高温动态拉伸下NG TiAl弹塑性力学行为的数值模拟
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摘要
TiAl基金属间化合物的优良高温力学性能使其可能成为新一代航空航天工程用的轻质高温结构材料。考虑到航空航天器的服役环境,要求TiAl基金属间化合物具有一定的抗冲击能力。这就使得TiAl基金属间化合物的高温冲击力学行为的研究变得十分重要。由于TiAl的高温冲击试验技术仍存在很多困难,因此有必要发展适当的模型对TiAl的高温动态力学行为进行模拟,以数值计算替代部分的实验工作。
本文基于率相关的晶体塑性理论,通过引入形变孪晶的饱和体积分数来对形变孪晶的演化给予限制,发展了更为合理的同时考虑位错滑移和形变孪晶作用,并计及温度影响的TiAl单晶本构模型。
在此基础上,建立了能够反映晶粒随机取向的多晶有限元模型,对不同温度(室温~840℃)不同拉伸应变率(10-3~1350s-1)下等轴(NG)组织TiAl的弹塑性力学行为进行了模拟。计算结果表明,模拟得到的应力应变曲线与试验结果吻合较好,这表明所采用的单晶本构模型能很好的反应材料的应变率强化效应、温度软化效应和应变硬化行为。
此外还考察了NG TiAl在不同温度不同应变率下形变孪晶与位错滑移两种微观变形机制随塑性变形的演化情况。结果表明,二者均是NG TiAl的主要变形模式。动态加载条件下更有利于形变孪晶的产生,但温度对二者的影响不是很明显。在塑性变形的发展过程中,形变孪晶在塑性变形开始时起主导作用,随着塑性变形的进一步增大,位错滑移的贡献增加,最终两者达到平衡。
The excellent mechanical behavior of TiAl intermetallics at elevated temperature makes it a possible new generation structure material serving as aeronautical material. Considering the working environment of aerospace vehicles, the capability of suffering impact loadings is required. So it is highly important to research on the dynamic mechanical properties of TiAl intermetallics at elevated temperature. The dynamic experiment at elevated temperature has many difficulties till now, so it is necessary to construct a proper model to simulate the dynamic mechanical behavior of TiAl at elevated temperature.
In this study, based on rate-dependent crystal plasticity theory, the TiAl single crystal constitutive equation, which incorporates the influence of temperature and the effects of both dislocation slip and deformation twinning, is constructed. A revised evolution equation of twinning is suggested by introducing the saturate twinning volume fraction.
On the basis of the single crystal constitutive equation, a polycrystalline model which contains enough randomly orientated elements is constructed. Then the elasto-plastic behavior of NG TiAl is simulated at different temperature(Room temperature~840℃) and different tensile strain-rate(10-3~1350 s-1). The calculation results show that the simulated curves are consistent with experimental ones, that is, the applied constitutive equations and the polycrystalline model can well describe the materials’temperature and strain-rate dependence and work-hardening behavior.
Besides, the contributions of dislocation slip and deformation twinning to the plastic deformation of NG TiAl are investigated. The results show that both mechanisms are the major plastic deformation mechanisms of NG TiAl. Dynamic loading is more propitious to the occurrence of deformation twinning. However, the influence of temperature on both mechanisms is not obvious. In the process of plastic deformation, twinning is predominant at the beginning of plastic deformation. However, with the increasing plastic strain, the contribution of dislocation movement increases and co-develops with twinning at last.
本文基于率相关的晶体塑性理论,通过引入形变孪晶的饱和体积分数来对形变孪晶的演化给予限制,发展了更为合理的同时考虑位错滑移和形变孪晶作用,并计及温度影响的TiAl单晶本构模型。
在此基础上,建立了能够反映晶粒随机取向的多晶有限元模型,对不同温度(室温~840℃)不同拉伸应变率(10-3~1350s-1)下等轴(NG)组织TiAl的弹塑性力学行为进行了模拟。计算结果表明,模拟得到的应力应变曲线与试验结果吻合较好,这表明所采用的单晶本构模型能很好的反应材料的应变率强化效应、温度软化效应和应变硬化行为。
此外还考察了NG TiAl在不同温度不同应变率下形变孪晶与位错滑移两种微观变形机制随塑性变形的演化情况。结果表明,二者均是NG TiAl的主要变形模式。动态加载条件下更有利于形变孪晶的产生,但温度对二者的影响不是很明显。在塑性变形的发展过程中,形变孪晶在塑性变形开始时起主导作用,随着塑性变形的进一步增大,位错滑移的贡献增加,最终两者达到平衡。
The excellent mechanical behavior of TiAl intermetallics at elevated temperature makes it a possible new generation structure material serving as aeronautical material. Considering the working environment of aerospace vehicles, the capability of suffering impact loadings is required. So it is highly important to research on the dynamic mechanical properties of TiAl intermetallics at elevated temperature. The dynamic experiment at elevated temperature has many difficulties till now, so it is necessary to construct a proper model to simulate the dynamic mechanical behavior of TiAl at elevated temperature.
