Archives: Case Studies

Machining distortion modeling

Part distortion during machining is a significant problem in many industries, particularly where rigorous dimensional tolerances are required. Distortion of finished parts can lead to significant economic loss and should be managed for effective design and production. This case study demonstrates some of the basic concepts related to the impact of residual stress on part distortion during machining. A representative problem is defined, and a model is used to estimate part distortion due to machining of raw material containing bulk residual stress.

This study considers a 304.8 x 203.2 x 12.7 mm (12.0 x 8.0 x 0.5 inch) aluminum plate as the starting raw material for the analysis. From the plate an example part will be machined that has the same in-plane dimensions as the starting plate (304.8 mm x 203.2 mm) and includes a 2.54 mm (0.1 inch) thick frame around a 2.54 mm (0.1 inch) thick web.


Raw plate and final part geometry. Non-bracketed dimensions are in inches and bracketed dimensions are in mm.

Aluminum plate is often stress relieved by stretching, and typically exhibits low levels of residual stress post-stress relief. For the sake of this analysis, the raw material is assumed to have the residual stress distribution shown in Figure 2a (similar to the residual stress measured by Prime and Hill [1]). The residual stress values are low compared to the yield strength of the material, ranging from about -20 to 20 MPa (-3 to 3 ksi).

In addition to the bulk residual stress present in the raw material, the machining process also induces stress. The machining-induced residual stress assumed for this demonstration is shown in Figure 2b, and exhibits a typical distribution with compressive residual stress near the machined surface that spans over a thin layer (0.2 mm) before it reaches magnitudes near zero. The peak compressive residual stress at the machined surface is -50 MPa (~ 7.3 ksi). The bulk residual stress in Figure 2a is assumed to be present in the raw plate for the analysis, while the machining-induced residual stress in Figure 2b is applied locally to the machined surfaces.


(a) Bulk residual stress (similar to [1] along rolling and transverse direction, (b) idealized machining induced residual stress

A finite element model including the bulk and machining-induced residual stresses was used to predict the distortion of the finished part. The model is elastic and superposes bulk and machining residual stress to provide an equilibrium solution. Figure 3a shows the deformed shape (using a magnification factor of 30 to better illustrate the deformation). The displacement pattern shows bowing of the finished part with respect to its intended shape, with positive displacements near the center. A 2D map of the displacement of the bottom surface of the finished part is shown in Figure 3b. Line plots along the x direction at y = 101.6 mm and along the y direction at x = 152.4 mm are shown in Figure 3c. The distortion range is approximately 1.4 mm. It is important to note that even though the bulk residual stress in the raw material is low (about 5% of the yield strength), it still has potential to cause significant distortion in finished parts, as illustrated here.


(a) Undeformed/deformed 3D shape of final part with zoffset = 0, (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top

Since the raw plate is thicker than the final part, the final part can be extracted from different positions through the thickness of the raw plate (e.g., Figure 4). The position from within the raw plate that the final part is removed from can have a significant impact on the distortion (due to the different bulk residual stress levels at different locations through the thickness). The position is defined by an offset distance from the bottom surface of the raw plate, zoffset. In the first example, the zoffset = 0, i.e., the bottom surface of the final part is aligned with the bottom surface of the raw plate (z = 0).


Location of machining of baseline/final part within the raw plate

The model used here can be modified to consider different part placements within the raw material in a straightforward manner. A significantly different result was obtained considering zoffset = 2.54 mm (0.1inch), which is shown in Figure 5. An opposite pattern of distortion is observed in Figure 5a compared to the case where zoffset = 0 (Figure 3a). The 2D map shown in Figure 5b shows displacements that range from 1.1 mm to -0.6 mm. Figure 5c shows the displacement along the left-right and bottom-top paths, and includes the results obtained with zoffset = 0 for comparison. Compared to zoffset = 0, zoffset = 2.54 mm exhibits displacement along the x direction that ranges from positive-negative-positive values and with higher magnitudes. The displacement along the y direction is similar for both offsets, but have opposite signs.


