Abstract
In this paper we develop a simple micromechanical model of a prestressed polycrystalline aggregate, in which the texture-induced and stress-induced anisotropies of the aggregate are precisely defined; here the word ‘texture’ always refers to the texture of the aggregate at the given prestressed configuration, not to that of a perhaps fictitious natural state of the aggregate. We use this model to derive, for a prestressed orthotropic aggregate of cubic crystallites, a birefringence formula which shows explicitly the effects of the orthotropic texture on the acoustoelastic coefficients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one reflecting purely the influence of stress on the birefringence, and the other encompassing all the effects of texture. The same formula, on the other hand, provides for each material specific quantitative criteria under which the ‘separation of stress-induced and texture-induced birefringence’ would become meaningful in an approximate sense.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.I. Crecraft, The measurement of applied and residual stresses in metals using ultrasonic waves. J. Sound Vib. 5 (1967) 173–192.
Y.H. Pao, W. Sachse and H. Fukuoka, Acoustoelasticity and ultrasonic measurements of residual stress. In: W.P. Mason and R.N. Thurston (eds.), Physical Acoustics, Vol. 17. Orlando: Academic Press (1984), pp. 61–143.
R.B. Thompson, W.-Y. Lu and A. V. Clark, Ultrasonic Methods. In: J. Lu and M.R. James (eds), SEM Monograph on Techniques for Residual Stress Measurement. Society for Experimental Mechanics (in press).
R.A. Toupin and B. Bernstein, Sound waves in deformed perfectly elastic materials. Acoustoelastic effect. J. Acoust. Soc. Am. 33 (1961) 216–225.
T. Tokuoka and M. Saito, Elastic wave propagations and acoustical birefringence in stressed crystals. J. Acoust. Soc. Am. 45 (1968) 1241–1246.
T. Tokuoka and Y. Iwashimizu, Acoustical birefringence of ultrasonic waves in deformed isotropic elastic materials. Int. J. Solids Structures 4 (1968) 383–389.
Y. Iwashimizu and K. Kubomura, Stress-induced rotation of polarization directions of elastic waves in slightly anisotropic materials. Int. J. Solids Structures 9 (1973) 99–114.
E. Imanishi, M. Sasabe and Y. Iwashimizu, Experimental study on acoustical birefringence in stressed and slightly anisotropic materials. J. Acoust. Soc. Am. 71 (1982) 565–572.
T.-T. Wu, M. Hirao and Y.-H. Pao, Acoustoelastic birefringences in plastically deformed solids: Part II-experiment. ASME J. Appl. Mech. 58 (1991) 18–23.
M. Hirao, H. Ogi and H. Fukuoka, Advanced ultrasonic method for measuring rail axial stresses with electromagnetic acoustic transducer. Res. Nondestr. Eval. 5 (1994) 211–223.
Y.H. Pao, Theory of acoustoelasticity and acoustoplasticity. In: J.D. Achenbach and Y. Rajapakse (eds), Solid Mechanics Research for Quantitative Non-Destructive Evaluation. Martinus Nijhoff Publishers, Boston (1987), pp. 257–273.
H.J. Bunge, Texture Analysis in Materials Science. Butterworth's, London (1982).
C.M. Sayers, Ultrasonic velocities in anisotropic polycrystalline aggregates. J. Phys. D. 15 (1982) 2157–2167.
C.M. Sayers, Ultrasonic determination of texture and residual stress in polycrystalline metals. In: J.D. Achenbach and Y. Rajapakse (eds), Solid Mechanics Research for Quantitative Non-Destructive Evaluation. Martinus Nijhoff Publishers, Boston (1987), pp. 319–333.
G.C. Johnson, Acoustoelastic response of polycrystalline aggregates exhibiting transverse isotropy. J. Nondestructive Evaluation 3 (1982) 1–8.
G.C. Johnson, Acoustoelastic response of a polycrystalline aggregate with orthotropic texture. ASME J. Appl. Mech. 52 (1985) 659–663.
