An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test
This paper presents the estimation of the parameters of the Cowper-Symonds material model of a commercial copper alloy from a single Split Hopkinson Pressure Bar Test using an inverse method. Parameters were identified by minimizing the error between the transmitted strain signal predicted by a fini...
- Autores:
-
Hernandez, Camilo
Blanco, David L.
Maranon, Alejandro
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2023
- Institución:
- Escuela Colombiana de Ingeniería Julio Garavito
- Repositorio:
- Repositorio Institucional ECI
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.escuelaing.edu.co:001/3155
- Acceso en línea:
- https://repositorio.escuelaing.edu.co/handle/001/3155
https://doi.org/10.1007/s40870-022-00364-5
https://link.springer.com/article/10.1007/s40870-022-00364-5
- Palabra clave:
- UNS C83600
Mechanical characterization
High-strain rates
Split Hopkinson Pressure Bar Test
Taylor test
Inverse problem
Parameter identifcation
- Rights
- openAccess
- License
- https://creativecommons.org/licenses/by-nc/4.0/
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| dc.title.eng.fl_str_mv |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| title |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| spellingShingle |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test UNS C83600 Mechanical characterization High-strain rates Split Hopkinson Pressure Bar Test Taylor test Inverse problem Parameter identifcation |
| title_short |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| title_full |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| title_fullStr |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| title_full_unstemmed |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| title_sort |
An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test |
| dc.creator.fl_str_mv |
Hernandez, Camilo Blanco, David L. Maranon, Alejandro |
| dc.contributor.author.none.fl_str_mv |
Hernandez, Camilo Blanco, David L. Maranon, Alejandro |
| dc.contributor.researchgroup.spa.fl_str_mv |
Grupo de Investigación en Diseños sostenibles en ingeniería mecánica |
| dc.subject.proposal.eng.fl_str_mv |
UNS C83600 Mechanical characterization High-strain rates Split Hopkinson Pressure Bar Test Taylor test Inverse problem Parameter identifcation |
| topic |
UNS C83600 Mechanical characterization High-strain rates Split Hopkinson Pressure Bar Test Taylor test Inverse problem Parameter identifcation |
| description |
This paper presents the estimation of the parameters of the Cowper-Symonds material model of a commercial copper alloy from a single Split Hopkinson Pressure Bar Test using an inverse method. Parameters were identified by minimizing the error between the transmitted strain signal predicted by a finite element model and those observed experimentally. The Taylor Test was used to validate the identified parameters by comparing the experimental final length of impacted specimens and the ones predicted by a finite element model using the identified parameters. Also, identified parameters were contrasted with those found by a traditional curve-fitting approach. It was found that finite element models using the identified parameters are better able to predict plastic deformation than those using parameters from traditional curve-fitting. |
| publishDate |
2023 |
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2023 |
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2024-07-10T19:58:11Z |
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2024-07-10T19:58:11Z |
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Artículo de revista |
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https://doi.org/10.1007/s40870-022-00364-5 |
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https://repositorio.escuelaing.edu.co/handle/001/3155 https://doi.org/10.1007/s40870-022-00364-5 https://link.springer.com/article/10.1007/s40870-022-00364-5 |
