Case Study highlight: Broad Application for Modeling Failure

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.

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

Click here to visit the case study page and read more about this powerful tool. If you have further questions, don’t hesitate to contact us for more information.

Broad Application for Modeling Failure

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.


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

Starting from an assumed initial flaw, BAMF 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, BAMF 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. BAMF 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 multi-point fracture mechanics approach to defining individual control points around the crack front

Multi-point 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.

Broad Application for Modeling Failure provides a straightforward approach for including residual stress in crack growth assessments. Residual stress input data for BAMF may come from measurement or process modeling (e.g., ERS-toolbox®). The MPFM capabilities in BAMF 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 (BAMF) and experimentally observed fatigue crack shape for a cold expanded hole test specimen.


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

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

For more information about the study described above, our fatigue analysis and testing abilities, or any of our residual stress engineering services, please contact us.

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 Hill Engineering and ESRD agreement for joint BAMF/StressCheck marketing

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 Hill Engineering and ESRD agreement for joint BAMF/StressCheck marketing

Strain gage in a bottle

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

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

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

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

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.