W. Voigt, Lehrbuch der Kristallphysik. B.G. Teubner, Leipzig (1928).
R. Chang, Relationships between the nonlinear elastic constants of monocrystalline and polycrystalline solids of cubic symmetry. Appl. Phys. Lett. 11 (1967) 305–308.
G.R. Barsch, Relation between third-order elastic constants of single crystals and polycrystals. J. Appl. Phys. 39 (1968) 3780–3793.
R.-J. Roe, Description of crystallite orientation in polycrystalline materials. III. General solution to pole figures. J. Appl. Phys. 36 (1965) 2024–2031.
P. Haupt, Y.-H. Pao and K. Hutter, Theory of incremental motion in a body with initial elastoplastic deformation. J. Elasticity 28 (1992) 193–221.
W. Rudin, Real and Complex Analysis, 3rd edition. McGraw-Hill, New York (1987).
W. Rudin, Functional Analysis. McGraw Hill, New York (1973).
H.J. Bunge, Representation of preferred orientations. In: H.-R. Wenk (ed.), Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern Texture Analysis. Academic Press, Orlando (1985), pp. 73–104.
C.-S. Man and D.E. Carlson, On the traction problem of dead loading in linear elasticity with initial stress. Arch. Rational Mech. Anal. 128 (1994) 223–247.
M.E. Gurtin, Topics in Finite Elasticity. SIAM, Philadelphia (1981).
A. Hoger, On the residual stress possible in an elastic body with material symmetry. Arch. Rational Mech. Anal. 88 (1985) 271–289.
A. Hoger, On the determination of residual stress in an elastic body. J. Elasticity 16 (1986) 303–324.
B.D. Coleman and W. Noll, Material symmetry and thermostatic inequalities in finite elastic deformations. Arch. Rational Mech. Anal. 15 (1964) 87–111.
C.-S. Man and W.Y. Lu, Towards an acoustoelastic theory for measurement of residual stress. J. Elasticity 17 (1987) 159–182.
B.A. Auld, Acoustic Fields and Waves in Solids, Vol. 1. John Wiley, New York (1973).
C.-S. Man, Acoustoelastic measurement of residual stress. In: R.C. Batra and M.F. Beatty (eds), Symposium on Elasticity to Honor Prof. J.L. Ericksen. CIMNE, Barcelona (in press).
J.F. Thomas, Third order elastic constants of aluminum. Phys. Rev. 175 (1968) 955–962.
V.P.N. Sarma and P.J. Reddy, Third-order elastic constants of aluminum. Phys. Stat. Sol. (a) 10 (1972) 563–567.
H. Fukuoka and H. Toda, Preliminary experiment on acoustoelasticity for stress analysis. Arch. Mech. 29 (1977) 673–686.
O. Kobori, and Y. Iwashimizu, Effects of stress and temperature on ultrasonic velocity. In: S.K. Datta, J.D. Achenbach and Y.S. Rajapakse (eds), Elastic Waves and Ultrasonic Nondestructive Evaluation. Elsevier, Amsterdam (1990), pp. 339–343.
R.-J. Roe, Inversion of pole figures for materials having cubic crystal symmetry. J. Appl. Phys. 37 (1966) 2069–2072.
P.R. Morris and A.J. Heckler, Crystallite orientation analysis for rolled cubic materials. In: J.B. Newkirk et al. (eds), Advances in X-ray analysis, Vol. 11. Plenum, New York (1968), pp. 454–472.
R.B. King and C.M. Fortunko, Determination of in-plane residual stress states in plates using horizontally polarized shear waves. J. Appl. Phys. 54 (1983) 3027–3035.
G.C. Johnson and W.C. Springer, A comparison of measured and predicted second-and thirdorder elastic constants of a textured aggregate. Int. J. Solids Structures 25 (1989) 609–619.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Man, CS., Paroni, R. On the separation of stress-induced and texture-induced birefringence in acoustoelasticity. J Elasticity 45, 91–116 (1996). https://doi.org/10.1007/BF00042485
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00042485