Shakedown-reliability based fatigue strength prediction of parts fabricated by directed energy deposition considering the microstructural inhomogeneities. (English) Zbl 1539.74400
Summary: For mechanical components made by additive manufacturing (AM) techniques such as directed energy deposition (DED), micropores and other defects prevalently exist in the microstructure and they significantly reduce the reliability of these parts. To allow the influence of these microstructural features over the load bearing capacity to be considered in the design stage of AM structures, in the present paper we developed a multiscale numerical approach. The goal of this approach is to predict the failure probability of AM structures subjected to time-varied loadings, and it is realized through combining statistical homogenization, shakedown analyses, and reliability methods such as first-order reliability method and Monte Carlo simulation. Based on this strategy, we employed statistics of material parameters obtained from micromechanical models as inputs, implemented numerical tools and applied them to two exemplary structures, the plate with a hole and an aircraft bracket. Through a series of case studies carried out using different methods and under different assumptions of material randomness, the paper confirmed the robustness of the derived results and explained the mechanism of how micropores influence the structural reliability. The method developed in this paper can be a viable means for the design and optimization of metallic and metal matrix composite structures produced by AM techniques.
MSC:
| 74R99 | Fracture and damage |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74E05 | Inhomogeneity in solid mechanics |
| 74M25 | Micromechanics of solids |
| 74K99 | Thin bodies, structures |
Keywords:
additive manufacturing; multiscale analysis; failure probability; statistical homogenization; first-order reliability method; Monte Carlo method; holed plate; aircraft bracketSoftware:
GurobiReferences:
| [1] | ABAQUS/CAE Users Manual : Version 2020. Simulia, Dassault Systémes (2020) |
| [2] | Arregui, Laura; Garmendia, Iker; Pujana, Joseba; Soriano, Carlos, Study of the geometrical limitations associated to the metallic Part Manufacturing by the LMD process, Procedia CIRP, 68, 363-368 (2018) |
| [3] | Barbieri, Loris; Muzzupappa, M., Performance-driven engineering design approaches based on generative design and topology optimization tools: a comparative study, APPLIED SCIENCES-BASEL, 12, 4, 2106 (2022) |
| [4] | Barrera, O.; Cocks, A. C.F.; Ponter, A. R.S., The Linear Matching Method applied to composite materials: a micromechanical approach, Compos. Sci. Technol., 71, 6, 797-804 (2011) |
| [5] | Benedetti, M.; Fontanari, V.; Bandini, M.; Zanini, F.; Carmignato, S., Low- and high-cycle fatigue resistance of Ti-6Al-4V ELI additively manufactured via selective laser melting: mean stress and defect sensitivity, Int. J. Fatig., 107, 96-109 (2018) |
| [6] | Bhandari, Litton; Gaur, V., On study of process induced defects-based fatigue performance of additively manufactured Ti6Al4V alloy, Addit. Manuf., 60, Article 103227 pp. (2022) |
| [7] | Bonneric, M.; Brugger, C.; Saintier, N.; Moreno, A. C.; Tranchand, B., Contribution of the introduction of artificial defects by additive manufacturing to the determination of the Kitagawa diagram of Al-Si alloys, Procedia Struct. Integr., 38, 141-148 (2022) |
| [8] | Cai, X.; Tang, K.; Ferro, P.; Berto, F., Coordinated effect of microstructure and defect on fatigue accumulation in dual-phase Ti-6Al-4V: quantitative characterization, Int. J. Fatig., 167, Article 107305 pp. (2023) |
| [9] | Cao, Mengzhen; Liu, Y.; Dunne, F. P.E., A crystal plasticity approach to understand fatigue response with respect to pores in additive manufactured aluminium alloys, Int. J. Fatig., 161, Article 106917 pp. (2022) |
| [10] | Chen, Geng; Bezold, A.; Broeckmann, C.; Weichert, D., On the statistical determination of strength of random heterogeneous materials, Compos. Struct., 149, 220-230 (2016) |