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eng |
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eng |
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Journal of Dynamic Behavior of Materials |
| dc.relation.references.spa.fl_str_mv |
Sun Y, Burgueño R, Vanderklok AJ, Tekalur SA, Wang W, Lee I (2014) Compressive behavior of aluminum/copper hybrid foams under high strain rate loading. Mater Sci Eng A 592:111–120. Acharya S, Gupta R, Ghosh J, Bysakh S, Ghosh K, Mondal D, Mukhopadhyay AK (2017) High strain rate dynamic compressive behaviour of Al6061-T6 alloys. Mater Charact 127:185–197. Wang L, Qiao J, Ma S, Jiao Z, Zhang T, Chen G, Zhao D, Zhang Y, Wang Z (2018) Mechanical response and deformation behavior of al0. 6cocrfeni high-entropy alloys upon dynamic loading. Mater Sci Eng A 727:208–213. Zhang W, Chen X, Zhuo B, Li P, He L (2018) Efect of strain rate and temperature on dynamic mechanical behavior and microstructure evolution of ultra-high strength aluminum alloy. Mater Sci Eng A 730:336–344. Kavanagh KT, Clough RW (1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7(1):11–23. Mariani S, Gobat G (2019) Identifcation of strength and toughness of quasi-brittle materials from spall tests: a sigma-point kalman flter approach. Inverse Probl Sci Eng 27(9):1318–1346. Vaz M Jr, Tomiyama M (2020) Identifcation of inelastic parameters of the aisi 304 stainless steel: a multi-test optimization strategy. Inverse Probl Sci Eng 28(11):1551–1569. Field JE, Walley SM, Proud WG, Goldrein HT, Siviour CR (2004) Review of experimental techniques for high rate deformation and shock studies. Mater Sci Eng A 30(7):725–775. Chen WW, Song B (1989) Split Hopkinson (Kolsky) bar: design testing and applications. Springer, New York. Gilat A, Seidt J, Matrka T, Gardner K (2019) A new device for tensile and compressive testing at intermediate strain rates. Exp Mech 59(5):725–731. Sasso M, Newaz G, Amodio D (2008) Material characterization at high strain rate by hopkinson bar tests and fnite element optimization. Mater Sci Eng A 487(1–2):289–300. Sedighi M, Khandaei M, Shokrollahi H (2010) An approach in parametric identifcation of high strain rate constitutive model using hopkinson pressure bar test results. Mater Sci Eng A 527(15):3521–3528. Milani AS, Dabboussi W, Nemes JA, Abeyaratne RC (2009) An improved multi-objective identifcation of Johnson-Cook material parameters. Int J Impact Eng 36(2):294–302. ASTM: ASTM standard E478-08(2008)-Standard test methods for chemical analysis of copper alloys. ASTM: ASTM designation B62-09(2009)-Standard specifcation for composition bronze or ounce metal castings. ASTM: ASTM standard E9-09 (2009)-standard test methods of compression testing of metallic materials at room temperature. Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc Sect B 62(11):676–700. Hopkinson B (1914) A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets. Proc R Soc Lond Ser A 89(612):411–413. Davies RM (1948) A critical study of the Hopkinson pressure bar. Philos Trans R Soc Lond Ser A 240(821):375–457. Taylor GI (1948) The use of fat-ended projectiles for determining dynamic yield stress. I. Theoretical considerations. Proc R Soc Lond Ser A 194(1038):289–299. Meyers MA (1994) Dynamic Behavior of Materials. Wiley-Interscience, New York. Whifn AC (1948) The use of fat-ended projectiles for determining dynamic yield stress. II. Tests on various metallic materials. Proc R Soc Lond A 194:300–322. Wilkins ML, Guinan MW (1973) Impact of cylinders on a rigid boundary. J Appl Phys 44(3):1200–1206. Hawkyard JB (1969) A theory for the mushrooming of fat-ended projectiles impinging on a fat rigid anvil, using energy considerations. Int J Mech Sci 11(3):313–333. ANSYS: ANSYS LS-DYNA User’s Guide: ANSYS Release 12.0. ANSYS Inc., (2009). ANSYS