Ultrasonic Determination of Texture and Residual Stress in Polycrystalline Metals
01 Jan 1987-pp 319-333
TL;DR: In this paper, the long wavelength limit of a polycrystalline aggregate is modelled as an elastic continuum with elastic constants determined by the elastic constants of the grains and the crystallite orientation distribution function (CODF).
Abstract: In a polycrystalline aggregate the elastic constants in the specimen reference frame vary from grain to grain due to the random orientation of the grains. Polycrystalline metals are therefore elastically inhomogeneous, and the elastic constant mismatch at the grain boundaries leads to scattering of the ultrasonic wave. In the long wavelength limit, however, the metal can be modelled as an elastic continuum with elastic constants determined by the elastic constants of the grains and the crystallite orientation distribution function (CODF). This function gives the probability of a crystallite having a given orientation with respect to the specimen frame, and gives a quantitative description of the texture, or crystallographic alignment, of the material. In a strongly textured metal the yield stress varies as a function of direction and this can lead to non-uniform flow in deep drawing for example. As a result there is a need for a non-destructive measurement of texture in process control, and there is considerable interest in the use of ultrasonics for this purpose. In section 2 it is shown how information on the CODF can be obtained from ultrasonic velocity measurements.
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TL;DR: In this article, a simple micromechanical model of a prestressed polycrystalline aggregate was developed, in which the texture-induced and stress-induced anisotropies of the aggregate were precisely defined.
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.
35 citations
TL;DR: In this paper, the authors measured the birefringence and the difference between Poisson's ratios measured using a shear wave polarized along the length of a plate and another wave polarized on the width of the plate, linearly related to the degree of deformation and hardness.
Abstract: Poisson's ratio and birefringence, both measured by ultrasound, are used to follow the evolution of the anisotropy in ASTM A-36 steel plates cold-rolled between 5 and 50% deformation, and then subjected to recrystallization at 900 and 1000 oC. Times of flight of longitudinal and shear waves along the thickness of the plates were measured. As orthotropy increases, both birefringence and the difference between Poisson's ratios measured using a shear wave polarized along the length and another wave polarized along the width of the plate, are linearly related to the degree of deformation and cold-rolled hardness. In addition, the ultrasonic methods used clearly detected the complex changes in anisotropy produced by the austenization and recrystallization heat treatments. Thus, Birefringence or Poisson's ratio, measured by ultrasound, can be used to follow-up nondestructively changes in the anisotropy of rolled plates as a function of both, degree of deformation and recrystallization heat treatment.
4 citations
01 Jan 1995
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Cites background from "Ultrasonic Determination of Texture..."
...For instance, from acoustic velocity measurements made in different directions, the texture of a material can be determined [4,5]....
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References
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TL;DR: In this article, the orientation distribution of crystallites in anisotropic polycrystalline samples can be derived from a set of plane-normal distributions obtained by x-ray diffraction measurements.
Abstract: A method is presented here by which orientation distribution of crystallites in anisotropic polycrystalline samples can be derived from a set of plane‐normal distributions obtained by x‐ray diffraction measurements. It is the generalization of the similar procedure proposed previously for analysis of samples having fiber texture. It thus represents a completely general solution to the problem of pole figure inversion, applicable to samples having any arbitrary symmetry elements. The plane‐normal distribution function is expanded in a series of spherical harmonics, the coefficients of which, Qlmi, can be determined by numerical integration of experimental diffraction data. The crystallite distribution function is expanded in a series of generalized spherical harmonics which appear as solutions to the Schrodinger wave equation of a symmetric top. The coefficients of the crystallite distribution function, Wlmn, are then obtained as linear combinations of Qlmi. Symmetry properties of Wlmn arising from crystallographic or statistical symmetry elements existing in the sample are examined. The methods of estimating the series truncation errors and of minimizing the experimental error by a least‐squares method, previously proposed in connection with fiber texture analysis, are still applicable here with appropriate generalizations. In addition it is shown that the effect of diffraction line broadening due to finite size or imperfection of crystallites can also be allowed for at least approximately.
757 citations
683 citations
TL;DR: In this article, a rigorous treatment is given of the problem of wave propagation in an elastic continuum when the influence of the initial stress is taken into account, and it is shown that a uniform hydrostatic pressure does not change the laws of propagation.
Abstract: A rigorous treatment is given of the problem of wave propagation in an elastic continuum when the influence of the initial stress is taken into account. After a short review of the theory various cases of initial stress are considered. It is shown that a uniform hydrostatic pressure does not change the laws of propagation. A hydrostatic pressure gradient produces a buoyancy effect which causes coupling between rotational and dilatational waves. Bromwich's equations for the effect of gravity on Rayleigh waves are derived from the general theory and the physical transition from Rayleigh waves in a very rigid medium to pure gravity waves in a liquid is discussed. The case of the vertical uniform stress is also considered and it is shown that the effect of the initial stress on the waves in this case cannot be accounted for by elastic anisotropy alone. Reflections may be produced by a discontinuity in stress without discontinuity of elastic properties.
265 citations
TL;DR: In this article, the ultrasonic velocities in polycrystalline aggregate of cubic crystals with orthorhombic symmetry are derived using the formalism of Roe (1965, 1966) for treating the texture of poly crystal aggregates.
Abstract: The ultrasonic velocities in a polycrystalline aggregate of cubic crystals with orthorhombic symmetry are derived. Use is made of the formalism of Roe (1965, 1966) for treating the texture of polycrystalline aggregates. It is shown how information about the crystallite orientation distribution function can be derived from ultrasonic velocity measurements. This enables the construction of ultrasonic pole figures, which may be compared with those obtained from neutron diffraction. Application is made to the effect of texture on ultrasonic propagation in austenitic welds.
213 citations
TL;DR: In this article, the orientation distribution of all crystallites in the sample is deduced by a procedure described in a previous paper, in which the crystallite distribution function is expanded in a series of generalized Legendre functions.
Abstract: X‐ray diffraction measurements on anisotropic polycrystalline samples give a set of functions (pole‐figures) describing the orientation distribution of individual plane‐normals. From the set of these plane‐normal distributions it is possible to deduce the orientation distribution of all crystallites in the sample (inversion of pole‐figures) by a procedure described in a previous paper, in which the crystallite distribution function is expanded in a series of generalized Legendre functions. The expansion coefficients Wlmn which characterize the crystallite distribution have to satisfy restrictions imposed by the crystallographic and statistical symmetry elements existing in the sample. When the crystallites belong to the cubic crystal class, it is required not only that some of Wlmn be identically equal to zero but also that the remaining nonzero Wlmn be linearly related to each other (for given l and m). The matrix equation expressing the linear dependence among Wlmn is solved numerically by a computer an...
196 citations