| [11] | Chen, G.; Bezold, A.; Broeckmann, C., Influence of the size and boundary conditions on the predicted effective strengths of particulate reinforced metal matrix composites (PRMMCs), Compos. Struct., 189, 330-339 (2018) |
| [12] | Chen, G.; Jiang, K.; Zhang, L.; Bezold, A.; Weichert, D.; Broeckmann, C., A Bayesian statistics based investigation of binder hardening’s influence on the effective strength of particulate reinforced metal matrix composites (PRMMC), Int. J. Mech. Sci., 159, 151-164 (2019) |
| [13] | Chen, G.; Zhang, L.; Bezold, A.; Broeckmann, C.; Weichert, D., Statistical investigation on influence of grain size on effective strengths of particulate reinforced metal matrix composites, Comput. Methods Appl. Mech. Eng., 352, 691-707 (2019) · Zbl 1441.74054 |
| [14] | Chen, G.; Wang, H.; Bezold, A.; Broeckmann, C.; Zhang, D. W.; L, Strengths prediction of particulate reinforced metal matrix composites (PRMMCs) using direct method and artificial neural network, Compos. Struct., 223, Article 110951 pp. (2019) |
| [15] | Chen, G.; Xin, S.; Zhang, L.; Broeckmann, C., Statistical analyses of the strengths of particulate reinforced metal matrix composites (PRMMCs) subjected to multiple tensile and shear stresses, Chin. J. Mech. Eng., 34, 1, 142 (2021) |
| [16] | Chen, Yisheng, Topology optimization design and experimental research of a 3D-printed metal aerospace bracket considering fatigue performance, Appl. Sci., 11, 15, 6671 (2021) |
| [17] | Chinh, P. D., Shakedown theory for elastic plastic kinematic hardening bodies, Int. J. Plast., 23, 7, 1240-1259 (2007) · Zbl 1294.74017 |
| [18] | Chinh, Pham Duc, On shakedown theory for elastic-plastic materials and extensions, J. Mech. Phys. Solid., 56, 1905-1915 (2008) · Zbl 1162.74327 |
| [19] | Dang Van, K., Introduction to Fatigue Analysis in Mechanical Design by the Multiscale Approach, 57-88 (1999) · Zbl 0938.74062 |
| [20] | Dang Van, K.; Griveau, B., On a New Multiaxial Fatigue Limit Criterion-Theory and Application,” Biaxial and Multiaxial Fatigue(A 90-16739 05-39), 479-496 (1989), Mechanical Engineering Publications, Ltd.: Mechanical Engineering Publications, Ltd. London |
| [21] | Dang Van, K.; Papadopoulos, I. V., High-cycle Metal Fatique: from Theory to Applications (1999), Springer · Zbl 0924.00021 |
| [22] | DebRoy, T., Additive manufacturing of metallic components-Process, structure and properties, Prog. Mater. Sci., 92, 112-224 (2018) |
| [23] | Delissen, Arnoud; Boots, E.; Laro, D.; Kleijnen, H.; van Keulen, F.; Langelaar, M., Realization and assessment of metal additive manufacturing and topology optimization for high-precision motion systems, Addit. Manuf., 58, Article 103012 pp. (2022) |
| [24] | Fatemi, A.; Molaei, R.; Sharifimehr, S.; Phan, N.; Shamsaei, N., Multiaxial fatigue behavior of wrought and additive manufactured Ti-6Al-4V including surface finish effect, Int. J. Fatig., 100, 347-366 (2017) |
| [25] | Gurobi Optimizer Reference Manual, 2021 (2021) |
| [26] | Gheysen, J.; Tingaud, D.; Villanova, J.; Hocini, A.; Simar, A., Exceptional fatigue life and ductility of new liquid healing hot isostatic pressing especially tailored for additive manufactured aluminum alloys, Scripta Mater., 233, Article 115512 pp. (2023) |
| [27] | Giugliano, Dario; Barbera, D.; Chen, H., Effect of fiber cross section geometry on cyclic plastic behavior of continuous fiber reinforced aluminum matrix composites, Eur. J. Mech. Solid., 61, 35-46 (2017) |
| [28] | Gupta, Alok C.; Bennett, C. J.; Sun, W., An Experimental Investigation on the Progressive Failure of an Additively Manufactured Laser Powder Bed Fusion Ti-6Al-4V Aero-Engine Bracket under Low Cycle Fatigue (2022), Engineering Failure Analysis |
| [29] | Gupta, Alok; Bennett, C. J.; Sun, W., Fatigue Property-Performance Relationship of Additively Manufactured Ti-6Al-4V Bracket for Aero-Engine Application: an Experimental Study (2022), Procedia Structural Integrity |
