摘要
从能量方程求得具体的裂纹扩展方程是困难的,因为在一般情况下,我们还不知道断裂过程中各种能量以什么样的比例存在于系统中。鉴于此,我们考虑将动量方程用于裂纹扩展研究。建立一个以动量定律而不是以能量原理为基础的断裂模型。这种模型的建立是基于这样的认识,即裂纹体在断裂过程中,即使其整体动量,动量矩是守恒的情况下,其局部动量、动量矩也是不守恒的。或者说,动量平衡方程是非局部的,通常的局部化假设在裂纹扩展展过程中是不成立的。在此基础上种文中以裂纹尖端局部区域为研究对象,从多方面论证了该区域作用有不平衡力,正是这个不平衡力的大小,方向等的变化控制着裂纹扩展过程,建立了变质量断裂模型。该模型以随裂纹尖端运动的局部区域作为变质量系统,研究该系统质量和作用在该系统上力的变化,以此研究裂纹扩展过程,从而给出了裂纹扩展遵循的一般方程。本文用自行研制的裂纹扩展速度测定仪测得的裂纹扩展速度,在平面应力Ⅰ型裂纹条件下,在一定程度上验证了理论的正确性。
It's difficult to get equations for cracking expansion from energy equation, becauseunder general situation, we don't know what concrete rate all kinds of energy in fracturepropagation exsist in the system.Therefore, let's consider to use momentum equation forthe expansion research, so as to set up a fracture model using momentum law instead ofenergy principle as its base. The foundation of such model is based on the cognition thatas for the cracking body in fracture, even if the whole momentum and its moment areconservative, the local momentum and its moment are unconservative. That's to say, themomentum balance equation is nonlocal and general assumption of localization is untena-ble in the process of cracking expansion. Therefore with the object of researching thelocal zone of the cracking tip, this paper proves from many aspecte that in this zone exs-ists unbalanced force. It is the variation of the magnitude and direction of the unbalanc-ed force that establishes the fracture model of variable,mass. The model is regarded asvariable mass system, in the local zone of cracking tip motion, then we can research thequality of system and the variation of force acted on the system, so as to research theprocess of cracking expansion. Thus general epuations followed by cracking expansion canbe obtained. Using the cracking expansion speed measured with the recognizer made byourselves, under the condition of the plane stress cracking model I, this paper proves thecorrection of the theory to a certain extent.
出处
《湘潭大学自然科学学报》
CAS
CSCD
1989年第1期178-187,共10页
Natural Science Journal of Xiangtan University
关键词
变质量
断裂模型
裂纹扩展
fracture model of variable mass
nonreversible large deformation local momentum nonconservative
non-loeafieldtheory
the propagation velocity of crack
