- Email: [email protected]
Fatigue Surface Crack Growth in Aluminum Alloys under Different Temperatures
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 160 (2016) 199 – 206
XVIII International Colloquium on Mechanical Fatigue of Metals (ICMFM XVIII)
FATIGUE SURFACE CRACK GROWTH IN ALUMINUM ALLOYS UNDER DIFFERENT TEMPERATURES R. Yarullin, I. Ishtyryakov * Kazan Scientific Center of Russian Academy of Sciences, Kazan, Russia
Abstract The variation of crack growth behavior is studied under cyclic axial tension fatigue loading for the different temperatures conditions. The subject for studies is cylindrical hollow specimens of B95 and D16 aluminum alloys with semi-elliptical surface cracks. By experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, crack opening displacements (COD), crack growth rate and aspect ratio were obtained. These relationships are useful for automation of experimental studies of surface crack growth. For the same specimen configuration and the different crack front position as a function of cyclic tension loading and temperatures conditions, the following constraint parameters were analyzed, namely, the non-singular T-stress, Tz -factor and the stress triaxiality parameter h in the 3D series of elastic-plastic computations. The governing parameter of the elastic-plastic stress fields In-factor distributions along various crack fronts was also determined from numerical calculations. The plastic stress intensity factor (SIF) approach was applied to the fatigue crack growth on the free surface of the hollow specimens as well as the deepest point of the semi-elliptical surface crack front. As result principal particularities of the fatigue surface crack growth rate as a function of temperature conditions are established. ©2016 2016The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the University of Oviedo. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the University of Oviedo Keywords: surface crack; aluminum alloys; tension fatigue loading; crack growth; different temperatures
1. Introduction The circular cylindrical metallic components of aircraft structure, power engineering elements, pressure vessel and piping are subjected to temperature variations from -60°C (213K) to more than 250°C (523K). In most cases,
* Corresponding author. Tel.: +7-843-236-31-02; fax: +7-843-236-31-02. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the University of Oviedo
doi:10.1016/j.proeng.2016.08.881
200
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
part-through flaws appear on the free surface of the cylinder and defects are approximately considered as semielliptical cracks. The fatigue growth analysis of surface cracks under different environmental conditions is very important for many engineering applications in order to quantify the structural safety according to the so-called damage tolerant design. Therefore fracture mechanics properties and material data at such temperature extremes are needed for material selection and design. Some researches provides detailed plastic limit load solutions for cylinders containing part-through external and internal surface cracks under combined axial tension, internal pressure and global bending [1]. The numerical analysis has been carried out to calculate the aspect ratio changes for different values of the geometrical parameters for both cylinder and surface flow [2]. The fatigue failure of cylindrical specimens often develops from surface flaws, and thus several analyses have been carried out to determine the stress intensity factors along the front of an edge defects and crack growth rate study on this base [3-8]. The sensitivity of aluminium alloys to environment changes have begun to explore else in the mid-1970s. During that time some researchers reported a significant reduction in the toughness and crack growth of several 7000 series aluminium sheet materials at low temperature [9-11]. Other researchers [12] have reported that the temperature dependence of fatigue crack formation and microstructure-scale growth from constituent particles in 7075-T651 and 7050-T651 is quantified via load induced fracture surface marker bands. The Paris law constants and threshold stress intensity range (ΔKth) have been measured for S460 and S980 structural grade base plate material at room temperature and -70°C. These results support the conclusions found in the literature that the fatigue crack growth rate decreases with lower temperatures until the Fatigue Ductile-Brittle Transition (FDBT), and then it increases again [13]. The growth of fatigue cracks at elevated temperatures (25–800°C) was studied [14]. The fatigue crack growth behaviour of a ferrite stainless steel has been investigated as a function of test temperature, thermal exposure and frequency at intermediate growth rates. In general, fatigue crack growth rates increased with increasing temperature and in the temperature range 500-700 °C growth rates were described by a kinetic process with an activation energy of 48 kJ/mole. Furthermore, other environmental effects should be taken into