Mechanical properties modeling of severely plastically deformed biodegradable ZK60 magnesium alloy for bone implants

Zhang, Yan; Wang, Ning; Li, Jingyi; Mesbah, Mohsen; Wong, Kuan Yew; Fallahpour, Alireza; Nasiri-Tabrizi, Bahman; Yang, Jiangfei

doi:10.1590/1679-78256151

Yan Zhang

Department of Trauma Orthopedics, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, Shandong Province, 250021, China. E-mail: doctorzhangyan1@sina.com

http://orcid.org/0000-0001-7202-9900

Ning Wang

Radiology Department, Shandong Provincial Hospital Affiliated to Shandong First Medical University, No.324 Jingwu Road, Huaiyin District, Jinan, Shandong 250000, China. E-mail: wnxtt1234@sina.com, yangjiangfei9120@sina.com

http://orcid.org/0000-0002-0104-4633

Jingyi Li

Operation room, The Affiliated Hospital of Qingdao University, Huangdao District, Qingdao, Shandong province, 266000, China. E-mail: Grc7729@sina.com

http://orcid.org/0000-0001-7234-2542

Mohsen Mesbah

Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. E-mail: mohsen_mesbah2005@yahoo.com

http://orcid.org/0000-0002-2380-0137

Kuan Yew Wong

School of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Malaysia. E-mail: wongky@mail.fkm.utm.my, fallahpour.a@gmail.com

http://orcid.org/0000-0002-2944-6749

Alireza Fallahpour

School of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Malaysia. E-mail: wongky@mail.fkm.utm.my, fallahpour.a@gmail.com

http://orcid.org/0000-0001-7841-2513

Bahman Nasiri-Tabrizi

School of Biosciences, Faculty of Health and Medical Sciences, Taylor’s University, Subang Jaya, Malaysia. E-mail: b.nasiritabrizi@gmail.com

http://orcid.org/0000-0003-0459-7169

Jiangfei Yang ^** Corresponding author

Radiology Department, Shandong Provincial Hospital Affiliated to Shandong First Medical University, No.324 Jingwu Road, Huaiyin District, Jinan, Shandong 250000, China. E-mail: wnxtt1234@sina.com, yangjiangfei9120@sina.com

http://orcid.org/0000-0002-7450-0628

* Corresponding author

Author’s Contributions:

Conceptualization, Y Zhang and B Nasiri-Tabrizi; methodology, M Mesbah; software, KY Wong and A Fallahpour; validation, KY Wong, M Mesbah and B Nasiri-Tabrizi; formal analysis, N Wang; investigation, Y Zhang and Y Li; resources, Y Li; data curation, A Fallahpour; writing-original draft preparation, Y Zhang, B Nasiri-Tabrizi, A Fallahpour; writing-review and editing, N Wang and Y Li; visualization, Y Zhang; supervision, J Yang and B Nasiri-Tabrizi; project administration, J Yang; funding acquisition, J Yang. All authors have read and agreed to the published version of the manuscript.

Editor:

Marcílio Alves.

	Minimum	Maximum
	Data used in the GP and GEP models
Input Parameters
SPD Method	M1	M3
The number of passes	0	8
Temperature (K)	273	573
Output Parameters
δ (%)	4	35.1
σ_YS (MPa)	120	320
σ_UTS (MPa)	221	397

Alloy	Input Parameters			Output Parameters			Ref.
Alloy	SPD Method	Pass	T (K)	δ (%)	σ_YS (MPa)	σ_UTS (MPa)
ZK60-1	M1 ¹	0	273	6	176	241	(Mesbah et al., 2019Mesbah, M., Fattahi, A., Bushroa, A., Faraji, G., Wong, K., Basirun, W., Fallahpour, A., Nasiri-Tabrizi, B., 2019. Experimental and Modelling Study of Ultra-Fine Grained ZK60 Magnesium Alloy with Simultaneously Improved Strength and Ductility Processed by Parallel Tubular Channel Angular Pressing. Metals and Materials International, 1-21.)
ZK60-2	M1	1	573	11	262	332	(Mesbah et al., 2019Mesbah, M., Fattahi, A., Bushroa, A., Faraji, G., Wong, K., Basirun, W., Fallahpour, A., Nasiri-Tabrizi, B., 2019. Experimental and Modelling Study of Ultra-Fine Grained ZK60 Magnesium Alloy with Simultaneously Improved Strength and Ductility Processed by Parallel Tubular Channel Angular Pressing. Metals and Materials International, 1-21.)
ZK60-3	M1	2	573	14	320	397	(Mesbah et al., 2019Mesbah, M., Fattahi, A., Bushroa, A., Faraji, G., Wong, K., Basirun, W., Fallahpour, A., Nasiri-Tabrizi, B., 2019. Experimental and Modelling Study of Ultra-Fine Grained ZK60 Magnesium Alloy with Simultaneously Improved Strength and Ductility Processed by Parallel Tubular Channel Angular Pressing. Metals and Materials International, 1-21.)
ZK60-4	M1	3	573	4	230	267	(Mesbah et al., 2019Mesbah, M., Fattahi, A., Bushroa, A., Faraji, G., Wong, K., Basirun, W., Fallahpour, A., Nasiri-Tabrizi, B., 2019. Experimental and Modelling Study of Ultra-Fine Grained ZK60 Magnesium Alloy with Simultaneously Improved Strength and Ductility Processed by Parallel Tubular Channel Angular Pressing. Metals and Materials International, 1-21.)
ZK60-5	M2 ²	4	523	17	233	316	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-6	M2	4	473	21	216	290	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-7	M2	4	423	30	268	300	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-8	M2	8	423	24	216	283	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-9	M2	1	523	20	175	290	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-10	M2	2	523	25	175	325	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-11	M2	3	523	29	175	320	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-12	M2	4	523	30	140	300	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-13	M2	4	513	28.1	120	221	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-14	M2	8	513	35.1	125	226	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-15	M2	2	523	24	180	277	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)
ZK60-16	M3 ³	1	473	30	286	338	(Dumitru et al., 2014Dumitru, F.-D., Higuera-Cobos, O.F., Cabrera, J., 2014. ZK60 alloy processed by ECAP: Microstructural, physical and mechanical characterization. Materials Science Engineering: A 594, 32-39.; He et al., 2010He, Y., Pan, Q., Qin, Y., Liu, X., Li, W., Chiu, Y., Chen, J.J., 2010. Microstructure and mechanical properties of ZK60 alloy processed by two-step equal channel angular pressing. Journal of Alloys and Compounds 492, 605-610.; Mostaed et al., 2014Mostaed, E., Hashempour, M., Fabrizi, A., Dellasega, D., Bestetti, M., Bonollo, F., Vedani, M., 2014. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. Journal of the Mechanical Behavior of Biomedical Materials 37, 307-322.; Orlov et al., 2011Orlov, D., Raab, G., Lamark, T.T., Popov, M., Estrin, Y., 2011. Improvement of mechanical properties of magnesium alloy ZK60 by integrated extrusion and equal channel angular pressing. Acta Materialia 59, 375-385.; Vinogradov, 2017Vinogradov, A., 2017. Effect of severe plastic deformation on tensile and fatigue properties of fine-grained magnesium alloy ZK60. Journal of Materials Research 32, 4362-4374.)

