Intermethod Comparison and Evaluation of Measured Near Surface Residual Stress in Milled Aluminum

Background

While near surface residual stress (NSRS) from milling is a driver for distortion in aluminum parts there are few studies that directly compare available techniques for NSRS measurement.

Objective

We report application and assessment of four different techniques for evaluating residual stress versus depth in milled aluminum parts.

Methods

The four techniques are: hole-drilling, slotting, cos(α) x-ray diffraction (XRD), and sin²(ψ) XRD, all including incremental material removal to produce a stress versus depth profile. The milled aluminum parts are cut from stress-relieved plate, AA7050-T7451, with a range of table and tool speeds used to mill a large flat surface in several samples. NSRS measurements are made at specified locations on each sample.

Results

Resulting data show that NSRS from three techniques are in general agreement: hole-drilling, slotting, and sin²(ψ) XRD. At shallow depths (<?0.03 mm), sin²(ψ) XRD data have the best repeatability (<?15 MPa), but at larger depths (>?0.04 mm) hole-drilling and slotting have the best repeatability (<?10 MPa). NSRS data from cos(α) XRD differ from data provided by other techniques and the data are less repeatable. NSRS data for different milling parameters show that the depth of NSRS increases with feed per tooth and is unaffected by cutting speed.

Conclusion

Hole-drilling, slotting, and sin²(ψ) XRD provided comparable results when assessing milling-induced near surface residual stress in aluminum. Combining a simple distortion test, comprising removal of a 1 mm thick wafer at the milled surface, with a companion stress analysis showed that NSRS data from hole-drilling are most consistent with milling-induced distortion.

     

A new rosette design for more reliable hole-drilling residual stress measurements

A new six-element strain gage rosette is presented that can greatly improve residual stress measurement accuracy when using the hole-drilling method. The proposed rosette consists of three pairs of sector-shaped radial and circumferential gages connected as half-bridges. This rosette design increases effective strain sensitivity by a factor of 2.3 compared with a standard ASTM rectangular rosette, and can identify stresses at one-third greater depths from the measurement surface. Experimental measurements confirm theoretical strain response calculations within 3–4 percent. Apart from a small increase in time to complete the electrical connections, the practical use of the proposed rosette is identical to that of a conventional three-element rosette.     

Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator

Background

Measurement precision and uncertainty estimation are important factors for all residual stress measurement techniques. The values of these quantities can help to determine whether a particular measurement technique would be viable option.

Objective

This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator.

Methods

Two repeatability studies were performed on test specimens extracted from aluminum and titanium shot peened plates. Each repeatability study included 12 hole-drilling measurements performed using a bespoke automated milling machine. Repeatability standard deviations were determined for each population. The repeatability studies were replicated using a commercially available manual hole-drilling milling machine (RS-200, Micro-Measurements). An updated uncertainty estimator was developed and was assessed using an acceptance criterion. The acceptance criterion compared an expected percentage of points (68%) to the fraction of points in the stress versus depth profile where the measured stresses ± its total uncertainty contained the mean stress of the repeatability studies.

Results

Both repeatability studies showed larger repeatability standard deviations at the surface that decay quickly (over about 0.3 mm). The repeatability standard deviation was significantly smaller in the aluminum plate (max ≈ 15 MPa, RMS?≈?6.4 MPa) than in the titanium plate (max ≈ 60 MPa, RMS?≈?21.0 MPa). The repeatability standard deviations were significantly larger when using the manual milling machine in the aluminum plate (RMS?≈?21.7 MPa), and for the titanium plate (RMS?≈?18.9 MPa).

Conclusions

The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate.

     

Incremental Computation Technique for Residual Stress Calculations Using the Integral Method

The Integral Method for determining residual stresses involves making surface deformation measurements within a sequence of small increments of material removal depth. Typically, the associated matrix equation for solving the residual stresses within each depth increment is ill-conditioned. The resulting error sensitivity of the residual stress evaluation makes it essential that data measurement errors are minimized and that the residual stress solution method be as stable as possible. These two issues are addressed in this paper. The proposed method involves using incremental deformation data instead of the total deformation data that are conventionally used. The technique is illustrated using an example ESPI hole-drilling measurement.     

