Calculation Of Residual Stresses Research Articles

The use of oscillation on PSD-based instruments for X-ray measurement of residual stress

Measurements of surface residual stress by X-ray diffraction can be accomplished very rapidly using a position-sensitive detector (PSD) to record the diffraction profile. It is shown that when the sample and detector are fixed during data accumulation, the profile shape may be distorted by large grain size or preferred orientation, which results in substantial error in the calculation of residual stress. Sample oscillation decreases the sensitivity of the PSD system to such microstructural variables in many cases. Instruments employing a PSD to measure surface residual stress should be designed with the capability of oscillating either the sample or the measuring head (X-ray tube and detector).

Residual stresses in cyclically loaded two-phase solid

Abstract A plane-stress finite element model of a two-phase solid is analyzed for residual stresses that develop under cyclic loading. One phase is assumed to be dilute and to yield at stresses below those of the matrix. Simple triangular constant strain finite elements are used and the soft material is assumed to be a linear work hardening one. The load is applied incrementally and the stiffness matrix is updated at each step to its tangential values. The emphasis is on the residual stresses which develop within the soft element and in the neighborhood. Several distributions of soft material were examined. In the cases we consider, the residual stresses change sign on each load cycle, that is, they are not constant. They are also an appreciable percentage of the yield stress of the soft phase. The residual stresses primarily develop in the first cycle and settle down in just a few cycles. The location of a soft element is somewhat of a factor in how far away its effect is felt by other elements. In addition to the calculation of residual stresses, the temperature changes are also calculated. The plastic work is converted into heat in the soft elements and this in turn is conducted to the cooler elastic matrix. It is found that adiabatic conditions can be assumed for steel specimens for strain rates above .033 sec−1 and at rates above .23 sec−1 for aluminum.

Residual stress distribution by the bending strip method

A new method for the calculation of residual stress in the cross section of an electrodeposit formed on one of the sides of a bending strip cathode is proposed. The relations for the cases of deposition and of dissolution of the deposit are given. In addition, suitable conditions for verification of the numerical values obtained are proposed. An example is given to show the advantages of the new method over previous methods. A precise relation is derived for determining the average residual stress in the cross section of the deposit.

Measurement of residual stresses by the hole-drilling method: Influences of transverse sensitivity of the gages and relieved-strain coefficients

The general expression of the error due to the transverse sensitivity of the gages and the relieved-strain coefficients, in a determination of residual stresses by the hole-drilling method in thin plates, is given. It has been shown that the transverse sensitivity of the gages can be ignored. A moderate amount of error, however, is introduced in the measurement of residual stresses when the relieved-strain coefficients from methods other than double integration over the area of the grid are used. The error due to the use of improper relieved-strain coefficients from rigorous relationships for calculation of residual stresses has been compared with the same part of the error from nonrigorous relationships. Abandonment of the use of nonrigorous relationships is recommended.

Theoretical Calculation of Residual Stresses in Case-Hardened Gears with Different Thicknesses of Hardened Layer

Theoretical Calculation of Residual Stresses in Case-Hardened Gears with Different Thicknesses of Hardened Layer

Theoretical Calculation of Residual Stress in Case-Hardened Gears with Different Thicknesses of Hardened Layer

In this paper, the authors investigate whether stresses of gears generated by case-hardening can be calculated theoretically or not by finite element method under the assumption that the gears have different thicknesses of hardened layer and the coefficient of thermal expansion and yield stress for gear material are known. The theoretically calculated results show that a certain thickness of hardened layer gives the maximum compression residual stress on the root fillet. And the residual stresses are in approximate agreement with those measured by X-ray method. Further it is shown that the endurance limits obtained from the bending fatigue test using a pulsator are influenced by the residual stress. Therefore from this theoretical analysis and experiments the possibility that adequate thickness of hardened layer is estimated for case-hardened gears is confirmed.

Viscoelastic and plastic relaxation of residual stresses around macroparticle reinforcements in metal matrices

Equations are presented for the calculation of residual stresses generated by temperature changes in metal matrix composites. The interfacial contact pressures and plastic zone sizes for various cooling rates imposed on an Al 2O 3 sphere embedded in 355 aluminium are evaluated. The results show that stress relaxation and alloy viscosity are important factors affecting the final composite residual stress state.

