniform temperature of 1100oF, and the temperature gradient after heating the flange plate to a surface temperature of 1200oF though the use of an acetylene torch. After the thermal analysis was completed, the resulting temperatures were imported into the structural model. The plate thicknesses analyzed were one, one and a half, and two inches, assuming both 50 and 70 ksi yield strengths. To achieve a 90 degree six-inch radius bend the plate was bent in five separate locations. The result of this analysis showed that with the introduction of temperature gradients into thefabrication process, the strains along the plate??s extreme fibers increased. The model further showed that for both a one and a half and two-inch thick plate the extreme fiber strains exceeded ten percent, which further adds to the increased risk of the flange plate cracking during fabrication. The highest residual stresses through the plate??s thickness occurred during cold bending. The residual stresses through the plate??s thickness decreased when the fabrication process was carried out at elevated temperatures. When steel exceeds a strain of 10 to 16 percent during the fabrication process, the plate becomes susceptible to cracking. This strain limit was exceeded for plate thicknesses of one and a half and two inches.

Recently, wet sand blasting on coated cutting tool inserts has drawn interest to the tooling industry due to its positive effects on cutting performance and tool life. This performance boost has partly been attributed to the buildup of compressive residual stresses in the coating during the blasting process. However, the mechanism of forming residual stresses in ceramic coatings during sand blasting is not fully understood. This work utilize x-ray diffraction as the main tool to study the formation and relaxation of residual stresses after wet sand blasting and annealing on 001, 012 and 110 textured α-Al2O3 coatings. To minimize the influence of stress gradients in the samples, all stress measurements were set up with a fixed analysis depth of 2 µm. Sand blasting was made with an alumina based slurry at 2, 3.2 and 4 bar pressure and the anneal was done at temperatures from 400 to 1000 °C for 2 hours or more. The coating hardness was evaluated by nanoindentation. Finally, the activation energy for the relaxation of residual stresses was estimated using the Zener-Wert-Avrami function. The results reveal the highest compressive residual stress with up to -5.3 GPa for the 012 texture while the stresses for the 001 and 110 textures peaked at -3.1 and -2.0 GPa, respectively. Further, a hardness gradient was present after blasting of the 001 and 012 textured samples indicating a higher stress at the surface of the coating. The 110 textured sample is the most brittle resulting in flaking of the coating during sand blasting. The different deformation mechanisms are related to difference in active slip planes between coatings with different textures. Both the stress and hardness decreased after heat treatment and the activation energy for stress relaxation was found to be as 1.1 ± 0.3 eV, 1.9 ± 0.2 eV and 1.2 ± 0.1 eV for the 001, 012 and 110 textures, respectively.

応用力学論文集v.15

The Thirteenth East Asia-Pacific Conference on Structural Engineering and Construction, September 11-13, 2013, Sapporo, Japan (EASEC-13)

The finite element method is used to investigate the effects of welding-induced residual stress and distortion on the strength and behaviour of ship hull structures. A finite element welding simulation consisting of sequentially coupled transient thermal and nonlinear structural analyses is used to predict the three-dimensional residual stress and distortion fields in welded stiffened plates. Three types of stiffener commonly used in commercial and naval applications are considered. The welding simulation is followed by a 'shakedown' analysis to study the possibility of residual stress relief caused by cyclic loads. The strength and behaviour of stiffened plates under axial load is characterized by normalized plots of average axial stress versus axial strain, commonly referred to as load-shortening curves. These curves are used to evaluate the effects of welding-induced residual stress and distortion on stiffened plate behaviour with and without considering stress relief by shakedown. Load-shortening curves generated by finite element analysis are also compared with load-shortening curves produced using analytical methods including those prescribed in ship structural design standards published by the International Association of Classification Societies (IACS). To conclude, a hull girder ultimate strength analysis is carried out using Smith's method with load-shortening curves generated by several different methods. Results indicate that welding-induced residual stress and distortion decrease the ultimate strength of flat-bar, angle, and tee-stiffened plates investigated in this study by as much as 17%, 15% and 13%, respectively. Stiffened plate ultimate strength values calculated using IACS common structural rules agreed reasonably well with results from numerical models in most cases. There was however, a significant discrepancy between the numerical load-shortening curves and the IACS curves in the post-ultimate regime, where the IACS curves overestimated the post-ultimate strength of stiffened plates by as much as 30%. To investigate stress relief by shakedown, axial stresses of 25% and 50% of the yield stress were applied and residual stresses were reduced by approximately 20% and 40%, respectively. In some cases, these reductions in residual stress led to increases in stiffened plate ultimate strength as high as 7%. Analysis of a box girder using load-shortening curves from a finite element model including residual stresses and distortions predicted by welding simulation predicted a bending moment capacity within 2.7% of the experimentally measured value. Using load-shortening curves from the IACS common structural rules, the ultimate strength was overestimated by 17%. / Thesis .pdf/A

