Measurement-driven, model-based estimation of residual stress and its effect on fatigue crack growth. Part 2: fatigue crack growth testing and modeling

This paper assesses the accuracy of fatigue crack growth (FCG) predictions for high-strength aluminum samples containing residual stress (RS) and complex two-dimensional cracks subjected to constant amplitude load. FCG predictions use linear-elastic, multi-point fracture mechanics. A first prediction includes RS estimated by the model described in Part 1; a second prediction includes RS measured by the contour method. FCG test data show a significant influence of RS. Ignoring the RS results in a +60% error in predicted FCG life (non-conservative). Including RS improves predictions of crack growth significantly (errors better than +26% (estimated RS) and -14% (measured RS)).


Measurement-driven, model-based estimation of residual stress and its effects on fatigue crack growth. Part 1: validation of an eigenstrain model

The objective of this paper is to validate a measurement-driven, model-based approach to estimate residual stress (RS) in samples machined from quenched aluminum stock. Model input is derived from measurement of RS in the parent stock. Validation is performed for prismatic T-sections removed from bars at different locations. We find RS predicted agrees with RS measured, by contour and neutron diffraction methods, with root-mean-square model-measurement difference of 22 MPa. Follow-on work (in Part 2) applies the RS estimation to samples representative of aircraft structures and examines the effects of RS on fatigue crack growth in the RS-bearing samples.


Near Surface Residual Stress Measurement Using Slotting

There are various experimental measurement techniques used to measure residual stress and this work describes one such method, the slotting method, and its application to measure near surface residual stresses. This work examines its application to macro-scale specimens. A series of numerical experiments were performed to understand the size required to assume that the specimen is infinitely large, namely the thickness, width, and height. To assess measurement repeatability, 12 slotting measurements were performed in a shot peened aluminum plate. The numerical experiments determined the specimen should have a thickness greater than or equal to 21.6 mm (0.85 in), a total specimen width (normal to the slot length) greater than or equal to 44.5 mm (1.75 in), and total height (parallel to the slot) greater than or equal to 38.1 mm (1.5 in) for the specimen to be assumed to be infinite. Slotting measurement repeatability was found to have a maximum repeatability standard deviation of 30 MPa at the surface that decays rapidly to 5 MPa at a depth of 0.3 mm from the surface. Comparison x-ray diffraction measurements were performed. Infinite plate dimensions and slot length were determined as well as measurement repeatability. Slotting was shown to have significantly better repeatability than X-ray diffraction with layer removal for this application.


Measurement Layout for Residual Stress Mapping Using Slitting

Residual stress spatial mapping has been developed using various measurement methods, one such method comprising a multiplicity of one-dimensional slitting method measurements combined to form a two-dimensional (2D) map. However, an open question is how to best distribute the individual slitting measurements for 2D mapping. This paper investigates the efficacy of different strategies for laying out the individual slitting measurements when mapping in-plane residual stress in thin stainless steel slices removed from a larger dissimilar metal weld. Three different measurement layouts are assessed: independent measurements on nominally identical specimens (i.e., one slitting measurement per specimen, with many specimens), repeatedly bisecting a single slice, and making nominally sequential measurements from one side of the specimen towards the other side of the specimen. Additional comparison measurements are made using neutron diffraction. The work shows little difference between the independent and bisecting slitting measurement layouts, and some differences with the sequential measurements. There is good general agreement between neutron diffraction measurement data and the data from the independent and bisecting layouts. This work suggests that when using slitting to create a 2D map of in-plane residual stress, a cutting layout that repeatedly bisects the specimen works well, requires a small number of specimens, and avoids potential errors from geometric asymmetry or measurement sequence.


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

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. This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator. 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. 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. 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). The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate.


DART – automated residual stress measurement

Near-surface residual stress data is critical when assessing material performance, optimizing design, validating models, evaluating field failures, and executing quality assurance programs. Hill Engineering’s DART™ is an industry-leading tool for efficient, precise, and reliable near-surface residual stress measurements. The DART™ overcomes limitations of existing residual stress measurement equipment and includes everything required to perform state-of-the-art measurements in accordance with industry specifications.

