materials Article Effect of Specimen Thickness and Stress Intensity Factor Range on Plasticity-Induced Fatigue Crack Closure in A7075-T6 Alloy Kenichi Masuda 1,* , Sotomi Ishihara 1,2 and Noriyasu Oguma 1 1 Department of Mechanical Engineering, University of Toyama, Gofuku 3190, Toyama 930-8555, Japan; [email protected] (S.I.); [email protected] (N.O.) 2 National Institute of Technology, Toyama College, Toyama 939-8630, Japan * Correspondence: [email protected]; Tel.: +81-76-445-6772 Abstract: Fatigue crack growth experiments are performed using A7075-T6 compact tension (CT) specimens with various thicknesses t (1–21 mm). The stress intensity factor at the crack opening level Kop is measured, and the effects of t and the stress intensity factor range DK on Kop are investigated. In addition, the change in Kop value due to specimen surface removal is investigated. Furthermore, we clarify that the radius of curvature of the leading edge of the fatigue crack decreases as t becomes thinner. Using the three-dimensional elastoplastic finite element method, the amount of plastic lateral contraction (depression depth d) at the crack tip after fatigue loading is calculated quantitatively. The following main experimental results are obtained: In the region where DK is 5 MPam1/2 or higher, the rate of fatigue crack growth da/dN at a constant DK value increases as t increases from 1 to 11 mm. The da/dN between t = 11 and 21 mm is the same. Meanwhile, in the region where DK is less than 5 MPam1/2, the effect of t on da/dN is not observed. The effects of t and DK on the da/dN–DK relationship are considered physically and quantitatively based on d. Keywords: fatigue crack growth behavior; aluminum alloy; CT specimen; plasticity-induced fatigue Citation: Masuda, K.; Ishihara, S.; crack closure; specimen thickness; plane stress and plane strain; 3D elastoplastic finite element Oguma, N. Effect of Specimen method; plastic lateral contraction at the fatigue crack tip Thickness and Stress Intensity Factor Range on Plasticity-Induced Fatigue Crack Closure in A7075-T6 Alloy. Materials 2021, 14, 664. 1. Introduction https://doi.org/10.3390/ma14030664 The importance of fatigue crack closure (FCC) on fatigue crack growth (FCG) behavior is acknowledged by many researchers. In many materials, even if the minimum stress Academic Editor: Tomasz Ta´nski intensity factor (K ) is on the tension side, a crack will not open unless the K value Received: 28 December 2020 min reaches the opening stress intensity factor K of the crack (K > K ). Therefore, K Accepted: 26 January 2021 op op min op Published: 31 January 2021 values must be evaluated well to accurately predict FCG behavior. Elber introduced the important concept of FCC [1,2] in the 1970s. He conducted FCG experiments using alu- Publisher’s Note: MDPI stays neutral minum alloy 2024-T3 under a constant stress ratio—R value and demonstrated that Kop − with regard to jurisdictional claims in increased with the stress intensity factor width DK (= Kmax Kmin). Here, Kmax is the max- published maps and institutional affil- imum stress intensity factor. He proposed that the plastic stretch (plastic wake) occurring iations. behind the crack tip contributed to the increase in Kop. Similar results were observed in other low- and medium-strength aluminum alloys [3], and this type of FCC behavior is called plasticity-induced fatigue crack closure (PIFCC). After the initial study by Elber, other types of FCCs were discovered, such as roughness-induced fatigue crack closure (hereinafter RIFCC) [4–6], oxide-induced crack closure, and corrosion product-induced Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. crack closure [7–10]. In RIFCC, unlike PIFCC, Kop levels do not change significantly or This article is an open access article remain constant with increasing DK. distributed under the terms and In a review paper regarding the PIFCC phenomenon [11], Schivje indicated that the conditions of the Creative Commons Kop level in the plane-stress region (specimen surface region) was higher than that in the Attribution (CC BY) license (https:// plane-strain region (inside the specimen). Ishihara et al. [12] conducted FCG experiments creativecommons.org/licenses/by/ using A6061 and carbon steel S25C. They reported that A6061 exhibited PIFCC behavior, 4.0/). and the slope of Kop–DK was almost 0.5, whereas carbon steel S25C exhibited RIFCC Materials 2021, 14, 664. https://doi.org/10.3390/ma14030664 https://www.mdpi.com/journal/materials Materials 2021, 14, 664 2 of 16 behavior and the slope of Kop–DK was almost 0. In addition, they measured the fracture surface roughness (Ra) near the specimen surface and specimen inside as a function of DK to specifically observe the interaction between the specimen surface and the specimen inside. Their results showed that the Ra near the specimen surface increased with DK, but the Ra inside the specimen decreased. Newman et