Inc. Cowper GR, Symonds PS (1957) Strain hardening and strainrate efects in the impact loading of cantilever beams. Technical Report 28, Brown University Division of Applied Mathematics. Hernandez C, Maranon A, Ashcroft I, Casas-Rodriguez J (2013) A computational determination of the Cowper-Symonds parameters from a single Taylor test. Appl Math Modell 37(7):4698–4708. Hernandez C, Buchely M, Maranon A (2015) Dynamic characterization of Roma Plastilina No. 1 from Drop Test and inverse analysis. Int J Mech Sci 100:158–168. Acosta C, Hernandez C, Maranon A, Casas-Rodriguez J (2016) Validation of material constitutive parameters for the AISI 1010 steel from Taylor impact tests. Mater Des 110:324–331. Lambert G, Gao H (1995) Line moments and invariants for real time processing of vectorized contour data. In: Braccini C, DeFloriani L, Vernazza G (eds) Image analysis and processing. Lecture notes in computer science. Springer, New York, pp 347–352. Hu MK (1962) Visual pattern recognition by moment invariants. IRE Trans Inform Theory 8(2):179–187. Wen W, Lozzi A (1993) Recognition and inspection of manufactured parts using line moments of their boundaries. Pattern Recognit 26(10):1461–1471. ASTM: ASTM Standard E8/E8M-22-Standard test methods for tension testing of metallic materials (2022). Shin H, Kim J-B (2019) Evolution of specimen strain rate in split Hopkinson bar test. Proc Inst Mech Eng Part C 233(13):4667–4687. Gray G III, Blumenthal WR (2000) Split-hopkinson pressure bar testing of soft materials. ASM Handbook 8:488–496. |
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Hernandez, Camilo102b737cea49dba2f49906ecbbafe5dd600Blanco, David L.94263308a331e3abf3b21940643c3e3dMaranon, Alejandro2c99cbb293bab3ddd019fcb66437f513600Grupo de Investigación en Diseños sostenibles en ingeniería mecánica2024-07-10T19:58:11Z2024-07-10T19:58:11Z20232199-7446https://repositorio.escuelaing.edu.co/handle/001/3155https://doi.org/10.1007/s40870-022-00364-52199-7454https://link.springer.com/article/10.1007/s40870-022-00364-5This paper presents the estimation of the parameters of the Cowper-Symonds material model of a commercial copper alloy from a single Split Hopkinson Pressure Bar Test using an inverse method. Parameters were identified by minimizing the error between the transmitted strain signal predicted by a finite element model and those observed experimentally. The Taylor Test was used to validate the identified parameters by comparing the experimental final length of impacted specimens and the ones predicted by a finite element model using the identified parameters. Also, identified parameters were contrasted with those found by a traditional curve-fitting approach. It was found that finite element models using the identified parameters are better able to predict plastic deformation than those using parameters from traditional curve-fitting.Este artículo presenta la estimación de los parámetros del modelo de material Cowper-Symonds de una aleación de cobre comercial a partir de una prueba de presión de Hopkinson de una sola barra dividida utilizando un método inverso. Los parámetros se identificaron minimizando el error entre la señal de deformación transmitida predicha por un modelo de elementos finitos y las observadas experimentalmente. La prueba de Taylor se utilizó para validar los parámetros identificados comparando la longitud final experimental de las muestras impactadas y las predichas por un modelo de elementos finitos utilizando los parámetros identificados. Además, los parámetros identificados se contrastaron con los encontrados mediante un enfoque de ajuste de curvas tradicional. Se encontró que los modelos de elementos finitos que utilizan los parámetros identificados son más capaces de predecir la deformación plástica que los que utilizan parámetros del ajuste de curvas tradicional.12 páginasapplication/pdfengSpringer