Hill Engineering’s DART™

A single DART™ can perform near-surface residual stress measurements using multiple techniques including hole drilling
and TRUEslot® methods. This flexibility is helpful when requirements change or new applications arise. The DART™ executes hole-drilling residual stress profile measurements in accordance with ASTM E837, providing a depth profile of the three in-plane residual stress components in a single measurement. TRUEslot® is a novel technique, like hole-drilling, but simpler and more precise. TRUEslot® provides a depth profile of one stress component per measurement.

Hole drilling measurement example

Hole drilling results example

Residual stress measurements with the DART™ are easy to complete. A user interface guides you through set-up, then takes over for automated measurement execution and residual stress calculation.

With measurements completing in less than 60 minutes, the DART™ excels in the production quality management environment. Automated data capture, processing, and archiving provide you with residual stress results instantly.

Featuring advanced cutting strategies and real-time quality checks, the DART™ gives you confidence in your residual stress data.

• Hole drilling residual stress measurements according to ASTM E837
• TRUEslot® residual stress measurements
• Positional accuracy: ± 0.001 in.
• Works on most materials including: aluminum, titanium, steel, stainless steel, and nickel alloys
• Custom fixtures can be integrated to meet the needs of individual applications
• NFPA 79 compliant


Each DART™ includes a complete software package that enables efficient and repeatable residual stress measurements for high-volume or single-use applications. DART™ software is designed for ease-of-use, while maintaining flexibility to meet your measurement needs and providing controls to maximize reliability. An operator defines the measurement location, the type of measurement (TRUEslot® or hole-drilling), and inputs the key measurement details. Following set-up, the software automatically controls the incremental material removal process, acquires the experimental data, computes residual stress, and outputs a test report. The entire process is significantly more efficient than other available tools.

DART™ produces the highest-quality residual stress data available
Precise engineering and extensive use of automation within the DART™ provides a demonstrated 50%+ improvement in measurement repeatability relative to other hole drilling test equipment. Hole drilling and TRUEslot® measurements performed using a DART™ have been shown to be 60%+ more repeatable than X-ray diffraction measurements.

DART™ outperforms its competitors in RS measurement repeatability

The DART™ has proven to meet our high internal standards for data quality and is currently in use in multiple facilities throughout the world. It could be in your facility soon.

To place an order for DART™ related goods or services, please contact us.

Download a DART™ brochure here

DART™ and TRUEslot® are protected by US Patent 10,900,768 and are patent pending for other international jurisdictions.

Contour method uncertainty

The contour method is a residual stress measurement technique that provides a two-dimensional map of residual stress on a plane. Hill Engineering’s uncertainty estimate for contour method measurements is summarized here. For additional information, refer to the references below.

The contour method uncertainty estimate accounts for two main, random uncertainty sources present in contour method measurements. This includes the uncertainty associated with random noise in the surface height profiles called the displacement error, and the uncertainty associated with choosing a specific analytical model to fit the surface profiles called the model error.

The displacement error is estimated using a Monte Carlo approach that applies normally distributed noise to the each of the original measured surfaces. The normally distributed noise is prescribed to have approximately the same magnitude as the surface roughness that arises from EDM cutting. Stress results are found using five different sets of random noise added to the surface height profiles, and the standard deviation of those five residual stress results at each spatial location is taken as the displacement error.

The model error is estimated by taking the standard deviation of the residual stress results using displacement surface profiles that have been fit with different analytical models (centered around what was determined to be the best fit). Each case uses a different number of fitting coefficients.

The total contour method uncertainty is then taken as the root-sum-square of the displacement and model errors with a minimum value of uncertainty set as a floor. The floor used is the mean of the total uncertainty (prior to the application of the floor), which is evaluated over a regular grid. The uncertainty estimate is assumed to have a normal distribution, which implies that one standard deviation represents a 68% confidence interval.

An illustrative example of the contour method uncertainty calculation is provided below from a measurement on a dissimilar metal welded plate.

Stainless steel dissimilar metal dimensions and measurement locations (dimensions in mm)

The measured residual stress in the test specimen is shown below.

Measured residual stress (σzz)

The model error for the measurement (below) is largest along the part boundary (95th percentile is at 41.0 MPa). The displacement error (also shown below) is largest along the part boundary (95th percentile is at 11.8 MPa). The displacement error is much smaller than the model error. The total uncertainty has nearly the same distribution as the model error (95th percentile is at 42.5 MPa) with a 17.5 MPa floor covering most of the cross-section.

