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.

     

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.

     

Validation of a Contour Method Single-Measurement Uncertainty Estimator

This work validates an analytical single-measurement uncertainty estimator for contour method measurement by comparing it with a first-order uncertainty estimate provided by a repeatability study. The validation was performed on five different specimen types. The specimen types cover a range of geometries, materials, and stress conditions that represent typical structural applications. The specimen types include: an aluminum T-section, a stainless steel plate with a dissimilar metal slot-filled weld, a stainless steel forging, a titanium plate with an electron beam slot-filled weld, and a nickel disk forging. For each specimen, the residual stress was measured using the contour method on replicate specimens to assess measurement precision. The uncertainty associated with each contour method measurement was also calculated using a recently published single-measurement uncertainty estimator. Comparisons were then made between the estimated uncertainty and the demonstrated measurement precision. These results show that the single-measurement analytical uncertainty estimate has good correlation with the demonstrated repeatability. The spatial distributions of estimated uncertainty were found to be similar among the conditions evaluated, with the uncertainty relatively constant in the interior and larger along the boundaries of the measurement plane.     

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.     

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

Background

In-plane vibration is significant to a structure and has been accurately solved by many numerical methods; however, there are still not enough studies on its experimental measurement.

Objective

This work aims to propose a non-contact and fast way to measure dense full-field in-plane vibration of a plate structure, which has high frequencies and low response magnitudes.

Methods

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs is developed to conduct full-field scanning of a plate with free boundary conditions under sinusoidal excitation to measure its 3D vibrations. Calibration among the three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles to ensure that three laser spots can continuously and synchronously move along the same two-dimensional scan trajectory on the plate. The demodulation method is used to process the measured response to obtain in-plane operating deflection shapes (ODSs) of the plate.

Results

Four in-plane ODSs are obtained in the frequency range of 0–5000 Hz. Modal assurance criterion (MAC) values between in-plane ODSs from 3D CSLDV and step-wise scanning laser Doppler vibrometer (SLDV) measurements are larger than 95%. MAC values between ODSs from 3D CSLDV measurements and corresponding mode shapes from the finite element model of the plate are larger than 91%.

Conclusions

Results from 3D CSLDV measurements have good accuracy compared to those from SLDV measurements and numerical calculation, and the 3D CSLDV system can scan much more measurement points in much less time than the SLDV system.

     

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.

     

Intralaboratory Repeatability of Residual Stress Determined by the Slitting Method

This paper presents repeated slitting method measurements of the residual stress versus depth profile through the thickness of identically prepared samples, which were made to assess repeatability of the method. Measurements were made in five 17.8 mm thick blocks cut from a single plate of 316L stainless steel which had been uniformly laser peened to induce a deep residual stress field. Typical slitting method techniques were employed with a single metallic foil strain gage on the back face of the coupon and incremental cutting by wire EDM. Measured residual stress profiles were analyzed to assess variability of residual stress as a function of depth from the surface. The average depth profile had a maximum magnitude of −668 MPa at the peened surface. The maximum variability also occurred at the surface and had a standard deviation of 15 MPa and an absolute maximum deviation of 26 MPa. Since measured residual stress exceeded yield strength of the untreated plate, microhardness versus depth profiling and elastic–plastic finite element analysis were combined to bound measurement error from inelastic deformation.     

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.     

A shear rheometer for measuring shear stress and both normal stress differences in polymer melts simultaneously: the MTR 25

The MTR 25 is a multitask rheometer (for shear and squeeze flow) with 25 kg of normal force and a partitioned plate. Torque and normal force are measured at both, the inner disk and the outer ring of the plate. The first and second normal stress differences can be determined from a single test. The axial stiffness is high (10⁷ N/m) by using rigid springs and strain gauges for the load cell. Monodisperse polystyrene (M _w = 206 kg/mol, 180°C) has been sheared in the range from 0.05 to 47 s^− 1. The viscosity and first normal stress difference are highly reproducible. The second normal stress difference scatters and mirrors the instability at the rim. A critical comparison is made between the MTR 25 method and the single transducer evaluation method (RMS 800 method, Schweizer, Rheol Acta 41:337–344, 2002): Both yield excellent and coinciding viscosity and first normal stress difference data. The RMS 800 method gives more stable second normal stress difference data, since the normal force from the outer ring, which is influenced by edge fracture, is not used. Data for the RMS 800 method can be acquired on the MTR 25. The high normal force capacity permits larger samples and higher shear rates than on the RMS 800.