Residual Stress Determination Using Cross-Slitting and Dual-Axis ESPI

Hole-drilling and Electronic Speckle Pattern Interferometry (ESPI) are used to measure residual stresses in metal specimens. The slitting method is chosen as an alternative to the more commonly used hole-drilling method because it involves less material removal and leaves large areas of highly deformed material available to be measured. However the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias. Conventional ESPI has a similar bias because it responds to surface displacements in a specific sensitivity direction. In this paper, a novel cross-slitting method with dual-axis ESPI measurements is proposed to address both directional biases. Cross-slitting is introduced as a means of releasing all in-plane stress components. The dual-axis ESPI system uses diagonal-mirror and shutter devices to provide surface displacement measurements in orthogonal in-plane directions. The combination of the cross-slit and dual-axis measurement gives isotropic sensitivity to the in-plane residual stress components. Experimental measurements are described that illustrate the capability and effectiveness of the cross-slitting/ESPI technique.     

Using Optical Interferometry to Restart the Ring-Core Method

Residual stresses are a well-known technical problem because they add to the stress field induced by external loads, thus causing mechanical components to fail at a load level significantly lower than expected. Of the various techniques developed to measure them, the ring-core method is one of the few which in principle can be restarted (by removing the core and re-installing the strain gauge rosette). Thus, it is theoretically able to measure residual stress at significantly greater depth than other methods. Although the idea is interesting, its practical implementation is quite difficult: in particular, re-installing the rosette and re-wiring is almost impossible when depth becomes significant, thus the incremental measurement is more a theoretical possibility than a real experimental approach. In this work we propose to replace the strain gauge rosette with an optical (interferometric) technique. In this way the incremental approach becomes viable, although, depending on the optical technique used, some practical problems have to be addressed.     

Incremental Hole Drilling for Residual Stress Analysis of Thin Walled Components with Regard to Plasticity Effects

The incremental hole-drilling method is widely used in residual stress depth distribution analysis. However, two specific difficulties with the generalization of the incremental method exist, including the consideration of the sample thickness and residual stress states close to the local material’s yield strength. The stress concentration effect of the hole can lead to plastic deformation in the vicinity of the hole, which results in an overestimation of residual stresses. Typically, the effect of the component’s thickness and the plasticity effects are analyzed separately and correction approaches are proposed. In the current paper, we analyze the combined effects of plasticity and thickness on residual stress analysis using the incremental hole-drilling method. A systematic study was performed on steel samples with (i) isotropic and (ii) anisotropic elastic and elasto-plastic material behavior with varying thicknesses ranging between 1 mm and 4 mm. Electronic speckle pattern interferometry (ESPI) hole-drilling experiments were conducted on beam samples loaded using a 4-point bending fixture. Finite element simulations were conducted to gain insight into the effects of incremental hole-drilling. The results indicate that reducing the component’s thickness increases the plastic deformation in the vicinity of the hole and results in significant stress deviations. Thin components bend during hole-drilling as a result of the loss of stiffness, which amplifies the plasticity effect.     

Residual Stress Determination Using Hole Drilling and 3D Image Correlation

In recent years, the hole drilling method for determining residual stresses has been implemented with optical methods such as holographic interferometry and ESPI to overcome certain limitations of the strain rosette version of hole drilling. Although offering advantages, the interferometric methods require vibration isolation, a significant drawback to their use outside of the laboratory. In this study, a 3D image correlation approach was used to measure micron-sized surface displacements caused by the localized stress relief associated with hole drilling. Residual stresses were then found from the displacements using non-dimensional relations previously derived by finite element analysis. A major advantage of image correlation is that it does not require interferometric vibration isolation. Experiments were performed to check the ability of this new approach for uniaxial and equi-biaxial states of stress. Stresses determined by the approach were in good agreement with computed values and those determined by hole drilling using holographic interferometry.     

