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Machining distortion modeling with multi-step models including residual stress

Distortion of finished parts during machining is a significant problem which typically results from release and redistribution of residual stress in the material once the part is unclamped from the machine table. If not accounted for, can lead to parts out of tolerance that need rework or become scrap. Hill Engineering’s machining process simulation capability solves the problem of reducing uncertainty in machining planning and improving machining processes by providing results from validated models to support decisions for contract machining vendors who want to produce high-quality parts efficiently and OEMs who want to maximize the productivity of their supply chain.

This case study focuses on machining modeling of a representative aircraft specimen using multi-step finite element analysis. Machining modeling was used to identify a machining strategy that requires less machine time (e.g., fewer part set-ups) to arrive at the final geometry, while also reducing the distortion of the finished part. The results illustrate how multi-step machining models can be used to provide upfront estimates of distortion, as well as guidance to optimize machining processes and obtain improved machining outcomes.

The part geometry considered in this case study is shown in Figure 1, and was designed to be representative of an aircraft part. The overall dimensions are 25 x 10 x 2.5 inches. The pockets, stiffener walls, holes, and tapering along the 25 inch dimension and 2.5 inch dimension provide a complex and representative geometry. The part is assumed to be machined from a 27 x 12 x 3.5 inch plate of aluminum alloy 7050-T7451 (stress relieved by stretching). While this material state typically exhibits low levels of residual stress, distortion during machining can still occur depending on the part geometry, machining strategy, and required tolerances.

Part geometry (dimensions in inches)

The plate considered for machining this part provides extra material coverage on all sides. Figure 2 shows the amount of machining cover on each side, given the part is aligned with the mid-thickness of the stock plate with equal spacing relative to the sides of the stock. One inch of extra material is available on all sides when looking from a top view, while one-half inch of extra material is available along the thickness direction.

Part geometry within stock material when placed at the mid-thickness of the plate

The assumed residual stress in the stock plate material is shown in Figure 3. This is based on slitting method results published in [1] for 3-inch-thick plate of aluminum alloy 7050-T7451. The residual stress distributions are relatively symmetric and were normalized and scaled for the specific stock plate thickness used in the current study (3.5 inches). The rolling direction of the stock plate was assumed to be along the 27-inch dimension of the plate.

Residual stress measured in aluminum alloy 7050-T7451 plate (adapted from [1])

The baseline machining strategy considered is illustrated in Figure 4, in which the part is placed near the top surface of plate. Step 1 includes a rough machining pass on the bottom surface of the plate to obtain a flat surface for subsequent machining. Then, the part is flipped on the machine table. Step 2 involves an initial rough machining of the pockets and stiffener walls. Step 3 flips the part once again and finalizes machining of the bottom flat surface of the part. Finally, the part is flipped for the last time, and machining of the pockets, holes, and stiffener walls is finalized to arrive at the final geometry. This machining strategy includes a total of 3 flips on the machine table.

Part placement and baseline machining strategy

Multi-step finite element models were employed to obtain estimates of the distortion and residual stress at the end of each machining step. For brevity, the displacement of the finished part only (step 4) is shown here. Figure 5 shows a contour plot of the displacement along the z-axis (U3, perpendicular to the bottom flat surface of the part) on a scale that varies from -0.025 to 0.025 inches. The displacement U3 range (maximum minus minimum value) is about 0.030 inches. Maximum displacement is observed near the corner region of the part that contains the 3-inch diameter hole (shown in Figure 1).

Contour plot of displacement along the z-axis (U3) for the finished part from the baseline strategy

Modeling was performed to simulate many different machining approaches. The optimal machining strategy places the part at the bottom surface of the stock plate as illustrated in Figure 6. The first step involves rough machining of the pockets and stiffener walls. The part is then flipped, and final-machined on the bottom flat surface. The second and final flip on the machine table provides the setup to final-machine the pockets, holes, and stiffener walls. This machining strategy uses a total of 2 flips (one less than the previous strategy).

