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Interactions of plasticity and oxide crack closure mechanisms near the fatigue crack growth threshold
International Journal of Fatigue 26 (2004) 923–927 www.elsevier.com/locate/ijfatigue
Interactions of plasticity and oxide crack closure mechanisms near the fatigue crack growth threshold John A. Newman a,, Robert S. Piascik b a
US Army Research Laboratory, Vehicle Technology Directorate, Mail Stop 188E, Hampton, VA 23681, USA b NASA Langley Research Center, Mail Stop 188E, Hampton, VA 23681, USA Received 13 June 2003; received in revised form 5 December 2003; accepted 16 February 2004
Abstract An advanced analytical model developed earlier has been utilized to predict interactions between plasticity and oxide crack closure mechanisms that influence near-threshold fatigue crack growth behavior. Near-threshold closure is complex because multiple closure mechanisms are likely, including plasticity and oxide-induced crack closure. A series of experiments has been performed to validate analytical results. Analytical and experimental results suggest that interactions between plasticity and oxide result in high closure levels near the fatigue crack growth threshold. At sufficiently low DK, the combined effects of plasticity and oxide completely closes fatigue cracks resulting in high fatigue crack growth threshold values. Published by Elsevier Ltd. Keywords: Fatigue crack growth threshold; Oxide-induced crack closure; Plasticity-induced crack closure
1. Introduction The accelerated fatigue crack growth rates (da/dN) observed with increases in load ratio (R ¼ K min =K max ) are largely explained by crack closure, where crack faces prematurely contact during fatigue loading [1]. It is widely assumed that closed cracks are shielded from fatigue damage and that da/dN is related to an effective cyclic crack-tip stress intensity range factor, DKeff ¼ K max K cl , where cracks are closed for K < K cl . Elber originally proposed that crack closure was caused by residual crack-wake plastic strains [1]. This mechanism was termed plasticity-induced crack closure (PICC) as other closure mechanisms were identified. Crack opening can also be influenced by oxide-induced crack closure (OICC) that occurs when voluminous oxides form on the crack surfaces [2]. OICC is especially significant in corrosive environments, or near the fatigue crack growth (FCG) threshold where crack-opening displacements are small [3]. Roughness-induced crack closure (RICC) is another mechanism whose signifi Corresponding author. Tel.: +1-757-864-8945; fax: +1-757-8648911. E-mail address: [email protected] (J.A. Newman).
0142-1123/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.ijfatigue.2004.02.001
cance is generally limited to threshold [4]; however, the scope of this paper is limited to the effects of two closure mechanisms, PICC and OICC. For Paris regime FCG, PICC is the dominant closure mechanism and OICC is a second-order effect [5]. Experimental results have shown high closure levels occur near the FCG threshold [2,3], however, analytical PICC models do not adequately predict this phenomenon in the absence of load history effects [5], possibly because OICC and RICC effects are neglected. Near the FCG threshold PICC and OICC are potentially first-order effects and both must be considered to achieve a more complete understanding of near-threshold crack closure. Analytical and experimental results are presented in this paper to show the combined effects of PICC and OICC near the FCG threshold. 2. Closure model To provide a more complete description of nearthreshold crack closure, the authors developed an analytical model that includes the contributions of PICC, RICC, and OICC [6,7]. Analytical results have shown that RICC effects become negligible, even at the FCG
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Fig. 1. Schematics of idealized crack closure behavior. (a) Constant-amplitude fatigue cycle; (b) crack configuration for maximum load; (c) crack configuration for minimum load.
threshold, when thick crack-mouth oxides are present [6]. Therefore, it is reasonable to neglect the contribution of RICC when considering crack growth in an aggressive environment, and the scope of this paper is limited to the interactions between PICC and OICC near the FCG threshold. The idealized crack-tip behavior is illustrated in Fig. 1 (neglecting roughness effects). In Fig. 1a, a constant-amplitude load cycle is shown, where the maximum and minimum crack-tip stress intensity factors (Kmax and Kmin) are identified and the corresponding crack-tip conditions are shown schematically in Figs. 1b and 1c, respectively. Here, crack-wake plasticity and oxide are shown as the shaded and solid regions, respectively. The crack-tip is shown to be open at Kmax and closed at Kmin. Crack
closure levels are analytically determined in terms of competing effects that tend to open (i.e. crack-opening displacements) and close the crack (i.e. both plasticity and oxide crack-wake effects); crack closure occurs when the crack opening is equal to the thickness of the crack-wake products. The analytical model requires three input parameters: elastic modulus (E), yield stress (ry), and oxide thickness (t). Crack opening displacements, calculated as the sum of elastic and plastic components, tend to increase with increasing distance from the crack tip, which makes crack closure more likely to occur near the crack tip. Analytical Rcl (=Kcl/Kmax) results for aluminum alloy 8009 (E ¼ 88 GPa; ry ¼ 420 MPa; R ¼ 0:05) are plotted in Fig. 2a as a function of DK for three
Fig. 2. Analytical crack closure results for aluminum alloy 8009 at R ¼ 0:05 and with different oxide layer thicknesses [6]. (a) Effect of oxide layer thickness; (b) conditions for fully closed crack.
