MODERN SITUATION IN PHOTOACOUSTICS IN APPLICATION TO THE PROBLEM OF MECHANICAL STRESS MEASUREMENTS

Experimental results obtained by the photoacoustic method for Vickers indentation zones in ceramics and metals are presented. The influence of the given external stresses on the photoacoustic images of Vickers indentations is demonstrated both for ceramics and metals. Obtained experimental results are compared with the available theoretical models of the photoacoustic effect in stressed materials. Introduction The problem of residual stress detection and measurement is urgent in modern engineering, mechanics and material physics. A good deal of effort has been undertaken in developing various methods for the residual stress detection [1]. Such methods as Raman spectroscopy, optical, ultrasonic, magnetic, X-ray and neutron diffraction methods are already applied effectively for this purpose in many cases. Hole drilling and compliance methods are actively developed at present for residual stress detection. Recently holographic and speckle interferometry has attracted serious attention for solving the problem [2]. At present thermoelastic stress analysis (TSA) is also a well-known experimental technique providing information on surface stress fields in structures [3]. Most of these methods are limited in application. For instance, Raman spectroscopy is mainly used in science and technology of semiconductors for which the phonon spectra have a relatively simple structure and line shifts with stresses are well known. The TSA and holographic interferometry are of more general applicability, but have comparatively low spatial resolution. From this viewpoint photoacoustic (PA) methods are attractive for modern diagnostics and imaging of near surface structures. The PA methods have micrometer resolution, are non-destructive and appeared to be useful for the detection of cracks and voids, delaminations and possible second phase material inclusions in the near surface layer of components. The first PA detection of residual stress took place about sixteen years ago [4]. Since then, there were a number of attempts for similar applications of the PA effect [5-9]. Nevertheless, residual stress detection by the PA methods has not been widely accepted. In our opinion, this situation is primarily due to the lack of in-depth systematic studies of the PA effect in solids with residual stresses including direct confirmation of stress influence on the PA signal. Accounting this we have performed detailed experimental and theoretical investigation of the PA effect in stressed solids. The aim of the work is to present our crucial results instantiating modern situation in the field of the PA detection and imaging of residual stresses. Some of the experimental results were presented and discussed in details elsewhere [10-13]. The paper presents also new results demonstrating the influence of external stresses on the PA images of Vickers indented ceramics and metals. We hope that presented results show the near-term outlook of some possible PA microscopy applications for residual stress detection. Theoretical Model of Photoacoustic Thermoelastic Effect in Stressed Solids To consider the theoretical foundation of the PA approach to the problem of residual stress detection we use the modern theory of thermoelasticity for elastic solids. By introducing the thermoelastic parameter instead of the coefficient of linear expansion in the equation of motion, the latter may be represented as [14] ( ) ( ) gradT K C u graddiv u u ε ε ρ μ λ μ λ μ ρ 2 3 2 + − + + ∇ = r r & &r , (1) where u r denotes deformations of the body, λ and μ are Lame’s elastic constants, ρ and Cε are the density and specific heat of the body, respectively; ε K is the thermoelastic parameter of the material, T is the temperature of the body. It is of general importance both for the PA technique that the thermoelastic parameter depends on stress [15]. By thermodynamic methods it was shown in [15] that in adiabatic conditions the thermoelastic parameter is related to the first stress invariant σ by the relation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ − = + = σ α ρ ε ε ε ε T E E C K K K T 2 ) 1 ( ) 0 ( 1 1 , (2) where αT is the coefficient of linear thermal expansion, E is Young's modulus, σik are the components of the stress tensor, ii σ σ = is the first stress invariant. ε ε ρ α C K T = ) 0 ( is the well-known relation for the thermoelastic parameter in the unstressed state of the body; ) 1 ( ε K accounts the influence of the stress on the thermoelastic parameter in the explicit form. A modulated laser radiation focused at the sample surface produces a cyclic local heat source Q. We suggest here that the pump laser radiation is strongly absorbed by the sample and Q is the surface heat source. The heat source generates thermal waves in the sample. The details of our PA microscopy setup for investigation of stressed materials are shown in Fig.1. Thermal waves are strongly damped and their propagation is limited by the length ω κ 2 = T l , where ω is the frequency of the pump beam modulation. According to Eq. (1) the periodic temperature gradient produces periodic local deformations in the body. It is important that the term with the temperature gradient includes the thermoelastic parameter. It means that laserinduced deformations of the body depend on local stresses in the small vicinity of the laser spot. In the PA microscopy these deformations are detected by a piezoelectric transducer attached to a sample under investigation. We have shown elsewhere [16, 17] that the PA images display mainly the near-surface thermoelastic properties of the sample. To get an expression for the PA signal we need to know the strain of the sample in the place of the piezoelectric transducer attachment. To obtain this strain Eq. (1) have to be solved. But in the general case it is a complicated mathematical problem. Therefore, we have analyzed this problem within the framework of the perturbation theory in quasi-static approximation. This approach assumes that elastic and thermoelastic inhomogeneties of the object are small and the length of acoustic waves exceeds essentially the length of thermal waves in a material. The second assumption is true for the most of the PA microscopy experiments. In this case the PA signal determined by thermoelastic inhomogeneties of a sample can be represented in the form of the volume integral SAMPLE PIEZOELECTRIC DETECTOR LASER