Hole-drilling method using grating rosette and Moiré interferometry

The hole-drilling method is one of the most wellknown methods for measuring residual stresses. To identify unknown plane stresses in a specimen, a circular hole is first drilled in the infinite plate under plane stress, then the strains resulting from the hole drilling is measured. The strains may be acquired from interpreting the Moire signature around the hole. In crossed grating Moire interferometry, the horizontal and vertical displacement fields （u and v） can be obtained to determinate two strain fields and one shearing strain field. In this paper, by means of Moire interferometry and three directions grating （grating rosette） developed by the authors, three displacement fields （u, v and s） are obtained to acquire three strain fields. As a practical application, the hole-drilling method is adopted to measure the relief strains for aluminum and fiber reinforced composite. It is a step by step method; in each step a single laminate or equivalent depth is drilled to find some relationships between the drilling depth and the residual strains relieved in the fiber reinforced composite materials.     

Tikhonov regularization with Incremental Hole-Drilling and the Integral Method in Cross-Ply Composite Laminates

Background: Incremental hole-drilling with the integral method has been extensively used in composite laminates but is sensitive to small measurement errors. Error sensitivity can be reduced by limiting the number of depth increments used in the calculation procedure. This approach is limited if a rapidly varying residual stress distribution exists since the calculated stress in each incremental depth is considered constant. Distortion of stress results can consequently occur due to averaging effects if the depth increments become too large. Tikhonov regularization is usually applied in isotropic materials to smooth the resulting residual stress distribution and reduce stress uncertainties, but has only been applied to composite laminates using the slitting technique. Objective: The intention of this work is to extend the use of Tikhonov regularization to incremental hole-drilling of composite laminates using the integral method. Methods: Finite element modelling is used to calculate the necessary calibration coefficients for unit pulses of uniform stress. Monte Carlo simulation is used to the determine uncertainties in the calculated residual stress distributions. Tikhonov regularization is optimised to reduce the stress uncertainty, while ensuring that the stress solution is not distorted. Results: The method is demonstrated on a GFRP (Glass fibre reinforced plastic) laminate of [0₂/90₂]_s construction and the calculated residual stress field is compared with those obtained by the standard integral method and series expansion. Conclusions: It is found that Tikhonov regularization significantly improves the accuracy of the standard integral method in composite laminates and shows good agreement with the series expansion method.

     

Universal Calibration Constants for Strain Gauge Hole-Drilling Residual Stress Measurements

Experimental Mechanics - There is a large geometrical variation among the commercially available strain gauge rosettes used for hole-drilling residual stress measurements. Detailed calibration data...     

Thermal Stress Measurement in Continuous Welded Rails Using the Hole-Drilling Method

The absence of expansion joints in Continuous Welded Rail has created the need for the railroad industry to determine the in-situ thermal stress levels for rail buckling and breakage prevention. This paper explores the hole-drilling method as a possible solution to this problem. A new set of calibration coefficients to compute the stress field relieved by fine hole depth increments required by the high strength steel was determined. The new calibration coefficients were experimentally validated on an aluminum plate subjected to a known uniaxial load. The thermal stress levels of constrained rails were estimated after compensation for the residual stress components, based on statistical relationships developed experimentally between the longitudinal and the vertical residual stresses. The results showed that the hole-drilling procedure, with appropriate calibration coefficients and residual stress compensation, can estimate the in-situ rail thermal stresses with an expected accuracy that is within the industry acceptable levels.     

Plasticity Effects in the Hole-Drilling Residual Stress Measurement in Peened Surfaces

The incremental hole-drilling technique (IHD) is a widely established and accepted technique to determine residual stresses in peened surfaces. However, high residual stresses can lead to local yielding, due to the stress concentration around the drilled hole, affecting the standard residual stress evaluation, which is based on linear elastic equations. This so-called plasticity effect can be quantified by means of a plasticity factor, which measures the residual stress magnitude with respect to the approximate onset of plasticity. The observed resultant overestimation of IHD residual stresses depends on various factors, such as the residual stress state, the stress gradients and the material’s strain hardening. In peened surfaces, equibiaxial stresses are often found. For this case, the combined effect of the local yielding and stress gradients is numerically and experimentally analyzed in detail in this work. In addition, a new plasticity factor is proposed for the evaluation of the onset of yielding around drilled holes in peened surface layers. This new factor is able to explain the agreement and disagreement found between the IHD residual stresses and those determined by X-ray diffraction in shot-peened steel surfaces.     