(top) Displacement error, (middle) model error, and (bottom) total uncertainty for the stainless steel DM welded samples

If you would like more information about using the contour method to determine a 2D map of residual stress in your parts please contact us.

Mechanical stress relief of aluminum alloys

As we discuss in a related case study, aluminum alloy heat treatment is a three-step process designed to achieve the desired properties. The process involves: 1) solution heat treatment (SHT) at an elevated temperature below the melting point, 2) quenching in a tank of fluid (e.g., 140-180°F water), and 3) age hardening. While providing good properties, the heat treatment has the negative side effect of creating bulk residual stress and distortion. These side-effects are a direct result of non-uniform cooling during the rapid quench. One approach to mitigate this problem is the application of a post-heat treatment mechanical stress relief process. In addition to modeling the heat treatment process, our analysis tools can support evaluation and optimization of mechanical stress relief processes.

Mechanical stress relief is practical for many aluminum alloy products as a means of reducing bulk residual stress. For products with a uniform cross section, such as most extrusions, plate, and bar stock, the material can be stretched on the order of 1% to 5% using special equipment. The figure below shows an example extrusion section with bulk residual stress (top) along with the remaining residual stress after mechanical stress relief (bottom). Note, the use of different color scales because the residual stress magnitude changes so significantly. This figure illustrates our capability to model post-quench and post-stretch residual stress.

Illustration of predicted post-quench (top) and post-mechanical-stress-relief-stretch (bottom) in the long direction of an example aluminum extrusion

For other products such as forgings, an alternative stress-relief process using a compressive cold work stress relief can be employed. For a hand forging this is usually achieved using open-dies comprised of mostly flat surfaces. Post-quench, the hand forging is subjected to 1% to 5% compression often in an overlapping fashion.

On the other hand, an impression-die forging usually requires a more complex process that involves a cold-work die set. Such die sets are designed to impress 1% to 5% cold-work. Typically, the compression is on the order of 1% in thinner web sections and 3% in thicker rib sections. Since the forging will be at room temperature for the compression (therefore the term – cold-work) it does require higher press loads than one sees in the hot forging operation. The following figure illustrates the elements of a cold-work die set.

Illustration of a typical cold-work die set for mechanical stress relief of an aluminum forging

In a previous case study, we demonstrated our capability to predict post-quench residual stress and distortion for an example forging. The effect of mechanical stress relief using compression dies on that same example forging is shown below. The post-quench residual stress (left) reaches as high as 20.0 ksi in this aluminum 7075 simulation. The post-cold-work residual stress (right) is significantly reduced. The reduced residual stress level in the stress-relieved state has significant advantages in terms of ease of machining (reduced distortion) and improved part performance.

Predicted residual stress post-quench (left) and post-cold-work-stress-relief (right) for an example aluminum forging

If this example relates to your production challenges, or if you have any questions about how these results might affect your projects, please do not hesitate to contact us. We would also be happy to answer any questions that you may have.

Rapid Forge Design

Hill Engineering’s Rapid Forge Design™ software is an automated tool for fast and reliable design of 2-piece, closed-die impression forgings. Rapid Forge Design™ reads the final part geometry and automatically designs a forging according to accepted industry guidelines and user inputs. Rapid Forge Design™ is intended for use by forging suppliers and forging consumers/OEMs.

The Rapid Forge Design™ software comes with a user-friendly, graphical interface that allows for forging designs using a simple, 3-step, menu guided approach.

Download a fully-functional demo version of Rapid Forge Design™.


Illustration of Rapid Forge Design™ user interface

The inputs to Rapid Forge Design™ are the 3D geometry of the machined part (to be manufactured from the forging) and critical, user-defined parameters that allow for customization of the resulting forging design (e.g., minimum thickness and minimum radius values).

The forging design is generated by Rapid Forge Design™ according to a set of prescribed, industry-accepted design rules. After the user inputs are provided, the automated forging design process is completed by Rapid Forge Design™ in minutes without any further user intervention. With this approach, Rapid Forge Design™ enables the design of forgings with significantly less effort than existing manual processes.

