“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

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	“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure
	Wang HY(汪海英); Wang HY(汪海英); Ke FJ; Bai YL(白以龙)
	2005-08-01
会议名称	The Seventh International Conference on Mesomechanics
通讯作者	白以龙
中文摘要	Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V. It is found that the trans-scale length ratio c/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V)including the *5 N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* 4) N N t =1 n c and tV=c/V. Clearly, the dimensionless number De=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.
会议录	The Seventh International Conference on Mesomechanics,2005-08-01,
学科主题	力学
内容类型	会议论文
源URL	[http://dspace.imech.ac.cn/handle/311007/13897]
专题	力学研究所_力学所知识产出(1956-2008)
通讯作者	Bai YL(白以龙)
推荐引用方式 GB/T 7714	Wang HY,Wang HY,Ke FJ,et al. “Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure[C]. 见:The Seventh International Conference on Mesomechanics.