account to assess the structural component safety: for example, the humidity and salt air content play an important role especially under fatigue loading. In this paper, only the temperature effects are considered and the fatigue crack propagation is examined. Firstly, experimental results of fatigue crack growth for a crack starting from a semi-elliptical edge notch in cylindrical hollow specimens under low/high and room temperature are given. The influence of different temperature conditions on fatigue life of cylindrical specimens is discussed. The relations of crack opening displacement and crack length on the free surface of specimens are obtained. Using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. Secondly, constrain parameters behaviour and governing parameter of elastic-plastic stress field distribution along the crack front was obtained using FEM analysis. Third, crack growth interpretation is performed using the traditional elastic and new plastic stress intensity factors [15-17]. Different crack growth rate is observed in the direction of the deepest point of the crack front with respect to the free surface of the hollow cylindrical specimen as a function of temperature conditions. 2. Experimental study The test materials are most popular in aircraft industry aluminum alloys D16T and B95AT (analogue of 2024 and 7075 aluminum). All tests were carried out at room (23°C or 296K), low (-60°C or 213K) and high (250°C or 523K) temperature. Low/high temperature tests were performed by using following equipment: Bi-00-101 UTM Test System with fatigue rated axial dynamic load cell (capacity +/- 50kN) and Bi-06-303 series axial extensometer; Climatic Chamber CM Envirosystems with temperature range: -60°C to 250°C (Fig.1). The first step of experimental study was determination the main mechanical properties of considered alloys. The tension testing was performed in accordance with ASTM E8. Obtained main mechanical properties are listed in Table 1, where E is the Young’s modulus, σs is the nominal ultimate tensile strength, σ0 is the monotonic tensile yield strength, σu is the true ultimate tensile strength, δ is the elongation, ψ is the reduction of area, n is the strain hardening exponent and α is the strain hardening coefficient. The distributions of this data for both materials are
201
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
presented in Fig. 2 as a function of test temperature. The results show that the D16T alloy is more sensitive to temperature changes. For both alloys the increasing of test temperature is leading to degradation in mechanical properties.
Fig. 1. Low/high temperature test equipment. Table 1. Main mechanical properties of aluminum alloys under different temperature. Material D16T B95AT
Temperature, K 213 296 523 213 296 523
σ0, MPa 406 438 294 506 520 415
σS, MPa 545 594 339 621 586 422
σu, MPa 633 665 371 694 775 436
α
n
E, GPa
δ, %
ψ, %
2.56 1.54 1.44 1.64 1.44 -
5.32 5.86 8.39 7.71 10.37 -
79.232 76.557 75.246 75.935 75.274 72.737
15 11 4 11 14 6
17 11 27 13 36 37
Fig. 2. Main mechanical properties distributions as a function of temperature for both aluminum alloys.
The next step of experimental study was crack growth rate tests of cylindrical hollow specimens with semielliptical surface cracks. The hollow cylindrical specimen geometry configuration is shown in Fig. 3. The diameter is equal to 28 mm in the test section and the length is equal to 130 mm. Using electro spark method surface edge cracks were cut with initial flaw depths b0 3.0 mm for elliptical-arc initial edge notch. The geometric parameters of the specimen test section and of the growing crack are shown in Figs. 3. In this figure, b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2a. The crack length b is
202
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
obtained by measuring the distance between the advancing crack break through point and the notch break through point. The depth of the initial curvilinear edge notch is denoted by a and the initial notch length by h. Both the optical microscope measurements and the crack opening displacement (COD) method are used to monitor and calculate both crack depth and crack length during the tests. The COD is measured on the free hollow specimen cylindrical surface, in the central plane of symmetry as shown in Fig. 1. All tests are carried out with sinusoidal loading form with load control. For the cyclic tension fatigue tests, the specimens are tested with an applied maximum nominal stress equal to 65 MPa and with a frequency value 10 Hz.
Fig. 3. Details of the hollow specimen geometry and initial notch.
The stress ratio R=0.1 was periodically interspersed with marker loading R=0.5 to mark the fracture surface. In this manner the marker loading does not induce load history effects or overload retardation [8]. The typical fracture surface marks on the post mortem cross section of specimens are shown in Fig. 4 for different temperature conditions.
Fig. 4. Fracture surface of the hollow specimens at different temperatures: (a) 213K, (b) 296K, (c) 523K.
