Analysis of residual stresses in cylindrically anisotropic materials

Metal-forming operations leave residual stresses in formed parts due to nonuniform deformation occurring during the process. An exact method of determining the longitudinal, radial and circumferential (tangential) residual stresses in axisymmetric specimens was proposed by Mesnager¹ and further developed by Sachs². The boring-out technique can be complemented by a similar procedure in which strains are measured on the inner surface of the tube when material is removed from the outer surface.The work proposed in this paper extends previous analyses of residual stresses to the case where the material exhibits cylindrical elastic anisotropy, i.e., the principal axes of anisotropy correspond to the longitudinal, radial and circum-ferential directions of the tube. In addition, the present analysis considers the case in which a residual-shear stress, developed by twisting the tube about its axis, exists in the tube. When such shearing stresses are present, the principal axes of the residual-stress distribution are not parallel to the principal axes of the tube.     

On residual-stress measurements in light truck wheels using the hole-drilling method

An investigation of the effect of drilling speed, milling-cutter wear, drilling mode, and applied drilling force on residual-stress measurements in a light truck wheel using a milling guide manufactured by Measurements Group, Inc. is described. The milling variables chosen were used to minimize the residual stresses induced by the introduction of a hole into the wheel material. An improved hole-drilling procedure was developed and found to be successful in the residual-stress measurements for a light truck wheel.     

Measuring Multiple Residual-Stress Components using the Contour Method and Multiple Cuts

The conventional contour method determines one component of residual stress over the cross section of a part. The part is cut into two, the contour (topographic shape) of the exposed surface is measured, and Bueckner’s superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple residual-stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The multiple-cut contour method results agree very well with independent measurements using neutron diffraction and with a computational, finite-element model of the indentation process.     

Examination of the ring method for determination of residual stresses

A semidestructive method for determining residual stresses on the surface of an isotropic material is examined. The method requires that a ring be cut around the point where residual stresses are to be found. Calibration is done by using a specimen with a known residual-stress distribution. Sensitivity of the technique is found to be much better than that of the conventional semidestructive method of hole drilling.     

Residual-stress measurement in SS304 seamless tube

This paper involves the experimental measurement of residual stresses in a nonwelded nuclear-grade 304 stainless-steel seamless tube subjected to one-sided quenching of its outside surface. Because this grade of tube is used extensively in nuclear power plants, the residual stresses measured are of interest to the nuclear industry. The Sach's boring method was used to obtain residual stresses. The longitudinal and tangential residual stresses at the inner wall were found to be 69 MPa to 138 MPa compressive. The results indicate that the residual-stress distribution would allow the tube to be highly resistant to the formation and propagation of stress-corrosion cracks.     

Residual Stresses in a Shaft after Weld Repair and Subsequent Stress Relief

To evaluate the possibility of repairing and/or modifying shaft surfaces by welding, remachining, and low-temperature stress relieving without introducing high residual stresses, residual-stress measurements were made on an 8.0 in. diameter shaft of Type 347 stainless steel. The measurements were made on the shaft surface before welding, after welding and remachining, and after a 750°F stress relief. This report shows the residual-stress patterns in and near the weld area at the various stages of the investigation. Measurements were made using the hole-drilling method. The holes were 0.060 in. diameter and 0.06 in. deep. They were made using a unique, stress free abrasive jet machining technique.*     

Residual-stress measurements in time-controlled quenched austenitic stainless steel

This paper presents experiments to determine the residual stresses generated during the low-speed quenching of austenitic stainless steel. Austenitic stainless steel was chosen because it does not undergo any phase transformation during quenching. As a result, the resultant residual-stress pattern depends only on plastic deformation taking place during the quench. Different quenching rates were used in the experiment to quantify their effect on the generation of residual stresses. These stresses were measured along the surface of the specimen in a direction parallel to the quench direction and in depth below the surface.     

Application of an advanced XRD instrument for surface stress-tensor measurements on steel sheets

The three-dimensional residual-stress condition of several martensitic stainless-steel sheets given various combinations of surface treatments was studied by an X-ray-diffraction method. The stress tensors in the near-surface region, approximately 12 micrometers (0.012 mm) deep, were calculated after obtaining the strain tensors through application of the differential method and an advanced X-ray-diffraction stress-measurement instrument. The advanced instrument collected the data in a few hours—a task that normally requires several days to a few weeks-and provided accuracies on the order of ±14 MPa (2 ksi). The surface treatments to the sheets included various combinations of mechanical polishing and vapor blastiing; all produced substantial compressive stresses in the plane and perpendicular to the surface. The mill-annealed specimen showed nearly zero residual stress prior to mechanical polish or vapor blasting. The resulting tensor-stress data were compared with data obtained through single-exposure-technique calculations which assume a plane-stress state on the surface.     

Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress

We utilize the recently developed surface Cauchy-Born model, which extends the standard Cauchy-Born theory to account for surface stresses due to undercoordinated surface atoms, to study the coupled influence of boundary conditions and surface stresses on the resonant properties of gold nanowires with surfaces. There are two major purposes to the present work. First, we quantify, for the first time, variations in the nanowire resonant frequencies due to surface stresses as compared to the corresponding bulk material which does not observe surface effects within a finite deformation framework depending on whether fixed/free or fixed/fixed boundary conditions are utilized. We find that while the resonant frequencies of fixed/fixed nanowires are elevated as compared to the corresponding bulk material, the resonant frequencies of fixed/free nanowires are reduced as a result of compressive strain caused by the surface stresses. Furthermore, we find that for a diverse range of nanowire geometries, the variation in resonant frequencies for both boundary conditions due to surface stresses is a geometric effect that is characterized by the nanowire aspect ratio. The present results are found to agree well with existing experimental data for both types of boundary conditions.The second major goal of this work is to quantify, for the first time, how both the residual (strain-independent) and surface elastic (strain-dependent) parts of the surface stress impact the resonant frequencies of metal nanowires within the framework of nonlinear, finite deformation kinematics. We find that if finite deformation kinematics are considered, the strain-independent surface stress substantially alters the resonant frequencies of the nanowires; however, we also find that the strain-dependent surface stress has a significant effect, one that can be comparable to or even larger than the effect of the strain-independent surface stress depending on the boundary condition, in shifting the resonant frequencies of the nanowires as compared to the bulk material.     

A Comparison of Residual-stress Measurements Using Blind-hole, Abrasive-jet and Trepan-ring Methods

This article describes the results of residual-stress measurements which were made on an artillery-projectile metal part to determine whether the state of the stress could be a factor in promoting a failure that had occurred during ballistic test firing. An additional objective of the work was to evaluate the suitability of several different methods for measuring residual stresses by the performance of these measurements on the same metal part.     

Residual stresses in reverse-bend test samples for stress-corrosion testing

Cracking of Inconel Alloy 600 (registered trademark) u-bend tubes used in pressure-water-reactor (PWR) steam generators has been a major concern in the nuclear-power industry over the past several years. The mechanism of cracking has been determined to be intergranular stress-corrosion cracking with residual stresses a major contributor. A simple specimen known as a reverse u-bend (RUB) has been used by a number of laboratories to simulate the high stresses and plastic strain extant in the most susceptible regions of the u-bend tubes. This paper presents the results of residual-stress measurements on four RUB samples, each from a different laboratory.The results indicate that the individual RUB fabrication procedures used by different laboratories tend to produce different residual-stress patterns in the highly strained regions over 700 tensile to nearly 700-MPa compressive on different samples. Stress gradients on the order of 140 MPa/mm were found on some samples. The residual-stress patterns were seen to qualitatively predict the stress-corrosion-cracking pattern experienced on similar samples.Electric Power Research Institute.     

Moiré interferometry determination of residual stresses in the presence of gradients

The full-field technique of high-sensitivity moiré interferometry in conjunction with a multiple-hole-drilling procedure is applied to residual-stress measurements in the presence of gradients. The method arrives at residual-stress estimates starting from in-plane displacement components. Successful applications of the method to problems simulating the nonuniform transverse residual stresses of welded joints are reported.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Residual stresses in thick electrodeposits of a nickel-cobalt alloy

Some electroplated metals contain residual stresses which can cause warpage or premature failure of parts plated or electrofomed with these materials. Noticeably absent from the literature are residual-stress data for finished parts. Typically for plated or electroformed parts, residual stresses are determined independently on thin strips and then piece parts are plated. This research describes a technique which can be used to measure stress on finished parts. The method involves drilling a hole in the part and measuring the resulting change of strain in the vicinity of the hole. Viability of this technique was demonstrated by measuring the stress in a nickel-cobalt deposit plated on an aluminum cylinder. Two separate runs, one 50 deg removed from the other, provided almost identical results; stress was 160 MN/m² (23,200 psi). Two other runs in a region where plating was somewhat thinner provided slightly lower results probably because all boundary-condition requirements were not met. The computed residual-stress values compared quite favorably with independent rigid-strip measurements of 131 MN/m² (19,000 psi) obtained for the solution before and after plating of the cylinder.     

