Dale L. Ball

A Model for the Inclusion of Notch Plasticity Effects in Fatigue Crack Growth Analysis

Notches or other stress concentrations are by far the most common sites for the initiation and growth of fatigue cracks in aircraft structures. The growth of these cracks is directly influenced by the material stress-strain response in the vicinity of the notch. Specifically, when the applied (remote) stress is sufficient to cause local plastic deformation at the notch, the response (local) stresses can no longer be found using elastic stress concentration factors, and they become dependent on the prior loading history. This is to say that the response stresses can no longer be treated as state variables. The occurrence of fatigue crack growth at notches which experience local yielding one or more times during their design lifetime is, in fact, quite common in many cyclically loaded structures. Some of the assumptions inherent in “traditional” Linear Elastic Fracture Mechanics (LEFM) based fatigue crack growth analysis may be inappropriate for such problems. In particular, the assumption that the stress distribution on a critical plane remains proportional to the elastic distribution throughout the loading history becomes incorrect when one or more of the applied loads causes plastic deformation and introduces or alters a residual stress field in this region. This paper first describes an elastic-plastic stress-strain response algorithm which may be used to estimate response stress distributions on a critical plane on a cycle-by-cycle basis. This is followed by a discussion of the manner by which stress intensity factors may be calculated based on these response stress distributions using Greens functions. Finally, the use of these stress intensity factors for the calculation of crack growth rate and, ultimately, crack growth life, is demonstrated.

From Integrated Computational Materials Engineering to Integrated Computational Structural Engineering

Recent advances in the simulation of the quench, cold-work and machining processes for large aluminum forgings are opening the way for a new paradigm in the design, manufacture and sustainment of aircraft structures. The use of large forgings permits the unitization of smaller parts (brackets, fittings, lugs, etc.) with primary structural components like spars and bulkheads. This is being done in order to reduce part count, which in turn leads to significant reductions in manufacturing cost. Unitization can also translate into weight reduction / avoidance when comparing against built-up structure, but it raises a number of issues for structural durability and damage tolerance, notably reduced repair / replace capability and reduced crack arrest capability. The viability of the unitization concept is dependent not only on the availability of material systems that retain their mechanical properties in very thick sections, but also on the designer’s ability to retain durability and damage tolerance, and to understand and mitigate the effects of residual stresses.

The Impact of Forging Residual Stress on Fatigue in Aluminum

Large aluminum forgings are seeing increased application in aerospace structures, particularly as an enabler for structural unitization. These applications, however, demand an improved understanding of the forging process induced bulk residual stresses and their impact on both design mechanical properties and structural performance. In recent years, significant advances in both computational and experimental methods have led to vastly improved characterization of residual stresses. As a result, new design approaches which require the extraction of residual stress effects from material property data and the formal inclusion of residual stresses in the design analysis, have been enabled. In particular, the impact of residual stresses on durability and damage tolerance can now be assessed, and more importantly, accounted for at the beginning of the design cycle. In an effort to support the development of this next-generation design capability, the AFRL sponsored Metals Affordability Initiative (MAI) consortium 1 has conducted a detailed experimental and analytical study of fatigue crack initiation and fatigue crack growth in aluminum coupons with known, quench induced residual stresses. In this study, coupons were designed and manufactured such that simple ‘design features,’ such as holes and machined pockets, were installed in locations with varying levels of bulk residual stress. The residual stresses at the critical locations in the coupons were measured using multiple techniques and modeled using detailed finite element analysis. Fatigue crack initiation (FCI) and fatigue crack growth (FCG) tests were performed using both constant amplitude and spectrum loading and the results were compared against computed FCI and FCG lives.

Fatigue Life Variability in Large Aluminum Forgings with Residual Stress

As part of a larger residual stress modeling and standardization program, a computational assessment of the variability in fatigue crack growth life that can result from variability in residual stresses has been conducted. A detailed finite element analysis of the forge/quench/coldwork/machine process was performed in order to predict the bulk residual stresses in a fictitious aluminum bulkhead. The residual stress profiles on ten critical planes were used to calculate residual stress intensity factors for a range of crack types that are typical for aircraft structural details. These stress intensity factors were used in a standard, linear-elastic-fracture-mechanics-based fatigue crack growth algorithm in order to predict fatigue life for typical fighter aircraft spectrum loading. Calculations were made for residual stress profiles which reflected variability due to machined part placement within the parent forging. For the conditions considered in this study (forging process, machined part placement, critical location / crack geometry, material and fatigue spectrum) we have found that variability in fatigue crack growth life due to part placement is on the order of +/- 20% about the mean. Furthermore, we have found from scaling the residual stress distributions for these conditions, that fatigue crack growth life sensitivity is on the order of 15% to 50% change in crack gowth life with every 5ksi change in peak residual stress.