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.     

An Uncertainty Estimator for Slitting Method Residual Stress Measurements Including the Influence of Regularization

This paper describes the development of a new uncertainty estimator for slitting method residual stress measurements. The new uncertainty estimator accounts for uncertainty in the regularization-based smoothing included in the residual stress calculation procedure, which is called regularization uncertainty. The work describes a means to quantify regularization uncertainty and then, in the context of a numerical experiment, compares estimated uncertainty to known errors. The paper further compares a first-order uncertainty estimate, established by a repeatability experiment, to the new uncertainty estimator and finds good correlation between the two estimates of precision. Furthermore, the work establishes a procedure for automated determination of the regularization parameter value that minimizes total uncertainty. In summary, the work shows that uncertainty in the regularization parameter is a significant contributor to the total uncertainty in slitting method measurements and that the new uncertainty estimator provides a reasonable estimate of single measurement uncertainty.

     

Micron-Scale Residual Stress Measurement by Micro-Hole Drilling and Digital Image Correlation

This paper reports a new technique, namely the incremental micro-hole-drilling method (IμHD) for mapping in-plane residual or applied stresses incrementally as a function of depth at the micron-scale laterally and the sub-micron scale depth-wise. Analogous to its macroscale counterpart, it is applicable either to crystalline or amorphous materials, but at the sub-micron scale. Our method involves micro-hole milling using the focused ion beam (FIB) of a dual beam FEGSEM/FIB microscope. The resulting surface displacements are recorded by digital image correlation of SEM images recorded during milling. The displacement fields recorded around the hole are used to reconstruct the stress profile as a function of depth. In this way residual stresses have been characterized around a drilled hole of 1.8microns. diameter, enabling the profiling of the stress variation at the sub-micron scale to a depth of 1.8 microns. The new method is used to determine the near surface stresses in a (peened) surface-severe-plastically-deformed (S²PD) Zr₅₀Cu₄₀Al₁₀ (in atomic percent, at.%) bulk metallic glass bar. In plane principal stresses of -800 MPa ± 90 MPa and −600 MPa ± 90 MPa were measured, the maximum compressive stress being oriented 15° to the axis of the bar.     

Displacement Uncertainty Quantifications in T3-Stereocorrelation

Background Uncertainty quantifications are required for any measurement result to be meaningful.

Objective The present work aims at deriving and comparing a priori estimates of displacement uncertainties in T3-stereocorrelation for a setup to perform high temperature tests.

Methods Images acquired prior to the actual experiment (i.e.,at room temperature) were registered using 3-noded triangular elements (T3-stereocorrelation) to determine displacement uncertainties for different positions of the experimental setup.

Results The displacement uncertainties were then compared to their a priori estimates.

Conclusions For the analyzed experiment, it is shown that noise floor estimates only differed by a factor 2 when compared to a posteriori measurements of standard displacement uncertainties.

