Residual stress states in engineering structures are usually determined by measuring components of stress tensors with depth below the material surface. There are destructive and nondestructive methods to measure strain tensor components and convert them into stress tensor components by a variety of techniques derived from constitutive (material) equations. In this study, four methods for determining the strain tensor components are presented: X-ray diffraction method (XRDM), magnetic Barkhausen noise method (MBNM), hole drilling method (HDM), and cut-and-section method (CSM); the first two are nondestructive, and the third and fourth are semidestructive and destructive, respectively. A complementarity of the experimental and two numerical methods such as boundary element method and finite element method is explained. An application of the experimental and numerical methods to measure residual stress states in an industrial component, an L-shaped part of a supporting column in a high voltage structure, is presented.

Using X-ray grazing incidence diffraction (GID) it is possible to perform a nondestructive analysis of the heterogeneous stress field for different volumes below the surface of the sample. The stress can be measured at very small depths, of the order of a few μm. The penetration depth of radiation is almost constant in a wide 2θ range for a given incidence angle α. It can be easily changed by an appropriate selection of α angle (or also by using a different type of radiation). There are, however, some factors which have to be corrected in this technique. The most important is the refraction of X-ray wave: it changes the wavelength and direction of the beam. Both effects modify a pick position. A corresponding correction was calculated and tested on ferrite powder and on 316L austenite stainless steel sample.

The sin2ψ method can be formulated as a single system of simultaneous linear equations. Using this it is easy to show that the sin2ψ method is not a least-squares method. It further helps to compare the accuracies of the stress tensors obtained by the sin2ψ method and the method of least squares. Quantitative comparisons have been made for different fictitious measurements. It is shown that the unnecessary loss in accuracy by using the sin2ψ method is quite significant and by no means negligible. The same course of action has been applied to compare the so-called Dölle-Hauk method with a least-squares method; the result is similar. Some other methods for X-ray stress determination, most often similar to the sin2ψ method, and their shortcomings are also discussed briefly, together with the corresponding, more effective and more versatile least-squares method.

Hard turning, i.e., turning hardened steels, may produce the unique “hook” shaped residual stress (RS) profile characterized by surface compressive RS and subsurface maximum compressive RS. However, the formation mechanism of the unique RS profile is not yet known. In this study, a novel hybrid finite element modeling approach based on thermal-mechanical coupling and internal state variable plasticity model has been developed to predict the unique RS profile patterns by hard turning AISI 52100 steel (62 HRc). The most important controlling factor for the unique characteristics of residual stress profiles has been identified. The transition of maximum residual stress at the surface to the subsurface has been recovered by controlling the plowed depth. The predicted characteristics of residual stress profiles favorably agree with the measured ones. In addition, friction coefficient only affects the magnitude of surface residual stress but not the basic shape of residual stress profiles.

The peak profile shape analysis has been preferentially used in the evaluation of X-ray and synchrotron powder diffraction pattern. However, neutron diffraction facilities of new generation frequently offer the instrumental resolution high enough to efficiently study the effects of broadening of neutron diffraction profiles. The present paper describes the procedure for a detailed evaluation of Bragg peak shape based on the method of transformed model fitting (TMF) which has been recently developed particularly for the treatment of neutron diffraction profiles. Microstructure modeling is performed in the reciprocal space and the convolution of the model with the instrumental resolution curve is fitted to the profiles recorded in the diffraction experiment.

Weld residual stress (RS) measurements are often undertaken on test-pieces which have been cut out from large components, yet it remains unclear to what extent the RSs in test-pieces are representative of those present in the original component. Similarly weld mechanical performance tests are frequently undertaken on cross-weld test-pieces without a proper understanding of the level or influence of retained RS. We present a systematic study of the relaxation of longitudinal RS in thin-plate butt welds produced using different materials and welding methods (FSW, laser-MIG, and pulsed-MIG). In each case the RSs were measured repeatedly in the same location as the welds were progressively and symmetrically cut down. Although cutting inevitably leads to stress redistribution, significant relaxation of the longitudinal RS was only observed when the weld length or width was reduced to below a certain value. This critical value appears to correlate with the lateral width of the tensile zone local to the weld-line and may be considered to be the characteristic length as defined in St. Venant’s principle. Further, it was found that the level of stress relaxation as a function of weld length for all the welds studied could be collapsed onto a single empirical curve using a simple approach based on the characteristic length scales of the weld. Given the range of materials and welding methods used, this relation appears to be of general use for thin-plate welds although further work is required to test the limits of its applicability.