(a) Undeformed/deformed 3D shape of final part with zoffset = 2.54 mm (0.1inch), (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top comparing zoffset = 0 and 2.54 mm

Another aspect that influences the part distortion is the thickness of the web of the large pocket. The previous results considered a thickness of 2.54 mm (0.1inch), as illustrated in the final part drawing in Figure 1. Reducing the thickness to 0.635 mm (0.025inch) and considering the zoffset = 0 configuration causes significant changes in the results, as observed in Figure 6. A similar pattern of distortion is observed in Figure 6a and Figure 6b compared to Figure 3a and Figure 3b, however the magnitudes of displacement are significantly lower. A line plot comparing the results obtained with both thicknesses is shown in Figure 6c. Overall, the model with reduced thickness (red lines) provides lower displacement magnitudes along both paths (left-right and bottom-top) compared to the initial model with 2.54 mm thickness, and exhibits peak displacement that is lower by about 50%.


(a) Undeformed/deformed 3D shape of final part with zoffset = 0, (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top comparing thickness = 0.635 mm (0.025inch) and 2.54 mm (0.1inch)

This case study provided an example problem for the estimation of part distortion due to residual stress release from machining, considering a typical bulk residual stress distribution and machining-induced residual stress distribution. The results show significant part distortion, even though the considered bulk residual stress had very low magnitude compared to the yield strength of the material. The results also show that part distortion varies significantly depending on the machining location within the raw stock material.

For more information concerning this case study or any of the residual stress measurement techniques employed at Hill Engineering, feel free to contact us.

[1] M. B. Prime and M. R. Hill, “Residual stress, stress relief, and inhomogeneity in aluminum plate,” Scripta Materialia, pp. 77-82, 2002.

3D Scanning

3D scanners are powerful tools with many applications ranging from dimensional inspection to reverse engineering. Typically, 3D scanners are used to create a 3D representation of the geometry of a complex part. Initially the part geometry may be represented by thousands or millions of individual points. These points can then be used to reconstruct a model of the part.

Many of our projects at Hill Engineering benefit from 3D scanning technology. In addition, Hill Engineering offers 3D scanning services for others on a fee-for-service basis. Some typical applications that require the use of a 3D scanner include:

• Quality assurance inspection: checking the geometry of manufactured parts to ensure consistency with drawing requirements
• Reverse engineering: generating a CAD model of a physical object for use in future design or manufacturing
• Machining distortion: evaluating the effects of different machining and manufacturing processes on the final machined shape of parts
• Engineered residual stress: evaluating the effects of residual stress surface treatments on the deformation of parts

At Hill Engineering we use a Nikon ModelMaker H120 3D scanner. The cutting-edge ModelMaker H120 incorporates blue laser technology, ultra-fast frame rate, specially developed Nikon optics and the ability to measure the most challenging materials. The following is a summary of the system specifications:
• Measuring range: 78.75 inches (2.0 m)
• Measurement accuracy: 0.0011 inches (0.028 mm)
• Minimum resolution: 0.0014 inches (0.035 mm)

Figure 1 – Photograph of Nikon ModelMaker H120 scanning a case

The illustrations below show example 3D scans that illustrate the capability of the Nikon ModelMaker H120 3D scanner. The first example shows an image taken from a 3D scan of a cordless drill. The second example shows a comparison between a scan of a new computer mouse and a used computer mouse. The colors show the regions of wear from continued use (red is worn).

Figure 2 – Illustration of a 3D scan of a cordless drill

Figure 3 – Comparison between a 3D scan of a new mouse and a used mouse showing regions of wear

Inspecting your parts using state-of-the-art 3D laser scanners provides the geometric insight needed to take the right engineering and quality assurance decisions. Hill Engineering’s in-house 3D scanning services provides a fast and reliable solution to meet your 3D scanning needs. Results are supplied in the form of easy-to-interpret graphic reports, complemented with complete measurement datasets. Please contact us with additional questions about 3D scanning services.