| [30] | Hamid, Mehdi; Saleh, M. S.; Afrouzian, A.; Panat, R.; Zbib, H. M., Modeling of porosity and grain size effects on mechanical behavior of additively manufactured structures, Addit. Manuf., 38, Article 101833 pp. (2021) |
| [31] | Heitzer, Michael; Staat, M., Limit and shakedown analysis with uncertain data, Lect. Notes Econ. Math. Syst., 253-267 (2002) · Zbl 1001.90024 |
| [32] | Heitzer, M.; S. M., Reliability Analysis of Elasto-Plastic Structures under Variable Loads, 269-288 (2000), Springer Netherlands |
| [33] | Hu, Y. N., The effect of manufacturing defects on the fatigue life of selective laser melted Ti-6Al-4V structures, Mater. Des., 192, Article 108708 pp. (2020) |
| [34] | Hu, D.; Pan, J.; Mao, J.; Guo, X.; Ji, H.; Wang, R., An anisotropic mesoscale model of fatigue failure in a titanium alloy containing duplex microstructure and hard α inclusions, Mater. Des., 193, Article 108844 pp. (2020) |
| [35] | Juan Guillermo Santos Macías; Elangeswaran, C.; Zhao, L.; Buffière, J.-Y.; Van Hooreweder, B.; Simar, A., Fatigue crack nucleation and growth in laser powder bed fusion AlSi10Mg under as built and post-treated conditions, Mater. Des., 210, Article 110084 pp. (2021) |
| [36] | Jun-Hyok, Ri, Un-Il Ri, Hyon-Sik Hong, and Chang-Man Kwak, “Eigenstress-based shakedown analysis for estimation of effective strength of composites under variable load,”, Compos. Struct., 280, Article 114851 pp. (2022) |
| [37] | Kavousi, M.; McGarry, P.; McHugh, P.; Leen, S., Geometrical and crystal plasticity modelling: towards the establishment of a process-structure-property relationship for additively manufactured 316L struts, Eur. J. Mech. Solid., 102, Article 105115 pp. (2023) · Zbl 1529.74011 |
| [38] | Koiter, W. T., A new general theorem on shake-down of elastic-plastic structures, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B, B59 (1956) · Zbl 0074.40801 |
| [39] | Laleh, Majid, A critical insight into lack-of-fusion pore structures in additively manufactured stainless steel, Addit. Manuf., 38, Article 101762 pp. (2021) |
| [40] | Li, H. X., Microscopic limit analysis of cohesive-frictional composites with non-associated plastic flow, Eur. J. Mech. Solid., 37, 281-293 (2013) · Zbl 1347.74016 |
| [41] | Li, Chunxu; Pisignano, D.; Zhao, Y.; Xue, J., Advances in medical applications of additive manufacturing, Engineering, 6, 11, 1222-1231 (2020) |
| [42] | Liu, J.; Chen, Q.; Liang, X.; To, A., Manufacturing cost constrained topology optimization for additive manufacturing, Front. Mech. Eng., 14 (2019) |
| [43] | Liu, Zhiyuan, Additive manufacturing of metals: microstructure evolution and multistage control, J. Mater. Sci. Technol., 100, 224-236 (2022) |
| [44] | Luo, Y. W., Pore-affected fatigue life scattering and prediction of additively manufactured Inconel 718: an investigation based on miniature specimen testing and machine learning approach, Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 802, 140693 (2021), 140693 |
| [45] | Maconachie, Tobias, SLM lattice structures: properties, performance, applications and challenges, Mater. Des., 183, Article 108137 pp. (2019) |
| [46] | Madhavadas, Vaishnav, A review on metal additive manufacturing for intricately shaped aerospace components, CIRP Journal of Manufacturing Science and Technology, 39, 18-36 (2022) |
| [47] | Magoariec, H.; Bourgeois, S.; Débordes, O., Elastic plastic shakedown of 3D periodic heterogeneous media: a direct numerical approach, Int. J. Plast., 20, 8, 1655-1675 (2004) · Zbl 1066.74576 |
| [48] | Martin, Kumke; Watschke, H.; Vietor, T., A new methodological framework for design for additive manufacturing, Virtual Phys. Prototyp., 11, 1, 3-19 (2015) |
| [49] | Masuo, H., Influence of defects, surface roughness and HIP on the fatigue strength of Ti-6Al-4V manufactured by additive manufacturing, Int. J. Fatig., 117, 163-179 (2018) |
| [50] | Melan, Ernst, Zur Plastizität des räumlichen Kontinuums, Ing. Arch., 9, 2, 116-126 (1938) · JFM 64.0840.01 |
| [51] | Moore, J. A.; Rusch, J. P.; Nezhad, P. S.; Manchiraju, S.; Erdeniz, D., Effects of martensitic phase transformation on fatigue indicator parameters determined by a crystal plasticity model, Int. J. Fatig., 168, Article 107457 pp. (2023) |
