基于塑性强化效应的典型材料极限承载能力分析
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摘要
课题来源于“十一五”国家科技支撑计划课题“大型高参数高危险性成套装置长周期运行安全保障关键技术研究及工程示范”。针对承压结构的塑性跨塌失效和局部失效,考虑金属材料应变强化效应,分析典型承压结构的最大及许用载荷,为在役承压设备承载能力挖潜,延长承压设备的安全使用寿命,节约能源。本研究从塑性理论出发,运用试验手段和有限元方法对材料力学性能和本构关系进行分析研究,主要解决了三方面的问题:
其一是典型材料的本构关系,采用实芯圆棒大变形扭转及拉伸试验获得材料的本构关系,并从理论上解决了扭转大变形的应力计算问题,给出了特种设备常用的三类材料(低合金钢、低碳钢、不锈钢)大变形扭转本构关系的数学模型及公式适用范围。
其二是多向应力状态下,典型材料本构关系数学模型的建立、不同应力状态对本构关系的影响程度分析。采用不同的拉伸、扭转应力比例,对实心圆棒试件进行拉扭组合试验,根据全量理论得到了三种材料的等效应力应变σ-ε数学关系;并对拉扭应力状态下材料本构关系进行对比分析、屈服准则验证及后继屈服的探索研究,得到了材料最大等效应变(εmax)与应力状态表征参数三轴应力度TS值的数学模型(ε_(max)-TS)。
其三是在不同应力状态(TS值)下,典型结构发生局部破坏的微观特征分析及定量化的局部应变控制准则适应性的试验验证。通过对带缺陷结构进行有限元计算分析和微观金相试验验证,从宏观和微观角度找出材料应变强化和结构许用载荷之间的关系。进一步验证了ASME局部应变失效控制条件的工程适应性。
结果表明:
①与传统单向拉伸测试材料本构关系的方法相比,实芯圆棒在扭转试验中得到的等效应力-应变本构关系适用范围更大,其数学模型可涵盖拉伸真应力应变(适用范围内)结果;②拉伸扭转二向应力联合作用下,材料的破坏形式及本构关系与三轴应力度TS有关,在先拉后扭的加载路径下,随着TS值增大,材料的塑性变形能力降低。在主应力空间中,屈服时全部实验数据点基本落在Mises轨迹上,强化时,等效应变在15-20%以内,试验点与Mises后继屈服轨迹基本吻合,在该塑性变形阶段具有等向强化模式。当等效应变大于20%以后,试验点偏离Mises后继屈服轨迹,TS值越大,偏移量越大;③应力状态(TS值)对材料的塑性变形有影响,但影响程度依不同材料有很大差异。拉伸、扭转及拉扭联合作用的综合试验结果表明:低合金钢(16MnR)的塑性变形能力对TS值非常敏感,拉伸与扭转实验的最大等效应变相差1000%,不锈钢(304)类则对TS值不敏感,拉伸与扭转仅相差25%;④按照ASME应变控制准则计算得到的结构破坏载荷与试验结果吻合较好,16MnR材料在缺陷半径为0.06mm及5mm时,误差仅为1%及3%。结构局部应力集中部位的破坏与材料的最大允许应变有关,其局部应变控制破坏方式或整体失稳破坏方式的决定,受应力状态的影响。⑤三种材料冲击吸收功均随材料塑性变形的增加成不同指数降低,其规律因材料而异。Q235材料有预应变状态下基本不具备抗冲击能力,故不适于在塑性状态下工作。
The subject attaches to the "Eleventh Five-Year" plan to support national science and technology issues, "Key security technology research and demonstration project of complete equipments based on large-scale high parameters and high-risk in long-term running." Aiming at plastic collapse failure and local failure of bearing structure, Strain-hardening effect of metallic materials is considered, and the maximum and allowable loads are analyzed, in order to extend the safe life of pressure equipment and save energy, the potential carrying capacity of pressure equipment in service need to be excavated.
