Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024-T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk.     

Laser surface-contouring and spline data-smoothing for residual stress measurement

We describe non-contact scanning with a confocal laser probe to measure surface contours for application to residual stress measurement. (In the recently introduced contour method, a part is cut in two with a flat cut, and the part deforms by relaxation of the residual stresses. A cross-sectional map of residual stresses is then determined from measurement of the contours of the cut surfaces.) The contour method using laser scanning is validated by comparing measurements on a ferritic steel (BS 4360 grade 50D) weldment with neutron diffraction measurements on an identical specimen. Compared to lower resolution touch probe techniques, laser surface-contouring allows more accurate measurement of residual stresses and/or measurement of smaller parts or parts with lower stress levels. Furthermore, to take full advantage of improved spatial resolution of the laser measurements, a method to smooth the surface contour data using bivariate splines is developed. In contrast to previous methods, the spline method objectively selects the amount of smoothing and estimates the uncertainties in the calculated residual stress map.     

Controlling the Cut in Contour Residual Stress Measurements of Electron Beam Welded Ti-6Al-4V Alloy Plates

The multiple cut contour method is applied to map longitudinal and transverse components of residual stress in two nominally identical 50 mm thick electron beam welded Ti-6Al-4V alloy plates, one in the as-welded condition and a second welded plate in a post weld heat treated (PWHT) condition. The accuracy and resolution of the contour method results are directly linked to the quality of the electro-discharge machining cut made. Two symmetric surface contour artefacts associated with cutting titanium, surface bowing and a flared edge, are identified and their influence on residual stresses calculated by the contour method is quantified. The former artefact is controlled by undertaking a series of cutting trials with reduced power settings to find optimal cutting conditions. The latter is mitigated by attaching 5 mm thick sacrificial plates to the wire exit side of the test specimen. The low level of noise in the measured stress profiles for both the as-welded and PWHT plates demonstrates the importance of controlling the quality of a contour cut and the added value of undertaking cutting trials.     

Evaluation of Errors Associated with Cutting-Induced Plasticity in Residual Stress Measurements Using the Contour Method

Cutting-induced plasticity can lead to elevated uncertainties in residual stress measurements made by the contour method. In this study plasticity-induced stress errors are numerically evaluated for a benchmark edge-welded beam to understand the underlying mechanism. Welding and cutting are sequentially simulated by finite element models which have been validated by previous experimental results. It is found that a cutting direction normal to the symmetry plane of the residual stress distribution can lead to a substantially asymmetrical back-calculated stress distribution, owing to cutting-induced plasticity. In general, the stresses at sample edges are most susceptible to error, particularly when the sample is restrained during cutting. Inadequate clamping (far from the plane of cut) can lead to highly concentrated plastic deformation in local regions, and consequently the back-calculated stresses have exceptionally high values and gradients at these locations. Furthermore, the overall stress distribution is skewed towards the end-of-cut side. Adequate clamping (close to the plane of cut) minimises errors in back-calculated stress which becomes insensitive to the cutting direction. For minimal constraint (i.e. solely preventing rigid body motion), the plastic deformation is relatively smoothly distributed, and an optimal cutting direction (i.e. cutting from the base material towards the weld region in a direction that falls within the residual stress symmetry plane) is identified by evaluating the magnitude of stress errors. These findings suggest that cutting process information is important for the evaluation of potential plasticity-induced errors in contour method results, and that the cutting direction and clamping strategy can be optimised with an understanding of their effects on plasticity and hence the back-calculated stresses.     

冷拔无缝钢管残余应力测量的杂交实验方法

提出了一种数值模拟和实验杂交的实验方法,测量了钢管内表面的残余应力。采用非线性有限元法模拟了冷拔钢管的成型过程,得到了钢管脱模以后的残余应力,通过释放切口处单元的刚度模拟了含有残余应力钢管的切割过程,研究了切割方法对残余应力的影响,数值计算和实验结果表明切割方法对二次残余应力有很大影响。采用X射线测量仪测量了钢管内表面的残余应力。研究结果表明,计算结果基本符合实验结果,误差可以被工程接受。     

Comparison Between Surface and Near-Surface Residual Stress Measurement Techniques Using a Standard Four-Point-Bend Specimen

Background

Determination of near-surface residual stresses is challenging for the available measurement techniques due to their limitations. These are often either beyond reach or associated with significant uncertainties.

Objective

This study describes a critical comparison between three methods of surface and near-surface residual stress measurements, including x-ray diffraction (XRD) and two incremental central hole-drilling techniques one based on strain-gauge rosette and the other based on electronic speckle pattern interferometry (ESPI).