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values of oxide thickness (t ¼ 0, 100 G, and 500 G plotted as solid, dotted, and dashed curves, respectively) [6]. For the special case of no oxide layer, the value of Rcl is constant (0.251). Although crack-tip and crackwake plasticity are proportional to DK and 1/ry, no other terms (e.g. oxide layer) appear in the analytical closure equations so DK and ry are algebraically cancelled. This is true only for the special case where RICC does not occur and t ¼ 0. Higher Rcl are observed with increasing oxide thickness, t. As DK increases and crack-tip opening displacement increases, Rcl values decrease and asymptotically approach the horizontal solid line. As DK decreases (near the FCG threshold), the oxide layer causes Rcl to increase until fully closed crack conditions occur, i.e. Rcl ¼ 1 and DKeff ¼ 0. The fully closed DK value (DKfc) is indicated for t ¼ 100 G (dotted curve) in Fig. 2a. The value of DKfc increases with increasing t, e.g., DKfc is greater for t ¼ 500 G than for t ¼ 100 G. The relationship between DKfc and t is plotted in Fig. 2b. As indicated, fully closed crack conditions occur in the shaded region below the solid curve. 3. Experimental procedure Fatigue crack growth tests were performed using computer-controlled servo-hydraulic testing machines. Back-face strain data were continuously monitored to determine crack length, and loads were adjusted to achieve programmed stress intensity factors. Closure loads were determined from compliance (load and displacement) data. Displacements were measured (1) near the crack tip, termed local determinations, and (2) at the specimen back face, far from the crack tip, termed global determinations. Experimental studies have shown that global closure determinations do not adequately characterize crack closure, especially near the FCG threshold [8,9]. Therefore, local closure determinations were made using an alternate non-contacting near-tip displacement measurement system called digital image displacement system (DIDS) [10]. During fatigue loading a series of high-magnification (500) digital images of the crack-tip region were recorded and analyzed to obtain local closure determinations. Results show that DIDS is better suited to detect neartip closure events than global compliance methods [8]. FCG tests were performed using eccentricallyloaded-single-edge-notch tension specimens made from aluminum alloy 8009 sheet material (2.3 mm thick, 38.1 mm wide) in the L–T orientation [11]. Alloy 8009 was used because the resulting fatigue crack surfaces are very smooth and nearly featureless, thus eliminating RICC as a closure mechanism [12]. As needed, OICC was eliminated by performing tests in ultra-high vacuum (UHV, <105 Pa).