The research, in which test method and FEM are used to analyze the mechanical property and constitutive relation of typical materials, starts from plasticity theory, and three major problems are solved:
First of all, in this article, the constitutive relation is obtained from the experimental of large deformation torsion of solid rods and unidirectional tension, and the problem about stress calculation of large deformation torsion is figure out in terms of theory. Taking low alloy steel 16MnR, mild steel Q235 and austenitic stainless steel 304 for example, not only the mathematic model of constitutive relation, but also the scope of the formula adapted is given.
Second, the equivalent constitutive of typical material in a multi-state stress is established, and the effect of stress state is analyzed. The method is that according to total strain theory, combinatorial tests of torsion and tension, in varying proportions, are carried out to attain the equivalent constitutive mathematic modelσ-ε, and the results are compared and analyzed to find the rule of effect of stress state. Then yield criterion is validated and subsequent yield is studied, from this work, the relation between maximal equivalent strain and triaxial stress coefficient which is a characterization of stress state is changed into mathematic modelε_(max)-TS.
Finally, in a multi-state stress, the FEM is applied to calculate limit load of typical structure according to strain control criterion, meanwhile the microscopic feature is observed to represent the limit load. The method of combining macroscopic calculation and microscopic test is first used to find the relation between strain-hardening of material and allowable load of structure, further more, projects adaptation of ASME local strain failure control factors is validated.
The results show that:
①Comparing with the unidirectional tension constitutive relation, large deformation torsion equivalent constitutive extend to a greater scope, and they tally with each other very well.②Under the combined effects of torsion and tension, modes of material failure and constitutive relation are associate with triaxial stress coefficient, for example, in the loading way of first tension and then torsion, the plastic deformation capacity of material cut down along with the increase of triaxial stress coefficient. In principal stress space, all the test points fall over Mises yield locus, when strain is strengthen between 15% and 20%, test points almost tally with subsequent yield locus, but they deviate after 20%, the greater the triaxial stress coefficient, the further the test points deviate.③Plastic deformation is greatly effected by stress state, and the incidence changes with different materials. Test results demonstrate that: plastic deformation capacity of low alloy steel (16MnR) is sensitive to triaxial stress coefficient, and the fall of maximal equivalent strain can be 1000%; but austenitic stainless steel 304 reverses, only 25%.④Test results coincide well with FEM results calculated on the basis of ASME local strain control criterion. For instance, the errors of 16MnR specimens with defect radius of 0.06mm and 5mm are only 1% and 3%. On one hand, local destruction of structure is associated with materials maximal allowable strain, on the other hand, the way of destruction is affected by stress state.⑤There are different reduces on impact absorbing energy of three typical materials with the increase of plastic deformation, and the rule vary with materials. For example, basically Q235 with pre-strain do not have the capacity to bear impact load, so it is not adapt to the work in plastic state.
