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实际工程结构和零件的弹塑性断裂,包括脆性断裂和疲劳断裂,经常发源干应力集中超过屈服限的塑性应变区中的小裂纹。甚至用来模拟切口地区中疲劳断裂的光滑试件应变疲劳实验中,寿命也主要是由微裂纹在循环塑性应变介质中的扩展速率决定的。此外,断裂韧度K_(1c)和扩展速率da/dN在一定条件下也和宏观裂纹顶端塑性区中微裂纹的扩展有关。因此,塑性应变区中裂纹扩展的分析方法是弹塑性断裂力学迫切需要解决的课题。但目前用于弹塑性条件下测定K_(1c)的J积分方法局限于考虑只有韧带屈服的深裂纹试件的弹塑性分析。本文根据J积分守恒性和塑性应力应变集中近似分析法,J积分的形变功率或能量率近似分析法,因次分析法等,从不同角度导出了塑性区中裂纹的J积分近似公式J=2πY~2α∫σde。应用这个公式于应变裂纹容限分析时,可以导出由大量含小裂纹宽板屈服后断裂实验归纳出的张开位移经验关系,例如Wells关系δ=2πae和Burdekin关系Φ≡δ/2παe_Y=(e/e_Y)-0.25。应用这个公式于应变疲劳寿命分析,则导出了由大量应变疲劳寿命实验归纳出的Coffin-Manson关系,并提出了能在更宽的寿命范围内进行疲劳寿命计算和分析的总形变功判据。在应变裂纹容限和应变疲劳寿命分析中的这些推导结果和大量实验数据归纳出的经验关系的一致性证明了本文所提出的塑性区中裂纹J积分近似公式的可靠性。当然,这公式的近似程度还需要今后用有限元法计算来进一步核实。
Elastoplastic fractures of actual engineering structures and parts, including brittle fracture and fatigue fracture, often generate small cracks in the plastic strain zone where the dry stress concentration exceeds the yield strength. Even in the fatigue tests of smooth specimens, which simulate the fatigue fracture in the incised area, the life span is mainly determined by the rate of microcrack propagation in the cyclic plastic strain medium. In addition, the fracture toughness K_ (1c) and the expansion rate da / dN are also related to the propagation of microcracks in the plastic zone at the top of macrocracks under certain conditions. Therefore, the analysis method of crack propagation in plastic strain zone is an urgent problem to be solved by elastoplastic fracture mechanics. However, the J-integral method currently used for the determination of K_ (1c) in elasto-plastic conditions is limited to the analysis of the elasto-plastic behavior of deep cracked specimens considering the yield of only the ligaments. In this paper, the J-integral approximate formula of crack in plastic zone is derived from different angles according to J-integral conservation and plastic stress-strain approximate analysis, J-integral deformation power or energy rate approximate analysis, ~ 2α∫σde. Applying this formula to the analysis of strain-crack allowance, we can derive the empirical relationship of open displacement derived from a large number of fracture experiments after yielding with small cracked wide plates. For example, wells relation δ = 2πae and Burdekin’s relation Φ≡δ / 2παe_Y = (e /e_Y)-0.25. Applying this formula to strain fatigue life analysis, the Coffin-Manson relationship deduced from a large number of strain fatigue life experiments is deduced and the total deformation work criterion for calculating and analyzing the fatigue life over a wider life span is proposed. The consistency of the empirical relationships summarized in the strain crack tolerance and strain fatigue life analysis and the large amount of experimental data proves the reliability of the J-integral approximation formula for the crack in the plastic zone proposed in this paper. Of course, the approximate degree of this formula also needs to be further verified by the finite element method calculation in the future.