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4. Experimental results and discussion Analytical and experimental results are compared to determine the validity of the closure model and to study the combined effects of PICC and OICC. First, the special case where only PICC occurs is examined before considering both PICC and OICC. This allows the PICC portion of the analytical model to be evaluated separately and provides a standard for comparison with the combined effects of PICC and OICC. 4.1. Plasticity-induced crack closure For the special case where PICC is the sole closure mechanism, analytical results (see Fig. 2 for t ¼ 0) indicate that Rcl is not affected by DK or ry (although the crack-tip displacements and crack-wake plasticity are). However, analytical results suggest that Rcl does vary with R, as seen in Fig. 3a. Here, material parameters appropriate for aluminum 8009 were used, although for this special case the same curve would be obtained for any material parameters. The diagonal dotted line corresponds to R ¼ Rcl ; closure only affects FCG for conditions above this line. As seen in the lower left corner of Fig. 3a, the analytical results cross the diagonal dotted line at approximately R ¼ 0:31, so closurefree conditions are expected at higher R values. Global closure data from aluminum 8009 constant pffiffiffiffi DK ¼ 6:6 MPa m FCG tests, performed in room-temperature laboratory air, are shown as triangular symbols in the figure. A comparison of the laboratory air and UHV results of Fig. 3b indicate the closure contribution of the laboratory-air oxide layer is negligible for pffiffiffiffi DK > 2 MPa m [6,7]. Good agreement is seen between analytical and experimental results and no closure was detected for value of R > 0:30. FCG tests (R ¼ 0:05) were conducted in UHV conditions to study the PICC mechanism in the absence OICC. The global and local closure data for UHV and laboratory air tests are compared with data from the open literature (McEvily [13] in Fig. 3b). The analytical result discussed earlier in Fig. 2a is plotted (solid line) and compared to the test data (symbols). The results in Fig. 3b show that experimental data, for both UHV and laboratory air environment, are in good agreement with the analytical result. Here, the closure contribution of the thin oxide layer produced in room-temperature laboratory air is not detectable, and PICC is pffiffiffiffi the dominant effect for DK > 2 MPa m. The results of Fig. 3b strongly suggest that Rcl is constant when PICC is dominant, and OICC and RICC effects are negligible. This finding is consistent with the analytical result that crack-wake plasticity and crack-tip displacements counteract each other resulting in a constant Rcl, in the absence of OICC and RICC, as shown in Figs. 2a and 3b.
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Fig. 3. Comparison of analytical results and experimental data for aluminum alloy 8009 at room temperature where PICC is the dominant closure mechanism [6]. (a) Relationship between Rcl and R; (b) Rcl results for R ¼ 0:05.
4.2. Plasticity- and oxide-induced crack closure To study the combined effects of PICC and OICC, FCG tests were conducted with an artificially produced oxide layer. Here, alumina particles (Al2O3) were injected into the crack opening to simulate a thick oxide layer. This approach was taken since laboratory air oxide layers were shown to have a negligible closure contribution. Alumina particles were selected because they are inert (i.e. do not readily react with aluminum), are available in large quantities in near uniform sizes, and are easily mixed with alcohol to form a slurry that could be injected into the crack opening with a syringe. After establishing a steady-state FCG rate during constant-DK tests (R ¼ 0:05), the crack was held at Kmax (to create the largest crack opening without crack-tip
overloads) while the alumina slurry was injected into the crack opening. After the alcohol evaporated, fatigue loading was resumed for approximately 10 cycles to make closure determinations, but without appreciable crack growth. Closure data are plotted in Fig. 4 for two alumina particles sizes (a) 0.05 lm diameter and (b) 0.30 lm diameter. Global and local closure data are shown as triangular and circular symbols, respectively, and analytical results are shown as the dashed curves. The analytical and experimental data are in good agreement for pffiffiffiffi pffiffiffiffi DK > 4 MPa m (Fig. 4a) and DK > 12 MPa m (Fig. 4b). Detailed fractographic studies, described elsewhere, showed that the differences between analytical and experimental results at lower DK are due to the
Fig. 4. Analytical and experimental crack closure results with an artificially produced oxide layer in cracked aluminum alloy 8009 (R ¼ 0:05, laboratory air, room temperature) specimens where PICC and OICC occur [6].
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wake roughness effects, and in an inert vacuum environment to eliminate crack-mouth oxide. To exacerbate oxide-induced closure effects, Al2O3 particulate slurry was used to simulate a thick crack-mouth oxide layer. Key findings of this study are as follows: . Crack-mouth oxide layers produce increases in closure levels (Rcl) as DK decreases; increases in Rcl are especially pronounced at low DK near the FCG threshold. At sufficiently low DK the crack becomes completely closed (i.e. DKeff ¼ 0) resulting in higher FCG threshold values. . For the special case where plasticity is the only closure mechanism, Rcl varies with load ratio, but does not vary with DK, elastic modulus, or yield stress. Fig. 5. Comparison of analytical and experimental crack closure results for pipe steel in a H2S brine solution (R ¼ 0:1, 4 Hz, room temperature) where PICC and OICC occur [14].