The compressive stress distribution below the specimen surface of severely surface deformed steels by shot peening was investigated by using laboratory X-rays and high-energy X-rays from a synchrotron radiation source, SPring-8 in the Japan Synchrotron Radiation Research Institute. Medium carbon steel plates were heat treated in two different conditions. The Vickers hardness of materials A and B after heat treatment is 408 and 617 HV, respectively. The specimens were shot peened with fine cast iron particles of the size of 50 μm. The coverage was selected to be 5000%. For the synchrotron radiation, by using the monochromatic X-ray beam with several energy levels, the stress values at the arbitrary penetration depth were measured by the constant penetration depth method. The shot-peened specimens were fatigued under four-point bending. The improvement of fatigue strength of material A was not so large because of large surface roughness. On the other hand, for material B, the surface roughness was smaller and the fatigue strength was higher than that of ground specimens.

Residual stresses impact on a wide variety of industrial sectors including the automotive, power generation, industrial plant, construction, aerospace, railway and transport industries, and a range of materials manufacturers and processing companies. The X-ray diffraction (XRD) technique is one of the most popular methods for measuring residual stress (Kandil et al., 2001) used routinely in quality control and materials characterization for validating models and design. The VAMAS TWA20 Project 3 activity on the “Measurement of Residual Stresses by X-ray Diffraction” was initiated by NPL in 2005 to examine various aspects of the XRD test procedure in support of work aimed at developing an international standard in this area. The purpose of this project was to examine and reduce some of the sources of scatter and uncertainty in the measurement of residual stress by X-ray diffraction on metallic materials, through an international intercomparison and validation exercise. One of the major issues the intercomparison highlighted was the problem associated with measuring residual stresses in austenitic stainless steel. The following paper describes this intercomparison, reviews the results of the exercise and details additional work looking at developing best practice for measuring residual stresses in austenitic stainless steel, for which X-ray measurements are somewhat unreliable and problematic.

After heat treating, finish machining of the hardened steel represents the last manufacturing step of machine elements. The practically most important operation of grinding is applied to achieve edge zone compressive residual stresses, best surface quality, and dimensional accuracy. Metal removal involves high plastic deformation work. Glide and intersection processes raise the density and produce lower energy substructures of dislocations. The temperature and time behavior of postmachining thermal treatment is analyzed on ground and honed martensitic SAE 52100 rolling bearing steel. Microstructure stabilization is reflected in a large XRD peak width decrease in the surface. The kinetics are modeled by rate-controlling carbide dissolution as the carbon source for Cottrell-type segregation at dislocations. This thermal static strain aging is verified by the formation of a slight white etching surface layer. The model is also extended to consider superimposed thermal dislocation recovery. Both effects are separable. In rolling contact fatigue tests under mixed friction conditions, air reheating below the tempering temperature, which avoids hardness loss, leads to a significant lifetime increase. The effect also occurs after cold working.

Generating compressive stresses in aerospace materials is an important consideration for enhancing fatigue life. Shot peening and cold expansion of holes are two techniques for imparting beneficial compressive stresses. X-ray diffraction is a direct method for measuring elastic strains. Diffraction peak widths are an indication of plastic strain. Elastic and plastic strains can be used to better assess the true condition of a component. This paper presents elastic and plastic strain information from shot peened and cold expanded aerospace materials. Examination of surface data showed which shot peened samples had the deeper layer of compressive stresses. Likewise, elastic and plastic strain data enabled successful ranking of the holes in terms of the maximum amount of cold working.

The aim of this study is to analyze the mechanics of a new class of metal/ceramic composites on a mesoscopic length scale. These composites are produced by melt infiltration of porous ceramic preforms produced by freeze casting and subsequent sintering. This production route has a high application potential since it offers a cost-effective way to obtain composites with ceramic content in the 30 to 70 vol. % range. The as-produced material exhibits a hierarchical domain structure with each domain composed of alternating layers of metallic and ceramic lamellae. Residual stresses present in all phases of the composite produced by infiltrating alumina preforms with a eutectic aluminum-silicon alloy have been measured. Integral as well as spatially resolved measurements were carried out on single-domain samples at the high-energy, energy-dispersive diffraction (EDDI) beamline at the synchrotron radiation source BESSY (Berlin, Germany). Results show that strongly fluctuating residual stresses are introduced by the production process, which can be rationalized by taking into account the thermal expansion mismatch of alloy and preform.

