Homogenization of material properties in additively manufactured structures

Abstract

Additive manufacturing transforms material into three-dimensional parts incrementally, layer by layer or path by path. Subject to the build direction and machine resolution, an additively manufactured part deviates from its design model in terms of both geometry and mechanical performance. In particular, the material inside the fabricated part often exhibits spatially varying material distribution (heterogeneity) and direction dependent behavior (anisotropy), indicating that the design model is no longer a suitable surrogate to consistently estimate the mechanical performance of the printed component. We propose a new two-stage approach to modeling and estimating effective elastic properties of parts fabricated by fused deposition modeling (FDM) process. First, we construct an implicit representation of an effective mesoscale geometry-material model of the printed structure that captures the details of the particular process and published material information. This representation of mesoscale geometry and material of the printed structure is then homogenized at macro scale through a solution of an integral equation formulated using Green's function. We show that the integral equation can be converted into a system of linear equations that is symmetric and positive definite and can be solved efficiently using conjugate gradient method and Fourier transform. The computed homogenized properties are validated by both finite element method and experiment results. The proposed two-stage approach can be used to estimate other effective material properties in a variety of additive manufacturing processes, whenever a similar effective mesoscale geometry-material model can be constructed.

Quantitative analysis of 0% infill density surface profile of printed part fabricated by personal FDM 3D printer

“…Rapid prototyping (RP) refers to a collection of new technologies, such as fused deposition modeling (FDM), direct metal deposition (DMD), selective laser sintering (SLS), inject modeling (IJM) and stereolithography (SLA), which can be used to create any desired 3D physical model of a printed part, element, device or artefact faster than before without machining or tooling [1] by layer manufacturing from computer aided design (CAD) data [2] and without a significant increase in time or cost [3]. This rapid growth of the market has placed 3D printers not just in enormously varied industrial settings but also in schools, universities, and homes, and it is therefore often preferable to call these devices a 'personal 3D printer' or 'desktop 3D printer' [4,5].…”

Mechanical Characterization of Additively Manufactured Parts by FE Modeling of Mesostructure

“…The stiffness properties should satisfy the reciprocal relation ν 12 /E 1 = ν 21 /E 2 , where ν 12 obtained from previous case and ν 21 = −ε 11 /ε 22 is calculated from this case.…”

“…Rodriguez et al [20] employed a numerical homogenization approach and a strength of material approach to find the elastic moduli of a material. Liu and Shapiro [21] proposed a new approach to find the elastic moduli of the parts fabricated by FDM, in which mesostructure is accounted for homogenization at macro scale level using Green's function. An experimental fatigue damage analysis of FDM processed parts was carried out in [22].…”

Comparison of As-Built FEA Simulations and Experimental Results for Additively Manufactured Dogbone Geometries

“…Liu et al [48] use a different approach to predict mechanical behavior, a homogenization method to compensate for the heterogeneity FDM parts. An implicit representation of the effective mesoscale structure is created and is then homogenized at a macro scale using a solution through an integral equation using Green's function [48].…”