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.

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Repeatability of Contour Method Residual Stress Measurements for a Range of Materials, Processes, and Geometries

This article examines the precision of the contour method using five residual stress measurement repeatability studies. The test specimens evaluated include the following: 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. These specimens were selected to encompass a range of typical materials and residual stress distributions. Each repeatability study included contour method measurements on five to ten similar specimens. Following completion of the residual stress measurements, an analysis was performed to determine the repeatability standard deviation of each population. In general, the results of the various repeatability studies are similar. The repeatability standard deviation tends to be relatively small throughout the part interior, and there are localized regions of higher repeatability standard deviations along the part perimeter. The repeatability standard deviations over much of the cross section range from 5 MPa for the aluminum T-section to 25 MPa for the nickel disk forging. There is a strong correlation between the elastic modulus of the material and the repeatability standard deviation. These results demonstrate the precision of the contour method over a broad range of specimen geometries, materials, and stress states.

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PSR Biaxial Residual Stress Mapping Validation

This paper further explores the primary slice removal technique for planar mapping of multiple components of residual stress and describes application to specimens with a range of alloys, geometries, and stress distributions. Primary slice release (PSR) mapping is a combination of contour and slitting measurements that relies on decomposing the stress in a specimen into the stress remaining in a thin slice and the stress released when the slice is removed from a larger body. An initial contour method measurement determines a map of the out-of-plane stress on a plane of interest. Subsequently, removal of thin slices and a series of slitting measurements determines a map of one or both in-plane stress components. Four PSR biaxial mapping measurements were performed using an aluminum T-section, a stainless steel plate with a dissimilar metal slot-filled weld, a titanium plate with an electron beam slot-filled weld, and a nickel disk forging. Each PSR mapping measurement described herein has one (or more) complementary validation measurement to confirm the technique. Uncertainty estimates are included for both the PSR mapping measurements and the validation measurements. Agreement was found between the PSR mapping measurements and validation measurements showing that PSR mapping is a viable technique for measuring residual stress fields.

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Mapping multiple residual stress components with PSR biaxial mapping

The contour method provides a spatially resolved two-dimensional map of the component of residual stress acting normal to a plane through a part. Hill Engineering recently developed an extension to the contour method, called PSR biaxial mapping, which generates two-dimensional maps of additional residual stress components over the same plane. When combined with traditional contour method measurements, PSR biaxial mapping is a very powerful residual stress measurement tool.

The basic steps for a PSR biaxial mapping residual stress measurement are illustrated below. First, the contour method is used to measure the residual stress component normal to a plane of interest. Next, a thin slice of material adjacent to the contour method measurement plane is removed. The residual stress in the thin slice is altered during the contour method measurement and subsequent slice removal. This change in residual stress is called the PSR stress. The residual stress in the removed thin slice is determined using a series of slitting measurements. The residual stress in the removed slice is referred to as the slice stress. The residual stress in the original configuration (prior to extracting the slice) is expressed as the sum of the slice stress (residual stress measured in the removed slice) and the PSR stress (residual stress released when the slice is removed from the body).

Figure 1 – Experimental steps used in a PSR mapping measurement

An example PSR biaxial mapping residual stress measurement is shown for a nickel alloy forging (Udimet-720Li). The forging had a diameter of approximately 151 mm (5.9 in) and a maximum height of 70 mm (2.7 in). The contour method was used to measure the hoop residual stress in the forging. Following completion of the contour method measurement, wedge shaped slices were removed adjacent to the contour measurement plane. Slitting measurements were used to develop a 2D map of the radial residual stress in the slices. The measured radial stress in the slices was combined with the PSR stress to determine the radial residual stress at the measurement plane in the original configuration.

Plots of the measured two-dimensional maps of the hoop residual stress (contour method) and radial residual stress (PSR biaxial mapping) are shown below. The hoop residual stress is tensile towards the center of the forging and near the inner diameter (maximum value of approximately 450 MPa) and has compensating compressive residual stress towards the outer diameter and along the top and bottom of the forging. The radial residual stress is also tensile near the center of the forging (maximum value of approximately 200 MPa) and compressive at the top and bottom.