其一是典型材料的本构关系,采用实芯圆棒大变形扭转及拉伸试验获得材料的本构关系,并从理论上解决了扭转大变形的应力计算问题,给出了特种设备常用的三类材料(低合金钢、低碳钢、不锈钢)大变形扭转本构关系的数学模型及公式适用范围。
其二是多向应力状态下,典型材料本构关系数学模型的建立、不同应力状态对本构关系的影响程度分析。采用不同的拉伸、扭转应力比例,对实心圆棒试件进行拉扭组合试验,根据全量理论得到了三种材料的等效应力应变σ-ε数学关系;并对拉扭应力状态下材料本构关系进行对比分析、屈服准则验证及后继屈服的探索研究,得到了材料最大等效应变(εmax)与应力状态表征参数三轴应力度TS值的数学模型(ε_(max)-TS)。
其三是在不同应力状态(TS值)下,典型结构发生局部破坏的微观特征分析及定量化的局部应变控制准则适应性的试验验证。通过对带缺陷结构进行有限元计算分析和微观金相试验验证,从宏观和微观角度找出材料应变强化和结构许用载荷之间的关系。进一步验证了ASME局部应变失效控制条件的工程适应性。
结果表明:
①与传统单向拉伸测试材料本构关系的方法相比,实芯圆棒在扭转试验中得到的等效应力-应变本构关系适用范围更大,其数学模型可涵盖拉伸真应力应变(适用范围内)结果;②拉伸扭转二向应力联合作用下,材料的破坏形式及本构关系与三轴应力度TS有关,在先拉后扭的加载路径下,随着TS值增大,材料的塑性变形能力降低。在主应力空间中,屈服时全部实验数据点基本落在Mises轨迹上,强化时,等效应变在15-20%以内,试验点与Mises后继屈服轨迹基本吻合,在该塑性变形阶段具有等向强化模式。当等效应变大于20%以后,试验点偏离Mises后继屈服轨迹,TS值越大,偏移量越大;③应力状态(TS值)对材料的塑性变形有影响,但影响程度依不同材料有很大差异。拉伸、扭转及拉扭联合作用的综合试验结果表明:低合金钢(16MnR)的塑性变形能力对TS值非常敏感,拉伸与扭转实验的最大等效应变相差1000%,不锈钢(304)类则对TS值不敏感,拉伸与扭转仅相差25%;④按照ASME应变控制准则计算得到的结构破坏载荷与试验结果吻合较好,16MnR材料在缺陷半径为0.06mm及5mm时,误差仅为1%及3%。结构局部应力集中部位的破坏与材料的最大允许应变有关,其局部应变控制破坏方式或整体失稳破坏方式的决定,受应力状态的影响。⑤三种材料冲击吸收功均随材料塑性变形的增加成不同指数降低,其规律因材料而异。Q235材料有预应变状态下基本不具备抗冲击能力,故不适于在塑性状态下工作。
The subject attaches to the "Eleventh Five-Year" plan to support national science and technology issues, "Key security technology research and demonstration project of complete equipments based on large-scale high parameters and high-risk in long-term running." Aiming at plastic collapse failure and local failure of bearing structure, Strain-hardening effect of metallic materials is considered, and the maximum and allowable loads are analyzed, in order to extend the safe life of pressure equipment and save energy, the potential carrying capacity of pressure equipment in service need to be excavated.
The research, in which test method and FEM are used to analyze the mechanical property and constitutive relation of typical materials, starts from plasticity theory, and three major problems are solved:
First of all, in this article, the constitutive relation is obtained from the experimental of large deformation torsion of solid rods and unidirectional tension, and the problem about stress calculation of large deformation torsion is figure out in terms of theory. Taking low alloy steel 16MnR, mild steel Q235 and austenitic stainless steel 304 for example, not only the mathematic model of constitutive relation, but also the scope of the formula adapted is given.
Second, the equivalent constitutive of typical material in a multi-state stress is established, and the effect of stress state is analyzed. The method is that according to total strain theory, combinatorial tests of torsion and tension, in varying proportions, are carried out to attain the equivalent constitutive mathematic modelσ-ε, and the results are compared and analyzed to find the rule of effect of stress state. Then yield criterion is validated and subsequent yield is studied, from this work, the relation between maximal equivalent strain and triaxial stress coefficient which is a characterization of stress state is changed into mathematic modelε_(max)-TS.
Finally, in a multi-state stress, the FEM is applied to calculate limit load of typical structure according to strain control criterion, meanwhile the microscopic feature is observed to represent the limit load. The method of combining macroscopic calculation and microscopic test is first used to find the relation between strain-hardening of material and allowable load of structure, further more, projects adaptation of ASME local strain failure control factors is validated.