Part placement and optimized machining strategy

The part distortion for the optimized machining strategy is shown in Figure 7 (using the same color scale as in Figure 5). Compared to the baseline strategy (Figure 5), a different displacement pattern is observed, although the maximum values are near the same region (i.e., near the corner of the part with the 3-inch diameter hole). The displacement range is 0.013 inches for the optimized machining strategy, which is significantly lower than observed from the baseline approach (0.030 inches). It is important to note that the optimized strategy (which places the part near the bottom of the stock) not only provided a finished part with lower amount of distortion, it also required less machine time (fewer flips), which represents an improvement in efficiency of the machining process.

Contour plot of displacement along the z-axis for the finished part from the optimized strategy

This case study considered multi-step machining models of a representative aircraft specimen, including the residual stress in the incoming stock material, to assess the distortion of the finished part. Two different machining strategies were presented, which included differences in part placement within the stock material, and sequence of machining steps. The results identify an optimized machining strategy that uses fewer flips on the machine table (setups) to arrive at the final geometry, while also reducing the distortion of the finished part. The results illustrate how multi-step machining models can be used to provide upfront estimates of distortion and guidance to optimize machining processes in order to obtain improved outcomes. Please contact us for additional information.

Case Study highlight: Broad Application for Modeling Failure

by Robert Pires

Our latest case study discusses our Broad Application for Modeling Failure (BAMF) software.

Broad Application for Modeling Failure (BAMF) enables fatigue crack growth analysis of parts with non-standard geometry, loading, and residual stress conditions through the implementation of multi-point fracture mechanics (MPFM). This user-friendly software environment provides structural analysts and engineers a tool to accurately and efficiently complete challenging fatigue crack growth problems.

BAMpF®

BAMpF® (Broad Application for Multipoint Fatigue) enables fatigue crack growth analysis of parts with non-standard geometry, loading, and residual stress conditions through the implementation of multipoint fracture mechanics (MPFM). This user-friendly software environment provides structural analysts and engineers a tool to accurately and efficiently complete challenging fatigue crack growth problems.

Starting from an assumed initial flaw, BAMpF® implements a multi-point fracture mechanics approach that allows crack shapes to evolve naturally as a function of the underlying, spatially varying stress fields and stress intensity factors. As illustrated in the figure below, the user specifies the number of points along the crack front to be used in the analysis. For each individual point, BAMpF® queries the stress intensity factor specific to the part geometry and loading through an interface with StressCheck® (a leading finite element software tool), provides the necessary inputs to AFGROW (a leading fatigue life assessment tool), and stores the expected fatigue crack growth for a given number of cycles. BAMpF® then combines the growth of each individual point into a new crack shape that serves as the starting point for the next increment of the analysis. This process is repeated until the fatigue crack reaches a critical size.

Illustration of multipoint fracture mechanics approach to defining individual control points around the crack front

Multipoint fracture mechanics improves the accuracy of fatigue crack growth calculations relative to traditional analysis methods by eliminating assumptions and constraints related to the shape of the crack (e.g. elliptical crack shapes are not required by MPFM). The use of MPFM is especially important when non-standard conditions like complex loading, complex geometry, and/or residual stresses are present as these factors tend to drive the evolution of the fatigue crack shape away from the circular/elliptical constraints imposed by the traditional analysis methods.

BAMpF® provides a straightforward approach for including residual stress in crack growth assessments. Residual stress input data for BAMpF® may come from measurement or process modeling (e.g., ERS-Toolbox®). The MPFM capabilities in BAMpF® enable accurate fatigue analysis of parts with laser shock peening (LSP), cold-expanded (CX) holes, of other bulk residual stress fields. For example, the figure below shows a comparison between the predicted (BAMpF®) and experimentally observed fatigue crack shape for a cold expanded hole test specimen.

Fatigue crack growth analysis (BAMpF®) and experimental results for a cold expanded hole test specimen

Some of the key features and capabilities of BAMpF® include:
• Natural fatigue crack shape progression
• Fully 3D analysis
• Complex loading
• Multi-crack interactions and link-up
• Residual stress

BAMpF® has received software certification from the United States Airforce.

For more information about the study described above, our fatigue analysis and testing abilities, our residual stress engineering services, or to place an order for BAMpF&reg related goods and services, please contact us.