Figure 2 – Two-dimensional maps of residual stress in the nickel disk forging: (a) hoop direction stress and (b) radial direction stress

PSR biaxial mapping has been used to measure 2D residual stress maps for a variety of applications including: a quenched aluminum extrusion, a stainless steel welded plate, a complex nuclear power plant nozzle mockup containing a dissimilar metal weld, an aluminum T-section, a stainless steel plate with a dissimilar metal weld, a titanium plate with an electron beam weld, and a nickel alloy forging.

Additional information about bulk residual stress measurement using PSR biaxial mapping can be found in the references below. Also, please feel free to read about other residual stress measurement techniques on our website or to contact us with additional questions.

Reference information:
M. D. Olson and M. R. Hill, “A New Mechanical Method for Biaxial Residual Stress Mapping,” Experimental Mechanics, volume 55, number 6, 2015, pp. 1139–1150.

Contour method repeatability

The contour method provides a spatially resolved two-dimensional map of the component of residual stress acting normal to a plane through a part. A typical contour method residual stress measurement involves three primary steps: 1) Cutting a part in half on the plane where residual stress is to be measured (typically using a wire EDM); 2) Measuring the resulting deformation on the cut surface caused by residual stress release; and 3) Performing an analysis to relate measured deformation to residual stress.

For this case study, the repeatability of the contour method under a variety of relevant conditions was determined. Repeatability is a measure of the precision of a measurement technique, but does not address measurement accuracy. The test specimens evaluated 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, a nickel disk forging, and an aluminum plate. These specimens were selected to encompass a range of typical materials and residual stress distributions. Each repeatability study included contour method measurements on 5 to 12 similar specimens. Following completion of the contour method measurements, an analysis was performed to determine the repeatability standard deviation of each population. In general, the results of the various contour method residual stress measurement repeatability studies are similar. The repeatability standard deviation tends to be relatively small throughout the part interior, with localized regions of higher repeatability along the part perimeter. These results provide expected precision data for the contour method over a broad range of specimen geometries, materials, and stress profiles.

Aluminum T section specimens were fabricated from bars cut from a thick 7050-T7451 aluminum plate. Prior to cutting, the aluminum plate had been stress relieved by stretching. The bars were then heat treated, including a quench, to induce high residual stress indicative of the -T74 temper. After heat treatment, T-sections were machined from the bars to represent an airframe structural member. Each T-section had a length of 254 mm (10.0 in), a height of 50.8 mm (2.0 in), a width of 82.55 mm (3.25 in), and a leg thicknesses of 6.35 mm (0.25 in).

Contour method measurements were performed at the mid-length of 10 specimens. The mean longitudinal residual stress is shown in Figure 1a. There is compressive residual stress at the left, right, and top edges with tensile stress at the center. The measured residual stress is similar between the 10 measurements and is quantified by the low repeatability standard deviation (Figure 1b). The repeatability standard deviation has a low distribution at most points (average of 5 MPa), with localized regions at the edges of the bottom and center flanges where the repeatability standard deviations is larger (95th percentile at 13 MPa).

Figure 1 – (a) Mean and (b) repeatability standard deviation for the aluminum T-section specimens

Five contour method measurements were performed on the stainless steel dissimilar metal weld specimen. The results (Figure 2a) show the mean longitudinal residual stress is tensile in the weld area and heat-affected zone (maximum = 380 MPa), and near the left and right edges of the plate (maximum = 400 MPa). There is compensating compressive residual stress toward the top of the plate at the left and right edges (minimum = -260 MPa). Most points have low repeatability standard deviations (average of 17 MPa), but there are localized regions near the part boundary where the repeatability standard deviation is larger (95th percentile at 36 MPa) as shown in Figure 2b.

