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基于断裂力学的甘蔗切割裂纹应力强度因子分析

Analysis of Crack Stress Intensity Factor of Sugarcane Cutting Based on Fracture Mechanics

  • 摘要: 甘蔗属于一年生或多年生宿根热带和亚热带草本植物,宿根切割质量对于甘蔗来年的长势有重要影响。本文探究甘蔗茎秆的切割机理并基于断裂力学理论研究甘蔗裂纹的起裂与扩展过程,为提高宿根切割质量提供理论基础。基于根切器与茎秆的相互作用关系,构建刀具切割茎秆的力学模型,探究切割力等影响因素并基于高速摄像技术观察茎秆切割过程;发现影响切割性能(弯矩、切割力等)的因素主要与甘蔗茎秆及根切器的机械力学特性(直径、密度及茎秆倾斜角度等)、根切器的运动参数(切割频率、切割深度)以及土壤情况等因素有关。高速摄像试验结果表明,多刀切割会增加甘蔗宿根破头、拔根的概率,其由于在一刀切割完成后,茎秆产生凹坑、裂纹等缺陷,在茎秆自身重力及外载的作用下缺陷发生扩展,导致宿根发生破坏。基于断裂力学理论从茎秆内部裂纹入手,分析裂纹起裂条件和影响断裂角的因素并探究裂纹参数对于裂纹尖端应力强度因子以及扩展量的影响。研究结果表明:裂纹角度及数量的改变导致裂纹的开裂类型为复合型裂纹,其中Ⅰ-Ⅱ复合型裂纹为主要开裂类型;应力强度因子随裂纹角度的改变有较大的波动以及裂纹开裂方向和扩展量的变化是由于裂纹角度的改变影响了最大主应力与裂纹扩展面之间的夹角;当裂纹角度小于等于75°时,裂纹将沿原有方向继续扩展后发生弯折,当裂纹角度大于75°时,裂纹将沿着垂直于原有裂纹的方向发生扩展;随着裂纹数量的增多,裂纹间的屏蔽效应增强,导致裂纹尖端材料的应力得到释放,裂尖附近的相对位移减小,裂纹的扩展量逐渐减小。

     

    Abstract: Sugarcane belongs to annual or perennial tropical and subtropical herbs, and the cutting quality of sugarcane stubble has a crucial impact on the growth of cane in the following year. Sugarcane cutting process is a high-speed, transient, and nonlinear dynamic problem. Aiming to explore the cutting mechanism of sugarcane stalks and study the cracking and propagation process of sugarcane cracks based on the fracture mechanics theory, which was to provide a theoretical basis for improving the cutting quality of sugarcane stalk, the mechanical model(bending moment, cutting force, etc.) of the base cutter cutting the stalk was established by analyzing the interaction between the cutter and the stalk, to explore the influencing factors of cutting force; and the high-speed camera technology was adopted to observe the cutting quality of sugarcane stubble cuts with one and multi-times cutting. It was found that the factors affecting the cutting performance were mainly related to the mechanical properties(diameter, density, stalk inclination angle, etc.) of sugarcane stalks and base cutters, the kinematic parameters(cutting frequency, cutting depth) of base cutters, and soil conditions. However, the multi-time base cutting would increase the probability of stubble damage, which was mainly caused by defects and cracks on the stalks after first cutting, and the cracks would extent under its own gravity and external load. Therefore, the internal cracks of the sugarcane stalk were first studied based on the fracture mechanics theory, the crack initiation conditions and the factors affecting the fracture angle were analyzed, and the influence of crack parameters on the stress intensity factor and the expansion amount were explored. The results showed that the change of crack angle and number led to the composite crack, and theⅠ-Ⅱ composite crack was the main crack type. The stress intensity factor fluctuated greatly with the crack angle changing, and the change of crack direction and extension was due to the angle between the maximum principal stress and the crack propagation surface was affected by the crack angle; when the crack angle was less than or equal to 75°, the crack would continue to expand along the original direction and then bend, however, the crack would expand along the direction perpendicular to the original crack when the crack angle was greater than 75°. During the propagation process of two cracks, the cracks propagated along a 45° direction from the original crack. This was due to the relative slip of the material inside the stem under the influence of the cracks. The shear stress reached its maximum value at the 45° direction. With the increase of number of cracks, the shielding effect between cracks was increased, which would result in the release of the stress in the material at the crack tip, the relative displacement near the crack tip was decreased, and the crack growth was decreased gradually.

     

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