Date on Master's Thesis/Doctoral Dissertation
12-2024
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Industrial Engineering
Degree Program
Industrial Engineering, PhD
Committee Chair
Yang, Li
Committee Member
Chou, Kevin
Committee Member
Segura, Luis Javier
Committee Member
Chen, Yanyu
Committee Member
Chen, Xiaoyu
Author's Keywords
additive manufacturing; cellular structures; analytical modeling; mechanical performances; failure behaviors; L-PBF thin features
Abstract
Lightweight cellular structures with their higher per mass performance capability, multifunctional designability and property tolerability are gaining much wider adaptation in many engineering applications ranging from aerospace, defense, biomedical, automotive to sports. However, to achieve the desired performance levels careful design must be carried out. The experimental-based empirical design often involves high manufacturing cost, and there are also certain information/knowledges about the cellular deigns that could not be easily obtained experimentally, such as the deformation local fracture initiation. Similarly, numerical modeling-based design approach commonly suffers from high computation cost and the lack of inverse designability. In addition, numerical models often employ assumptions that might affect the fidelity of the models. Ideally, analytical modeling-based design approach, in which the design relationships are explicitly expressed as formulations, could provide a computationally-efficient and informative design alternative. The analytical model usually does not require extensive experimentation either, and can save iteration times during the product development. Commonly utilized homogenization modeling approach assumes infinite number of unit cells in different spatial directions and neglect the real-world non-ideal scenarios such as boundary constraints. The stress heterogeneity distribution results in significant deviations from classical homogenized models and even lead toward earlier failure. However, limited studies have been carried out on local stress heterogeneity effects. Here, the intrinsic stochastic material quality/property variabilities within elements (thin walls/ struts) of additive manufacturing (AM) cellular structures further complicates the issue. To address these non-ideal scenarios, a model that could fully capture the heterogeneity of the structures based on full-size cellular structure needs to be developed. An important aspect investigated in this work is the material plasticity. The performances of cellular structured made with brittle (elastic) materials have been investigated extensively in previous works from our research group. However, most common AM materials in structural applications exhibit ductile plasticity behaviors, which necessitates heterogeneous plasticity-based models. However, modeling analysis of cellular structures with plastic materials has been mostly carried out by experimental or numerical works, and the capturing of plasticity behavior within cellular structure in analytical modeling is challenging and complex. The development of high-fidelity full-scale plasticity-based analytical model is needed. Cellular structures are interconnected networks of thin features (walls/struts), and the quality/ property of these thin features can have significant influence on determining macroscopic performance of overall cellular structure. Despite the structural optimization of cellular structures, they could still suffer from underperformance due to the poor quality of fabricated thin features serving as a root cause. However, research is mostly focused on understanding and optimizing performance of overall cellular structures. Therefore, the need for fabrication of high-quality cellular structures clearly suggests for more research works on understanding how better-quality thin features can be manufactured. Extensive experimental and simulations studies on thin features to gain knowledge on process-geometry-property/quality relationships can be helpful. For example, although powder feedstock stochasticity has shown significant relationships to mechanical properties with the bulk PBF-AM parts, studies on effect of powder feedstock on thin features has not been explored previously, indicating the need for tailored studies on powder feedstock effect on thin features property/quality. For considering the plastic deformation behaviors of non-ductile materials in structural applications, stiffness matrix-based analytical modeling approach was developed using concentrated plastic hinge theory. Bilinear elastic-plastic constitutive material model was adopted. The preliminary study on different structures identified plastic hinge theory to be applicable to bending-dominated structures only. Additional limitations were observed for diamond and BCC structures at smaller opening angles. The detailed investigation on material-geometry-plasticity behavior indicated significant enhancement of strength and energy absorption capability with the incorporation of material plasticity, but their normalized values followed similar trend as elastic model. Compound effect of material plasticity, boundary constraints and unit cell topology design on mechanical performance were observed. Among the investigated cellular structures, material plasticity introduced significant yield/failure characteristics changes for auxetic structures. More importantly, the stress-state plots obtained from these plasticity models are expected to provide valuable insights for design iterations for different engineering applications. The selective reinforcement strategy of most critical element(s) within the cellular structure was adopted in this dissertation to investigate the effect of local stress