【作者】 索忠林；

【导师】 宋玉泉；

【作者基本信息】 吉林大学 ， 材料加工工程， 2006， 博士

【摘要】 本论文主要讨论和研究了理想试样的超塑性变形的稳定性。文中建立了描述拉伸变形过程的模型,定义和讨论了变形过程的四个失稳状态,指出Considère、Hart、Ghosh和Jonas所提出的稳定性准则描述的是应变速率敏感性材料在不同变形路径下的失稳发生。γ= 1描述的是恒应变速率拉伸变形中的失稳,γ= 1 + m描述的是恒速率拉伸变形中的失稳,而γ= 1 ? m描述的是定载荷拉伸变形过程中的失稳。由于在定载荷拉伸变形过程中,载荷是恒定的,因此载荷不能做为判断失稳的参考量,故Hart将试样截面积的变化做为判断失稳的参考量。结合数学模型给出了应变速率波动模型,利用数学模型解出了全面反映力学参量与材料参数之间关系的超塑性流动方程。对理想试样的四个失稳状态的失稳应变进行了预测,借助于数值计算的技巧给出了非理想试样断裂应变的预测公式。更多还原

【Abstract】 Nowadays,the world’s development mainly represents on two aspects:science and technology, war industry. While the development andadvancement of them more and more rely on manufacture and application ofnew materials. Then superplastic metals have important roles on above twofields. Therefore,superplastic theory and application need to be studied deeply,in order to give universal answer and regular guidance for the questions inmanufacture. We should understand further the conjunction betweenmacro-mechanical law and micro-physics mechanism , which is veryimportant to develop new materials, simplify superplastic pretreatment andnormalize forming technics.Superplastic deformation has strong structure sensitivity,and there isclose relationship between stress state and deformation path. Uniaxial tensileis the simplest one-dimension stress state, therefore the relationship betweenmaterial mechanical parameter and deformation path and conditionalparameter can be confirmed by tensile experiment directly. The essencedifference between superplastic deformation of superplastic material andplastic deformation of ductile material is: When load is instable duringsuperplastic deformation, geometrical instability will not happensimultaneously which appears after homogeneous deformation;At the sametime of geometrical instability, stress instability will happen;and failureinstability will not be caused directly after geometrical instability, but arelatively long quasi-stable deformation will be rebuilt. This is themechanical essence of material’s superplasticity. Based on reviewing ofsuperplastic tensile deformation instability at home and abroad this paper hasa systemic study on tensile instability.The author’s works and achievements are as follows:1、The achievements about superplastic uniaxial tensile deformation inthree aspects since 1885 is reviewed and summarized:①the definition of instability and its determinant rules;②the development of necking and the influence of defect on instabilitydiffusion;③the predicts of instability strain and failure strain.The author point out that there has not form a systemic theory andmethod,that is the shortage of superplastic theory;And the orientation of thedevelopment of superplastic theory is emphasized, one is to develop advancedobservation and experiment equipments, the other is to establish mathematicalmodel which could accurately describe deformation course, and then get abroadly applied constructive equation which reflects superplastic flow.2、Constructive equation which reflects superplastic flow is establishedsuccessfully, combining the Hart’s state equation and basic formulae ofsuperplastic deformation. The stability of the model is analysed from the pointof nonlinear systemic kinetics, and it is pointed out that the system will go tobe instable if without control when load attains maximum value.3、Quasi-uniform deformation stage of superplastic deformation isdivided into: load instability,geometry instability,stress instability and failureinstability,then these are analyzed. We got a conclusion that different rules ofinstability is consistent,their expressions are only the beginning of instabilityunder different deformation path or instable state, and there is nocomparability between the strains corresponding to instability point of eachinstability rules.4、Superplastic uniaxial tensile sample is regarded as a nonlinear kineticsystem,and we obtain strain rate fluctuate model of this system. Load is thedriving force for the system. When initial load is given, initial strain rate canbe confirmed by load and strain hardening property of material;While strainrate sensitivity index is determined by strain rate,test temperature and grainsize of material,and its value represents recovery ability of strain rate,thebigger the value, the higher the recovery ability;Constructive equation isgiven which includes initial condition, stress, strain, strain rate, strain ratesensitivity index and strain hardening index and can represent superplasticdeformation course specifically;Furthermore the important results aboutsuperplastic tensile deformation previously were reappeared by theconstructive equation.5、Necking question of non perfect sample was studied;Instable strainand failure strain were forecasted,then we obtain ideal theoretic predictorformula.In 1964,Backofen put forward constructive equation representingsuperplastic tensile deformation process. Then, Hart gave state equationdescribing superplastic deformation process in 1967. The equation combinedstress, strain, strain rate, strain rate sensitivity index and strain hardeningindex. However, it is too ambiguous to reflect the relationship betweendifferent mechanical variables and material parameters. The mathematicalmodel in the first chapter made up for the shortage of the state equation. Themathematical model which was given by the author is a standard second-ordernonlinear differential equation , which provided theoretical basis forcontrolling tensile deformation process automatically. In addition,if we canconfirm the relationship between material parameter and strain or strain rate,then the model will be more definitely to confirm the relationship betweendifferent mechanical variables. Superplastic deformation process is toocomplex to express by one variable function, which is a commonunderstanding to people , thus Backofen’s constructive equation seemsextremely simple. On the other hand, Backofen’s constructive equation didn’trepresent the relationship between different mechanical variables overall. Wecan obtain a new constructive equation by regarding the material parametersas constant,and Backofen’s constructive equation is just a peculiar case of thenew constructive equation. The constructive equation in the third chapterrepresents the relationship of mechanical variables and material parameters. Itis the new constructive equation that can obtain a result consisting withstability criterion under different deformation path. There is innovation in thefirst chapter’s mathematical model and the third chapter’s constructiveequation,and they will contribute to perfect and develop superplasticdeformation theory. The mechanical analysis about four states of tensileinstability will help us understand deformation process better;Strain ratefluctuate model of superplastic tensile deformation represents strain ratesensitivity of superplastic material more clearly,and gives the effect thatstrain rate sensitivity index on strain rate fluctuate model,this model also canhelp us establish relational expression of strain rate sensitivity index.Moreover, the forecasting of instability strain and failure strain with singledefect or mixed defect sample enrich the theory of strain forecasting.The achievements and results of this paper will contribute to thedevelopment of superplastic theory.更多还原