In this study, based on rate-dependent crystal plasticity theory, the TiAl single crystal constitutive equation, which incorporates the influence of temperature and the effects of both dislocation slip and deformation twinning, is constructed. A revised evolution equation of twinning is suggested by introducing the saturate twinning volume fraction.
On the basis of the single crystal constitutive equation, a polycrystalline model which contains enough randomly orientated elements is constructed. Then the elasto-plastic behavior of NG TiAl is simulated at different temperature(Room temperature~840℃) and different tensile strain-rate(10-3~1350 s-1). The calculation results show that the simulated curves are consistent with experimental ones, that is, the applied constitutive equations and the polycrystalline model can well describe the materials’temperature and strain-rate dependence and work-hardening behavior.
Besides, the contributions of dislocation slip and deformation twinning to the plastic deformation of NG TiAl are investigated. The results show that both mechanisms are the major plastic deformation mechanisms of NG TiAl. Dynamic loading is more propitious to the occurrence of deformation twinning. However, the influence of temperature on both mechanisms is not obvious. In the process of plastic deformation, twinning is predominant at the beginning of plastic deformation. However, with the increasing plastic strain, the contribution of dislocation movement increases and co-develops with twinning at last.
引文
[1]颜鸣皋,吴学仁,朱知寿,航空材料技术的发展现状与展望[J],航空制造技术,2003,12,p.19-25
[2] Appel, F., R. Wagner, Microstructure and deformation of two-phaseγ-titanium aluminides[J], Materials Science and Engineering:R: Reports, 1998. 22(5): 187-268.
[3] Edward A. Loria, Gamma titanium aluminides as prospective structure materials[J], Intermetallics, 2000, 8, 1339-1345
[4] Z. Jin, C. Candy, G.T. Gray, et al, Mechanical behavior of a fine-grained duplexγ-TiAl alloy[J], Metallurgical and Materials Tansactions A, 2000, 31(3): 1007-1016.
[5] S.A. Maloy, G.T. Gray III, et al, High strain rate deformation of Ti48Al2Nb2Cr[J], Acta Materialia, 1996, 44(5), Pages 1741-1756.
[6] Yuanxin Zhou, Yuanming Xia, Tensile mechanical behavior of TiAl(FL) at high strain rate[J], Journal of Materials Science, 2000, 35(4), p.925-929.
[7] Mostafa Shazly, Vikas Prakash, Susan Draper, Mechanical behavior of Gamma-Met PX under uniaxial loading at elevated temperatures and high strain rates[J], International Journal of Solids and Structures, 2004, 41(22-23), Pages 6485-6503.
[8]昝祥,TiAl基金属间化合物高温动态力学行为基变形机理研究[D],中国科学技术大学,近代力学系,2008.6.
[9]昝祥,汪洋,夏源明.三种微观组织的Ti-46. 5Al-2Nb-2Cr高温动态力学行为的实验研究[J].实验力学. 2008, 23 (6): 477-484.
[10] R. J. Asaro, Crystal Plasticity [J], Journal of Applied Mechanics, December, 1983, 50: 921.
[11] Bimal K. Kad, Ming Dao, Robert J. Asaro, Numerical simulations of stress-strain behavior in two-phase a2 +γlamellar TiAl alloys[J], Materials Science and Engineering A, 1995, 192/193: 97-103.
[12] M. Werwer, A. Cornec, The role of superdislocations for modeling plastic deformation of lamellar TiAl[J],International journal of plasticity, 2006, 22: 1683-1698.