From the crack front shape obtained in this way, the relations between the relative crack depth a/D and the surface crack chord length b/D can be measured using a comparison microscope (Fig. 5). In addition, based on periodically measured increments of surface crack chord length 'b, the curve of surface crack propagation versus cycle numbers db/dN can be obtained. Afterwards, utilizing the relation of crack depth versus surface crack chord length, it is possible to obtain the crack growth rates da/dN in the depth direction. The evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using COD and the microscope. Fig. 6 shows relations between COD and crack length b on free surface for both alloys and three temperatures. It is found strong correlation between these two parameters which can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. It should be noted that the
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
measurements of crack length b by microscope on free surface of specimens for the test on climatic chamber are impossible. For these specimens crack length b was obtained on the base of experimental relations represented on Fig. 6.
Fig. 5. Aspect ratio versus crack depth (a) and crack length (b) for different temperature conditions.
Fig. 7 represents the surface crack growth rate db/dN versus COD on the hollow cylindrical specimens. It is found that the crack growth rate along the external surface direction as a function of COD described as a various curves with a small scatter band of the experimental results for both tested aluminum alloys. Also, looking at Fig.5b and considering changes in the general durability of the specimens in low/high temperature test, significant differences in the crack growth rate in the depth direction a and on the free surface b of hollow specimens under the above temperature conditions are expected.
Fig. 6. Relationship between COD and crack length on free surface of hollow specimen under different temperature conditions.
Fig. 7. Crack growth rate on the free surface of hollow specimen versus COD for different temperature conditions.
3. Numerical study FEM analysis was performed for semi-elliptical cracks in the cylindrical hollow specimens to determine the stress strain fields along the crack front. Typical finite element meshes for the cylindrical hollow specimens are illustrated in Fig. 8. Numerical analysis for the elastic constraint parameters in the form of the non-singular T-stress and TZ –factor, as well as the elastic-plastic constraint parameters, in the form of the local stress triaxiality h and In-factor along the experimental crack fronts in cylindrical hollow specimens for the cyclic tension testing at the room temperature conditions was performed in [8].
203
204
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
Fig. 8. Typical FEM-mesh for cylindrical hollow specimens with semi-elliptical surface crack.
Primarily, the numerical calculations of the present study are concerned with the determination of the elastic and elastic-plastic constraint parameters along the crack front in the cylindrical hollow specimens under different temperature conditions. All the stress-strain state and constraint parameters at the crack tip for each type of the tested specimens were calculated by using the corresponding static material properties listed in Table 1 and ranges of the testing loads. These distributions correspond to the crack front positions at the accumulated number of loading cycles: initial front, intermediate front and final failure front (Fig. 9).
Fig. 9. FEM crack front geometry: initial (a), intermediate (b, c), final (d).
The distributions of the elastic and elastic-plastic constraint parameters along the crack front in the hollow specimen for both alloys and three temperatures are plotted in Fig. 10, 11.
Fig. 10. Constraint parameter distributions along crack front (1-initial, 2-intermediate, 3-final) for different temperature conditions.
205
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
The constraint parameter is plotted against the normalized coordinate R. In this plot R = 0.0 is the crack border (the specimen free surface) while R = 1.0 is the mid-plane of the hollow specimen thickness. It can be observed that all constraint parameters essentially changed along the crack front from the free surface toward the mid-plane. It should be noted that the front with the number three in Fig. 10 corresponds to condition when the surface crack becomes completely through-thickness and intersects the cylinder wall. 1.2
1.2
D16T
B95AT 213K
1.1
296K 523K
In-factor
In-factor
1 1 0.9
0.8
213K
0.8
0.6
296K
0.7
523K
0.6
0.4 0
0.2
0.4
0.6
R
0.8
1
1.2
0
0.2
0.4
R
0.6
0.8
1
Fig. 11. In-factor distributions along crack front for different temperature conditions.