The alignment error of the hole-drilling method

The hole-drilling method is one technique for measuring residual stresses. All the existing equations for the calculation of residual stresses are based on the assumption that the hole is located at the rosette center. In this paper, the stress-strain relationship for the eccentric hole case has been derived and expressed in terms of the off-center distance and the polar angle. The alignment error is studied and demonstrated by two examples, namely, a uniaxial-stress field and a hydrostatic-stress field. The error analysis yielded the following typical result: ten percent of hole radius off-center will yield about five-percent measurement error for the standard rosette (EA-09-062-RE-120).

Residual stress distribution in nitrided En41B steel as function of case depth

AbstractSpecimens of a ‘Nitralloy’ type of En 41B steel were subjected to glow-discharge nitriding at 525°C for between 0.5 and 24h in order to produce specimens with differing nitride case depths. Microhardness tests were used to determine the specimen case depth and to indicate the reproducibility between batches of nitrided specimens. The residual stress distribution was obtained by the Sachs boring technique. ‘Change-in-strain’ at the specimen surface was measured by four precision strain gauges connected in two separate Wheatstone bridge circuits. Strain functions were calculated from the strain data and a computer program was produced which fitted robust, weighted least-squares polynomials to these strain functions. The triaxial residual stress condition was obtained on differentiation of the fitted polynomials. The residual stresses introduced into the specimen by drilling were minimized to a consistent level for which corrections were made in the calculation of residual stress. Conditions of high ...

Approximate calculation of residual welding stresses in cylindrical shells

Approximate calculation of residual welding stresses in cylindrical shells

Calculation of Residual Stresses in Plastic Deformation Processes

Three problems, namely, autofrettage process, plastic upsetting of a solid cylinder, and plane-strain and axisymmetric extrusion, are treated for residual stress calculation. A thick-walled cylinder consisting of two loosely fitted concentric cylinders of different materials is subjected to various levels of internal pressure. The residual stresses were calculated with an emphasis on the case where the inner surface of the cylinder yields again upon removal of the internal pressure. Comparison between the calculations and the measurements is given. The residual stresses in plastic upsetting of a solid cylinder were calculated by the finite-element method. An attempt was also made to simulate the real situation in extrusion by the finite-element method. An estimation of the residual stress distribution is then discussed for axisymmetric extrusion problems.

Computer Controlled X-Ray Diffraction Measurement of Residual Stress

AbstractThe system to be described includes hardware and software for the on-line computer control of the X-ray diffraction measurement of residual stress. This determination involves accurately measuring the angles at which a back-reflection line is diffracted, first by diffracting planes parallel to the sample surface, and then by planes at an angle (ψ) to the sample surface. The residual stress is calculated from the difference in the two measured diffraetion angles. The procedure executed by the computer consists of locating the peaks, selecting three angles for collection of X-ray counts, correcting the measured counts, fitting the equi-angular intensity measurements to a three-point parabola, calculating the peak angles, calculating the residual stress from the measured angles and typing a report. This automation has eliminated the tedium of the manual X-ray data accumulation and of the residual stress calculation. The online control has also permitted improvements in the technique not practicable with the manually performed measurement of residual stress.

Calculation of the residual stresses and strains in wound reinforced-plastic products

A method is proposed for determining the residual stresses and strains in wound glass-reinforced plastic products. The fabrication process is divided into five stages: winding, heating polymerization, cooling, and removal from the mandrel. The initial stresses that develop during winding and the subsequent stress increment associated with heating are taken into account. Polymerization is treated as a process during which the mechanical and thermophysical properties of the material change. Chemical shrinkage of the resin and its filtration through the fiberglass are disregarded. Equations are derived for the residual radial and peripheral stresses in the finished product, for the residual change in inside diameter, and for the temperature at which the product is released from the mandrel during the cooling process. The experimental data relating to two types of wound products are discussed. The results of a computation of the residual stresses and the residual changes in inside diameter are compared with the experimental data.

Analytical Solution For A New Hybrid Double-Ellipsoidal Heat Source In Semi-infinite Body

Weld pool simulation plays a significant role in thermal stress analysis, residual stress calculation as well as microstructure modeling of welded joints and structures. This paper aims to describe the analytical solution for a new hybrid double-ellipsoidal power density moving heat source in semi-infinite body & its application in weld pool simulation. The solution has been obtained by superimposing the solutions for various parts of the proposed hybrid doubleellipsoidal heat source. The weld pool geometry subjected to various heat source parameters has been calculated and compared with results predicted by the double ellipsoidal heat source and available experimental data. Very good agreement between the predicted weld pool geometry and the measured ones has been obtained. The results also show that the hybrid heat source could give an improved prediction for weld pool depth in comparison with the earlier double ellipsoidal heat source.