Al2O3 particles not reaching the crack-tip region as assumed in the analytical model [6]. In Fig. 5, analytical results are compared with analytical data from the open literature [14] for FCG testing on drill-pipe steel (R ¼ 0:1; E ¼ 210 GPa; ry ¼ 700 MPa) in a corrosive H2S brine solution where both PICC and OICC effects are expected. Closure data for decreasing DK and increasing DK testing are shown as triangular and circular symbols, respectively. Dark-colored crack-mouth oxide up to 1 lm thick was observed at the specimen surface for increasing DK conditions. Decreasing DK conditions appeared to produce less oxide. Analytical results are presented for t ¼ 0, 250 G, 500 G, and 1000 G (dotted, dashed, solid, and dash-dot-dot curves, respectively). The analytical and experimental results have very similar trends; the t ¼ 1000 G and 250 G curves are upper and lower bounds for all data. The values of DKfc for decreasing and increasing DK are indicated as A and B (at pffiffiffiffi pffiffiffiffi approximately 7 MPa m and 10 MPa m), and correspond to analytical results for t ¼ 360 G and 700 G, respectively. Although experimental measurements of oxide thickness are not available, the analytical result accurately predicts the trends (increasing Rcl with decreasing DK) observed in Fig. 5.
5. Conclusions Analytical closure model results were validated with experimental data where plasticity and oxide closure mechanisms were dominant. Fatigue crack growth tests were performed with aluminum alloy 8009, a fine-grain alloy with smooth crack surfaces to eliminate crack-
References [1] Elber W. Fatigue crack closure under cyclic tension. Engng Fract Mech 1970;2:37–45. [2] Suresh S, Zaminski GF, Ritchie RO. Oxide induced crack closure: An explanation for near-threshold corrosion fatigue crack growth behavior. Met Trans 1981;12A:1435–43. [3] Suresh S, Vasudevan AK, Bretz P. Mechanisms of slow fatigue crack growth in high strength aluminum alloys: Role of microstructure and environment. Met Trans 1984;15A:369–79. [4] Walker N, Beevers C. A fatigue crack closure mechanism in titanium. Fatigue Engng Mater Struct 1979;1:135–48. [5] Newman JC. An evaluation of plasticity-induced crack-closure concept and measurement methods. In: McClung RC, Newman JC, editors. ASTM STP 1343, 2000. p. 128–44. [6] Newman JA. The effects of load ratio on threshold fatigue crack growth of aluminum alloys. PhD dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2000. [7] Newman JA, Riddell WT, Piascik RS. A threshold fatigue crack closure model (Parts I and II). Fatigue Fract Engng Mater Struct 2003;26:603–25. [8] Newman JA, Piascik RS. Plasticity and roughness closure interactions near the fatigue crack growth threshold. In: Reuter WG, Piascik RS, editors. ASTM STP 1417, 2000. [9] Smith SW, Piascik RS. Determining closure free fatigue crack growth behavior in the near threshold regime. In: Reuter WG, Piascik RS, editors. ASTM STP 1372, 2000. p. 109–22. [10] Sutton MA, Zhao W, McNeill SR, Helm JD, Piascik RS, Riddell WT. Local crack closure measurements: Development of a measurement system using computer vision and a far field microscope. In: McClung RC, Newman JC, editors. ASTM STP 1343, 1999. p. 145–56. [11] Reynolds AP. Constant amplitude and post-overload fatigue crack growth behavior in PM aluminum alloy AA 800. Fatigue Fract Engng Mater Struct 1992;15:551–62. [12] Piascik RS, Newman JC, Underwood JH. The extended compact tension specimen. Fatigue Fract Engng Mater Struct 1997;20:559–63. [13] McEvily AJ. Fatigue fracture-surface roughness and the K-opening level. Int J Fatigue 1997;19:629–33. [14] Ruppen JA, Salzbrenner R. The effect of environment on crack closure and fatigue threshold. Fatigue Engng Mater Struct 1983;6:307–14.
