University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln NASA Publications National Aeronautics and Space Administration 2011 Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens Y. Yamada Ohio Aerospace Institute at NASA Glenn Research Center B. Ziegler Mississippi State University J.C. Newman Jr. Mississippi State University, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/nasapub Part of the Physical Sciences and Mathematics Commons Yamada, Y.; Ziegler, B.; and Newman, J.C. Jr., "Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens" (2011). NASA Publications. 99. https://digitalcommons.unl.edu/nasapub/99 This Article is brought to you for free and open access by the National Aeronautics and Space Administration at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in NASA Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Engineering Fracture Mechanics 78 (2011) 2597–2608 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens ⇑ Y. Yamada a, B. Ziegler b, J.C. Newman Jr. b, a Ohio Aerospace Institute at NASA Glenn Research Center, Cleveland, OH 44135, USA b Mississippi State University, Aerospace Engineering, Mississippi State, MS 39762, USA article info abstract Keywords: Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz Cracks (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and sim- Fatigue-crack growth ulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate Aluminum alloy crack-growth-rate data from threshold to near fracture over a wide range of stress ratios Crack closure (R = P /P = 0.1–0.75) using the new compression pre-cracking test methods. Compar- Stress–intensity factor min max Plasticity isons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike over- load tests. The life-prediction code, FASTRAN, which is based on the strip-yield model con- cept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T) specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fati- gue mode, unlike the single-shear mode (45o slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In 2004, Schijve et al. [1] presented the results of various fatigue-crack-growth-rate tests on the aluminum alloy D16Cz (clad) sheet, which was considered to have crack-growth properties similar to the 2024-T3 alloy. Later, these test results were compared to calculations made with the NASGRO [2] life-prediction code by Skorupa et al. [3]. In the NASGRO calculations, the strip-yield model options were used. In the mid-1990s, the strip-yield model options in NASGRO were developed by the National Aerospace Laboratory [4] in a joint effort between the European Space Agency and the National Aeronautics and Space Administration. The model equations were similar to those developed in the FASTRAN life-prediction code [5], which are based on Elber’s crack-closure concept [6] and the Dugdale strip-yield model [7]. The NASGRO code has two strip-yield model options: (1) variable constraint in the plastic-zone region, and (2) constant constraint in the plastic-zone region. Both options were used and the article stated that ‘‘no analysis option enabled to reproduce crack growth retardation observed after application of a single overload cycle ... Improving the predictions for variable-amplitude (VA) loading would require ⇑ Corresponding author. Tel.: +1 662 325 1521; fax: +1 662 325 7720. E-mail address: [email protected] (J.C. Newman Jr.). 0013-7944/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2011.06.015 2598 Y. Yamada et al. / Engineering Fracture Mechanics 78 (2011) 2597–2608 Nomenclature B thickness, mm c crack length, mm dc/dN crack growth rate, m/cycle E modulus of elasticity, MPa 1/2 Kcp compressive stress–intensity factor during pre-cracking, MPa m 1/2 KIe elastic fracture toughness or maximum stress–intensity factor at failure, MPa m 1/2 Kmax maximum stress–intensity factor, MPa m Pmax maximum applied load, N Pmin minimum applied load, N Po crack-opening load, N R load (Pmin/Pmax) ratio U crack-opening function, (1 À Po/Pmax)/(1 À R) w half-width of M(T) and width of C(T) specimens, mm a constraint factor DK stress–intensity factor range, MPa m1/2 1/2 DKeff effective stress–intensity factor range (UDK), MPa m 1/2 (DKeff)T effective stress–intensity factor range at constraint-loss region, MPa m ro flow stress (average of rys and ru), MPa rys yield stress (0.2% offset), MPa ru ultimate tensile strength, MPa choosing lower values of the fitting parameter (a) which, however, would worsen the predictions for constant-amplitude (CA) loading’’ [3]. The unexpected inconsistencies found in these comparisons and the emphasis on the constraint-loss regime has inspired the present work. Using material provided by the research group in Poland (M. Skorupa and T. Machniewicz, University of Science and Tech- nology), a series of fatigue-crack-growth tests were performed on compact, C(T), specimens machined from previously frac- tured middle-crack tension, M(T), specimens. Testing included constant-amplitude (CA) loading at several stress ratios (R), a single-spike overload test, and spectrum tests using Mini-Falstaff+, a spectrum derived from Mini-Falstaff [8,9] consisting of only tensile loads. Test data generated under CA loading on the C(T) specimens were combined with the test data by Schijve et al. [1] on M(T) specimens to develop a multi-linear curve describing the relationship between crack-growth rate (dc/dN) and the effective stress–intensity factor (DKeff) using proper constraint factors. The constraint factor models the elevation of the flow stress around a crack front due to the tri-axial stress state [10,11]. The constraint factor (a) is a key parameter in the correlation of fatigue-crack-growth-rate data and the prediction of crack growth under variable-amplitude loading. It was determined many years ago that CA test data was necessary, but not sufficient to establish the constraint factors [12,13]. Single-spike or repeated-spike overload tests are more sensitive to constraint factors than CA loading. It would be prudent to conduct tests under spike overloads or other VA loading to validate the selection of the constraint factors. Of course, the CA tests at various stress ratios (R) may be used to estimate an initial value of the constraint factor. In addition, a constraint- loss regime (transition from plane strain to plane stress) [14] occurs as the plastic-zone size approaches the sheet thickness, that allows slip-bands to develop through the thickness, and the crack surfaces develop full slant (single shear) or double- shear fracture [15,16]. This research work is organized in two papers. The objectives of the first paper were to present test data on compact, C(T), specimens, to develop the effective stress–intensity factor against rate relation, and to determine the proper con- straint factors for the D16Cz alloy. While the objectives of the second paper [17] were to present test data on the M(T) specimens [1] and to predict crack growth under a single-spike overload, variable-amplitude (block) loading, and the Mini-Falstaff spectrum loading. Herein, the FASTRAN life-prediction code was used to calculate the crack length against cycles for the C(T) specimens under CA loading, a single-spike overload (OL) and, finally, the code was used to predict the crack length against cycles on two spectrum tests. The following will present and discuss the specifics of the material, specimens tested, test data analyses, types of fatigue loading applied, the crack-growth analyses performed and a compar- ison of test and analyses. 2. Material The material used was the Russian alloy D16CzATWH, which appears to be similar to the American alloy 2124. It is a high purity clad alloy. Tensile testing performed by Schijve et al. [1] determined the mechanical properties to be rys = 335 MPa, ru = 457 MPa and an elongation of 22%. The high elongation (as compared to 2024-T3) is likely explained by the low impu- rity content (Fe and Si) and the crack-growth properties are considered to be similar to the 2024-T3 alloy [1]. Y. Yamada et al. / Engineering Fracture Mechanics 78 (2011) 2597–2608 2599 Grip marks 2w = 100 mm (a) Middle-crack-tension specimen w = 76.2 mm + c 2.5 mm 50 mm (b) Compact specimen Fig. 1. Layout and dimensions of C(T) specimen cut from M(T) specimen. 3. Specimens The material used in the current study was obtained from the research group in Poland (M.