简介概要

双剪统一强度理论计算塑性金属材料强度的唯一性

来源期刊:中南大学学报(自然科学版)2008年第6期

论文作者:刘光连

文章页码:1280 - 1284

关键词:双剪统一强度理论;屈服;塑性;金属

Key words:twin-shear unified strength theory; yield; plastic; metal

摘    要:研究了双剪统一强度理论及其有关关系式,得到塑性金属材料双剪统一强度理论参数b的计算式,对某一塑性金属材料,其值为常数,取值范围是b>-1;运用双剪统一强度理论计算某一塑性金属材料的强度时有唯一确定的强度计算值,而不是多个值,不能得出塑性金属材料的τss;分析材料的拉压强度比为1时双剪统一强度理论的2组等价变换式,对b<0的材料,双剪统一强度理论计算表明,材料的破坏不是由中间主剪应力引起,这与双剪统一强度理论的假设矛盾;该理论不适用于三向等值拉应力状态的计算。

Abstract: Twin-shear unified strength theory and its related functions were studied. The formula of parameter b in the twin-shear unified strength theory for a certain plastic metal was developed and its value was determined to be constant for a certain plastic metal and its value range is b>-1; only a certain value can be obtained when the strength of a plastic metal based on the twin-shear unified strength theory was calculated and the value of ts/ss could not be obtained. The results show that based on the analysis of the two equivalent equations of the twin-shear unified strength theory when the ratio of tensile strength to compressive strength equals 1, for materials with b<0, the fracture of materials is not caused by the intermediate principal shear stress, which does not agree with the hypothesis of the twin-shear unified strength theory, and this theory can not be applied in stress state such as equitriaxial tension.



详情信息展示

双剪统一强度理论计算塑性金属材料强度的唯一性

刘 光 连

(中南大学 机电工程学院,湖南 长沙,410083)

摘  要:研究了双剪统一强度理论及其有关关系式,得到塑性金属材料双剪统一强度理论参数b的计算式,对某一塑性金属材料,其值为常数,取值范围是b>-1;运用双剪统一强度理论计算某一塑性金属材料的强度时有唯一确定的强度计算值,而不是多个值,不能得出塑性金属材料的τss;分析材料的拉压强度比为1时双剪统一强度理论的2组等价变换式,对b<0的材料,双剪统一强度理论计算表明,材料的破坏不是由中间主剪应力引起,这与双剪统一强度理论的假设矛盾;该理论不适用于三向等值拉应力状态的计算。

关键词:双剪统一强度理论;屈服;塑性;金属

中图分类号:TH114         文献标识码:A         文章编号:1672-7207(2008)06-1280-05

 

Uniqueness in calculating strength of plastic metals based on twin-shear unified strength theory

LIU Guang-lian

(School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China)

Abstract: Twin-shear unified strength theory and its related functions were studied. The formula of parameter b in the twin-shear unified strength theory for a certain plastic metal was developed and its value was determined to be constant for a certain plastic metal and its value range is b>-1; only a certain value can be obtained when the strength of a plastic metal based on the twin-shear unified strength theory was calculated and the value of ts/ss could not be obtained. The results show that based on the analysis of the two equivalent equations of the twin-shear unified strength theory when the ratio of tensile strength to compressive strength equals 1, for materials with b<0, the fracture of materials is not caused by the intermediate principal shear stress, which does not agree with the hypothesis of the twin-shear unified strength theory, and this theory can not be applied in stress state such as equitriaxial tension.

Key words: twin-shear unified strength theory; yield; plastic; metal

                    


Yu于1961年提出了双剪应力屈服准则[1],1985 年发展为双剪应力强度理论[2],1991年提出了新的双剪统一强度理论[3]。双剪统一强度理论认为:“当作用于双剪单元体上的2个较大剪应力及其面上的正应力影响函数到达某一极限值时,材料开始发生破坏。”它的数学建模方程如下[3-6]


式中:b为反映中间主剪应力以及相应面上的正应力对材料破坏影响程度的参数;为材料的拉伸强度极限()与压缩强度极限()的比值,即

若认为材料的拉伸、压缩强度极限相等,即,则式(1)和(2)就是双剪统一屈服准则的计算式[4];若令,b=1,则式(1)和(2)就是双剪应力屈服准则的计算式[1-2, 4]

自2004年以来,双剪统一强度理论在国内外得到较多的引用[8-10]和应用[11-13]。双剪统一强度理论具有统一的理论模型和统一的数学表达式,适用于金属、岩石、聚合物等多种材料[4-5]

双剪统一强度理论不断得到发展,在系列剪应力强度理论基础上,出现了“新的普遍形式的统一强度理论”和它的各种特例[14]。在此,本文作者根据双剪统一强度理论推导过程中已经得到的有关关系式,研究双剪统一强度理论参数b的物理意义和该理论的强度计算式,分析参数b的取值范围和该理论的不足,指出新的强度理论仍然值得研究。

1  计算塑性金属材料强度的唯一性

参数b被认为是双剪统一强度理论的破坏准则参数[3-5]。在一般情况下,可取b=0,1/4,1/2,3/4,1,5/4,3/2共7种典型参数[4]。例如,文献[4]中举例计算了某一承受内压的低碳钢薄壁圆筒的壁厚,其拉压强度极限相等,分别取b=0,1/4,1/(1+),1/2,3/4和1,经计算得到的壁厚分别为12,10.8,10.4,10,9.43和9 mm。取b=0时算得的壁厚与第三强度理论得出的结果一致;取b=1/(1+)时,算得的壁厚与第四强度理论的计算结果(10.38 mm)接近。从这个算例看,即使是各向同性材料,在同一应力状态下,参数b可以有多种选择,是不确定的。究竟哪个是最优的取值,该理论似乎并不能确定。

双剪统一强度理论的参数b可以取不同的值进行设计计算,得出没有确定性的结果。事实上,对于一各向同性塑性金属材料的拉伸屈服强度、压缩屈服强度和剪切屈服强度都是材料常数。以此为前提,可以确定参数b。

为此,考虑塑性金属材料在纯扭转受力状况下,因材料剪切屈服而发生失效,失效条件为:

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