Interactions of plasticity and oxide crack closure mechanisms near the fatigue crack growth threshold John A. Newman a,, Robert S. Piascik b a
US Army Research Laboratory, Vehicle Technology Directorate, Mail Stop 188E, Hampton, VA 23681, USA b NASA Langley Research Center, Mail Stop 188E, Hampton, VA 23681, USA Received 13 June 2003; received in revised form 5 December 2003; accepted 16 February 2004
Abstract An advanced analytical model developed earlier has been utilized to predict interactions between plasticity and oxide crack closure mechanisms that influence near-threshold fatigue crack growth behavior. Near-threshold closure is complex because multiple closure mechanisms are likely, including plasticity and oxide-induced crack closure. A series of experiments has been performed to validate analytical results. Analytical and experimental results suggest that interactions between plasticity and oxide result in high closure levels near the fatigue crack growth threshold. At sufficiently low DK, the combined effects of plasticity and oxide completely closes fatigue cracks resulting in high fatigue crack growth threshold values. Published by Elsevier Ltd. Keywords: Fatigue crack growth threshold; Oxide-induced crack closure; Plasticity-induced crack closure
1. Introduction The accelerated fatigue crack growth rates (da/dN) observed with increases in load ratio (R ¼ K min =K max ) are largely explained by crack closure, where crack faces prematurely contact during fatigue loading [1]. It is widely assumed that closed cracks are shielded from fatigue damage and that da/dN is related to an effective cyclic crack-tip stress intensity range factor, DKeff ¼ K max K cl , where cracks are closed for K < K cl . Elber originally proposed that crack closure was caused by residual crack-wake plastic strains [1]. This mechanism was termed plasticity-induced crack closure (PICC) as other closure mechanisms were identified. Crack opening can also be influenced by oxide-induced crack closure (OICC) that occurs when voluminous oxides form on the crack surfaces [2]. OICC is especially significant in corrosive environments, or near the fatigue crack growth (FCG) threshold where crack-opening displacements are small [3]. Roughness-induced crack closure (RICC) is another mechanism whose signifi Corresponding author. Tel.: +1-757-864-8945; fax: +1-757-8648911. E-mail address: [email protected] (J.A. Newman).
0142-1123/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.ijfatigue.2004.02.001
cance is generally limited to threshold [4]; however, the scope of this paper is limited to the effects of two closure mechanisms, PICC and OICC. For Paris regime FCG, PICC is the dominant closure mechanism and OICC is a second-order effect [5]. Experimental results have shown high closure levels occur near the FCG threshold [2,3], however, analytical PICC models do not adequately predict this phenomenon in the absence of load history effects [5], possibly because OICC and RICC effects are neglected. Near the FCG threshold PICC and OICC are potentially first-order effects and both must be considered to achieve a more complete understanding of near-threshold crack closure. Analytical and experimental results are presented in this paper to show the combined effects of PICC and OICC near the FCG threshold. 2. Closure model To provide a more complete description of nearthreshold crack closure, the authors developed an analytical model that includes the contributions of PICC, RICC, and OICC [6,7]. Analytical results have shown that RICC effects become negligible, even at the FCG
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Fig. 1. Schematics of idealized crack closure behavior. (a) Constant-amplitude fatigue cycle; (b) crack configuration for maximum load; (c) crack configuration for minimum load.
threshold, when thick crack-mouth oxides are present [6]. Therefore, it is reasonable to neglect the contribution of RICC when considering crack growth in an aggressive environment, and the scope of this paper is limited to the interactions between PICC and OICC near the FCG threshold. The idealized crack-tip behavior is illustrated in Fig. 1 (neglecting roughness effects). In Fig. 1a, a constant-amplitude load cycle is shown, where the maximum and minimum crack-tip stress intensity factors (Kmax and Kmin) are identified and the corresponding crack-tip conditions are shown schematically in Figs. 1b and 1c, respectively. Here, crack-wake plasticity and oxide are shown as the shaded and solid regions, respectively. The crack-tip is shown to be open at Kmax and closed at Kmin. Crack
closure levels are analytically determined in terms of competing effects that tend to open (i.e. crack-opening displacements) and close the crack (i.e. both plasticity and oxide crack-wake effects); crack closure occurs when the crack opening is equal to the thickness of the crack-wake products. The analytical model requires three input parameters: elastic modulus (E), yield stress (ry), and oxide thickness (t). Crack opening displacements, calculated as the sum of elastic and plastic components, tend to increase with increasing distance from the crack tip, which makes crack closure more likely to occur near the crack tip. Analytical Rcl (=Kcl/Kmax) results for aluminum alloy 8009 (E ¼ 88 GPa; ry ¼ 420 MPa; R ¼ 0:05) are plotted in Fig. 2a as a function of DK for three
Fig. 2. Analytical crack closure results for aluminum alloy 8009 at R ¼ 0:05 and with different oxide layer thicknesses [6]. (a) Effect of oxide layer thickness; (b) conditions for fully closed crack.
