Compressibility of an Isolated Spheroidal Cavity in an Isotropic Elastic Medium
Compressibility of an Isolated Spheroidal Cavity in an Isotropic Elastic Medium
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DOI：
10.1115/1.3169108
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发表时间：
1985-09
期刊：
影响因子：
--
通讯作者：
R. Zimmerman
中科院分区：
文献类型：
--
作者：
R. Zimmerman
无限大、各向同性、弹性介质中的球形空腔为经常存在于岩石、陶瓷和多孔金属中的空隙提供了一个有用的模型。在其限制形式中，球体可以表示球体、无限长的圆柱体或扁平的“硬币形”裂纹。这种空隙的一个重要性质是其”孔隙压缩性”，在此用Cpp表示，并定义为由于向其表面施加单位大小的流体静压而导致的空腔体积的分数变化。虽然在过去的文献[1-3]中已经研究了球形空腔周围的弹性场问题，但这些研究的重点通常是应力集中。因此，孔隙压缩系数的某些特性似乎没有引起人们的注意。一个是长球体的孔隙压缩性，其形状可以从球体到圆柱体的范围内，是为所有意图和目的的剪切模量的函数，几乎独立的基质材料的压缩性。此外，渐近表达式的孔隙压缩性的扁球体的消失小的纵横比（通常模型的硬币形裂纹）实际上是高度准确的扁球体的纵横比的几乎整个范围内。
A spheroidal cavity in an infinite, isotropic, elastic medium provides a useful model for the voids that are often present in rocks, ceramics, and porous metals. In its limiting forms, the spheroid can represent a sphere, an infinitely long cylinder, or a flat," penny-shaped" crack. An important property of such a void is its" pore compressibility," denoted here by Cpp, and defined as the fractional change in the volume of the cavity resulting from the application to its surface of a hydrostatic pressure of unit magnitude. Although the problem of the elastic field around a spheroidal cavity has been examined in the past [1-3], the focus of these studies has usually been on stress concentrations. Consequently, there are certain features applicable to pore compressibility that seem to have escaped notice. One is that the pore compressibility of a prolate spheroid, whose shape can range from a sphere to a cylinder, is for all intents and purposes a function only of the shear modulus, and nearly independent of the compressibility of the matrix material. Also, the asymptotic expression for the pore compressibility of an oblate spheroid of vanishingly small aspect ratio (the usual model for the penny-shaped crack) is actually highly accurate over nearly the entire range of oblate spheroid aspect ratios.