Residual Stress Measurement in Composite Laminates Using Incremental Hole-Drilling with Power Series

Current methods for incremental hole-drilling in composite laminates have not been successfully applied in laminates of arbitrary construction or where significant variation of residual stress exists within a single ply. This work presents a method to overcome these limitations. Series expansion is applied to each ply orientation separately so that the discontinuities in the residual stresses at ply interfaces can be correctly captured. Temperature variations described by power series are used to set up eigenstrains and consequent stresses which vary in the through-thickness direction. The calibration coefficients at each incremental hole depth are calculated through the use of finite element modelling. The inverse solution employs a least-squares approach which makes the resulting solution insensitive to measurement uncertainty. Robust uncertainties in the residual stress distributions are determined using Monte Carlo simulation. The residual stress distribution is found from that combination of series orders in the different ply orientations that has the lowest RMS uncertainty, selected only from those combinations that have converged. The method is demonstrated on a GFRP laminate of [0₂/+45/?45]_s construction where it is found that transverse cracking of the plies at the inner surface of the hole may have impacted on the accuracy of the results.     

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 Analysis of Orthotropic Materials by the Through-hole Drilling Method

The present study deals with the development and the application of the through-hole drilling method for the residual stress analysis in orthotropic materials. Through a systematic theoretical study of the stress field present on orthotropic plates with a circular hole, the relationships between the relaxed strains measured by a rectangular strain gauge rosette and the Cartesian components of the unknown residual stresses are obtained. The theoretical formulas of each influence coefficient allow the user an easy application of the method to the analysis of uniform-residual stresses on a generic homogeneous orthotropic material. Furthermore, to extend the method to the analysis of the residual stresses on orthotropic laminates, caused by initial in-plane loadings, an alternative formulation is implemented. The accuracy of the proposed method has been assessed through 3D numerical simulations and experimental tests carried out on unidirectional, cross-ply and angle-ply laminates.     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP     

Evaluation of the High-Speed Drilling Technique for the Incremental Hole-Drilling Method

The incremental hole-drilling method is frequently used for residual stress depth distribution analyses, due to its fast and economical experimental execution. Depending on the planned use of the component, the drilled hole that is made to measure the residual stress can often be repaired or ignored if it does not affect the intended use of the part. Nevertheless an important experimental issue and assumption is the introduction of an ideal cylindrical hole into the component without additional plastic deformation. Although high-speed drilling is well established the consequences of the resulting hole geometries compared to ideal assumptions are not well known. Therefore, a detailed comparison between different bits and drilling techniques was carried out and is discussed in this paper in order to detect the best experimental conditions and to find out reasons especially for the lack of accuracy of the hole-drilling method for the first increments close to the specimens surface. It comes out that the orbital drilling with common used six-blade bits results in the best compromise of an ideal cylindrical hole and centricity to the center of the strain gage rosette. In the case of conventional drilling the hole geometry differs from the ideal one if six-blade bits were used due to the influence of chamfers at the cutting edges and a non 180° plane end face and also in the case of a two-blade bit due to a non 180° plane end face and the tendency to more eccentric holes. Diamond bits cannot be recommended under all tested conditions due to their geometrical undefined shape.     

大错位量散斑干涉法测量残余应力

本文提出大错位量激光散斑干涉法结合钻孔法测量残余应力,对单向拉伸残余应力进行了测量,试验结果与理论解非常吻合,并且实现了对真实构件表面残余应力的测量.     

Improvements in Residual Stress Measurement by the Incremental Centre Hole Drilling Technique

This paper presents results which advance and improve the usefulness, accuracy and efficiency of incremental centre hole drilling as a method of measuring near surface residual stress fields. Particular emphasis is placed on providing optimal values for the number of drilling step increments to be used and their corresponding size. Guidelines on the optimal values for the number and size of steps to use during measurements are presented for various ratios of hole radius to strain gauge rosette radius in the form of tabulated data. These guidelines are subsequently incorporated into a new data analysis program which permits very near surface residual stress fields to be accurately determined in real components. The benefits of the new approach are highlighted by reporting the results of measurements made on three industrial components, each of which has been subjected to a well-known engineering process. These components are a shot-peened spring-steel, a friction stir welded aluminium alloy, and a titanium alloy subjected to three different machining processes. The results reveal that the improvements to the incremental centre hole drilling technique can provide measured residual stresses from depths ranging from about 10 m to 1 mm.