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values of oxide thickness (t ¼ 0, 100 G, and 500 G plotted as solid, dotted, and dashed curves, respectively) [6]. For the special case of no oxide layer, the value of Rcl is constant (0.251). Although crack-tip and crackwake plasticity are proportional to DK and 1/ry, no other terms (e.g. oxide layer) appear in the analytical closure equations so DK and ry are algebraically cancelled. This is true only for the special case where RICC does not occur and t ¼ 0. Higher Rcl are observed with increasing oxide thickness, t. As DK increases and crack-tip opening displacement increases, Rcl values decrease and asymptotically approach the horizontal solid line. As DK decreases (near the FCG threshold), the oxide layer causes Rcl to increase until fully closed crack conditions occur, i.e. Rcl ¼ 1 and DKeff ¼ 0. The fully closed DK value (DKfc) is indicated for t ¼ 100 G (dotted curve) in Fig. 2a. The value of DKfc increases with increasing t, e.g., DKfc is greater for t ¼ 500 G than for t ¼ 100 G. The relationship between DKfc and t is plotted in Fig. 2b. As indicated, fully closed crack conditions occur in the shaded region below the solid curve. 3. Experimental procedure Fatigue crack growth tests were performed using computer-controlled servo-hydraulic testing machines. Back-face strain data were continuously monitored to determine crack length, and loads were adjusted to achieve programmed stress intensity factors. Closure loads were determined from compliance (load and displacement) data. Displacements were measured (1) near the crack tip, termed local determinations, and (2) at the specimen back face, far from the crack tip, termed global determinations. Experimental studies have shown that global closure determinations do not adequately characterize crack closure, especially near the FCG threshold [8,9]. Therefore, local closure determinations were made using an alternate non-contacting near-tip displacement measurement system called digital image displacement system (DIDS) [10]. During fatigue loading a series of high-magnification (500) digital images of the crack-tip region were recorded and analyzed to obtain local closure determinations. Results show that DIDS is better suited to detect neartip closure events than global compliance methods [8]. FCG tests were performed using eccentricallyloaded-single-edge-notch tension specimens made from aluminum alloy 8009 sheet material (2.3 mm thick, 38.1 mm wide) in the L–T orientation [11]. Alloy 8009 was used because the resulting fatigue crack surfaces are very smooth and nearly featureless, thus eliminating RICC as a closure mechanism [12]. As needed, OICC was eliminated by performing tests in ultra-high vacuum (UHV, <105 Pa).
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4. Experimental results and discussion Analytical and experimental results are compared to determine the validity of the closure model and to study the combined effects of PICC and OICC. First, the special case where only PICC occurs is examined before considering both PICC and OICC. This allows the PICC portion of the analytical model to be evaluated separately and provides a standard for comparison with the combined effects of PICC and OICC. 4.1. Plasticity-induced crack closure For the special case where PICC is the sole closure mechanism, analytical results (see Fig. 2 for t ¼ 0) indicate that Rcl is not affected by DK or ry (although the crack-tip displacements and crack-wake plasticity are). However, analytical results suggest that Rcl does vary with R, as seen in Fig. 3a. Here, material parameters appropriate for aluminum 8009 were used, although for this special case the same curve would be obtained for any material parameters. The diagonal dotted line corresponds to R ¼ Rcl ; closure only affects FCG for conditions above this line. As seen in the lower left corner of Fig. 3a, the analytical results cross the diagonal dotted line at approximately R ¼ 0:31, so closurefree conditions are expected at higher R values. Global closure data from aluminum 8009 constant pffiffiffiffi DK ¼ 6:6 MPa m FCG tests, performed in room-temperature laboratory air, are shown as triangular symbols in the figure. A comparison of the laboratory air and UHV results of Fig. 3b indicate the closure contribution of the laboratory-air oxide layer is negligible for pffiffiffiffi DK > 2 MPa m [6,7]. Good agreement is seen between analytical and experimental results and no closure was detected for value of R > 0:30. FCG tests (R ¼ 0:05) were conducted in UHV conditions to study the PICC mechanism in the absence OICC. The global and local closure data for UHV and laboratory air tests are compared with data from the open literature (McEvily [13] in Fig. 3b). The analytical result discussed earlier in Fig. 2a is plotted (solid line) and compared to the test data (symbols). The results in Fig. 3b show that experimental data, for both UHV and laboratory air environment, are in good agreement with the analytical result. Here, the closure contribution of the thin oxide layer produced in room-temperature laboratory air is not detectable, and PICC is pffiffiffiffi the dominant effect for DK > 2 MPa m. The results of Fig. 3b strongly suggest that Rcl is constant when PICC is dominant, and OICC and RICC effects are negligible. This finding is consistent with the analytical result that crack-wake plasticity and crack-tip displacements counteract each other resulting in a constant Rcl, in the absence of OICC and RICC, as shown in Figs. 2a and 3b.