Methods

These measurements were performed on standard four-point-bend beams of steel loaded to known nominal stresses, according to the ASTM standard. These were to evaluate the sensitivity of different techniques to the variation in the nominal stress, and their associated uncertainties.

Results

The XRD data showed very good correlations with the surface nominal stress, and with superb repeatability and small uncertainties. The results of the ESPI based hole-drilling technique were also in a good agreement with the XRD data and the expected nominal stress. However, those obtained by the strain gauge rosette based hole-drilling technique were not matching well with the data obtained by the other techniques nor with the nominal stress. This was found to be due to the generation of extensive compressive residual stress during surface preparation for strain gauge installation.

Conclusion

The ESPI method is proven to be the most suitable hole-drilling technique for measuring near-surface residual stresses within distances close to the surface that are beyond the penetration depth of x-ray and below the resolution of the strain gauge rosette based hole-drilling method.

     

Repeatability of the Contour Method for Residual Stress Measurement

This paper describes the results of a residual stress measurement repeatability study using the contour method. The test specimen is an aluminum bar (cut from plate), with cross sectional dimensions of 50.8 mm?×?76.2 mm (2 in?×?3 in) with a length of 609.6 mm (24 in). There are two bars, one bar with high residual stresses and one bar with low residual stresses. The high residual stress configuration (±150 MPa) is in a quenched and over-aged condition (Al 7050-T74) and the low residual stress configuration (±20 MPa) is stress relieved by stretching (Al 7050-T7451). Five contour measurements were performed on each aluminum bar at the mid-length of successively smaller pieces. Typical contour method procedures are employed with careful clamping of the specimen, wire electric discharge machining (EDM) for the cut, laser surface profiling of the cut faces, surface profile fitting, and linear elastic stress analysis. The measurement results provide repeatability data for the contour method, and the difference in repeatability when measuring high or low magnitude stresses. The results show similar repeatability standard deviation for both samples, being less than 10 MPa over most of the cross section and somewhat larger, around 20 MPa, near the cross section edges. A comparison with published repeatability data for other residual stress measurement techniques (x-ray diffraction, incremental hole drilling, and slitting) shows that the contour method has a level of repeatability that is similar to, or better than, other techniques.     

Evaluation of Residual Stresses Induced by Robotized Hammer Peening by the Contour Method

Welded components suffer from high tensile residual stresses close to the weld beads. These stresses seem to be the origin of premature cracking which could result in a catastrophic rupture during operation and a reduction of the lifespan of these components. In this context, the Hydro-Québec’s Research Institute (IREQ) developed a technique of residual stresses relaxation by robotized hammer peening which makes it possible to release stresses close to surface and preserve the mechanical and dimensional properties of manufactured components. Robotized hammer peening was used to induce compressive residual stresses on initially stress free samples of austenitic stainless steel 304L. Hammer peening layers from one to nine were performed and the resulting residual stresses were evaluated thanks to the contour technique. Complete 2D residual stress fields on samples cross sections were obtained. The ability of hammer peening to relax residual stresses within welded plates was then quantified on austenitic stainless steel 304L plates welded with a 308 steel and hammer peened. These tests show the efficiency of hammer peening as a method to relax tensile residual stresses and induce compressive ones to a depth of a few millimetres. Process parameters were optimized such as the number of hammer peening layers to be applied to reduce processing time and maximization of the intensity and spatial distribution of the compressive residual stresses.     

3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.     

A Novel Cutting Strategy for Measuring Two Components of Residual Stresses Using Slitting Method

An exact knowledge of residual stresses that exist within the engineering components is essential to maintain the structural integrity. All mechanical strain relief (MSR) techniques to measure residual stresses rely on removing a section of material that contains residual stresses. Therefore, these techniques are destructive as the integrity of the components is compromised. In slitting method, as a MSR technique, a slot with an increasing depth is introduced to the part incrementally that results in deformations. By measuring these deformations the residual stress component normal to the cut can be determined. Two orthogonal components of residual stresses were measured using the slitting method both experimentally and numerically. Different levels of residual stresses were induced into beam shaped specimens using quenching process at different temperatures. The experimental results were then compared with those numerically predicted. It was shown that while the first component of residual stress was being measured, its effect on the second direction that was normal to the first cut was inevitable. Finally, a new cutting configuration was proposed in which two components of residual stresses were measured simultaneously. The results of the proposed method indicated a good agreement with the conventional slitting.     