Analysis of axially symmetrical residual stresses in bars and tubes

A new method has been developed for the determination of residual stresses in a cylinder. Boring out or removing layers from outside induces changes in the length and diameter of the remaining bar. The initial distributions of the stresses are derived from measurements of the length change only. Details of equations required for the calculations are described. The method rests on an assumption that the radial displacement just below a surface is equal to the radial displacement at a new surface after removal of the surface layer of material. This assumption leads to relations between the three residual-stress components. The numerical calculations of these relations agree well with the experimental data for quenched cylinders obtained by using the Sachs method in other investigations. A brief general discussion is given on the equilibrium conditions of the residual stresses determined.     

Polychromatic X-ray method for residual-stress measurements in a subsurface layer

The classical sin² method with characteristic X-rays is widely used to measure residual stress nondestructively in the steel members of a structure or a machine. With this method it is, however, difficult to measure the three-dimensional stress distribution with a steep gradient that occurs along the depth direction in a subsurface layer of the material after surface treatment such as grinding or cold rolling. This paper presents a new polychromatic X-ray method for residual-stress measurements in a subsurface layer. The relationship between the diffracted beam peak of the polychromatic X-ray and the strain along the depth direction in a subsurface layer was obtained by theoretical analysis. It was modeled by numerical simulation to obtain probable values of the parameters, and these were used along with experimental X-ray data to derive an experimental value for the stress gradient. This was compared with the values predicted from plate bending theory.Paper was presented at the 1994 SEM Spring Conference on Experimental Mechanics held in Baltimore, MD on June 6–9.     

Residual stresses in turned AISI 4340 steel

The residual-stress distribution in the surface region of workpieces of annealed AISI 4340 steel that is turned under unlubricated conditions is determined using a deflection etching technique. The absolute value of the residual stresses at the machined surface are low and increase with an increase in depth beneath the machined surface to a maximum. They then decrease with a further increase in depth eventually becoming vanishingly small. Peak residual stresses are tensile at cutting speeds of 0.5 and 1.0 ms⁻¹ and are compressive at a cutting speed of 1.5 ms⁻¹ for all feed rates and depths of cut. Peak residual stresses and depth of the stressed region increase with an increase in feed rate and depth of cut, but decrease with an increase in cutting speed. The results of this investigation can be interpreted in terms of the variation of tool forces with cutting conditions.     

Multiple trenching: a simple self-calibrating method of residual-stress measurement

A simple semidestructive residual-stress-measurement technique, particularly suitable for measurement parallel to edges or on outside radii of components, is presented. The nature of the technique obviates reliance upon calibration constants such as have been obtained for the hole-drilling and ring-cutting methods for residual-stress measurement. Use of such calibration constants might seriously underestimate stress values for relatively shallow surface stresses such as may be produced by, for example, grinding or thermochemical treatment.     

Residual stresses in roller-expanded thin tubes

The residual-stress distribution of through-the-wall thickness in the roller-expanded region of thin-walled incoloy-800 Fe–Ni–Cr alloy tubing was determined. Such tubes are commonly used in the fabrication of steam generators for nuclear-power stations. For the present study, the test specimens consisted of short lengths of tubing which were roller-expanded into tubesheet simulation blocks. Some of the specimens were then heat treated. The measurement method involved the installation of strain-gage rosette strips on the inner tube wall. Strain measurements were first taken after the removal of the tubesheet simulation block. Residual stresses were then released by progressive chemical etching of the outer tube wall. In some cases the inner tube wall was etched instead and this required the removal of the inner strain-gage strip and its replacement by one attached to the outer wall. A calculation procedure based on the Sachs approach, first proposed for straight unrolled tubes, was used for determining the residual-stress distribution in the vicinity of the roller-expanded zone and through-the-wall thickness. Surface residual stresses of the order of 250 MPa were determined in the as-received specimens. Residual stresses in the stress-relieved heat-treated specimens were generally lower by about 40 percent. Contact stresses were nearly eliminated by the heat-treating process. The residual stresses in the various specimens of the same type compared to within a standard deviation of 35 MPa.