基于位错理论的TC4钛合金的动态本构模型与数值模拟
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摘要
为描述Ti-6Al-4V(TC4)两相钛合金在高应变率、高温载荷条件下的复杂力学行为,基于细观塑性变形机理和位错动力学理论,从细观尺度构建一种两相钛合金粘塑性本构模型,并阐释各本构参数与微结构特征量之间的关联及其表征的物理意义。为确定本构参数并提高参数的识别效率与精度,提出一种基于拉丁超立方抽样、Spearman秩相关分析的参数敏感度整体分析方法,并在参数敏感度分析结果和基本遗传算法的基础上,建立基于改进小生境算法、可疑峰值点判断策略和局域精确搜索技术的改进遗传算法,得到了TC4两相钛合金的本构参数。采用应力补偿更新算法,通过显式用户子程序接口VUMAT将两相钛合金本构模型嵌入ABAQUS有限元软件中,实现了钛合金在高应变率、高温条件下动态本构行为的数值模拟。对比模拟结果与实验数据发现,所构建的本构模型描述材料高应变率条件下力学行为的准确性优于Johnson-Cook模型的。
A new physically-based constitutive model of dual-phase Ti-6 Al-4 V alloy(TC4) was developed based on the microscopic mechanism of plastic deformation and the theory of thermally activated dislocation motion. The relationships among constitutive parameters and microstructure characteristics, as well as the physical meanings were illustrated. In order to determine the constitutive parameters and improve the efficiency and precision of parameters identification, an overall analysis method of parameter sensitivity based on Latin Hypercube Sampling(LHS) method and spearman rank correlation method was presented. Furthermore, the constitutive parameters of the material were determined by a global genetic algorithm composed of an improved niche genetic algorithm, a global peak determination strategy and local accurate searching techniques. By adopting a stress compensation updating algorithm, a subroutine VUAMT of the proposed constitutive model of dual-phase titanium alloy was programmed on plat of ABAQUS/Explicit.Then finite element simulation of dynamic responses of TC4 alloy under loading conditions of high strain rate and high temperature was investigated. The comparison results indicate that the proposed model is more suitable and accurately to describe the mechanical behavior of material subjected to high strain rate than Johnson-Cook model.
A new physically-based constitutive model of dual-phase Ti-6 Al-4 V alloy(TC4) was developed based on the microscopic mechanism of plastic deformation and the theory of thermally activated dislocation motion. The relationships among constitutive parameters and microstructure characteristics, as well as the physical meanings were illustrated. In order to determine the constitutive parameters and improve the efficiency and precision of parameters identification, an overall analysis method of parameter sensitivity based on Latin Hypercube Sampling(LHS) method and spearman rank correlation method was presented. Furthermore, the constitutive parameters of the material were determined by a global genetic algorithm composed of an improved niche genetic algorithm, a global peak determination strategy and local accurate searching techniques. By adopting a stress compensation updating algorithm, a subroutine VUAMT of the proposed constitutive model of dual-phase titanium alloy was programmed on plat of ABAQUS/Explicit.Then finite element simulation of dynamic responses of TC4 alloy under loading conditions of high strain rate and high temperature was investigated. The comparison results indicate that the proposed model is more suitable and accurately to describe the mechanical behavior of material subjected to high strain rate than Johnson-Cook model.
引文
[1]张长清,谢兰生,陈明和,商国强.高应变率下TC4-DT钛合金的动态力学性能及塑性本构关系[J].中国有色金属学报,2015,25(2):323-329.ZHANG Chang-qing,XIE Lan-sheng,CHEN Ming-he,SHANG Guo-qiang.Dynamic mechanical property and plastic constitutive relation of TC4-DT Ti alloy under high strain rate[J].The Chinese Journal of Nonferrous Metals,2015,25(2):323-329.
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[10]MACDOUGALL D A S,HARDING J.A constitutive relation and failure criterion for Ti6Al4V alloy at impact rates of strain[J].Journal of the Mechanics and Physics of Solids,1999,47(5):1157-1185.
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[12]FOLLANSBEE P S,KOCKS U F.A constitutive description of the deformation of copper based on the use of mechanical threshold stress as an internal state variable[J].Acta Metallurgica,1988,36(1):81-93.
[13]GAO C Y,ZHANG L C,YAN H X.A new constitutive model for HCP metals[J].Materials Science and Engineering A,2011,528(13-14):4445-4452.
[14]PEIERLS P E.The size of a dislocation[J].Proceedings of the Physical Society,1940,52(1):34-37.
[15]OROWAN E.Problems of plastic gliding[J].Proceedings of the Physical Society,1940,52(1):8-22.
[16]JOHNSON W G,GILMAN J J.Dislocation velocities,dislocation densities,and plastic flow in lithium fluoride crystals[J].Journal of Applied Physics,1959,30(2):129-144.
