CONTRIBUTED PAPERS NON-DESTRUCTIVE DETERMINATION OF LOAD AND RESIDUAL STRESSES BY THE X-RAY STRESS METHOD I. O. BENNING

Transcription

1 The Rigaku Journal Vol. 6/ No. 2 / 1989 CONTRIBUTED PAPERS NON-DESTRUCTIVE DETERMINATION OF LOAD AND RESIDUAL STRESSES BY THE X-RAY STRESS METHOD I. O. BENNING Dept. of Machinery, Fachhochschule Bochum 1. Introduction When mechanical stresses in a component are being discussed, the first thing one thinks about in most cases is load stresses, i.e. stresses caused by external load, such as forces, moments, internal pressures or temperature differences. Today, efficient methods for determining these stresses are available including both theoretical procedures, such as the FE method, and experimental procedures, such as strain gauge measurements. These procedures have achieved a high level of development to the extent that they can be used both with complex structures (FE method) and in experimental investigations under difficult environmental conditions (SG technique). In addition to such load stresses, internal stresses (residual stresses) can be present in a metallic component. These stresses are attributable to the components manufacture and are superimposed on the external loads. This paper describes an experimental method of examination which makes it possible to determine residual stresses in metallic materials non-destructively. The technique concerned here is lattice strain measurement by X-rays. Since residual stresses can have both a positive and a negative effect on component behaviour under operating load it is often advantageous to know the level and distribution of residual stresses. This method is used primarily to determine residual stresses, but it can also cover load stresses, e.g. it can meaningfully be used in cases where the zero condition of the component is not known. 2. Classification and Cause of Residual Stresses Stresses present in a body not subjected to external loads are called residual stresses. With regard to their value and distribution they are such that any forces and moments resulting from them become zero, i.e. these stresses form a state of equilibrium in themselves. Since this state of equilibrium can be present within areas of different size, three different types of residual stress are distinguished: Residual stresses I type: macrostresses, i.e. Constant over a large number of grains Residual stresses II type: constant over a single grain Residual stresses III type: constant over the atomic range. If residual stresses are also considered with Fig. 1 Different types of residual stresses in the microstructure. regard to safety the classification into macro residual stresses (type 1) and micro residual stresses (type 11 and 111) is useful [1]. What follows is concerned only with residual stresses of the first type (1). In DIN 8580 [2] the following procedures are distinguished in manufacturing technology: original forming further forming cutting joining coating and modification of material properties. 15 The Rigaku Journal

2 These procedures produce geometrically definite solid bodies in which a new or modified adhesion is created between the separate particles. It is only possible to produce such forms by plastic deformations which vary with regard to location or time. These are almost always incompatible with those of adjacent particles in the work piece,, and this results in a mutual obstruction of form and hence in residual stresses. Since the technological manufacturing process is the cause of residual stresses, a distinction can be drawn between the following: residual stresses due to original forming e.g. as a result of casting, die casting, extrusion residual stresses due to further forming e.g. from bending, straightening, drawing, rolling residual stresses due to machining e.g. as a result of such machining procedures as turning, milling, grinding or surface strain hardening (e.g. by rolling or sandblasting) residual stresses due to jointing e.g. from welding, soldering or sticking residual stresses due to coating e.g. by coating or cladding residual stresses due to heat treatment e.g. by hardening, or quenching and tempering. The occurrence of residual stresses can therefore mainly be attributed to the following: uneven and partly overelastic deformations, caused by uneven distribution of stress over the cross section, e.g. further forming thermal processes combined with plastic deformations, e.g. caused by jointing or heat treatment surface treatment by removal or addition of coatings, e.g. machining, cladding or refining structural changes with the effect of local changes in volume, e.g. during hardening. These types of residual stress can superimpose themselves on one another in the finished component and can in general only be estimated on a proportional basis. A number of part-processes, however, involve high residual stresses during manufacture. There is a possibility here of achieving the most favorable residual stress condition possible by selecting suitable process parameters. The prerequisite here is, however, that the level and distribution of the residual stresses are known. Normally experimental investigations are required for this purpose. 3. Procedures for Determining Residual Stresses In practice mainly the following methods are used to determine residual stresses: Fig. 2 Principle of the hole-drilling method. mechanical-electrical method, e.g. dessection, bore hole and ring-core method X-ray method US-method; magnetic methods calculation, e.g. FE-calculation. Whereas the mechanical-electrical methods (Fig. 2) result in at least partial destruction of the component and the more recent methods (US, magnetic methods) are still at the experimental stage, the X-ray procedure offers major advantages: non-destructive measurement directly on the surface (~10 µm) determination of stress distributions over the cross section are possible. Theoretical determination also still involves significant difficulties in spite of modern calculation procedures, such as FE. This is because a large number of parameters, such as component shape, temperature-related material characteristics, time-related temperature history or degree of forming have to be known. 4. Lattice Strain Measurement by X-rays X-ray stress measurement is based on the measurement of elastic lattice distortions using X-rays. This means that, in contrast to strain measurements in the macrorange with the common form of stress analysis, lattice strain measurements using X-rays are performed over atomic lengths. The measurements here relate to the changes in distance between certain lattice planes {h, k, 1} where such changes occur as a result of stresses in individual grains close to the surface of any polycrystalline material. Fig. 3 illustrates the difference between macrostrains and lattice strains for the area of the material close to the surface [3]. When subjected to a force the macroscopic dimensions and the distances between the lattice planes change. This can be determined by X-rays from the Vol. 6 No