Rapid Forge Design™ outputs the 3D geometry of the forging and a host of useful forging statistics and properties including volume, plan view area, periphery length, heat treatment section thickness, and other dimensional information. These metrics are essential to support the quoting process (material producers) and planning and costing activities (OEMs).

The preliminary forging designs produced by Rapid Forge Design™ can be used as the starting point for the finished forging’s more detailed design and tooling CAD files.

The Rapid Forge Design™ process is outlined in the flowchart below. The operator can input and customize important design parameters including: web thickness, draft wall cover, draft wall angle, plan view radius, fillet radius, and corner radius. Default values are provided based on alloy dependent industry standards. Help menus provide additional support and guidance, where necessary.




Summary of Rapid Forge Design™ workflow

Numerous examples taken from publicly available CAD files come with the software. The following are a few illustrations showing the ability of Rapid Forge Design™ to effectively produce forging designs for a wide variety of supplied final part geometry.


Illustration of forging designs produced by Rapid Forge Design™ (gold) along with the final machined part geometry that was used as the input for design (grey)

Download a fully-functional demo version of Rapid Forge Design™.

To place an order for Rapid Forge Design™ related goods and services, please contact us.

Aluminum forging quench modeling

Aluminum alloy heat treatment is a three-step process designed to achieve desired properties. The process involves: 1) solution heat treatment (SHT) at an elevated temperature below the melting point, 2) quenching in a tank of fluid (e.g., 140-180°F water), and 3) age hardening. While providing good properties, the heat treatment has the negative side effect of creating bulk residual stress and distortion. These side-effects are a direct result of non-uniform cooling during the rapid, time-dependent quench. Since there is an unavoidable difference in cooling rates between near-surface and internal areas, thinner versus thicker sections, locations first submerged versus those submerged last, and vertical versus horizontal surfaces, the generation of bulk residual stress and distortion is unavoidable. Oftentimes there are so many variables in play it can appear as though there is a high degree of randomness in the process if things are not carefully controlled. Our analysis tools can help.

The focus of this case study is the quench distortion of an aluminum aerospace forging. Using our modeling tools, we were able to capture the significant post-quench distortion in the forging, which is shown in the figure below. A rapid immersion quench, evenly applied, results in a very distorted and bowed output.

Illustration of predicted distortion of an aluminum forging during quench

Clearly, alternatives needed to be explored to mitigate the large amount of distortion. We considered several possibilities: slowing the cooling on one side (with a coating), removing the webbing before the quench (with machining), increasing the thickness of the webbing, or redesigning the forging with back-to-back symmetry by putting two parts into one forging. However, real-time physical experimentation of multiple options would be expensive and time consuming.

With modeling tools, we were able to quickly and effectively identify the most promising alternatives for improvement.

In this case, the biggest improvement came from removal of the webbing. The webbing is necessary for some of the initial forging operations, but does not need to be retained. It does not provide any coverage of the customer’s final post-machined part, and it is not necessary for heat treatment. Removing the webbing (i.e. cutting it off) prior to heat treatment requires an extra machining operation, but that is relatively inexpensive. As seen in the next figure, removing the webbing before quench resulted in a post-quench distortion that is remarkably reduced.

Illustration of predicted distortion for an alternate aluminum forging quench process that involves removing the webbing from the center prior to solution heat treatment and quench

The advantage of pre-production simulation is that problems can be found and solved beforehand, and the robustness of the proposed solutions can be tested and quantified.

Post-quench distortion is driven by bulk residual stress. That stress is created during the quench due to uneven cooling. Near surface cooling is much faster than the internal cooling of the part. This is unavoidable. However, using our modeling tools, the quench-induced residual stress can be predicted.

This predicted bulk residual stress is useful in follow-up simulations of post-machining distortion and part performance. The next figure shows the principal bulk residual stress as seen in section planes throughout the forging. Note that the residual stress reaches as high as 20.0 ksi in this aluminum 7075 simulation. This residual stress is post-quench and absent of any mechanical stress relief operations that are typically performed in subsequent steps.

Illustration of predicted post-quench bulk residual stress in an aluminum forging

If this example relates to your production challenges, or if you have any questions about how these results might affect your projects, please do not hesitate to contact us. We would also be happy to answer any questions that you may have.