heterogeneity and its distribution in different cellular topologies. The strength reinforcement model based on perfectly elastic material model was developed for reinforcement levels ranging from 5% to 500%. The continued reinforcement led towards more uniform stress distribution in the cellular structure which shifted the local element criticality. Furthermore, the local elemental criticality distribution in cellular structures were identified to be highly dependent on the unit cell topology. In addition, their failure characteristics exhibited dependency on multiple factors including unit cell topology, reinforcement level and pattern size. The effect of intrinsic AM stochastic material quality/property variabilities were also explored to investigate their impact on mechanical properties and failure patterns. Analytical models incorporated quality variabilities in terms of elastic modulus and strength variabilities ranging from 2% to 10%. The variability propagation effect and stochastic failure patterns were investigated on different 2D cellular structures where the strength was reinforced to 50%, 100% and 250% objectives. The study revealed a higher negative influence of material strength variability than material elastic modulus variability on both strength reinforcement achievability and failure patterns. Similarly, the variability propagation showed negative impact on strength reinforcement except for diamond structures. Diamond structures showed potential for positive reinforcement owing to their highly topology dominant stress concentration at center unit cell. Strength reinforcement probabilistic lower bound with 95% confidence intervals for each unit cell topology were also presented, however, the real-world application of these reinforced structures demand for design with safety factor in mind. Furthermore, the potential optimized design was suggested by investigating the distribution of first critical element within each cellular topology. Considering the highly complex nature of PBF-AM process and smaller dimensions of thin features, powder feedstock-geometry-process-property/quality (PGPP/Q) relationships were experimentally investigated using Ti6Al4V powders initially at high volumetric energy density of 75 – 92.6 J/mm3. Thin features (walls and struts) with dimensions ranging from 0.1mm to 0.5mm were studied. Interestingly, an increase in feature dimension increased the internal porosity within the thin features. The microstructure grain size showed dependency on the feature dimension. Both powder feedstock and feature dimensions showed significant influence on properties and quality of thin features. More importantly, the statistical analysis indicated the existence of complex PGPP/Q relationships. All the findings from this study were limited to higher-than-nominal energy density and demanded for extension of our experimental design to low and mid energy densities. For the second thin feature study, the process window was extended to cover the entire processing window such that the volumetric energy density ranges from 34 to 92.6 J/mm3. Optimal processing windows (internal porosity < 1%) for each feature dimension fabricated with different powder feedstock were identified. With the aim to explore the potential but less obvious relationships that are difficult to identify with classical statistical approaches, two graphical model-based machine learning (ML) approaches (Graphical Mediation analysis and Bayesian network structure learning) were explored. These data-driven approaches identified several cause-effect relationships which included direct relationships from input to flexural properties, indirect relationships from input though intermediate variables to flexural properties and the relationships among intermediate variables (not identified with statistical analysis). The mediation analysis and bayesian network complemented each other towards the identification of potential new PGPP/Q relationships, implying the feasible of these graphical ML approaches in exploring the complex relationships in PBF-AM processes. Based on the resulted directed acyclic graphs, several hypotheses were postulated. Although these hypotheses were not validated/verified in this study, they aim towards guiding/inspiring future more tailored studies rather than drawing final conclusions. Overall, this dissertation addressed several existing challenges and literature gaps related to the thin features and cellular structures. Elastic and plastic material models developed for cellular structures helped in gaining detailed knowledge and understanding on their mechanical performances and failure behavior along with some design guidelines. Studies on selectively reinforced structures, with or without stochastic material property variability, contributed towards understanding local stress heterogeneity. The knowledge from reinforced structure could help in understanding the performance behavior of complex structures with dimensional heterogeneity such as cellular structures with gradient design. Despite cellular topology studies, the thin features studies conducted in this dissertation provide detailed insights into the limitedly understood PGPP/Q relationship for PBF-AM thin features. The hypotheses enabled by the graphical ML modeling approach could serve as a inspiration for future studies on thin features such that the thin features and cellular structures can be repeatedly fabricated with better quality.
Recommended Citation
Koju, Naresh, "Modeling and understanding of additive manufacturing periodic cellular structures with heterogeneity: Property, quality and design strategy." (2024). Electronic Theses and Dissertations. Paper 4490.
Retrieved from https://ir.library.louisville.edu/etd/4490