Figure 2 – (a) Mean and (b) repeatability standard deviation for the stainless steel DM welded specimens

Six contour method measurements were performed on the titanium EB welded plate. The mean longitudinal stress (Figure 3a) has tensile stress in the weld area (maximum = 350 MPa) and compensating compressive stress in the heat-affected zone (minimum = -200 MPa). The repeatability standard deviation is low at most points (average of 8 MPa), with localized regions near the part boundary having higher repeatability standard deviations (95th percentile at 17 MPa) as shown in Figure 3b.

Figure 3 – (a) Mean and (b) repeatability standard deviation for the titanium EB welded plate specimens

Measurements were also performed on stainless steel forgings and a nickel disk forging, which are discussed in a more in-depth technical publication.

The results of the repeatability studies show consistent trends among samples, with low repeatability standard deviations over most of the specimen interior and localized regions of higher variability (typically along the part perimeter). The mean repeatability standard deviation ranged from 5 MPa for the aluminum T section to 35 MPa for the stainless steel forging, which represent the minimum and maximum values of the population.

The magnitude of the repeatability standard deviation increases with elastic modulus of the material, as shown in Figure 4a. The materials with the largest elastic moduli also have the largest repeatability standard deviations. Furthermore, when the repeatability standard deviation is normalized by elastic modulus (Figure 4b), the normalized repeatability standard deviation becomes consistent across all specimens, ranging from 70 x 10-6 MPa/MPa to 125 x 10-6 MPa/MPa, with an average value of approximately 100 x 10-6 MPa/MPa. Similarly, the 95th percentile of the normalized repeatability standard deviation is also relatively consistent, but covers a significantly larger range from 150 x 10-6 MPa/MPa to 275 x 10-6 MPa/MPa, with an average value of 220 x 10-6 MPa/MPa.

Figure 4 – Repeatability standard deviation (a) statistics and (b) statistics normalized by elastic modulus.

Reference information:

Repeatability of Contour Method Residual Stress Measurements for a Range of Material, Process, and Geometry, M. D. Olson, A. T. DeWald, and M. R. Hill, Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8, Springer, Cham, 2018, pp. 101–113.

The Contour Method (book chapter)

Chapter 5 of Practical Residual Stress Measurement Methods.

The contour method, which is based upon solid mechanics, determines residual stress through an experiment that involves carefully cutting a specimen into two pieces and measuring the resulting deformation due to residual stress redistribution. The measured displacement data are used to compute residual stresses through an analysis that involves a finite element model of the specimen. As part of the analysis, the measured deformation is imposed as a set of displacement boundary conditions on the model. The finite element model accounts for the stiffness of the material and part geometry to provide a unique result. The output is a two-dimensional map of residual stress normal to the measurement plane. The contour method is particularly useful for complex, spatially varying residual stress fields that are difficult (or slow) to map using conventional point wise measurement techniques. For example, the complex spatial variations of residual stress typical of welds are well-characterized using the contour method. A basic measurement procedure is provided along with comments about potential alternate approaches, with references for further reading.

Citation
Authors’ version at LANL

The Slitting Method (book chapter)

Chapter 4 of Practical Residual Stress Measurement Methods.

The slitting method is a technique for measuring through thickness residual stress normal to a plane cut through a part. It involves cutting a slit (i.e., a thin slot) in increments of depth through the thickness of the work piece and measuring the resulting deformations as a function of slit depth. Residual stress as a function of through thickness position is determined by solving an inverse problem using measured deformations. The chapter describes practical measurement procedures, provides a number of example applications, and summarizes efforts to determine the quality of the residual stress information obtained with the method.

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The effects of laser peening and shot peening on high cycle fatigue in 7050-T7451 aluminum alloy

The high cycle fatigue performance of 7050-T7451 aluminum was investigated for untreated as-machined, laser peened, and shot peened conditions. Constant amplitude, smooth (Kt=1) fatigue tests were conducted in four-point bending at a stress ratio of R=0.1. Results show that laser peening induces a layer of compressive residual stress more than three times deeper than for shot peening. Both treatments significantly increase fatigue performance.

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