<div>Defects are unavoidable, life-limiting and dominant sites of damage and subsequent failure in a material. Ni-based superalloys are commonly used in high temperature applications and inevitably found to have defects in the form of inclusions, voids and microscopic cracks which are below the resolution of standard inspection techniques. A mechanistic understanding of the role of defects in such industrially relevant bulk polycrystalline material is essential for philosophies of design and durability to follow and ensure structural integrity of components in the inevitable presence of such defects. The current understanding of defect-mediated damage, in bulk Ni superalloys, is limited by experimental techniques that can capture the local micromechanical state of the material surrounding the defect. In this work, we combine mechanical testing with in-situ, non-destructive 3-D X-ray characterization techniques to obtain rich multi-modal datasets at the microscale to interrogate complex defect-microstructure interactions and elucidate the mechanisms of failure around defects. The attenuated X-ray beam, after passage through the material, is utilized through computed micro-tomography to characterize the defects owing to its sensitivity to density differences in the material. The diffracted X-ray beam, after illuminating the material, is employed through high energy diffraction microscopy in various modes to interrogate the evolving micromechanical state around the discovered defects.</div><div>Three case studies are performed with specimens made of a Ni-based superalloy specially designed and fabricated to have internal defects in the form of: (i) an inclusion, (ii) a microscopic crack, and (iii) voids. In each case, the grain scale information is investigated to reveal heterogeneity in the local micromechanical state of the material as a precursor for the onset of failure. Models and simulations based on finite element or crystal plasticity are utilized, wherever necessary, to assess the factors essential to the underlying mechanism of failure. In the first case study, the detrimental effects of an inclusion in initiating a crack upon cyclic loading is interrogated and the state of bonding, residual stresses, and geometrical stress concentrations around the inclusion are demonstrated to be of utmost importance. In the second case study, the propagation of a short fatigue crack through the microstructure is examined to reveal the crystallographic nature of crack growth through the (i) alignment of the crack plane with the most active slip system, (ii) the correlation between the crack growth rate and the maximum resolved shear stresses, and (iii) the dependence of the crack growth direction on microplasticity within grains ahead of the crack front. In the third case study, the role of voids in ductile failure under tensile loading is explored to illuminate the activation and operation of distinct mechanisms of inter-void shear and necking under the control of the local state of stress triaxiality and the local plasticity within the grains at critical sites of fracture.</div><div>In summary, a grain scale description of the micromechanical state has been unambiguously determined through experiments to examine the heterogeneity around defects in the material. It has enabled us to identify and isolate the nature of factors essential to the activation of specific mechanisms at the onset failure. The grain scale thus provides an ideal physical basis to understand the fundamentals of defect mediated damage and failure instilling trust in the predictive capabilities of models that incorporate the response of the grain structure. The generated datasets can be used to instantiate and calibrate such models at the grain level for higher fidelity. </div>

Computational modeling is essential for material and structural analyses for a multitude of reasons, including for the improvement of design and reducing manufacturing costs. However, the cost of commercial finite element packages prevent companies with limited financial resources from accessing them. Free finite element solvers, such as Warp3D, exist as robust alternatives to commercial finite element analysis (FEA) packages. This and other open-source finite element solvers are not necessarily easy to use. This is mainly due to a lack of a preprocessing framework, where users can generate meshes, apply boundary conditions and forces, or define materials. We developed a preprocessor for Warp3d, which is referred to as <i>W3DInput</i>, to generate input files for the processor. <i>W3DInput</i> creates a general framework, at no cost, to go from CAD models to structural analysis. With this preprocessor, the user can import a mesh from a mesh generator software – for this project, Gmsh was utilized – and the preprocessor will step the user through the necessary inputs for a Warp3D file. By using this preprocessor, the input file is guaranteed to be in the correct order and format that is readable by the solver, and makes it more accessible for users of all levels. With this preprocessor, five use cases were created: a cantilever beam, a displacement control test, a displacement control test with a material defined by a user-defined stress-strain curve, a crystal plasticity model, and pallet. Results were outputted to Exodus II files for viewing in Paraview, and the results were verified by checking the stress-strain curves. Results from these use cases show that the input files generated from the preprocessor functions were correct.

