DISLOCATIONS AS A CAUSE OF MECHANICAL DAMPING IN METALS
DISLOCATIONS AS A CAUSE OF MECHANICAL DAMPING IN METALS
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DOI：
10.1098/rspa.1949.0072
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发表时间：
1949-01-01
影响因子：
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通讯作者：
ESHELBY, JD
中科院分区：
文献类型：
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作者：
ESHELBY, JD
齐纳已经证明了热弹性效应如何引起固体机械振动的阻尼。例如，在振动簧片中，相对侧交替地压缩和延伸。这引起了横跨簧片宽度的交替温差，并且由此产生的热流动导致机械能的耗散。在振动的金属单晶中，观察到额外的能量损失，这通常归因于位错的运动。在本文件中，提出了以下机制。位错在晶体内应力的最小值处被捕获在“势槽”中。当晶体振动时，位错在它们的势槽中振荡，与它们相关的运动应力系统在材料中产生波动的温度分布;这导致阻尼，如齐纳的情况。计算了位错以给定振幅振荡所产生的能量损失率，并讨论了它们的集合的影响。振动晶体中阻尼的实际估计需要（i）位错的振荡幅度与导致其移动的振动应力之间的关系的知识，以及（ii）材料中位错密度的知识。对（i）进行了初步讨论。数量（ii）是未知的，但是，它表明，阻尼只取决于单位面积的位错数的比率，单位面积的潜在槽数。如果从理论结果和铜单晶中观察到的阻尼计算这个比率，发现它是统一的顺序。本理论预测阻尼应随频率增加。这与有限的实验数据不符。还研究了两个辅助效应，即振动应力与定常位错周围应力相互作用产生的热弹性阻尼，以及振动位错发射弹性波产生的阻尼。这两种效应被证明是小的移动位错所造成的热弹性阻尼相比。
Zener has shown how thermoelastic effects give rise to damping of the mechanical vibrations of a solid. For example, in a vibrating reed opposite sides are alternately compressed and extended. This gives rise to an alternating temperature-difference across the width of the reed, and the resulting flow of heat leads to dissipation of mechanical energy. In a vibrating single crystal of a metal an additional energy loss is observed which is usually attributed to the motion of dislocations. In the present paper the following mechanism is proposed. Dislocations are trapped in 'potential troughs’ at the minima of the internal stress in the crystal. When the crystal vibrates the dislocations oscillate in their potential troughs and the moving stress-system associated with them produces a fluctuating temperature distribution in the material; this leads to damping as in Zener’s case. The rate of loss of energy produced by a dislocation oscillating with given amplitude is calculated and the effect of a collection of them is discussed. An actual estimate of the damping in a vibrating crystal requires (i) a knowledge of the relation between the amplitude of oscillation of a dislocation and the vibrational stress causing it to move, and (ii) a knowledge of the density of dislocations in the material. A tentative discussion of (i) is given. The quantity (ii) is unknown; however, It is shown that the damping depends only on the ratio of the number of dislocations per unit area to the number of potential troughs per unit area. If this ratio is calculated from the theoretical result and the observed damping in copper single crystals, it is found to be of the order of unity. The present theory predicts that the damping should increase with frequency. This is in disagreement with the limited experimental data available. Two subsidiary effects are also investigated, the thermoelastic damping arising from the interaction between the vibrational stresses and the stresses surroundingstationarydislocations, and the damping due to the emission of elastic waves from an oscillating dislocation. Both these effects are shown to be small compared with the thermoelastic damping caused by moving dislocations.