Image from a BAMpF® analysis showing the stress in a specimen with a small crack near a hole

Special thanks to our partners:

ESRD’s flagship software product, StressCheck® Professional, is an advanced FEA tool having numerous unique technical capabilities

AFGROW is a Damage Tolerance Analysis (DTA) framework that allows users to analyze crack initiation, fatigue crack growth, and fracture to predict the life of metallic structures

Announcing agreement with ESRD for joint BAMF/StressCheck marketing

by Adrian DeWald

Hill Engineering and Engineering Software Research and Development, Inc. (ESRD) have executed a joint marketing agreement to collaboratively promote the combined use of our software tools: Broad Application for Modeling Failure (BAMF) and StressCheck® for fatigue analysis. Continue reading Announcing agreement with ESRD for joint BAMF/StressCheck marketing

Strain gage in a bottle

by Robert Pires

A representative composite overwrapped pressure vessel. Image courtesy of CompositesWorld: https://www.compositesworld.com/articles/thermoplastic-composite-pressure-vessels-for-fcvs

We’re putting something in a bottle, and no, it’s not an SOS to the world. It’s a strain gage!

Hill Engineering has recently developed technology to orient and apply strain gages inside a pressure vessel with restricted interior access. Continue reading Strain gage in a bottle

Residual Stress 101 vlog

by Robert Pires

Today, we’ve released the newest episode of our vlog: Residual Stress 101. The video is a return to basics, discussing the core of what it is we do here at Hill Engineering.

If you haven’t checked out our YouTube channel, it might be time. Our mission is to post content that helps highlight the capabilities of our organization, so that everyone can see how and why residual stress is important to their manufacturing processes.

Today’s post is a broad overview of what residual stress is, including the several techniques for measuring residual stress found in our lab. Look for future content that delves further into each technique, and contact us if you have any further questions or want to see a video related to something we haven’t discussed.

BAMF version 7.0 release

by Josh Hodges

Following the inputs from our user community, we continue to develop new capability in the Broad Application for Modeling Failure (BAMF) software. We are happy to announce the new version of BAMF (7.0) is now available, which includes several significant enhancements that improve the usability of BAMF and adds to the state-of-the-art capability not available in other fatigue analysis tools. Continue reading BAMF version 7.0 release

Case Study: cold hole expansion process modeling

by Robert Pires

Cold hole expansion (Cx or cold expansion for short) of fastener holes is a technique that has been widely used in the aircraft industry to improve the fatigue performance of structural components. The cold hole expansion process introduces compressive residual stress near the vicinity of the hole that slows crack growth and can significantly improve fatigue performance. Continue reading Case Study: cold hole expansion process modeling

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

by Adrian DeWald

Hill Engineering recently published new research detailing our efforts to quantify uncertainty for slitting method residual stress measurements. This new approach provides a more accurate estimate of the measurement uncertainty associated with the slitting method, which is very helpful for probabilistic performance assessments. The paper is titled An Uncertainty Estimator for Slitting Method Residual Stress Measurements Including the Influence of Regularization and appears in Experimental Mechanics. The abstract text is available here along with a link to the publication. Continue reading New publication – An Uncertainty Estimator for Slitting Method Residual Stress Measurements Including the Influence of Regularization

Case Study: Cold hole expansion process modeling

Cold hole expansion (CX or cold expansion for short) of fastener holes is a technique that has been widely used in the aircraft industry to improve the fatigue performance of structural components. The cold hole expansion process introduces compressive residual stress near the vicinity of the hole that slows crack growth and can significantly improve fatigue performance. The process induces plastic deformation near the hole from pulling an oversized mandrel through the hole. The elastic recovery of the surrounding material results in compressive residual stress near the hole bore surface that is balanced by tensile residual stress farther from the hole. The benefits of cold expansion on fatigue performance have been illustrated in several research studies. A correlation of fatigue crack growth at cold expanded holes is illustrated in [1].

This case study focuses on nonlinear process modeling of cold expansion using finite element analysis. An aluminum coupon with dimensions 50.8 x 50.8 x 6.35 mm (2.0 x 2.0 x 0.25 inch) and a hole in the center of diameter 12.12 mm (0.477 inch) is considered. The hole undergoes a 3.16% applied expansion during the cold hole expansion process, i.e., at maximum expansion, the hole radius is enlarged by 3.16%. Figure 1 shows the coupon geometry.