Surface Rayleigh Waves in the Determination of Near-Surface Stresses of Structural Elements

A supersonic nondestructive method for determining stresses in near-surface layers of solids is stated on the basis of the acoustoelastic theory of surface Raylegh waves. Examples are presented of how this method is used to determine the operating and residual stresses in materials and structural elements. Features of the mutual use of surface and volume waves to obtain additional information on the stress distribution over the cross section of a specimen are indicated     

On Foundations of the Ultrasonic Nondestructive Method for Determination of Stresses in Near-Surface Layers of Solid Bodies

The ultrasonic nondestructive method for determining stresses in near-surface layers of solid bodies is based on the laws governing the propagation of elastic surface waves in bodies with initial (residual) stresses. These laws are established within the framework of the linearized three-dimensional theory of waves in bodies with initial (residual) stresses. The dispersion equations in associated problems are solved by computational methods. The nondestructive method and measuring instruments and devices are described. Some examples of nondestructive determination of welding-induced residual stresses and operating stresses in near-surface layers of materials are presented Presented at the International Conference on Computational and Experimental Engineering and Sciences (ICCES'04) (Madeira, Portugal, July 26–29, 2004) and published in the journal Computer Modeling in Engineering and Sciences (CMES). __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 130–144, August 2005.     

应用云纹干涉法测量冷挤压孔周残余应力分布

本文就冷挤压加工后紧固孔周的残余应力测量问题进行了研究。文中提出了径向切割法以释放欲求剖面的周向残余应力;采用高灵敏度的云纹干涉法测量残余应力释放后引起的附加变形;用载波错位法获得高反差的应变条纹图。     

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.     

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.     

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.     

A finite-element technique to analyze the data measured by the hole-drilling method

A finite-element technique to analyze the data obtained by the hole-drilling strain-gage method is presented. In this study, residual stresses are assumed as initial stresses existing in the structural material or component. It is also assumed that the elimination of the initial stresses in the region of the drilled hole changes the measured strains. After putting initial stresses into displacement finite-element equations and comparing the stiffness matrix and the initial stresses matrix with those of the previous increment, equations relating unknown initial stresses and measured strains were obtained. By solving these equations, residual stresses were obtained. In this paper three examples are studied. In the first two examples, calibration constants C1 to be used in determining residual stress were calculated which varied with depth. In the third example, the data obtained by using the hole-drilling method are analyzed. All examples show good agreement with previous studies. Using the present method allows greater flexibility of choice of specimen shape, materials, and experimental procedure than would be possible if only analytic solutions were used.     

Residual Stresses Induced by Cold Expansion of Adjacent and Cut-Out Holes

Fatigue life of fastener holes can be enhanced via a cold-expansion process to introduce a compressive residual stress field around the hole edge and to reduce crack growth propagation. Considering that aerospace components contain multiple rows of holes, the present investigation focuses on the evaluation of the three-dimensional residual stress distribution in adjacent cold-expanded (CE) holes. The redistribution of residual stresses caused by a cut introduced between two adjacent holes was also investigated. Finite element (FE) analysis and experimental technique were used to assess the residual stress distribution in a 6082-T6 aluminum plate with two adjacent holes expanded sequentially at 4 % nominal interference. The influence of center-to-center distance between holes was explored to assess the optimal level of separation between adjacent holes. Results suggested that residual stresses near second CE hole are markedly lower than those of first CE hole and that a cutting process does not affect the beneficial compressive residual stress around CE holes. These effects may delay fatigue crack propagation from CE holes or cut-out holes.     

Surface waviness removed by orthogonal machine cutting

A thermoelastoplastic analysis is made to study the surface waviness of orthogonal machine cutting. As a workpiece experiences heavy cutting, chips are formed incrementally in a steady fashion leaving a sinusoidal wavy surface as evidence of the varying thickness of the uncut chips. The finite difference method is applied to determine the temperature distribution in the chip and tool while a large deformation thermoelastoplastic finite element analysis is made to simulate the wave removing process whereby the wavy surface is modelled by saw-tooth shaped meshes. Determined are the chip geometry, residual stresses in the machined surface, temperature distributions in the chip and tool forces. The cutting forces are also calculated and they agree well with the test results.     

Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation

The life analysis of engine components needs to take into account the residual stress relaxation induced by cyclic service loads. The paper recalls a new class of constitutive equations for cyclic viscoplasticity, using a series of kinematic hardening models with thresholds. The equations are introduced within a recently enlarged thermodynamic framework. Some attention is focused to the relations with multisurface approaches and to a specific determination procedure of the model parameters. The new model is applied to the calculation of the near surface residual stress relaxation after shot peening, when the structure is submitted to cyclic service loads. The simulated stabilized residual stresses are in good accordance with experimental results obtained on an N18 disk alloy at 650°C. In comparison, the classical model without threshold predicts the complete vanishing of the residual stresses, which is not satisfactory.