3 Fig. 3 Definition of macro- and lattice strain. Fig. 5 Measurement of X-ray interference. Fig. 4 Principle of X-ray stress measurement. shift of the interference lines emanating from the lattice planes {h, k, l} (Fig. 4), because the angle of diffraction changes from θ 0 to θ when there is a change from D 0 to D: dθ = θ -θ 0 = -tan θ 0 dd/d The direction of strain measurement is therefore always the normal line on the measured planes of the grains covered. If a primary X-ray P(λ 0, I 0 ) impinges diagonally on the surface of a stress-free polycrystal and if there are a sufficient number of grains with statistically random orientation in the irradiated body of the material, then a symmetrical interference cone I occurs (Fig. 5). With the grains contributing to the interference, the normal lines for identical lattice planes also lie on a cone N symmetrical to P. If the material zone is subjected to stress, asymmetrical interference and normal cones arise in relation to P. The diffracted X-ray is registered, using the following methods: Film (vertical to the primary beam) Result: Interference ring with intensities of grains with definite orientation, Intensity measurement (counting tube, scintillation counter, OED) Fig. 6 Penetration depth of X-rays. Result: Local intersection through interference ring in the form of an I-9-distribution (interference or interference line profile; Fig. 5). Depending on the X-ray wave length used, the diffracted X-ray intensity contains information from various depths in the material tested. Fig. 6 takes the example of iron to show the relative intensity portions diffracted with various wave-lengths when lattice strain measurements are performed perpendicular to the surface (ψ = 0). With ψ 0 integration is performed over small edge zones. On the basis of this principle, the features of X- ray stress measurement can be described as follows: Performance of measurements on crystalline materials Distance between adjacent lattice planes Measuring direction normal to the reflecting lattice plane Measurement in reflection zone (70 < θ < 85 ) Small penetration depth (<20 µm) 17 The Rigaku Journal

