Estimation of elastic behaviors of metal components containing process induced porosity

Deng, Shiguang; Soderhjelm, Carl; Apelian, Diran; Suresh, Krishnan

doi:10.1016/j.compstruc.2021.106558

Cited by 5 publications

(11 citation statements)

References 49 publications

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“…We also define a transformation tensor F to project the associated functional spaces between the reference domain and perturbed domain in Equation ( 28) with the properties of F defined in Equation (29).…”

Section: Second-order Functional Derivativementioning

confidence: 99%

“…Since we have demonstrated both the first and second-order porosity sensitivities are implicit functions of the pore parameter in Equations ( 42) and (44), we need to integrate the sensitivity fields to calculate the effects of accumulative shape changes from Figure 3A-D in Section 5. To this end, we can directly account for the performance function of the porous domain in Figure 3A by the field variables computed on the reference domain in Figure 3D.…”

Section: Boundary Formulation Of Second-order Porosity Sensitivitymentioning

confidence: 99%

“…where i and j denote the pore indices in an interactive pore-pair, the integrand in Equation ( 55) is the first-order shape sensitivity in Equation (42), and the integrands in Equations ( 57) and (58) are computed by the second-order shape sensitivities in Equation (44).…”

Section: Pore Shape-dependent Bvpmentioning

confidence: 99%

“…To quantify the impacts of domain transformations on the performance function, we utilize pore shape (𝜂) dependent sensitivity fields (see Section 4) to compute the change of functions in a parameterized domain regarding infinitesimal perturbations. With the help of exterior formulations, the sensitivity fields in Equations ( 42) and (44), which are implicitly based on 𝜂, are now converted to explicit functions of 𝜂 in Equations ( 65)-(68). We integrate the sensitivities to 𝜂 in the range of 0 ≤ 𝜂 ≤ 1, and demonstrate the integrations of the first-order shape sensitivity and the second-order shape sensitivity in Equations ( 69) and (70), respectively.…”

Section: Second-order Porosity Estimatormentioning

confidence: 99%

“…Turevsky et al 28 developed a feature sensitivity by integrating shape sensitivities over geometric transformations to estimate the performance functions in a 2D Poisson problem where topological change was approximated by the shape sensitivity. In a recent work by Deng et al, 29 a first-order defeaturing estimator was developed to exploit the morphology F I G U R E 1 (A) Manufactured metallic component with more than 1300 pores whose morphologies and spatial distributions are reconstructed from 3D x-ray tomography; (B) an extremely fine FE mesh is created with more than 6.2 million tetrahedrons is created to capture the porous part's geometric details; (C) a cross-sectional view of the FE mesh illustrates the existence of irregularly shaped pores in proximity and ill-shaped elements near pore surface; (D) a reduced (i.e., defeatured) model without any pores; and (E) a sufficiently fine mesh on the reduced (i.e., defeatured) model only requires less than 0.25 million elements, that is, about 4% of its porous counterpart of manufacturing-induced pores. To estimate the influence of pores on part behaviors, topological and shape sensitivities were systematically integrated where each pore was assumed far away from neighbors so that interactions were neglected.…”

Section: Introductionmentioning

confidence: 95%

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Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

Deng

Soderhjelm

Apelian

et al. 2022

Numerical Meth Engineering

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Manufactured metallic components often contain nonuniformly distributed pores of complex morphologies. Since such porosity defects have a significant influence on material behaviors and affect the usage in high‐performance applications, it is significant to understand the impact of porosity characteristics on the behaviors of components. In this work, a gradient‐enhanced porosity defeaturing estimator, which allows for the modeling of pore geometry and spatial distribution, is proposed within a general elastostatic framework. In this approach, the first‐order shape sensitivity is implemented to account for the change in the elastic quantity of interests to variations of pore sizes and shapes, which is then supplemented by a second‐order shape sensitivity whose mixed partial derivative quantifies the interactions between pores in proximity. The efficacy of the proposed method comes from its posterior manner that it only relies on field solutions of reference models where pores are suppressed. In this context, meshing difficulty and solution convergence issues are avoided, which would otherwise arise in a direct finite element analysis on porous structures. The impact of porosity on structural elastic performance is approximated using a second‐order Taylor expansion where the topological difference between the porous and reference domains is estimated by topological sensitivity; the field variables on pore boundaries are approximated as explicit functions of design variables using exterior formulations. Numerical results show that the elastic performances of components are influenced by the existence of pores. The pore‐to‐pore interactions are significant when pores are close by.

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Section: Second-order Functional Derivativementioning

confidence: 99%

Section: Boundary Formulation Of Second-order Porosity Sensitivitymentioning

confidence: 99%

Section: Pore Shape-dependent Bvpmentioning

confidence: 99%

Section: Second-order Porosity Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 3 more Smart Citations

Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

Deng

Soderhjelm

Apelian

et al. 2022

Numerical Meth Engineering

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Development of Advanced Aluminum Alloy for Structural Castings

Beals

Niu

Brown³

2022

Light Metals 2022

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Reduced-order multiscale modeling of plastic deformations in 3D alloys with spatially varying porosity by deflated clustering analysis

et al. 2022

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Aluminum alloys are increasingly utilized as lightweight materials in the automobile industry due to their superior capability in withstanding high mechanical loads. A significant challenge impeding the large-scale use of these alloys in high-performance applications is the presence of manufacturing-induced, spatially varying porosity defects. In order to understand the impacts of these defects on the macro-mechanical properties of cast alloys, multiscale simulations are often required. In this paper, we introduce a computationally efficient reduced-order multiscale framework to simulate the behavior of metallic components containing process-induced porosity under irreversible nonlinear deformations. In our approach, we start with a data compression scheme that significantly reduces the number of unknown macroscale and microscale variables by agglomerating close-by finite element nodes into a limited number of clusters. Then, we use deflation methods to project these variables into a lower-dimensional space where the material’s elastoplastic behaviors are approximated. Finally, we solve for the unknown variables and map them back to the original, high-dimensional space. We call our method deflated clustering analysis and by comparing it to direct numerical simulations we demonstrate that it accurately captures macroscale deformations and microscopic effective responses. To illustrate the effect of microscale pores on the macroscopic response of a cast component, we conduct multi-scale simulations with spatially varying local heterogeneities that are modeled with a microstructure characterization and reconstruction algorithm.

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Estimation of elastic behaviors of metal components containing process induced porosity

Cited by 5 publications

References 49 publications

Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

Development of Advanced Aluminum Alloy for Structural Castings

Reduced-order multiscale modeling of plastic deformations in 3D alloys with spatially varying porosity by deflated clustering analysis

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