This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Tensile failure prediction for cellular latticestructure fabricated by material extrusion usingcohesive zone model

Park, Sang‑In; Watanabe, Narumi; Rosen, David W.

2018

Park, S.‑ I., Watanabe, N., & Rosen, D. W. (2018). Tensile failure prediction for cellular latticestructure fabricated by material extrusion using cohesive zone model. Proceedings of the3rd International Conference on Progress in Additive Manufacturing (Pro‑AM 2018),358‑363. doi:10.25341/D47G62

https://hdl.handle.net/10356/88568

https://doi.org/10.25341/D47G62

© 2018 Nanyang Technological University. Published by Nanyang Technological University,Singapore.

Downloaded on 28 Dec 2021 23:45:39 SGT

ABSTRACT: In material extrusion, the geometrical approximation process introduces defects such as voids and gaps in the build plane as well as along the building direction. These serve as crack initiation sites and increase possibility of fracture by crack propagation. As a result, structural members under tensile loading in lattice structures tend to fail at significantly lower stresses than strengths that are estimated only based on elastic or plastic failure criteria. In this paper, we present a failure prediction approach for material extruded cellular lattice structures under tensile loading. The approach is based on a cohesive zone model (CZM) and assesses two failure criteria: elastic failure and fracture. We constructed as-fabricated voxel models for lattice structures and inserted cohesive zone element at interfaces between layers. The failure strength was estimated using the voxel models and are compared with test results.

KEYWORDS: Cellular lattice structure, Material Extrusion, Cohesive Zone Model, Interlayer bonding strength, As-fabricated voxel model

INTRODUCTION

Recent advances in additive manufacturing (AM) processes provide new opportunities to fabricate cellular lattice structures more easily and accurately. Although technical issues in AM processes such as fabrication time and accuracy have been improved (Tumbleston et al. 2015), applications of cellular lattice structures are still limited due to their geometrical complexity. Many struts in lattice structures increase bounding surfaces, which should be approximated in AM process workflows. Geometrical approximations in the AM workflow result in geometrical degradation in fabricated lattice structures (Ahn et al. 2009, Karamooz Ravari et al. 2014). Degraded struts in the lattice structure do not show intended mechanical performance and, as a result, mechanical properties of lattice structures are also significantly degraded.

In material extrusion, as-manufactured parts generally have two types of defects. The slicing process introduces stairs steps, and filament-deposition process produces voids and gaps among filaments. These defects play a role of embedded cracks as well as stress concentration sites under tensile loading. Thus, the defects as cracks limit mechanical strength of manufactured lattice structures as they grow along filament or layer interfaces.

TENSILE FAILURE PREDICTION FOR CELLULAR LATTICE STRUCTURE FABRICATED BY MATERIAL EXTRUSION USING

COHESIVE ZONE MODEL

SANG IN PARK* WATANABE **

DAVID W ROSEN *, **

* Digital Manufacturing and Design (DManD) Centre,Singapore University of Technology and Design, Singapore

** The G. W. W. School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia

SANG-IN PARK*

NARUMI WATANABE**

DAVID W ROSEN*,**

358

Proc. Of the 3rd Intl. Conf. on Progress in Additive Manufacturing (Pro-AM 2018) Edited by Chee Kai Chua, Wai Yee Yeong, Ming Jen Tan, Erjia Liu and Shu Beng TorCopyright © 2018 by Nanyang Technological UniversityPublished by Nanyang Technological University ISSN: 2424-8967 :: https://doi.org/10.25341/D47G62

More importantly, these embedded cracks affect strength of cellular lattice structures more significantly than that of bulky parts. Large bounding surfaces in lattice structures increase the possibility of crack initiation. In addition to this, the relative size of crack region become large compared to bulky parts. Therefore, crack initiation and propagation easily occur and critically degrade strength of lattice structures. Cohesive zone model (CZM) is a numerical fracture analysis model devised to describe crack propagation and fracture in bonded interfaces. Several researchers utilized a cohesive zone model to investigate interlayer strength of additively manufactured parts. Liravi et al. developed a cohesive zone model to estimate a pulling-up force at failure in a bottom-up projection-based photo polymerization process (Liravi et al. 2015). Spackman et al. constructed CZM and proposed model-based design framework for a fiber-reinforced soft composite additive manufacturing process (Spackman et al. 2017). The authors selected CZM parameters based on calibration experiments. Fracture mechanics approach can be used to explain strength degradation between layers. Ahmadi et al. implemented CZM to assess mechanical properties of metal parts fabricated by a powder bed fusion process (Ahmadi et al. 2016). The authors utilized CZM to define interactions among melt pool boundaries based on their observation that melt pool boundaries are weaker than grain boundaries so that defects are initiated in melt pool boundaries. They predicted effects of microstructure on mechanical properties of fabricated parts based on numerical analysis with CZM. However, previous research has focused on experimental aspects of the approach. A numerical fracture analysis model can help to expedite the design process for material extruded lattice structure. The goal of this research is to estimate failure strength of a lattice structure considering fracture mechanics in addition to elastic failure. To achieve the goal, we propose a research framework presented in Figure 1. We developed a cohesive zone model, and we incorporated the developed model into an as-fabricated model of lattice structures. The strength degradation is assessed by analyzing as-fabricated voxel models with cohesive zone elements.