Bioactive glasses react with the human physiological solution in control of their biofunctionality. The stress state in bioactive glasses determines the chemomechanical reaction and their biofunctionality. Using the microindentation technique, the effect of the indentation deformation on the surface damage and material dissolution of 45S5 bioglass was investigated. The indentation-induced residual stresses were calculated. Complete anelastic recoveries of the indentation depths and the impression marks were observed for the first time, which was likely driven by the stored strain energy over the anelastic deformation zone. The indentation-induced local surface damages were revealed before and after the immersion tests in phosphate buffer solution (PBS). The growth of the cracks in the PBS solution displayed the stress-corrosion behavior with the crack-growth speed being a linear function of the indentation load. 45S5-bioglass was crystallized at temperature of 650 ºC. Microindentation technique also was used to study the localized mechanical behavior of the crystallized 45S5-bioglass. The crystallization had little effect on the indentation hardness, and the indentation hardness of the crystallized 45S5-bioglass is the same as that of the corresponding material in vitreous state. The fracture toughness is about 3 times less than that of annealed 45S5-bioglass in vitreous state, suggesting the preference of using bioactive glasses of vitreous state in the implant applications. Also, the effect of crystallization on the material dissolution was examined in phosphate buffer solution. We also studied the growth and mechanical behaviors of the Ca-P precipitate layers formed on 45S5 bioglass in simulated body fluid. The thickness of the Ca-P precipitate layers was proportional to the square root of the immersion time, and the ratio of Ca/P in the Ca-P precipitate layers increased with the immersion time and approached 1.67, corresponding to the stoichiometric hydroxyapaptite (HA).Using the indentation technique, the indentation behavior of the Ca-P precipitate layers was investigated. The indentation hardness of the HA layers formed in SBF was found to be 0.40 GPa, and the contact modulus was 12.0 GPa. The contact modulus of 12.0 GPa is close to that of cortical bone. In this thesis, the primary mechanical properties of the non-crystalline and crystalline bioglass 45S5 were revealed. The relationship between the dissolution rate and localized residual stresses are discussed. With such knowledge, the evaluation of implants with respect to manufacturing processes, control, and service conditions now has another variable to consider and evaluate against performance.

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The advancement of the structural steel manufacturing industry has led to the recent emergence of steel members with Elliptical Hollow Sections (EHS) and Semi Elliptical Hollow Sections (SEHS). Although these sections are gaining popularity among architects, the lack of design guidelines specifically tailored towards these sections inhibits their efficient structural use. Within this context, this thesis provides several steps towards the development of such guidelines. A review of the manufacturing process of hot-rolled steel sections is conducted with emphasis on hollow structural sections. The main factors affecting the formation of residual stresses during cooling of the sections are discussed. Lower bound plastic interaction relations for EHS subjected to combinations of axial force, bi-axial bending moments and torsion are then derived. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example. A simplified and conservative interaction equation is then proposed based on curve fitting of the results of the lower bound solution. Upper bound interaction relations are next developed for EHS subjected to combinations of axial force, bi-axial bending moments, torsion and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. An iterative solution technique is developed to solve the resulting highly non-linear system of interaction relations. The effects of residual stresses and initial imperfections on axial compressive resistance of hot-rolled EHS are then incorporated into the lower bound interaction relations. Towards that goal, the thermo-mechanical properties of steel were extracted from the literature. A thermo-mechanical finite element model was developed for prediction of residual stresses in rolled sections. The validity of the model was assessed by comparison against residual stress measurements available in the literature. The model is then applied to predict the residual stresses in hot-rolled EHS. A series of geometric and material nonlinear finite element analyses is conducted on columns of EHS sections. The analyses include predicted residual stresses and initial out-of-straightness imperfections in order to determine the inelastic buckling capacity of EHS members and generate column curves for EHS sections. The column curves are subsequently compared to those based on Canadian, American and European design codes. Two column curve equations are proposed in a format similar to that of the Canadian Standards for buckling about major and minor axes. The column curves were subsequently combined with the interaction relations developed to provide design rules for EHS members under combined loads. The last contribution of the thesis provides a formulation of lower bound interaction relations for SEHS subject to combinations of axial force, bi-axial bending moments and torsion. An iterative scheme for solving the parametric form of the interaction relations is developed and a grid of admissible stress resultant combinations is generated. A series of trial functions are fitted to the grid of internal force combinations and two simplified and conservative interaction equations are proposed.

In this thesis the finite element computer code QUEANA simulating the quenching of axisymetric parts and determining the residual stress state was improved by adding pre- and post-processors. The code was further verified by additional numerical experiments and comparison of the results with commercial software &ldquo / MARC&rdquo / . The possible applications of this code are optimization of industrial quenching processes by controlling the evolution of internal stresses and dimensional changes.