The Ohio State University, Department of Materials Science and Engineering, Edison Joining Technology Center, 1248 Arthur E. Adams Dr., Columbus, OH 43221, USA.
Ultrasonics. 2011 Aug;51(6):697-708. doi: 10.1016/j.ultras.2011.02.002. Epub 2011 Feb 19.
Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.
对于具有长形晶粒的立方多晶材料中的超声波，以简单的积分形式获得了纵波和横波衰减系数。详细描述了衰减与频率和晶粒形状的关系。给出了在任意方向相对于椭球轴传播的波在瑞利和随机频率极限下的椭球晶粒的显式解析解。在这些频率极限下，衰减表现出典型的频率依赖性。然而，在随机极限下对晶粒形状的依赖性是出乎意料的：它与椭球晶粒的横截面无关，仅取决于传播方向上的晶粒尺寸。在瑞利区域，衰减与椭球晶粒的有效体积成正比，与形状无关。在过渡区域，衰减对晶粒形状/尺寸和频率表现出复杂的行为。所得到的结果简化为具有等轴晶粒的多晶材料的衰减对参数的经典依赖性。