4 Fig. 7 Evaluation of the measurement results. Performance of measurements on single and multiphase materials Elastic strains. In order to determine the stresses it is necessary to link the measured lattice strains with the existing stress condition by means of the elasticity theory. Taking the system of coordinates in Fig. 7 as a basis, the linear elasticity theory gives the following for the plane stress condition (σ 1, σ 2 ) [4]: ε ϕψ = ε 1 cos 2 ϕsin 2 ψ+ε 2 sin 2 ϕcos 2 ψ+ε 3 cos 2 ψ. (2) Taking into account Hooke's relations and the surface stress component in the azimuth ϕ under ψ = 90 σ ϕ = σ 1 cos 2 ϕ + σ 2 sin 2 ϕ (3) the base equation for the X-ray stress measure-ment follows: Εϕψ = ½s 2 σ ϕ sin 2 ψ + s 1 (σ 1 + σ 2 ) (4) with the Voigt constants 1 1 s 2 = + ν ; s 2 E = ν 1. (5) E With the aid of the postulate ε ϕψ = θ θ dd = cot d (6) 0 D ϕψ the following relation for stress determination is obtained (Fig. 7) σ = E θ ϕ cot θ 0 (7) 2 1+ ν sin ψ Accordingly, for a given plane stress condition, the following applies for lattice strain: 1. Independently of the azimuth ϕ, the lattice strains are always distributed in a linear fashion over sin 2 ψ 2. The rise for the straight lines in the plane ϕ = const. is m ϕ = 1 s (8) 2 2 σ ϕ 3. The ordinate section for the straight lines is ε ϕψ=0 = ε 3 (σ 1 +σ 2 ). (9) With practical lattice strain measurements, conventional reflection methods are used with film recording, or diffractometer methods with scintillation counter or OED. With the diffractometer the line positions occurring are measured in 2θ ϕψ in a number of ψ directions directly in the I-2θ charts with ϕ = const. For this purpose the objects are inclined in relation to the primary beam in such a way that it is possible to measure in different ψ directions (sin 2 ψ) and to determine the rise in the related stress. It is assumed, however, that the X-ray constants (s 1, s 2 ) are known, and these should be determined in a calibration test (specimen with known stress condition, powder). Where the main stress directions are unknown, the distributions of lattice strain should be recorded in three different azimuth angles ϕ (e.g. ϕ, ϕ+ 45, ϕ + 90 ), from which the main stresses and the angle of direction can then be determined. The prerequisites for application of the sin 2 ψ method are: Direction of main stress parallel to the surface Vol. 6 No

5 Quasi isotropic elastic behaviour Homogeneous structure. If these conditions are not met, difficulties can arise in the application of this method (anisotropy, texture). 5. Possible Applications for X-ray Stress Measurement 5.1 General Because of this method's nondestructive character and the small penetration depth of X-ray beams (< 20 µm), it is particularly suitable for measurements in areas close to the surface. Volume measurements are also possible, however, if the material is removed layer by layer (electrolytically) at the measuring point. Up to a few years ago the use of this method was restricted to laboratory tests (size of the measuring instruments, evaluation). Thanks to the application of microelectronics it has been possible to significantly simplify the evaluation procedure and so this method has now become a part of practical measuring techniques (Figs. 8, 9 and 10). The possible applications for this method are as follows: Determination of load and residual stresses in loadbearing components, e.g. cranes and offshore installations Determination of residual stresses from casting and deformation (low-warping components) Optimization of welding procedures Examination of the necessity for heat treatment and subsequent check Lifetime assessment of highly stressed parts (turbine blades, generator shafts) or components subject to stress corrosion cracking Fig. 8 Measuring equipment for the laboratory. Fig. 9 Equipment for field measurement. 19 The Rigaku Journal

6 Fig. 10 Equipment in use on offshore constructions. Fig. 11 Residual stresses in a thick-walled elbow. Check of measures intended to lengthen lifetime, e.g. surface hardening, strain-hardening, auto-frettage Effect of surface treatment procedures, e.g. machining, cladding, coating Check of surface protection procedures in tribology Quantitative analysis of hardened components, e.g. determination of retained austenite Failure analysis. 5.2 Examples of applications In the manufacture of polyethylene, meandering tube reactors are used in which the process takes place under high pressures (3000bar). The tube bends in this installation are subject to cold bending during manufacture and so a residual stress condition sets in which Fig. 12 Evaluation of the fatigue strength (A=axial-; T=tangential direction. can be considerable in longitudinal direction (Fig. 11). When the stresses from autofrettage are superimposed on these residual stresses, the fatigue strength can be seriously impaired (Fig. 12). Rollers in briquetting plants are fitted with highstrength bands. These bands are subjected to special heat treatment to ensure a high degree of strength combined with adequate abrasion resistance (hardness), and such heat treatment may result in considerable residual stresses in the band. The design of the Vol. 6 No

7 Fig. 13 Mobile equipment in use on rollers in briketting plants. rollers must take account of these residual stresses (Fig. 13). References [1] Tietz, H.D.: Grundlagen der Eigenspannungen, VEB Deutscher Verlag für Grundstoffindustric, Leipzig (1982). [2] DIN 8580: Fertigungsverfahren; Übersicht, Ausgabe (1986). [3] Macherauch, E.: Praktikum in Werkstoffkunde; 6. Auflage, Vieweg-Verlag (1985). [4] HTM-Sonderdruck, Bd. 31, H. 1 (1976) und H. 2 (1982). (Received July, 1989) 21 The Rigaku Journal