[13] M. Werwer, A. Cornec, Numerical simulation of plastic deformation and fracture in polysynthetically twinned (PST) crystals of TiAl, Computational Materials Science, 2000, 19, pp.97-107
[14] S. M. Schlogl, F.D. Fischer, Micromechanical modelling of TiAl intermetallics, Computational Materials Science,1996, 7, pp. 34-39
[15] W.T. Marketz, F.D. Fischer, F. Kauffmann, Computational modeling and experimental study of the deformation behavior ofγ- TiAl-based alloy[J], Advanced Engineering materials, 2000, 2(10): 662-666.
[16] W.T. Marketz, F.D. Fischer, H. Clemens, Deformation mechanisms in TiAl intermetallics—experiments and modeling[J], International journal of plasticity, 2003, 19: 281-321.
[17] Suryar. Kalidindi, Incorporation of deformation twinning in crystal plasticity models[J], J. Mech. Phys. Solids, 1998, 46(2): 267 -290.
[18] H. Inui, Y. Toda, M. Yamaguchi, Plastic deformation of single crystals of a DO19 compoundwith an off-stoichiometric composition (Ti-36.5at.%Al) at room temperature[J], Philosophical Magazine A, 1993, Vol. 67, No.6, 1315-1332;
[19] F.D. Fischer, T. Schaden, F. Appel, Mechanical twins, their development and growth[J], European Journal of Mechanics A/Solids 2003, 22: 709–726.
[20] Shengqiang Cai, Ziran Li, Yuanming Xia, Evolution equations of deformation twins in metals—Evolution of deformation twins in pure titanium[J], Physica B, 2008, 403: 1660–1665.
[21] Huang, Y., A user-subroutine incorporating single crystal plasticity in the ABAQUS finite element program[D], Mech Report 178, Harvard University, Division of Engineering and Applied Sciences, 1991.
[22] Y. He, R.B. Schwarz, Elastic constants and thermal expansion of single crystalγ-TiAl from 300 to 750 K[J], Materials Science and Engineering A, 1997, 239/240: 157–163.
[23] M.H. Yoo, J. Zou, C.L. Fu, Mechanistic modeling of deformation and fracture behavior in TiAl and Ti3Al, Materials Science and Engineering A, 192/193 (1995) 14-23;
[24] Hans Conrad, Efect of interstitial solutes on the strength and ductility of titanium, Progress in Materials Science, Vol.26, pp.123-403;
[25] H. Inui, M. Matsumuro, D.H. Wu, Temperature dependence of yield stress, deformation mode and deformation structure in single crystals of TiAl (Ti-56 at.% Al) [J] , Philosophical Magazine A, 1997, 75(2), 395-423.
[26] T. Kawabata, T. Kanai, Positive temperature dependence of the yield stress in TiAl L10 type superlattice intermetallic compound single crystals, Acta Metal. , 1985, Vol.33,No.7, pp.1355-1366.
[27]黄文,纯钛高温动态拉伸力学性能研究[D],中国科学技术大学,近代力学系,2006.5.
[28]毛卫民,晶体材料织构定量分析,北京:冶金工业出版社,1995.
[29]程经毅,周光泉,位错的运动和产生与塑性变形的一般关系,塑性力学和细观力学文集,王自强,徐秉业,黄筑平编,1993,北京:北京大学出版社.
[2] Appel, F., R. Wagner, Microstructure and deformation of two-phaseγ-titanium aluminides[J], Materials Science and Engineering:R: Reports, 1998. 22(5): 187-268.
[3] Edward A. Loria, Gamma titanium aluminides as prospective structure materials[J], Intermetallics, 2000, 8, 1339-1345
[4] Z. Jin, C. Candy, G.T. Gray, et al, Mechanical behavior of a fine-grained duplexγ-TiAl alloy[J], Metallurgical and Materials Tansactions A, 2000, 31(3): 1007-1016.
[5] S.A. Maloy, G.T. Gray III, et al, High strain rate deformation of Ti48Al2Nb2Cr[J], Acta Materialia, 1996, 44(5), Pages 1741-1756.
[6] Yuanxin Zhou, Yuanming Xia, Tensile mechanical behavior of TiAl(FL) at high strain rate[J], Journal of Materials Science, 2000, 35(4), p.925-929.
[7] Mostafa Shazly, Vikas Prakash, Susan Draper, Mechanical behavior of Gamma-Met PX under uniaxial loading at elevated temperatures and high strain rates[J], International Journal of Solids and Structures, 2004, 41(22-23), Pages 6485-6503.