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.<br><br>First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.<br> <br>Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.<br> <br>As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.<br><br><br>

First, the theory of MSG is extended to aperiodic heterogeneous solid structures. Integral constraints are introduced to decompose the displacements and strains of the heterogeneous material into a fluctuating part and a macroscopic part, of which the macroscopic part represents the responses of the homogenized material. One advantage of this theory is that boundary conditions are not required. Consequently, it is capable of handling micro-structures of arbitrary shapes. In addition, periodic constraints can be incorporated into this theory as needed to model periodic or partially periodic materials such as textile composites. In this study, the newly developed method is employed to investigate the finite thickness effect of textile composites.<div><br></div><div>Second, MSG is enabled to deal with Timoshenko beam-like structures with spanwise heterogeneity, which provide higher accuracy than the previous available Euler–Bernoulli beam model. Its reduced form, the MSG beam cross sectional analysis, is found to be able to analyze generalized free-edge problems with arbitrary layups and subjected to general loads. In this method, the only assumption applied is that the laminate is long enough so that the Saint-Venant principle can be adopted. There is no limitation on the cross section of the laminate since no ad hoc assumption is involved with the microstructure geometry. This method solve the free-edge problem from a multiscale simulation point of view.<br></div><div><br></div>

<p>Raman spectroscopy is a molecular spectroscopy technique that uses monochromatic light to provide a fingerprint to identify structural components and chemical composition. Depending on the changes in the unit-cell parameters and volume under the application of stress and temperature, the Raman spectrum undergoes changes in the wavenumber of Raman-active modes that allow identification of sample characteristics. Due to the various advantage of mechanical Raman spectroscopy (MRS), the use of this technique in the characterization and modeling of chemical changes under stress and temperature have gained popularity. </p> <p> Quantitative information regarding the local behavior of interfaces in an inhomogeneous material during shock loading is limited due to challenges associated with time and spatial resolution. Recently, we have extended the use of MRS to high-strain rate experiments to capture the local thermomechanical response of mock energetic material and obtain material properties during shock wave propagation. This was achieved by developing a novel method for <i>in‑situ</i> measurement of the thermo‑mechanical response from mock energetic materials in a time‑resolved manner with 5 ns resolution providing an estimation on local pressure, temperature, strain rate, and local shock viscosity. The results show the solid to liquid phase transition of sucrose under shock compression. The viscous behavior of the binder was also characterized through measurement of shock viscosity at strain rates higher than 10⁶/s using microsphere impact experiments.</p> <p> This technique was further extended to perform Raman spectral imaging over a microscale domain of the sample with a nano-second resolution. This was achieved by developing a laser-array Raman spectral imaging technique where simultaneous deconvolution of Raman spectra over the sample domain was achieved and Raman spectral image was reconstructed on post-processing. We developed a Raman spectral imaging system using a laser array and analysis was performed over the interface of sucrose crystals bonded using an epoxy binder. This study provides the Raman spectra over the microstructure domain which enabled the detection of localized melting under shock compression. The distribution of shock pressure and temperature over the microstructure was obtained using mechanical Raman analysis. The study shows the effects of an actual interface on the propagation of shock waves where a higher dissipation of shock energy was observed compared to an ideal interface. This increase in shock dissipation is accompanied by a decrease in both the maximum temperature, as well as the maximum pressure within the microstructure during shock wave propagation.</p>