Coupon geometry used for cold hole expansion process modeling. Non-bracketed dimensions are in inches and bracketed dimensions are in mm.

The analysis considers the elastic-plastic behavior of the material, and uses a true stress-strain curve obtained from experimental tests using the specific material considered here. The material curve describes the material behavior under loading, and characterizes the hardening of the material as it is loaded past its initial yield strength.

Typically, fatigue cracks initiate at the edge of fastener holes. The hoop residual stress combines with applied loading to alter the crack driving force, and is important in a fatigue crack growth analysis considering cold expanded holes. The process model used here provides hoop residual stress as shown in Figure 2. A through-thickness map taken at the y = 25.4 mm (1.0 inch) plane is shown in Figure 2a, where high compressive residual stress is observed near the edges of the hole, while tensile residual stress arises farther from the hole edge to satisfy mechanical equilibrium. Figure 2b also shows the hoop residual stress, but at a xy midplane (z = 3.175 mm (0.125 inch)). The high compressive residual stress is localized near the hole edge, and is approximately axisymmetric. Taking a line plot of the hoop residual stress along a specified path provides more quantitative results, as illustrated in Figure 2c, where the path taken is at the y = 25.4 mm plane and at the mid-thickness of the plate (z = 3.175 mm (0.125 inch)). The curve in this plot is for the right side of the hole only (x > 30 mm).
The distribution shows peak compressive residual stress at the hole edge that decays and eventually becomes tensile. The peak compressive residual stress at the hole edge is -480 MPa (approximately -70 ksi). The size of the compressive residual stress zone, i.e., the distance at which the RS crosses 0 is about 4.4 mm (0.17 inch), which corresponds to about 0.7R (R = radius of the hole). Beyond the compressive residual stress zone, tensile residual stress develops with peak of about 115 MPa (approximately 17 ksi) at 7.2 mm (0.28 inch) away from the hole edge, which corresponds to 1.1R.

Hoop residual stress from process model with 3.16% applied expansion a) through thickness of coupon, b) on xy midplane at z = 3.175 mm (0.125 inch), c) line plot along x-direction at y = 25.4 mm, z = 3.175 mm

Having the process model established above, it is useful to evaluate the effect of the radial applied expansion level in the resulting hoop residual stress. Running the process model with a 4.16% applied expansion provides hoop residual stress as shown in Figure 3. Maps of the hoop residual stress are shown in Figure 3a and Figure 3b, and show slightly higher magnitudes of residual stress compared to the results in Figure 2a and Figure 2b. Figure 3c shows the line plot along the same path as for the previous model, and compares the results obtained with both levels of expansion. Overall, the higher level of expansion resulted in about 5% increase in peak compressive residual stress at the hole edge, and a 10% increase in the size of the compressive residual stress zone around the hole.

Hoop residual stress from process model with 4.16% applied expansion a) through thickness of coupon, b) on xy midplane at z = 3.175 mm (0.125 inch), c) line plot along x-direction at y = 25.4 mm, z = 3.175 mm

This case study focuses on process modeling using finite element analysis for prediction of residual stress from cold expansion of fastener holes. A process model is developed to simulate the expansion of the hole due to the mandrel pull-through operation, and the resulting hoop residual stress after elastic recovery of the material is presented. The model results show high compressive residual stress at the edge and vicinity of the hole, which decays with distance from the hole and eventually becomes tensile. Increasing the amount of applied expansion used in the model causes an increase in peak compressive residual stress at the hole edge, as well as an increase in size of the zone of compressive residual stress near the hole. Although only the hoop residual stress results are shown here, the process model provides full field solutions, and allows for evaluating residual stress from cold expansion through numerical simulation.

For more information about the study described above, our fatigue testing abilities, or any of our residual stress measurement techniques, please contact us.

[1] Stuart, D. H., Hill, M. R., and Newman Jr, J. C., 2011, “Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition,” Eng. Fract. Mech., 78(7), pp. 1389–1406.