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Fig. 3. Comparison of analytical results and experimental data for aluminum alloy 8009 at room temperature where PICC is the dominant closure mechanism [6]. (a) Relationship between Rcl and R; (b) Rcl results for R ¼ 0:05.
4.2. Plasticity- and oxide-induced crack closure To study the combined effects of PICC and OICC, FCG tests were conducted with an artificially produced oxide layer. Here, alumina particles (Al2O3) were injected into the crack opening to simulate a thick oxide layer. This approach was taken since laboratory air oxide layers were shown to have a negligible closure contribution. Alumina particles were selected because they are inert (i.e. do not readily react with aluminum), are available in large quantities in near uniform sizes, and are easily mixed with alcohol to form a slurry that could be injected into the crack opening with a syringe. After establishing a steady-state FCG rate during constant-DK tests (R ¼ 0:05), the crack was held at Kmax (to create the largest crack opening without crack-tip
overloads) while the alumina slurry was injected into the crack opening. After the alcohol evaporated, fatigue loading was resumed for approximately 10 cycles to make closure determinations, but without appreciable crack growth. Closure data are plotted in Fig. 4 for two alumina particles sizes (a) 0.05 lm diameter and (b) 0.30 lm diameter. Global and local closure data are shown as triangular and circular symbols, respectively, and analytical results are shown as the dashed curves. The analytical and experimental data are in good agreement for pffiffiffiffi pffiffiffiffi DK > 4 MPa m (Fig. 4a) and DK > 12 MPa m (Fig. 4b). Detailed fractographic studies, described elsewhere, showed that the differences between analytical and experimental results at lower DK are due to the
Fig. 4. Analytical and experimental crack closure results with an artificially produced oxide layer in cracked aluminum alloy 8009 (R ¼ 0:05, laboratory air, room temperature) specimens where PICC and OICC occur [6].
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wake roughness effects, and in an inert vacuum environment to eliminate crack-mouth oxide. To exacerbate oxide-induced closure effects, Al2O3 particulate slurry was used to simulate a thick crack-mouth oxide layer. Key findings of this study are as follows: . Crack-mouth oxide layers produce increases in closure levels (Rcl) as DK decreases; increases in Rcl are especially pronounced at low DK near the FCG threshold. At sufficiently low DK the crack becomes completely closed (i.e. DKeff ¼ 0) resulting in higher FCG threshold values. . For the special case where plasticity is the only closure mechanism, Rcl varies with load ratio, but does not vary with DK, elastic modulus, or yield stress. Fig. 5. Comparison of analytical and experimental crack closure results for pipe steel in a H2S brine solution (R ¼ 0:1, 4 Hz, room temperature) where PICC and OICC occur [14].
Al2O3 particles not reaching the crack-tip region as assumed in the analytical model [6]. In Fig. 5, analytical results are compared with analytical data from the open literature [14] for FCG testing on drill-pipe steel (R ¼ 0:1; E ¼ 210 GPa; ry ¼ 700 MPa) in a corrosive H2S brine solution where both PICC and OICC effects are expected. Closure data for decreasing DK and increasing DK testing are shown as triangular and circular symbols, respectively. Dark-colored crack-mouth oxide up to 1 lm thick was observed at the specimen surface for increasing DK conditions. Decreasing DK conditions appeared to produce less oxide. Analytical results are presented for t ¼ 0, 250 G, 500 G, and 1000 G (dotted, dashed, solid, and dash-dot-dot curves, respectively). The analytical and experimental results have very similar trends; the t ¼ 1000 G and 250 G curves are upper and lower bounds for all data. The values of DKfc for decreasing and increasing DK are indicated as A and B (at pffiffiffiffi pffiffiffiffi approximately 7 MPa m and 10 MPa m), and correspond to analytical results for t ¼ 360 G and 700 G, respectively. Although experimental measurements of oxide thickness are not available, the analytical result accurately predicts the trends (increasing Rcl with decreasing DK) observed in Fig. 5.
5. Conclusions Analytical closure model results were validated with experimental data where plasticity and oxide closure mechanisms were dominant. Fatigue crack growth tests were performed with aluminum alloy 8009, a fine-grain alloy with smooth crack surfaces to eliminate crack-
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