tailieunhanh - Acoustic Waves part 15

Tham khảo tài liệu 'acoustic waves part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Ultrasonics A Technique of Material Characterization 409 7 3. Porosity The porosity of the porous material can be examined with the knowledge of elastic moduli and Poisson s ratio as a function of pore volume fraction. These parameters can be evaluated with help of measured velocity and density. A simple expression of Young modulus and shear modulus for a porous material can be written as Y Y0 exp -ap-bp2 G G0 exp -ap-bp2 Here Y0 and G0 are the modulus of material without pore a b and c are the constants p is pore volume fraction which is equal to 1- d d0 and d is the bulk density determined experimentally from mass and volume while d0 is the theoretical density determined from XRD. The elastic moduli and Poisson ratio measured ultrasonically are compared with the theoretical treatment for the characterization. The elastic moduli of porous material are not only the function of porosity but also the pore structure and its orientation. The pore structure depends on the fabrication parameters like compaction pressure sintering temperature and time. If the pores are similar in shape and distributed in homogeneous pattern then a good justification of mechanical property can be obtained with this study. 5. Grain size There is no unique relation of average grain size with the ultrasonic velocity. The following typical graph Fig. 5 shows a functional relation among velocity V grain size D and wave number k . This has three distinct regions viz. decreasing increasing and oscillating regions. Both the I and II region are useful for the determination of grain size determination whereas region III is not suitable. kD Fig. 5. Ultrasonic velocity as a function of kD The obtained grain size with this study has good justification with grain size measured with metallography. The important advantage of using ultrasonic velocity measurements for the grain size determination is the accuracy in which ultrasonic transit time could be determined through electronic instrumentation. The .