[17]SIMPSON T W,LIN D K.Sampling strategies for computer experiments:design and analysis[J].International Journal of Reliability and Applications,2001,2(3):209-240.
[18]GAO C Y,LIU P H,ZHANG L C.An explicit integration algorithm for introducing user-defined Thermo-Viscoplastic constitutive models in FE Simulations[C]//Proceeding of Materials Science Forum.Switzerland:Trans Tech Publications,2011:204-207.
[19]FOLLANSBEE P S,GRAY G T.An analysis of the low temperature,low and high-rate deformation of Ti-6Al-4V[J].Metallurgical Transaction A,1989,20(5):863-874.
[2]MAJORELL A,STRIVATSA S,PICU R C.Mechanical behavior of Ti-6Al-4V at high and moderate temperaturesPart I:Experimental results[J].Materials Science and Engineering A,2002,326(2):297-305.
[3]王冰洁,郭鹏程,李世康,叶拓,曹淑芬,李落星.应变速率对AM80镁合金压缩变形行为的影响[J].中国有色金属学报,2015,25(3):560-567.WANG Bing-jie,GUO Peng-cheng,LI Shi-kang,YE Tuo,CAO Shu-fen,LI Luo-xing.Influence of strain rate on compression deformation behavior of AM80 magnesium alloy[J].The Chinese Journal of Nonferrous Metals,2015,25(3):560-567.
[4]CHIOU S T,TSAI H L,LEE W S.Impact mechanical response and micro structural evolution of Ti alloy under various temperatures[J].Journal of Materials Processing Technology,2009,209(5):2282-2294.
[5]KHAN A S,SUH Y S,KAZMI R.Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys[J].International Journal of Plasticity,2004,20(12):2233-2248.
[6]NEMAT-NASSER S,GUO W G,NESTERENKO V F,INFRAKANTI S S,GU Y B.Dynamic response of conventional and hot isostatically pressed Ti-6Al-4V alloys:Experiments and modeling[J].Mechanics of Materials,2001,33(8):425-439.
[7]ZERILLI F J,ARMSTRONG R W.High strain rate effects on polymer,metal and ceramic matrix composites and other advanced materials[C]//Proceeding of ASME International Mechanical Engineering Congress and Exposition.San Francisco:American Society of Mechanical Engineers,1995:121-126.
[8]SEO S,MIN O,YANG H.Constitutive equation for Ti-6Al-4V at high-temperatures measured using the SHPBtechnique[J].International Journal of Impact Engineering,2005,31(6):735-754.
[9]ZHAN H,WANG G,KENT D,DARGUSCH M.Constitutive modeling of the flow behavior of?(10)?titanium alloy at high strain rates and elevated temperatures using the Johnson-Cook and modified Zerilli-Armstrong models[J].Materials Science and Engineering A,2014,612(1):71-79.
[10]MACDOUGALL D A S,HARDING J.A constitutive relation and failure criterion for Ti6Al4V alloy at impact rates of strain[J].Journal of the Mechanics and Physics of Solids,1999,47(5):1157-1185.
[11]REGAZZONI G,KOCKS U F,FOLLANSBEE P S.Dislocation kinetics at high strain rates[J].Acta Metallurgica,1987,35(2):2865-2875.
[12]FOLLANSBEE P S,KOCKS U F.A constitutive description of the deformation of copper based on the use of mechanical threshold stress as an internal state variable[J].Acta Metallurgica,1988,36(1):81-93.
[13]GAO C Y,ZHANG L C,YAN H X.A new constitutive model for HCP metals[J].Materials Science and Engineering A,2011,528(13-14):4445-4452.
[14]PEIERLS P E.The size of a dislocation[J].Proceedings of the Physical Society,1940,52(1):34-37.
[15]OROWAN E.Problems of plastic gliding[J].Proceedings of the Physical Society,1940,52(1):8-22.
[16]JOHNSON W G,GILMAN J J.Dislocation velocities,dislocation densities,and plastic flow in lithium fluoride crystals[J].Journal of Applied Physics,1959,30(2):129-144.
[17]SIMPSON T W,LIN D K.Sampling strategies for computer experiments:design and analysis[J].International Journal of Reliability and Applications,2001,2(3):209-240.
[18]GAO C Y,LIU P H,ZHANG L C.An explicit integration algorithm for introducing user-defined Thermo-Viscoplastic constitutive models in FE Simulations[C]//Proceeding of Materials Science Forum.Switzerland:Trans Tech Publications,2011:204-207.
[19]FOLLANSBEE P S,GRAY G T.An analysis of the low temperature,low and high-rate deformation of Ti-6Al-4V[J].Metallurgical Transaction A,1989,20(5):863-874.