al. reported that FCG behavior in aluminum alloy 7075-T651 (t = 5.7 mm) showed PIFCC behavior [13]. Furthermore, Matos et al. [14] investigated the effect of specimen thickness t on Kop using aluminum alloy 6082-T6. They observed that the Kop for thin specimens was higher than that for thick specimens. In addition, Camas et al. [15] reported that the leading edge of the fatigue crack had a curvature, and that this curvature was affected by the specimen thickness. The conclusion of a review that we conducted on previous studies focusing on PIFCC for aluminum alloys indicates that knowledge regarding the effects of t and DK on FCG and FCC behaviors of aluminum alloys is limited to qualitative understanding. In particular, few studies have been carried out on the effect of DK on PIFCC. In this study, FCG and Kop behaviors of A7075-T6 were investigated experimentally using CT specimens with various thicknesses. Subsequently, the effect of t on Kop and the range of DK at which the effect of t occurs were clarified. The effect of t on the leading edge shape of the crack was experimentally investigated; furthermore, the effect of the leading edge shape of the crack on Kop is discussed herein. In addition, the PIFCC behavior involving plastic deformation was significantly affected by the DK level. It is assumed that the effect of RIFCC appeared in the low DK region. Therefore, we analyzed the DK value at which the transition from PIFCC to RIFCC occurred. The effects of t and DK on Kop were quantitatively and physically considered by analyzing the plastic lateral contraction (depression depth d) of the crack tip via the three-dimensional (3D) elastoplastic finite element method (FEM). 2. Materials, Specimens, and Experimental Methods 2.1. Material/Specimen The test material was aluminum alloy 7075-T6 (hereinafter A7075-T6). Its chemical composition and mechanical properties are shown in Tables1 and2, respectively. A tensile test was performed according to JIS standards, and two specimens were used. The difference between the results of the two tests was not large; thus, the average value of these is presented in Table2. The stress–strain curve obtained from the tensile test is shown in Figure1. The stress–strain curve was approximated by Ramberg–Osgood power law, and a strain-hardening exponent of 0.036 was obtained. Table 1. Chemical composition of the test material (wt%). Si Fe Cu Mn Mg Cr Zn Ti Al 0.40 0.50 1.60 0.30 2.50 0.24 5.50 0.20 Bal. Table 2. Mechanical properties of the test material. Yield Tensile Young’s Poisson’s Strain-Hardening Elongation Strength Strength Modulus Ratio Exponent 510 MPa 577 MPa 70 GPa 0.3 12% 0.036 Materials 2021, 14, x FOR PEER REVIEW 3 of 17 Materials 2021,, 14,, 664x FOR PEER REVIEW 33 of of 1617 Figure 1. Stress−strain curve for the present material A7075−T6. Figure 1. Stress− strain curve for the present material A7075−−T6. FigureFCG 1. Stress experimentsstrain curve were for performed the present using material American A7075 T6. society for testing and materials (ASTM) standard compact tension (CT) specimens; their shapes and dimensions are FCG experiments were performed using using American American society for testing and materials shown in Figure 2. FCG experiments and Kop measurements were performed using four ((ASTM)ASTM) standardstandard compact compact tension tension (CT) (CT) specimens; specimens their; their shapes shapes and dimensions and dimensions are shown are CTin Figurespecimens2. FCG with experiments t = 1, 6, 11, andand K21op mmmeasurements, and with specime were performedn width (W using) = 57.2 four mm CT fixed. speci- shown in Figure 2. FCG experiments and Kop measurements were performed using four FCG experimentt was performed using one or two CT specimensW for one specimen CTmens specimens with = with 1, 6, 11,t = 1, and 6, 11, 21 mm,and 21 and mm with, and specimen with specime widthn width ( ) = 57.2(W) = mm 57.2 fixed. mm fixed. FCG thickness,experiment t. Such was performeda method is using employed one or in two a usual CT specimensFCG experiment for one using specimen CT specimen thickness,s. FCG experiment was performed using one or two CT specimens for one specimen Then,t. Such the a methodrelationship is employed between in the a usual rate FCGof fatigue experiment crack using growth CT da/dN specimens. and Then,ΔK was the thickness, t. Such a method is employed in a usual FCG experiment using CT specimens. measuredrelationship by betweenperforming the a rate constant of fatigue ΔK experiment, crack growth a da/dNΔK increasing and DK experiment, was measured and bya Then, the relationship between the rate of fatigue crack growth da/dN and ΔK was ΔKperforming decreasing a constantexperiment.DK experiment,As for the measurement a DK increasing of K experiment,op, during a constant and a DK ΔK decreasing test, the measured by performing a constant ΔK experiment, a ΔK increasing experiment, and a valuesexperiment.