A Methodology for Partitioning Residual Stress Effects From Fatigue Crack Growth Rate Test Data

This paper described an improved fatigue crack growth rate (FCGR) material characterization process that partitioned residual stress effects from the material “true” FCGR behavior, leading to FCGR design curves that are free of residual stress bias. The material used in the program had high residual stress intentionally introduced. Two test methods from the literature were used to characterize the material: the adjusted compliance ratio (ACR) test method for closure correction, and the crack compliance test method for measuring the stress-intensity factor due to residual stress (Kres). Both test methods operated independently on compliance data collected during FCGR tests. Two independent data reduction methods were used to analyze the FCGR data. In the first, the closure corrected ACR data were combined with the Kres data using a power law relationship to normalize the curves into a residual stress free “master” curve, which was then transformed into a more traditional closure free ΔKeff curve. In the second, the Kres data were used in a superposition approach along with a closure model to reduce the data directly to the closure free ΔKeff curve. The two ΔKeff curves were shown to be in good agreement. The closure model was also used to reintroduce the stress ratio effect to generate the familiar da/dN-ΔK family of design curves that were free of residual stress bias. Validation examples were included where curves for the material with high residual stress were compared with data from similar material that had minimal residual stress, and those results were in good agreement. A summary of fatigue crack growth life predictions was also included to show that when residual stress effects are removed from FCGR characterization data and reintroduced in the fatigue life analysis, fatigue life is predictable within the usual 2x scatter factor for damage tolerance analysis.

A Detailed Evaluation of the Effects of Bulk Residual Stress on Fatigue in Aluminum

The fully effective utilization of large aluminum forgings in aerospace structures has been hampered in the past by inadequate understanding of, and sometimes inaccurate representation of, bulk residual stresses and their impact on both design mechanical properties and structural performance. In recent years, significant advances in both computational and experimental methods have led to vastly improved characterization of residual stresses. As a result, new design approaches which require the extraction of residual stress effects from material property data and the formal inclusion of residual stresses in the design analysis, have been enabled. In particular, the impact of residual stresses on durability and damage tolerance can now be assessed, and more importantly, accounted for at the beginning of the design cycle.

F-35 Full Scale Durability Modeling and Test

The F-35 Joint Strike Fighter program includes three aircraft variants, one of which has been designed and built according to US Air Force requirements, and the other two of which have been designed and built according to US Navy requirements. For all three variants, a system design and development (SDD) configuration aircraft is being subjected to a full-scale durability (FSD) test. In each case, the complete airframe is being subjected to two lifetimes of severe design spectrum loading, with maneuver, catapults/arrestments (carrier variant only) and buffet loads applied as separate, alternating 1000 flight hour blocks during the major test sequence. For the airframe tests, the buffet loads are applied quasi-statically; for the separate vertical tail component tests, they are applied dynamically. In addition, tests of doors and attachments (local tests) are conducted when the full airframe test is down for inspections (as required, for example, between the first and second lifetimes). In this paper, we describe the manner in which the airframe tests were designed, including fatigue spectrum development and test adequacy analyses. In addition, we provide a summary of the test findings to date, along with a description of the analytical simulation for a typical finding. The paper includes an analysis vs test correlation summary that provides an indication of the validity of the fatigue crack initiation (FCI) and fatigue crack growth (FCG) analysis methods used to design the aircraft.

The Relationships between Crack Closure, Specimen Compliance and ‘Effective’ Fatigue Crack Growth Rate

The recent utilization of new, large aluminum forgings for critical airframe structural components has prompted the need for improved fatigue crack growth rate (FCGR) characterization methods. This need is most evident for cases in which the FCGR data are confounded by the presence of manufacturing process induced bulk residual stresses. The test method that has been the most successful at removing these confounding effects is the adjusted compliance ratio (ACR) method. In this paper we review two of the relationships that play a pivotal role in the success of the method. The first is the relationship between specimen compliance and fatigue crack closure, and the second is the relationship between closure and the so called ‘effective’ fatigue crack growth rate. We conclude with a brief discussion of the manner in which ACR data may be used in design.