     

Surface Decoration for Improving the Accuracy of Displacement Measurements by Digital Image Correlation in SEM

In-situ straining experiments and residual stress evaluations by micromachining require accurate measurement of surface displacements. Such measurements can be conveniently done using Digital Image Correlation (DIC). Three surface decoration techniques are presented to enhance surface deformation and residual stress measurement capabilities on micron-scale samples within a Scanning Electron Microscope—Focused Ion Beam (SEM-FIB) instrument. They involve the use of Yttria-stabilized-zirconia nano particles applied chemically, nano platinum dots applied using FIB, and Focused Electron Beam (FEB) assisted deposition. The three decoration techniques create distinctive, random surface features that can be used with Digital Image Correlation to provide full field maps of surface displacements at high magnifications. A series of experiments using a FEGSEM-FIB demonstrated the effectiveness of the three surface decoration techniques for FEGSEM imaging at magnifications from 2,000× to 60,000×. The precision of the image correlation is substantially enhanced by the surface decoration, with displacement standard deviations reduced to the 0.005–0.03 pixel range, depending on the patch size used. By means of an example application, the use of surface decoration for microscopic hole-drilling residual stress measurements within a FIB-SEM is presented. The same trends in DIC uncertainty observed in the analysis of the surface decoration patterns carried through to the example application. Guidelines are given for appropriate choice of decoration method to suit various practical applications.     

Novel Crash Sled with a Translating Support Mass

Background

A novel crash sled has been developed with a translating support incorporating transducers that allow multiple methods of measuring energy absorption to fully characterize the dynamic crush response of composite components.

Objective

The main goal of the current investigation was to demonstrate functionality, repeatability, and accuracy of crush testing using a crash sled with a translating support mass.

Methods

A semi-automated algorithm for data reduction was developed based on impact mechanics principles. A preliminary set of tests was initially conducted using aluminum honeycomb specimens with a specified stable crushing force to quantify the accuracy and repeatability of the crush data. Following the success of these tests, triaxially-braided fiber-reinforced polymer (FRP) specimens were evaluated.

Results

Crush tests with the aluminum honeycomb specimens showed excellent outcomes for all three specimens. These data provided close agreement with cumulative energy absorption between individual instruments and stable crushing forces at expected values. For the FRP specimens, specific energy absorption (SEA) and force-displacement curves were successfully measured; however, data from the translating support mass accelerometer were excluded from the dataset due to clipping. The SEA of the corrugated specimens was greater than the SEA for the C-channel specimens at both test speeds.

Conclusions

The crash sled functionality was verified, the specimen geometry was found to contribute more to SEA than the impact speed in the speed range tested, and the support mass accelerometer will be upgraded to prevent clipping in future tests.

     

Evaluation of the VDA 238–100 Tight Radius Bend Test for Plane Strain Fracture Characterization of Automotive Sheet Metals

Accurate characterization of the fracture limit in plane strain tension of automotive sheet metals is critical for the design and crash performance of structural components. Plane strain bending using the VDA 238–100 V-bend test has potential for proportional fracture characterization by avoiding a tensile instability. The VDA 238–100 V-bend test was evaluated using DIC strain measurement to characterize the plane strain fracture limit under proportional plane stress loading and to evaluate the effect of the VDA pre-straining methodology for ductile alloys upon the material response. The load-based failure criterion of the V-bend test was evaluated with DIC to monitor the development of surface cracking. The influence of the non-linear strain path imposed by the pre-straining procedure for ductile materials was then evaluated for three automotive alloys: an advanced high strength dual phase steel, DP1180, a rare-earth magnesium, ZEK100, and an AA5182 aluminum. A fracture criterion based on the load threshold was reasonable for the three alloys considered. Pre-straining in uniaxial tension prior to plane strain bending affected each alloy differently. The DP1180 was not affected by the non-linear strain path whereas the cumulative equivalent strain for the AA5182 and ZEK100 increased by strains of 0.07 and 0.05 strain, respectively. The non-linear strain path within the VDA pre-straining methodology creates ambiguity in comparing the fracture limits of different materials. The plane strain fracture limit for proportional loading can be readily obtained in the V-bend test with DIC strain measurement.

     

Mechanical Stimuli for Left Ventricular Growth During Pressure Overload

Background

The mechanical stimulus (i.e., stress or stretch) for growth occurring in the pressure-overloaded left ventricle (LV) is not exactly known.

Objective

To address this issue, we investigate the correlation between local ventricular growth (indexed by local wall thickness) and the local acute changes in mechanical stimuli after aortic banding.