Calculation of Residual Stresses in Glass

Lee, Rogers, and Woo presented a theory for calculating the stresses produced in glass by tempering. Unlike earlier treatments, theirs takes account of the viscoelastic properties of glass. The purpose of this paper is to evaluate this theory by comparison with experimental data. Discrepancies were found to exist between calculated and observed stress distributions. For cases in which glass is quenched from initial temperatures well above the strain point, these discrepancies result from the numerical formulation of the theory, not from any shortcomings of the theory itself. A modification of this formulation brought calculated and observed stresses into good agreement. For quenching from lower initial temperatures, the present theory could not be brought into agreement with experimental data. The reasons for this are briefly considered in the context of the structural heterogeneity of tempered glass and its possible effects on residual stresses.

X-Ray Diffraction Study of the Effects of Uniaxial Plastic Deformation on Residual Stress Measurements

AbstractUniaxial Plastic Deformation (UPD) has been known to produce anomalies in residual stress measurements based on x-ray diffraction techniques. This study was undertaken to determine the magnitude of the effects, if any, on residual stress calculations from various materials subjected to UPD. An x-ray diffraction study using the two-exposure method ( ψ = 0° and ψ = U5°) was made on several iron, aluminum, and titanium alloys (AISI 4340, 4330M, 4130; 2024-13, 7075-T611; Ti-6Al-4V) before and after these alloys were deformed plastically by bending on a U-bend test fixture. The x-ray peak shifts, Δ2θ0-ψ, were recorded and the x-ray stress factors, Ki, calculated by three different methods. The results indicate that UPD of the calibration specimens will increase or decrease Ki depending on the alloy. These results are discussed together with observations on the additivity of residual and applied stresses, and the per cent differences in the stress measurements based on stress factors calculated by three different methods.

Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.

A Calculating Method of Residual Stresses from Extensively Diffused X-Ray Diffraction Lines

The X-ray diffraction patterns of materials which are used in the construction of industrial structures and machines generally have so widely diffused profiles that their K-alpha doublets can not be distinguished and these peaks are superposed.The calculation of residual stresses with the use of X-ray are carried out by measuring the peak positions of back reflection lines, but these broad lines contain some errors in the measurement of the peak shift.The shift of the peak positions are the movement of the whole profile and it would be calculated from Fourier's coefficients when the profiles are analysed by Fourier's method. This method of calculation is described in this paper.

The effects of residual stress, thermal stress-relief, and electrolytic polishing on the elastic properties of Australian wire: By John C. Williams, University of Tennessee, College of Dentistry, Memphis, Tenn.

The rapid solidification and subsequent thermal cycles that material is subjected to during additive manufacturing (AM) of a component result in a buildup of residual stresses, which lead to part distortion, and negatively impact the component's mechanical properties. We present a method for using neutron diffraction to validate thermomechanical models developed to predict the residual stresses in Inconel 625 walls fabricated by laser-based directed energy deposition. Residual stress calculations from neutron diffraction measurements depend strongly on the determination of stress-free lattice spacings. After measurement of stressed lattice spacings in Inconel 625 walls, reference samples were obtained by extracting thin slices from the walls and cutting comb-type slits into these slices. Reference lattice spacings were measured in these slices, as well as equivalent slices that were also subjected to stress-relieving heat treatment. These heat treatments changed the reference lattice spacings, and therefore affected residual strain measurements. Further, this study shows the importance of using location-dependent reference lattice spacing, as during AM, the thermal history, and therefore elemental composition and stress-free lattice spacing, vary with position. Residual stresses measured by neutron diffraction along the build direction using comb-type reference samples without heat treatment were in good agreement with thermomechanical modeling predictions.

Residual stresses in shot-peened aluminum bars

1. The X-ray method of measuring residual stresses has been shown to be applicable for measuring the residual stresses due to shot peening in aluminum alloys. 2. A slight change in the stress constant between peened and unpeened bars was noted. 3. For practical purposes, the experimental constant from an unpeened bar of otherwise identical composition and treatment should suffice for the calculation of residual stresses by the X-ray method in aluminum alloys. 4. X-ray techniques coupled with layer-removal techniques permit the approximate determination of the depth of peening.