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<p>Extrusion Deposition Additive Manufacturing is a process by which short fiber-reinforced polymers are extruded in a screw and deposited onto a build platform using a set of instructions specified in the form of a machine code. The highly non-isothermal process can lead to undesired effects in the form of residual deformation and part delamination. Process simulations that can predict residual deformation and part delamination have been a thrust area of research to prevent the repeated trial and error process before a useful part has been produced. However, populating the material properties required for the process simulations require extensive characterization efforts. Tackling this experimental bottleneck is the focus of the first half of this research.</p><p>The first contribution is a method to infer the fiber orientation state from only tensile tests. While measuring fiber orientation state using computed tomography and optical microscopy is possible, they are often time-consuming, and limited to measuring fibers with circular cross-sections. The knowledge of the fiber orientation is extremely useful in populating material properties using micromechanics models. To that end, two methods to infer the fiber orientation state are proposed. The first is Bayesian methodology which accounts for aleatoric and epistemic uncertainty. The second method is a deterministic method that returns an average value of the fiber orientation state and polymer properties. The inferred orientation state is validated by performing process simulations using material properties populated using the inferred orientation state. A different challenge arises when dealing with multiple extrusion systems. Considering even the same material printed on different extrusion systems requires an engineer to redo the material characterization efforts (due to changes in microstructure). This, in turn, makes characterization efforts expensive and time-consuming. Therefore, the objective of the second contribution is to address this experimental bottleneck and use prior information about the material manufactured in one extrusion system to predict its properties when manufactured in another system. A framework that can transfer thermal conductivity data while accounting for uncertainties arising from different sources is presented. The predicted properties are compared to experimental measurements and are found to be in good agreement.</p><p>While the process simulations using finite element methods provide a reliable framework for the prediction of residual deformation and part delamination, they are often computationally expensive. Tackling the fundamental challenges regarding this computational bottleneck is the focus of the second half of this dissertation. To that end, as the third contribution, a neural network based solver is developed that can solve parametric partial differential equations. This is attained by deriving the weak form of the governing partial differential equation. Using this variational form, a novel loss function is proposed that does not require the evaluation of the integrals arising out of the weak form using Gauss quadrature methods. Rather, the integrals are identified to be expectation values for which an unbiased estimator is developed. The method is tested for parabolic and elliptical partial differential equations and the results compare well with conventional solvers. Finally, the fourth contribution of this dissertation involves using the new solver to solve heat transfer problems in additive manufacturing, without the need for discretizing the time domain. A neural network is used to solve the governing equations in the evolving geometry. The weak form based loss is altered to account for the evolving geometry by using a novel sequential collocation sampling method. This work forms the foundational work to solve parametric problems in additive manufacturing.</p>

<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>

Mechanics of structure genome (MSG) is a unified homogenization theory that provides constitutive modeling of three-dimensional (3D) continua, beams and plates. In present work, the author extends the MSG to study the buckling of structures such as stiffened and sandwich panels. Such structures are usually slender or flat and easily buckle under compressive loads or bending moments which may result in catastrophic failure.<div><br><div>Buckling studies of stiffened and sandwich panels are found to be scattered. Most of the existed theories employ unnecessary assumptions or only apply to certain types of structures. There are few unified approaches that are capable of studying the buckling of different kinds of structures altogether. The main improvements of current approach compared with other methods in the literature are avoiding unnecessary assumptions, the capability of predicting all possible buckling modes including the global and local buckling modes, and the potential in studying the buckling of various types of structures.<br></div><div><br></div><div>For global buckling that features small local rotations, MSG mathematically decouples the 3D geometrical nonlinear problem into a linear constitutive modeling using structure genome (SG) and a geometrical nonlinear problem defined in a macroscopic structure. As a result, the original structures are simplified as macroscopic structures such as beams, plates or continua with effective properties, and the global buckling modes are predicted on macroscopic structures. For local buckling that features finite local rotations, Green strain is introduced into the MSG theory to achieve geometrically nonlinear constitutive modeling. Newton’s method is used to solve the nonlinear equilibrium equations for fluctuating functions. To find the bifurcated fluctuating functions, the fluctuating functions are then perturbed under the Bloch-periodic boundary conditions. The bifurcation is found when the tangent stiffness associated with the perturbed fluctuating functions becomes singular. Moreover, the arc-length method is introduced to solve the nonlinear equilibrium equations for post-local-buckling predictions because of its robustness. The imperfection is included in the form of geometrical imperfection by superimposing the scaled buckling modes in linear perturbation analysis on mesh.<br></div><div><br></div><div>Extensive validation case studies are carried out to assess the accuracy of the MSG theory in global buckling analysis and post-global-buckling analysis, and assess the accuracy of the extended MSG theory in local buckling and post-local-buckling analysis. Results using MSG theory and extended MSG theory in buckling analysis are compared with direct numerical solutions such as 3D FEA results and results in literature. Parametric studies are performed to reveal the relative influence of selective geometric parameters on buckling behaviors. The extended MSG theory is also compared with representative volume element (RVE) analysis with Bloch-periodic boundary conditions using commercial finite element packages such as Abaqus to assess the efficiency and accuracy of the present approach.<br></div></div>