| [52] | Motaman, S. Amir H., Optimal design for metal additive manufacturing: an integrated computational materials engineering (ICME) approach, JOM, 72, 3, 1092-1104 (2020) |
| [53] | Muth, A.; John, R.; Pilchak, A.; Kalidindi, S. R.; McDowell, D. L., Analysis of Fatigue Indicator Parameters for Ti-6Al-4V microstructures using extreme value statistics in the transition fatigue regime, Int. J. Fatig., 153, Article 106441 pp. (2021) |
| [54] | Ng, C. H.; Bermingham, M. J.; Dargusch, M. S., Controlling grain size, morphology and texture in additively manufactured β-titanium alloy with super transus hot isostatic pressing, Addit. Manuf., 59, Article 103176 pp. (2022) |
| [55] | Ngo, T. D.; Kashani, A.; Imbalzano, G.; Nguyen, K. T.Q.; Hui, D., Additive manufacturing (3D printing): a review of materials, methods, applications and challenges, Compos. B Eng., 143, 172-196 (2018) |
| [56] | Ngọc Trình Trần; Staat, M., Direct plastic structural design under lognormally distributed strength by chance constrained programming, Optim. Eng., 21, 1, 131-157 (2020) · Zbl 1433.90099 |
| [57] | Omiyale, B. O.; Olugbade, T. O.; Abioye, T. E.; Farayibi, P. K., Wire arc additive manufacturing of aluminium alloys for aerospace and automotive applications: a review, Mater. Sci. Technol., 38, 7, 391-408 (2022) |
| [58] | Ostoja-Starzewski, M., Material spatial randomness: from statistical to representative volume element, Probabilist. Eng. Mech., 21, 2, 112-132 (2006) |
| [59] | Ostoja-Starzewski, M., Microstructural randomness and scaling in mechanics of materials, (Modern Mechanics and Mathematics (2007), Chapman and Hall/CRC) |
| [60] | Paul, Gradl, Robust metal additive manufacturing process selection and development for aerospace components, J. Mater. Eng. Perform., 31, 8, 6013-6044 (2022) |
| [61] | Pingaro, M.; Bellis, M. L.D.; Reccia, E.; Trovalusci, P.; Sadowski, T., Fast statistical homogenization procedure for estimation of effective properties of ceramic matrix composites (CMC) with random microstructure, Compos. Struct., 304, Article 116265 pp. (2023) |
| [62] | Plotkowski, A., Microstructure and properties of a high temperature Al-Ce-Mn alloy produced by additive manufacturing, Acta Mater., 196, 595-608 (2020) |
| [63] | Ponche, Remi; Kerbrat, O.; Mognol, P.; Hascoet, J.-Y., A novel methodology of design for Additive Manufacturing applied to Additive Laser Manufacturing process, Robot. Comput. Integrated Manuf., 30, 4, 389-398 (2014) |
| [64] | Popova, Evdokia; Rodgers, T. M.; Gong, X.; Cecen, A.; Madison, J. D.; Kalidindi, S. R., Process-structure linkages using a data science approach: application to simulated additive manufacturing data, Integrating Materials and Manufacturing Innovation, 6, 1, 54-68 (2017) |
| [65] | Prithivirajan, V.; Sangid, M. D., The role of defects and critical pore size analysis in the fatigue response of additively manufactured IN718 via crystal plasticity, Mater. Des., 150, 139-153 (2018) |
| [66] | Prithivirajan, Veerappan; Ravi, Priya; Naragani, D.; Sangid, M. D., Direct comparison of microstructure-sensitive fatigue crack initiation via crystal plasticity simulations and in situ high-energy X-ray experiments, Mater. Des., 197, Article 109216 pp. (2021) |
| [67] | Qian, G.; Jian, Z.; Qian, Y.; Pan, X.; Ma, X.; Hong, Y., Very-high-cycle fatigue behavior of AlSi10Mg manufactured by selective laser melting: effect of build orientation and mean stress, Int. J. Fatig., 138, Article 105696 pp. (2020) |
| [68] | Romano, Simone; Nezhadfar, P. D.; Shamsaei, N.; Seifi, M.; Beretta, S., High cycle fatigue behavior and life prediction for additively manufactured 17-4 PH stainless steel: effect of sub-surface porosity and surface roughness, Theor. Appl. Fract. Mech., 106, Article 102477 pp. (2020) |
| [69] | M. Shahmardani et al., “Experimental assessment and micromechanical modeling of additively manufactured austenitic steels under cyclic loading,” Adv. Eng. Mater.s, vol. n/a, no. n/a, doi: 10.1002/adem.202300103.. |