Figure 1 Conceptual diagram for research framework TEST METHOD FOR CHARACTERIZING INTERLAYER BONDING STRENGTH In this research, we implemented the ASTM D5528-13 testing method to quantify inter-layer bonding fracture strength (ASTM 2013). This method utilizes a double cantilever beam (DCB) specimen as shown in Figure 2(a). Since this test method is devised for a continuous fiber-reinforced composite material, we modified a test specimen to assess interlayer bonding strength between filaments. A material extrusion device fills a part volume with thin ABS filaments based

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finite element analysis. The cohesive parameters were determined based on parametric studies of traction force opening displacement responses by changing the parameters. The values of the parameters were selected for minimizing differences in traction force-opening displacement responses. The selected penalty stiffness was 12.1 MPa, and the cohesive strength and fracture energy were 10.2 MPa and 1200 J/m2, respectively. The response using cohesive zone model is presented in Figure 4 with test results. The obtained cohesive parameters were applied to cohesive zones at interfaces in as-fabricated voxel models explained in the following section. AS-FABRICATED VOXEL MODEL WITH COHESIVE ELEMENTS As-fabricated voxel modeling is an approach to construct a voxel model of material extruded parts based on deposition paths. This approach is capable to include geometrical defects such as stair steps, void and gaps in the numerical model (Park and Rosen 2016). To incorporate the cohesive zone into as-fabricated voxel models, we inserted a layer of cohesive elements at the layer interfaces of the finite element model. Figure 8 shows an as-fabricated voxel model of a 2D rectangular lattice structure and corresponding cohesive elements. The specimens were built in five different building angles at 0, 30, 45, 60 and 90 degrees to investigate the effects of the building direction. To estimate strength of lattice structures, we conducted numerical tensile tests using the cohesive zone augmented as-fabricated models. The strength was calculated based on the maximum force. The estimation results were compared with test results. Figure 9 presents the comparison among estimated and experimentally tested results of the 2D rectangular lattice specimens. The strength was normalized with respect to desired strength, which is obtained without any degradation and fracture failure. Test specimen strength was reduced up to 87% compared with desired strength. Since the interlayer bonding strength is much lower than yield strength, the interlayer bonding strength limits the strength of lattice structure manufactured at high build angles. The as-fabricated voxel models with cohesive zone modeling provided good estimates for strength. At the 90-degree build angle, the model shows about 10% error. When a strut is built vertically, more layers are generated than at lower build angles. This can increase the possibility of other defects such as misalignment between layers. Thus, the test specimens showed additional degradation. When only elastic failure mode is considered, the estimates at build angles over 30-degree show large error. However, consideration of fracture failure mode enables accurate prediction of lattice structure strength.

Layers of cohesive elementsBuild angle

Figure 8 As-fabricated voxel model with cohesive zone elements

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Figure 9 Comparison of estimated strength of 2D rectangular lattice structure CONCLUSION A tensile failure prediction approach was presented based on cohesive zone and as-fabricated voxel modeling approaches. To obtain the cohesive parameters, DCB tests were conducted with modified specimens. The cohesive parameters were selected using parametric studies so that the values minimize the difference between DCB tests and numerical analysis results. The determined cohesive parameters were integrated into as-fabricated voxel models to estimate tensile strength of lattice structures. The proposed approach considering fracture failure was able to predict accurate strength, which cannot be estimated with only elastic yielding criteria. In future research, we will investigate three-dimensional lattice structures using the proposed approaches. ACKNOWLEDGMENTS The authors gratefully acknowledge support from the National Science Foundation, grants CMMI-1200758 and CMMI-1538744. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors also acknowledge support from the Digital Manufacturing and Design research centre at the Singapore University of Technology & Design under project RGDM1710205. REFERENCES Ahmadi, A., et al. (2016). "Effect of manufacturing parameters on mechanical properties of 316L stainless steel

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Processing Technology 209(15): 5593-5600. ASTM (2013). Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-

Reinforced Polymer Matrix Composites, ASTM International. Karamooz Ravari, M. R., et al. (2014). "Numerical investigation on mechanical properties of cellular lattice

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surface Stereolithography processes." Computer-Aided Design 69: 134-142. Park, S.-i. and D. W. Rosen (2016). "Quantifying effects of material extrusion additive manufacturing process on

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Spackman, C. C., et al. (2017). "A Cohesive Zone Model for the Stamping Process Encountered During Three-Dimensional Printing of Fiber-Reinforced Soft Composites." Journal of Manufacturing Science and Engineering 140(1): 011010-011010-011010.

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