Method		Parameters	Value
GEP	General	Chromosomes	20
		Function set	×, /, +, -, power (x, y), e, Cos, Sin*
		Number of genes	4
		Head size	6
		Linking function	+
	Fitness Function	MSE
	Genetic Operators	Mutation rate	0.09
		One-point recombination rate	0.2
		Two-point recombination rate	0.1
		Gene recombination rate	0.3
		Gene transportation rate	0.3
	Numerical Constant	Constants per gene	4
		Data type	Floating Point
		Lower bound	-10
		Upper bound	+10
GP	General	Number of population size	600
		Function set	+, -, ×, ÷, e, √, Arc Tan
		Value of reproduction	0.3
		Value of mutation	0.03
		Value of crossover	0.5
		Selection method	Roulette-wheel
		Type of initialization method	Half
		Number of generation	900
	Fitness function	MSE

Method		Parameters	Value
GEP	General	Chromosomes	45
		Function set	×, /, +, -, power (x, y), Log, Sin, Cos*
		Number of genes	3
		Head size	7
		Linking function	+
	Fitness Function	MSE
	Genetic Operators	Mutation rate	0.03
		One-point recombination rate	0.5
		Two-point recombination rate	0.3
		Gene recombination rate	0.4
		Gene transportation rate	0.4
	Numerical Constant	Constants per gene	3
		Data type	Floating Point
		Lower bound	-10
		Upper bound	+10
GP	General	Number of population size	750
		Function set	+, -, ×, ÷, Sin, √, Log, Cos
		Value of reproduction	0.4
		Value of mutation	0.01
		Value of crossover	0.7
		Selection method	Roulette-wheel
		Type of initialization method	Half
		Number of generation	680
	Fitness function	MSE

Method		Parameters	Value
GEP	General	Chromosomes	30
		Function set	×, /, +, -, power (x, y), Arc Tan, Sin, Cos*
		Number of genes	3
		Head size	8
		Linking function	+
	Fitness Function	MSE
	Genetic Operators	Mutation rate	0.02
		One-point recombination rate	0.3
		Two-point recombination rate	0.5
		Gene recombination rate	0.2
		Gene transportation rate	0.2
	Numerical Constant	Constants per gene	5
		Data type	Floating Point
		Lower bound	-10
		Upper bound	+10
GP	General	Number of population size	600
		Function set	+,-,×,÷,e,√, Arc Tan
		Value of reproduction	0.3
		Value of mutation	0.03
		Value of crossover	0.5
		Selection method	Roulette-wheel
		Type of initialization method	Half
		Number of generation	900
	Fitness function	MSE

Item	Formula	Condition	σ _YS	σ _UTS	δ
1	R	$0.8 < R$	0.99	0.963	0.922
2	$k = \frac{\sum_{i = 1}^{n} (h_{i} \times t_{i})}{h_{i}^{2}}$	$0.85 < k < 1.15$	1.11	1.01	0.995
3	$k^{'} = \frac{\sum_{i = 1}^{n} (h_{i} \times t_{i})}{t_{i}^{2}}$	$0.85 < k^{'} < 1.15$	1.04	1.007	1.003
4	$m = \frac{R^{2} - R_{o}^{2}}{R^{2}}$	$\| m \| < 0.1$	0.013	0.041	0.022
5	$n = \frac{R^{2} - R_{o^{'}}^{2}}{R^{2}}$	$\| n \| < 0.1$	0.009	0.007	0.022
6	$R_{m} = R^{2} \times (1 - \sqrt{\| R^{2} - R_{o}^{2} \|})$	$0.5 < R_{m}$	0.978	0.951	0.832

[1] * Corresponding author

Brasil

Brasil

Mechanical properties modeling of severely plastically deformed biodegradable ZK60 magnesium alloy for bone implants

Abstract

Graphical Abstract