| [70] | Staat, M., Limit and shakdedown analysis under uncertainty, Int. J. Comput. Methods, 11, 3, Article 1343008 pp. (2014) · Zbl 1359.74350 |
| [71] | Staat, M.; Heitzer, M., LISA-a European project for FEM-based limit and shakedown analysis, Nucl. Eng. Des., 206, 2, 151-166 (2001) |
| [72] | Staat, Manfred; Heitzer, M., Numerical Methods for Limit and Shakedown Analysis : Deterministic and Probabilistic Problems (2003) |
| [73] | Stanković, Tino; Mueller, J.; Egan, P.; Shea, K., A generalized optimality criteria method for optimization of additively manufactured multimaterial lattice structures, J. Mech. Des., 137, 11 (2015) |
| [74] | Tang, Ming; Pistorius, P. C., Fatigue life prediction for AlSi10Mg components produced by selective laser melting, Int. J. Fatig., 125, 479-490 (2019) |
| [75] | Thanh Ngoc Trần; Kreißig, R.; Staat, M., Probabilistic limit and shakedown analysis of thin plates and shells, Struct. Saf., 31, 1, 1-18 (2009) |
| [76] | Trần, Trình; Tran, T.; Matthies, H. G.; Stavroulakis, G.; Staat, M., Shakedown analysis of plate bending analysis under stochastic uncertainty by chance constrained programming (2016) |
| [77] | Tran, N. T.; Tran, T. N.; Matthies, H. G.; Stavroulakis, G. E.; Staat, M., Shakedown Analysis under Stochastic Uncertainty by Chance Constrained Programming, 85-103 (2018), Springer International Publishing |
| [78] | Trần, Trình; Matthies, H.; Stavroulakis, G.; Staat, M., Direct Plastic Structural Design by Chance Constrained Programming (2018) |
| [79] | Wang, X.; Chen, H.; Xuan, F., Direct method-based probabilistic shakedown analysis for the structure under multiple uncertain design conditions, Ocean Eng., 280, Article 114653 pp. (2023) |
| [80] | Wang, X.; Yang, J.; Chen, H.; Xuan, F., Physics-based probabilistic assessment of creep-fatigue failure for pressurized components, Int. J. Mech. Sci., 250, Article 108314 pp. (2023) |
| [81] | Weichert, D.; Hachemi, A.; Schwabe, F., Application of shakedown analysis to the plastic design of composites, Arch. Appl. Mech., 69, 9-10, 623-633 (1999) · Zbl 0968.74022 |
| [82] | Weingarten, Christian; Buchbinder, D.; Pirch, N.; Meiners, W.; Wissenbach, K.; Poprawe, R., Formation and reduction of hydrogen porosity during selective laser melting of AlSi10Mg, J. Mater. Process. Technol., 221, 112-120 (2015) |
| [83] | Wen, Hao Kan; Nadot, Y.; Foley, M.; Ridosz, L.; Proust, G.; Cairney, J. M., Factors that affect the properties of additively-manufactured AlSi10Mg: porosity versus microstructure, Addit. Manuf., 29, Article 100805 pp. (2019) |
| [84] | Wu, S. C.; Song, Z.; Kang, G. Z.; Hu, Y. N.; Fu, Y. N., The Kitagawa-Takahashi fatigue diagram to hybrid welded AA7050 joints via synchrotron X-ray tomography, Int. J. Fatig., 125, 210-221 (2019) |
| [85] | Xin, Shengzhen; Zhang, Lele; Chen, Min; Gebhardt, Christian; Chen, Geng, Understanding influence of micro pores on strengths of LMDed AlSi10Mg material using a direct method based statistical multiscale framework, Mater. Des., 214, Article 110409 pp. (2022) |
| [86] | Yan, W., Modeling process-structure-property relationships for additive manufacturing, Front. Mech. Eng., 13, 4, 482-492 (2018) |
| [87] | Zhang, J.; Shen, W. Q.; Oueslati, A.; De Saxcé, G., Shakedown of porous materials, Int. J. Plast., 95, 123-141 (2017) |
| [88] | Zhang, Jin; Oueslati, A.; Wanqing Shen; de Saxcé, G., Homogenization of ductile porous materials by limit and shakedown analysis, (Direct Methods: Methodological Progress and Engineering Applications (2021), Springer International Publishing: Springer International Publishing Cham) |
| [89] | Zhang, X. Z., Additive manufacturing of intricate lattice materials: ensuring robust strut additive continuity to realize the design potential, Addit. Manuf., 58, Article 103022 pp. (2022) |
| [90] | Zheng, Xiaoyu; Williams, Christopher; Spadaccini, Christopher M.; Shea, Kristina, Perspectives on multi-material additive manufacturing, J. Mater. Res., 36, 18, 3549-3557 (2021) |
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