Pathological phenomena often change the mechanical properties of the tissue. Therefore, estimation of tissue mechanical properties can be of clinical importance. Ultrasound elastography is a well-established strain estimation technique. Until recently, mainly 1D elastography algorithms have been developed. A few 2D algorithms have also been developed in the past. Both of these two types of technique ignore the tissue motion in the elevational direction, which could be a significant source of decorrelation in the RF data. In this thesis, a 3D elastography algorithm that estimates all the three components of tissue displacement is implemented and tested statistically. In this research, displacement fields of mechanical models are simulated. RF signals are then generated based on these displacement fields and used as the input of elastography algorithms. To evaluate the image quality of elastograms, absolute error, SNRe, CNRe and CNRasse are computed. The SNRe, CNRe and CNRasse values are investigated not only under different strain conditions, but also in different frame locations, which forms 3D strain filters. A statistical comparison between image qualities of the 3D technique and 2D technique is also provided. The results of this study show that the 3D elastography algorithm outperforms the 2D elastography algorithm in terms of image quality and robustness, especially under high strain conditions. This is because that the 3D algorithm estimates the elevational displacement, while the 2D technique only estimates the axial and lateral deformation. Since the elevational displacement could be an important source for the decorrelation in the RF data, the 3D technique is more effective and robust compared with the 2D technique.

In order to develop a better understanding of the property, microstructure evolution and thermal history of FSW Inconel 718's, the strain, strain rate and thermal cycles need to be determined. In order to estimate the strain field of a deformed body, a displacement function needs to be determined. A 3D deformation model was developed to determine the displacement coefficients. A rectangular box created in this model deforms following a linear displacement function. Three orthogonal planes cut this deformed box, which leads to three deformed planes. The shape parameters (L, H, θ¹ and θ²) on the three orthogonal planes can be expressed as the functions of displacement coefficients. Although the displacement coefficients can not be expressed in the forms of the shape parameters symbolically, a numerical solution can be found using numerical optimization methods. The shape parameters were obtained by assuming the displacement coefficients (three cases). Then, the numerical optimization was carried out to determine the displacement coefficients. The solved displacement coefficients are the same as the assumed ones, which shows that this inverse problem can be solved, and this model is robust to determine the displacement function numerically. This model was used to estimate the strain and strain rate at the boundary of the nugget zone of Friction Stir Welding (FSW) Inconel 718. A numerical/experimental methodology was developed to estimate the thermal history in the stir zone of FSW Inconel 718.The thermocouple experiment was conducted to measure the thermal cycles in Heat Affected Zone (HAZ). Using the measured temperature in HAZ and a numerical model, the peak temperature (1039 ºC) and cooling rate (58.18 ºC/s) were determined. The microstructure in different regions was characterized and co-related with the thermal cycles. In order to understand the microstructure evolution in the stir zone, the strain rate (12.612 s-1) was estimated using the mathematical model as mentioned above. According to the estimated thermal history and strain rate, the assumption that the dynamic recrystallizaiton occurred during FSW was made. The grain size in the nugget zone affects the hardness. The relationship among the microstructure, mechanical properties, and thermal cycles was discussed.

<div>In contrast to traditional steel and aluminum, short fiber reinforced polymer composites (SFRCs) provide promising alternatives in material selection for automotive and aerospace applications due to their potential to decrease weight while maintaining excellent mechanical properties. However, uncertainties about the influence of complex microstructures and defects on mechanical response have prevented widespread adoption of material models for</div><div>SFRCs. In order to build confidence in models’ predictions requires deepened insight into the heterogenous damage mechanisms. Therefore, this research takes a micro-mechanics standpoint of assessing the damage behavior of SFRCs, particularly micro-void nucleation at the fiber tips, by passing information of microstructural attributes within neighborhoods of incipient damage and non-damage sites, into a framework that establishes correlations between the microstructural information and damage. To achieve this, in-situ x-ray tomography of the gauge sections of two cylindrical injection molded dog-bone specimens, composed of E-glass fibers in a polypropylene matrix, was conducted while the specimens were monotonically loaded until failure. This was followed by (i) the development of microstructural characterization frameworks for segmenting fiber and porosity features in 3D images, (ii) the development of a digital volume correlation informed damage detection framework that confines search spaces of potential damage sites, and (iii) the use of a Gaussian process classification framework to explore the dependency of micro-void nucleation on neighboring microstructural defects by ranking each of their contributions. Specifically, the analysis considered microstructural metrics related to the closest fiber, the closest pore, and the local stiffness, and the results demonstrated that less stiff resin rich areas were more relevant for micro-void nucleation than clustered fiber tips, T-intersections of fibers, or varying porosity volumes. This analysis provides a ranking of microstructural metrics that induce microvoid nucleation, which can be helpful for modelers to validate their predictions on proclivity of damage initiation in the presence of wide distributions of microstructural features and</div><div>manufacturing defects. </div>