Four matrix-phase crystallographic directions of IN718 are investigated by in situ tensile tests using neutron diffraction. The elastic diffraction constants for all directions measured are compared to theoretical values calculated by the Kröner model. The differences between the microscopic and the macroscopic material response are given. The accumulation of microstrains in the different crystallographic directions is discussed. A comparison between the results of a single phase material (ingot IN718) and two differently thermal treated multiphase materials is presented.

The neutron diffraction technique was applied to measure strain distributions in a rebar in a reinforced concrete. At first, absorption coefficients of several kinds of concrete with different compounding ratios of water, cement, and aggregate were measured, and it was confirmed that the absorption coefficient of concrete was affected by the amounts of water and aggregate. In addition, it was also clarified by measuring strain change of the rebar under tensile loading that accuracy of the strain measurement in the rebar in the reinforced concrete was not affected by the neutron absorption by the concrete. Second, the size of the anchorage zone was evaluated by measuring strain distributions in the rebar under pull-out loading. The length of the anchorage zone measured by neutron diffraction was shorter than that measured by strain gauges. Moreover, detailed strain distributions in the rebar around cracks in the concrete were measured under tensile loading, and it was confirmed that the bond condition between rebar and concrete around cracks could be evaluated using the neutron diffraction technique.

We have used synchrotron X-ray diffraction experiments to measure the strain field introduced by a hydride blister grown on a section of a pressure tube from a CANDU nuclear reactor. After charging the tube section with a homogeneous hydrogen concentration of 300 wt ppm, the blister was produced by creating a small cold spot on its surface (∼200 °C), while the bulk was kept at a temperature of 338 °C over a period of 1008 h. The blister studied here is ellipsoidal in shape, with its long axis along the tube axial direction. The experiments were performed on the wiggler beam line ID15 at the European Synchrotron Radiation Facility (ESRF) using a polychromatic beam of high-energy X-rays (60 to 300 keV). Unlike conventional X-ray diffraction, in this mode the scattering angle is fixed and the diffracted beam is discriminated on the basis of the photon energy. The results show that the blister is composed by two crystallographic phases (δ-ZrH and α-Zr), with volume fractions varying with position. The maximum stresses appear at the blister-matrix interfaces. Near the tube outer surface, we found large compressive stresses of (−450±90) MPa along the blister long axis, and tensile stresses (+320±90) MPa along the tube hoop direction. The main uncertainty in these stresses results from the uncertainty in the elastic constants of the hydride phase. Large strains and broad peaks were observed for this phase, which were explained by a rather low Young’s modulus (35 GPa) for the hydride. The results are compared with finite element simulations found in the literature.

This paper deals with the implementation of a theoretically described method to determine residual stresses in real space directly by means of small gauge volumes. For this purpose, beam limiting masks were designed, manufactured, and investigated in first experiments. Image series taken with a position sensitive CCD camera demonstrate the ability to detect interferences from gauge volumes beneath the sample surface by defined slit geometries. The experiments show that due to the highly absorbing masks the amount of detectable photons is poor, and thus long exposure times are necessary to receive suitable data. For increasing measurement depths (altering masks) a decrease in the intensity can be detected which leads to the assumption that the diffracted photons originate from deeper regions in the material. A model was developed to simulate the diffraction conditions with different mask layouts and material properties. Modeling yields consistent results with experimental data, and thus provides a basis for further improvements of the experimental setup and the realization and assessment of residual stress measurements.

For residual stress evaluation in complex substrate-coating systems, energy-dispersive (ED) diffraction with energies up to 100 keV can be applied to analyze the near interface residual stress state in the substrate, because the high energy white beam penetrates the coating completely. By the example of an Al2O3/TiCN on WC coating system we have studied the feasibility for using the coating reflections being stored in the ED diffraction patterns together with the substrate diffraction lines to analyze the residual stress state in individual sublayers of which the coating system consists. The results indicate that the ED method is suitable to detect even steep intralayer stress gradients, if the diffraction conditions are adapted to the coating geometry.