Methods

LV geometric data were extracted from 3D echo measurements at baseline and 2 weeks in the aortic banding swine model (n?=?4). We developed and calibrated animal-specific finite element (FE) model of LV mechanics against pressure and volume waveforms measured at baseline. After simulation of the acute effects of pressure-overload, the local changes of maximum, mean and minimum myocardial stretches and stresses in three orthogonal material directions (i.e., fiber, sheet and sheet-normal) over a cardiac cycle were quantified. Correlation between mechanical quantities and the corresponding measured local changes in wall thickness was quantified using the Pearson correlation number (PCN) and Spearman rank correlation number (SCN).

Results

At 2 weeks after banding, the average septum thickness decreased from 10.6?±?2.92 mm to 9.49?±?2.02 mm, whereas the LV free-wall thickness increased from 8.69?±?1.64 mm to 9.4?±?1.22 mm. The FE results show strong correlation of growth with the changes in maximum fiber stress (PCN?=?0.5471, SCN?=?0.5111) and changes in the mean sheet-normal stress (PCN?=?0.5266, SCN?=?0.5256). Myocardial stretches, however, do not have good correlation with growth.

Conclusion

These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

     

Analysis of Damage and Failure in Anisotropic Ductile Metals Based on Biaxial Experiments with the H-Specimen

Background

Dependence of strength and failure behavior of anisotropic ductile metals on loading direction and on stress state has been indicated by many experiments. To realistically predict safety and lifetime of structures these effects must be taken into account in material models and numerical analysis.

Objective

The influence of stress state and loading direction on damage and failure behavior of the anisotropic aluminum alloy EN AW-2017A is investigated.

Methods

New biaxial experiments and numerical simulations have been performed with the H-specimen under different load ratios. Digital image correlation shows evolution of strain fields and scanning electron microscopy is used to visualize failure modes on fracture surfaces. Corresponding numerical studies predict stress states to explain damage and fracture processes on the micro-scale.

Results

The stress state, the load ratio and the loading direction with respect to the principal axes of anisotropy affect the width and orientation of localized strain fields and the formation of damage mechanisms and fracture modes at the micro-level.

Conclusions

The enhanced experimental program with biaxial tests considering different loading directions and load ratios is suggested for characterization of anisotropic metals.

     

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 1. A Theoretical Analysis

Background

This paper deals with the possible field of application of ultrasonic Surface Reflection Method (SRM) to achieve the mechanical characteristics of isotropic materials. This method is based on the measurement of the amplitude of the reflected wave at the interface between reference material and the material to be characterised. Objective: The purpose of Part 1 of this paper is to establish the theoretical conditions for the applicability of SRM.

Methods

First, the theoretical formulas necessary to obtain the mechanical properties of the material to be tested will be established. Then, on the basis of these analytical formulas, the validity of the results for the material to be studied will be discussed according to the choice of the mechanical properties of the reference material through uncertainty calculations. The measurand error of SRM is then compared to that of traditional methods (transmission, transmission in water bath, pulse-echo).

Results

The analytical solution to the inverse problem (the mechanical characteristics of the tested medium based on those of the reference medium and the waves’ amplitude) will be given. From this analytical solution, an analysis of the measurand error will be performed and a method for choosing the reference material will be proposed.

Conclusions

It appears that SRM is better suited than traditional methods in two specific cases: measurement of small deviations of mechanical properties from a reference material or characterisation of high damping materials. In Part 2 of this paper, the practical conditions of applicability of the method are described and then applied to different kinds of materials.

     

A Scaling Law for APM2 Bullets and Aluminum Armor Plates

In a previous paper, we presented a scaling law for the ballistic-limit velocity for the 7.62 mm APM2 bullet and five aluminum alloy plates. This scaling law predicts that the ballistic-limit velocity is proportional to the square root of the product of the plate thickness and a material strength term. In this note, we show that this same scaling law can be used to accurately predict ballistic-limit velocity for the larger 12.7 mm APM2 bullet.