The results show that:
①Comparing with the unidirectional tension constitutive relation, large deformation torsion equivalent constitutive extend to a greater scope, and they tally with each other very well.②Under the combined effects of torsion and tension, modes of material failure and constitutive relation are associate with triaxial stress coefficient, for example, in the loading way of first tension and then torsion, the plastic deformation capacity of material cut down along with the increase of triaxial stress coefficient. In principal stress space, all the test points fall over Mises yield locus, when strain is strengthen between 15% and 20%, test points almost tally with subsequent yield locus, but they deviate after 20%, the greater the triaxial stress coefficient, the further the test points deviate.③Plastic deformation is greatly effected by stress state, and the incidence changes with different materials. Test results demonstrate that: plastic deformation capacity of low alloy steel (16MnR) is sensitive to triaxial stress coefficient, and the fall of maximal equivalent strain can be 1000%; but austenitic stainless steel 304 reverses, only 25%.④Test results coincide well with FEM results calculated on the basis of ASME local strain control criterion. For instance, the errors of 16MnR specimens with defect radius of 0.06mm and 5mm are only 1% and 3%. On one hand, local destruction of structure is associated with materials maximal allowable strain, on the other hand, the way of destruction is affected by stress state.⑤There are different reduces on impact absorbing energy of three typical materials with the increase of plastic deformation, and the rule vary with materials. For example, basically Q235 with pre-strain do not have the capacity to bear impact load, so it is not adapt to the work in plastic state.
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53. CHEN Lijie, LIU Yinghua, YANG Pu, XU Bingye. Modified elastic compensation method for limit analysis of complex structures. Jixie Gongcheng Xuebao/Chinese Journal of Mechanical Engineering, 2007, Vol. 43, No.5:187-193.
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55. Bai Jie, Liu Yinghua, Chen Gang, Xu, Bingye. Plastic limit analysis of pipelines with part-through slots. Qinghua Daxue Xuebao/Journal of Tsinghua University, 2002, Vol.42, No.suppl:11-14.
56. Zhang Hongtao, Liu Yinghua, Xu Bingye. Plastic limit analysis of periodic heterogeneous materials by a static approach. Engineering Materials, 2004, Vol. 274-276, No.1:739-744.
57. Li N, Sang Z.F, Widera G.E.O. Study of plastic limit load on pressurized cylinders with lateral nozzle. Journal of Pressure Vessel Technology, Transactions of the ASME, 2008, Vol.130, No.4:0412101-0412107.
58. Kim Yun-Jae, Kim Jonghyun, Ahn Joonghyuk, Hong Seok-Pyo, Park Chi-Yong. Effects of local wall thinning on plastic limit loads of elbows using geometrically linear FE limit analyses. Engineering Fracture Mechanics, 2008, Vol.75, No.8:2225-2245.
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61. Duan Zhixiang, Shen Shiming. Analysis and experiments on the plastic limit pressure of elbows. International Journal of Pressure Vessels and Piping, 2006, Vol.83, No.10:707-713.
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63. Yun Jae Kim, Chang Kyun Oh, Man Sik Myung, Jin Moo Park. Fully plastic analyses for notched bars and plates using finite element limit analysis. Engineering Fracture Mechanics, Vol.73, No.13:1849-1864.
64. Yun Jae Kim, Chang Sik Oh. Finite element limit analyses of under-matched tensile specimens. Engineering Fracture Mechanics, Vol.73, No.10:1362-1378.
65. Yun Jae Kim, Kuk Hee Lee, Chi Yong Park. Plastic limit loads for piping branch junctions. Key Engineering Materials, 2007, Vol.345-346, pt.2:1377-1380.
66. Landi L., Braccesi C. A general elastic-plastic approach to impact analysis for stress state limit evaluation in ball screw bearings return system. International Journal of Impact Engineering. 2007, Vol.34, No.7:1272-1285.
67. Lee Sang Min, Choi Young Hwan, Chung Hae Dong, Chang Yoon Suk, Kim Young Jin. Plastic limit analysis of an elbow with various wall-thinning geometries. Key Engineering Materials, 2008, Vol.385-387:833-836.
68.杨丽红.基于实心圆轴扭转实验的大变形本构关系研究[D],哈尔滨工程大学, 2005.
69.何蕴增,邹广平.实心圆试件扭转试验确定大应变本构关系.力学学报, 2001, Vol.33, No.6: 828-833.
70.何蕴增,邹广平.实心圆轴扭转测定本构关系的概念和方法,实验力学. 2003, Vol.18.No.3:426-432.
71. Sewell, M.J., J. Mech. Phys. Solids, 22(1974), pp. 469-490.
72.王仁,熊祝华,黄文彬.塑性力学基础.科学出版社, 1982.
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