[8]昝祥,TiAl基金属间化合物高温动态力学行为基变形机理研究[D],中国科学技术大学,近代力学系,2008.6.
[9]昝祥,汪洋,夏源明.三种微观组织的Ti-46. 5Al-2Nb-2Cr高温动态力学行为的实验研究[J].实验力学. 2008, 23 (6): 477-484.
[10] R. J. Asaro, Crystal Plasticity [J], Journal of Applied Mechanics, December, 1983, 50: 921.
[11] Bimal K. Kad, Ming Dao, Robert J. Asaro, Numerical simulations of stress-strain behavior in two-phase a2 +γlamellar TiAl alloys[J], Materials Science and Engineering A, 1995, 192/193: 97-103.
[12] M. Werwer, A. Cornec, The role of superdislocations for modeling plastic deformation of lamellar TiAl[J],International journal of plasticity, 2006, 22: 1683-1698.
[13] M. Werwer, A. Cornec, Numerical simulation of plastic deformation and fracture in polysynthetically twinned (PST) crystals of TiAl, Computational Materials Science, 2000, 19, pp.97-107
[14] S. M. Schlogl, F.D. Fischer, Micromechanical modelling of TiAl intermetallics, Computational Materials Science,1996, 7, pp. 34-39
[15] W.T. Marketz, F.D. Fischer, F. Kauffmann, Computational modeling and experimental study of the deformation behavior ofγ- TiAl-based alloy[J], Advanced Engineering materials, 2000, 2(10): 662-666.
[16] W.T. Marketz, F.D. Fischer, H. Clemens, Deformation mechanisms in TiAl intermetallics—experiments and modeling[J], International journal of plasticity, 2003, 19: 281-321.
[17] Suryar. Kalidindi, Incorporation of deformation twinning in crystal plasticity models[J], J. Mech. Phys. Solids, 1998, 46(2): 267 -290.
[18] H. Inui, Y. Toda, M. Yamaguchi, Plastic deformation of single crystals of a DO19 compoundwith an off-stoichiometric composition (Ti-36.5at.%Al) at room temperature[J], Philosophical Magazine A, 1993, Vol. 67, No.6, 1315-1332;
[19] F.D. Fischer, T. Schaden, F. Appel, Mechanical twins, their development and growth[J], European Journal of Mechanics A/Solids 2003, 22: 709–726.
[20] Shengqiang Cai, Ziran Li, Yuanming Xia, Evolution equations of deformation twins in metals—Evolution of deformation twins in pure titanium[J], Physica B, 2008, 403: 1660–1665.
[21] Huang, Y., A user-subroutine incorporating single crystal plasticity in the ABAQUS finite element program[D], Mech Report 178, Harvard University, Division of Engineering and Applied Sciences, 1991.
[22] Y. He, R.B. Schwarz, Elastic constants and thermal expansion of single crystalγ-TiAl from 300 to 750 K[J], Materials Science and Engineering A, 1997, 239/240: 157–163.
[23] M.H. Yoo, J. Zou, C.L. Fu, Mechanistic modeling of deformation and fracture behavior in TiAl and Ti3Al, Materials Science and Engineering A, 192/193 (1995) 14-23;
[24] Hans Conrad, Efect of interstitial solutes on the strength and ductility of titanium, Progress in Materials Science, Vol.26, pp.123-403;
[25] H. Inui, M. Matsumuro, D.H. Wu, Temperature dependence of yield stress, deformation mode and deformation structure in single crystals of TiAl (Ti-56 at.% Al) [J] , Philosophical Magazine A, 1997, 75(2), 395-423.
[26] T. Kawabata, T. Kanai, Positive temperature dependence of the yield stress in TiAl L10 type superlattice intermetallic compound single crystals, Acta Metal. , 1985, Vol.33,No.7, pp.1355-1366.
[27]黄文,纯钛高温动态拉伸力学性能研究[D],中国科学技术大学,近代力学系,2006.5.
[28]毛卫民,晶体材料织构定量分析,北京:冶金工业出版社,1995.
[29]程经毅,周光泉,位错的运动和产生与塑性变形的一般关系,塑性力学和细观力学文集,王自强,徐秉业,黄筑平编,1993,北京:北京大学出版社.