NatureSuizahttps://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)http://purl.org/coar/access_right/c_abf2https://link.springer.com/article/10.1007/s40870-022-00364-5An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar TestArtículo de revistainfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1Workflowinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a8517821679N/AJournal of Dynamic Behavior of MaterialsSun Y, Burgueño R, Vanderklok AJ, Tekalur SA, Wang W, Lee I (2014) Compressive behavior of aluminum/copper hybrid foams under high strain rate loading. Mater Sci Eng A 592:111–120.Acharya S, Gupta R, Ghosh J, Bysakh S, Ghosh K, Mondal D, Mukhopadhyay AK (2017) High strain rate dynamic compressive behaviour of Al6061-T6 alloys. Mater Charact 127:185–197.Wang L, Qiao J, Ma S, Jiao Z, Zhang T, Chen G, Zhao D, Zhang Y, Wang Z (2018) Mechanical response and deformation behavior of al0. 6cocrfeni high-entropy alloys upon dynamic loading. Mater Sci Eng A 727:208–213.Zhang W, Chen X, Zhuo B, Li P, He L (2018) Efect of strain rate and temperature on dynamic mechanical behavior and microstructure evolution of ultra-high strength aluminum alloy. Mater Sci Eng A 730:336–344.Kavanagh KT, Clough RW (1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7(1):11–23.Mariani S, Gobat G (2019) Identifcation of strength and toughness of quasi-brittle materials from spall tests: a sigma-point kalman flter approach. Inverse Probl Sci Eng 27(9):1318–1346.Vaz M Jr, Tomiyama M (2020) Identifcation of inelastic parameters of the aisi 304 stainless steel: a multi-test optimization strategy. Inverse Probl Sci Eng 28(11):1551–1569.Field JE, Walley SM, Proud WG, Goldrein HT, Siviour CR (2004) Review of experimental techniques for high rate deformation and shock studies. Mater Sci Eng A 30(7):725–775.Chen WW, Song B (1989) Split Hopkinson (Kolsky) bar: design testing and applications. Springer, New York.Gilat A, Seidt J, Matrka T, Gardner K (2019) A new device for tensile and compressive testing at intermediate strain rates. Exp Mech 59(5):725–731.Sasso M, Newaz G, Amodio D (2008) Material characterization at high strain rate by hopkinson bar tests and fnite element optimization. Mater Sci Eng A 487(1–2):289–300.Sedighi M, Khandaei M, Shokrollahi H (2010) An approach in parametric identifcation of high strain rate constitutive model using hopkinson pressure bar test results. Mater Sci Eng A 527(15):3521–3528.Milani AS, Dabboussi W, Nemes JA, Abeyaratne RC (2009) An improved multi-objective identifcation of Johnson-Cook material parameters. Int J Impact Eng 36(2):294–302.ASTM: ASTM standard E478-08(2008)-Standard test methods for chemical analysis of copper alloys.ASTM: ASTM designation B62-09(2009)-Standard specifcation for composition bronze or ounce metal castings.ASTM: ASTM standard E9-09 (2009)-standard test methods of compression testing of metallic materials at room temperature.Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc Sect B 62(11):676–700.Hopkinson B (1914) A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets. Proc R Soc Lond Ser A 89(612):411–413.Davies RM (1948) A critical study of the Hopkinson pressure bar. Philos Trans R Soc Lond Ser A 240(821):375–457.Taylor GI (1948) The use of fat-ended projectiles for determining dynamic yield stress. I. Theoretical considerations. Proc R Soc Lond Ser A 194(1038):289–299.Meyers MA (1994) Dynamic Behavior of Materials. Wiley-Interscience, New York.Whifn AC (1948) The use of fat-ended projectiles for determining dynamic yield stress. II. Tests on various metallic materials. Proc R Soc Lond A 194:300–322.Wilkins ML, Guinan MW (1973) Impact of cylinders on a rigid boundary. J Appl Phys 44(3):1200–1206.Hawkyard JB (1969) A theory for the mushrooming of fat-ended projectiles impinging on a fat rigid anvil, using energy considerations. Int J Mech Sci 11(3):313–333.ANSYS: ANSYS LS-DYNA User’s Guide: ANSYS Release 12.0. ANSYS Inc., (2009). ANSYS Inc.Cowper GR, Symonds PS (1957) Strain hardening and strainrate efects in the impact loading of cantilever beams. Technical Report 28, Brown University Division of Applied Mathematics.Hernandez C, Maranon A, Ashcroft I, Casas-Rodriguez J (2013) A computational determination of the Cowper-Symonds parameters from a single Taylor test. Appl Math Modell 37(7):4698–4708.Hernandez C, Buchely M, Maranon A (2015) Dynamic characterization of Roma Plastilina No. 1 from Drop Test and inverse analysis. Int J Mech Sci 100:158–168.Acosta C, Hernandez C, Maranon A, Casas-Rodriguez J (2016) Validation of material constitutive parameters for the AISI 1010 steel from Taylor impact tests. Mater Des 110:324–331.Lambert G, Gao H (1995) Line moments and invariants for real time processing of vectorized contour data. In: Braccini C, DeFloriani L, Vernazza G (eds) Image analysis and processing. Lecture notes in computer science. Springer, New York, pp 347–352.Hu MK (1962) Visual pattern recognition by moment invariants. IRE Trans Inform Theory 8(2):179–187.Wen W, Lozzi A (1993) Recognition and inspection of manufactured parts using line moments of their boundaries. Pattern Recognit 26(10):1461–1471.ASTM: ASTM Standard E8/E8M-22-Standard test methods for tension testing of metallic materials (2022).Shin H, Kim J-B (2019) Evolution of specimen strain rate in split Hopkinson bar test. Proc Inst Mech Eng Part C 233(13):4667–4687.Gray G III, Blumenthal WR (2000) Split-hopkinson pressure bar testing of soft materials. ASM Handbook 8:488–496.UNS C83600Mechanical characterizationHigh-strain ratesSplit Hopkinson Pressure Bar TestTaylor testInverse problemParameter identifcationTEXTAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdf.txtAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdf.txtExtracted texttext/plain49089https://repositorio.escuelaing.edu.co/bitstream/001/3155/4/An%20Inverse%20Method%20to%20Estimate%20Cowper%e2%80%91Symonds%20Material%20Model%20Parameters%20from%20a%20Single%20Split%20Hopkinson%20Pressure%20Bar%20Test.pdf.txt45abbdd5773bab43f017eb64d41ba86fMD54open accessTHUMBNAILPortada - An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pngPortada - An Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pngimage/png215225https://repositorio.escuelaing.edu.co/bitstream/001/3155/3/Portada%20-%20An%20Inverse%20Method%20to%20Estimate%20Cowper%e2%80%91Symonds%20Material%20Model%20Parameters%20from%20a%20Single%20Split%20Hopkinson%20Pressure%20Bar%20Test.png6a971771f037abc2b5fdc2e466ca22d0MD53open accessAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdf.jpgAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdf.jpgGenerated Thumbnailimage/jpeg14931https://repositorio.escuelaing.edu.co/bitstream/001/3155/5/An%20Inverse%20Method%20to%20Estimate%20Cowper%e2%80%91Symonds%20Material%20Model%20Parameters%20from%20a%20Single%20Split%20Hopkinson%20Pressure%20Bar%20Test.pdf.jpg1d330c6e42f5442aaae39ace047b5c13MD55open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-81881https://repositorio.escuelaing.edu.co/bitstream/001/3155/2/license.txt5a7ca94c2e5326ee169f979d71d0f06eMD52open accessORIGINALAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdfAn Inverse Method to Estimate Cowper‑Symonds Material Model Parameters from a Single Split Hopkinson Pressure Bar Test.pdfArtículo de revistaapplication/pdf1207554https://repositorio.escuelaing.edu.co/bitstream/001/3155/1/An%20Inverse%20Method%20to%20Estimate%20Cowper%e2%80%91Symonds%20Material%20Model%20Parameters%20from%20a%20Single%20Split%20Hopkinson%20Pressure%20Bar%20Test.pdfcdcfd957b53b7cb31d9f8111ed72d57dMD51open access001/3155oai:repositorio.escuelaing.edu.co:001/31552024-07-11 03:00:41.336open accessRepositorio Escuela Colombiana de Ingeniería Julio Garavitorepositorio.eci@escuelaing.edu.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 |