The distributions along the crack front of the governing parameter for the elastic-plastic solution in the form of an In-integral measured above used to determination the plastic stress intensity factor (SIF) Kp in pure Mode I for cylindrical hollow specimens as follows:
ª K12 º « » 2 ¬D V 0 I n T ¼
KP
1 n 1
ª§ V · 2 SO Y 2 a w º 1 «¨¨ ¸¸ » «¬© V 0 ¹ D I n T »¼
1 n 1
;
V SO Y1 a w
K1
(1)
where K1 K1 / w is normalized by a characteristic size of cracked body elastic stress intensity factor and E' E for plane stress and E' E 1 Q 2 for plane strain. In the above equations, D and n are the hardening parameters, O a w is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen diameter), V is the nominal stress, and V0 is the yield stress. The procedure for calculating the governing parameter of the elastic–plastic stress–strain fields in the form of In for the different specimen geometries by means of the elastic–plastic FE-analysis of the near crack-tip stress-strain fields suggested by [15-17].
0.8
0.8
6
B95AT
D16T
0.7
plastic SIF
elastic SIF [MPa*m^0.5]
8
296K
0.6
296K
0.5
4
523K
0.7
523K
plastic SIF
0.6
213K
0.5
213K 0.4
0.4
0.3
0.3
2 0
0.2
0.4
R
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
0
0.2
R
Fig. 12. Elastic and plastic stress intensity factor distributions for initial crack front.
0.4
0.6
R
0.8
1
206
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
In Fig.12 shown the distributions of the elastic and plastic SIF's for the same tensile loading conditions along the same crack front. Fig. 12 gives a clear illustration of the necessity to take into account the plastic properties of the material in the interpretation of the characteristics of the material resistance to crack propagation. In contrast to the elastic SIF K1, the plastic SIF Kp shows very useful effect of the sensitivity to the plastic properties of the tested materials. It can be seen from Fig. 12 that the plastic SIF gradually increases by increasing the test temperature conditions. The data presented very obvious advantages of using the plastic stress intensity factors to characterize the material's resistance to cyclic crack growth. 4. Conclusions The main mechanical properties of aluminum alloys at different temperature conditions were obtained. It is found, that for both alloys the increasing of test temperature is leading to degradation in mechanical properties. The variation of crack growth behavior in cylindrical hollow specimens for the different temperatures conditions was studied. By experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, crack opening displacements (COD), crack growth rate and aspect ratio were obtained. For the same specimen configuration and the different crack front position as a function of cyclic tension loading and temperatures conditions the elastic and elastic-plastic constraint parameters were analyzed. The distributions of governing parameter of the elastic-plastic stress fields - In-factor and plastic stress intensity factors - Kp along various crack fronts was determined. It is stated that the elastic-plastic stress intensity factor, which is sensitive to the constraint effects and elastic-plastic material properties, is attractive as the self-dependent unified parameter for characterization of the material fracture resistance properties. References [1] Kim, Y.J., Shim, D.J., Nikbin, K., Kim, Y.Jin, Hwang, S.S., Kim, J.S., Finite element based plastic limit loads for cylinders with part-through surface cracks under combined loading, Int. J. of Pressure Vessels and Piping, 80 (2003) 527-540. [2] Shlyannikov, V.N., Fatigue shape analysis for internal surface flow in a pressurized hollow cylinder, Int. J. of Pressure Vessels and Piping, 77 (2000) 227-234. [3] Newman, J.C., Raju, I.S., An empirical stress-intensity factor equation for the surface crack, Eng. Fract. Mech., 15 (1-2) (1981) 185-192. [4] Carpinteri, A., Brighenti, R., Part-through cracks in round bars under cyclic combined axial and bending loading, Int. J. Fatigue, 18 (1) (1996) 33-39. [5] Yang, F.P., Kuang, Z.B., Shlyannikov, V.N., Fatigue crack growth for straight-fronted edge crack in a round bar, Int. J. Fatigue, 28 (2006) 431–437. [6] Predan, J., Mocilnic, V., Gubeljak, N., Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion, Eng. Fract. Mech., 105 (2013) 152-168. [7] Citarella, R., Lepore, M., Slyannikov, V., Yarullin, R., Fatigue surface crack growth in cylindrical specimen under combined loading, Eng. Fract. Mech., 131 (2014) 439-453. [8] Slyannikov, V., Yarullin, R., Ishtyryakov, I., Surface crack growth in cylindrical hollow specimen subject to tension and torsion, Frattura ed Integrita Structurale, 33 (2015) 335-344. [9] Pettit, D.E., Van Orden, J.M., Evaluation of Temperature Effects on Crack Growth in Aluminum Sheet Material, Fracture Mechanics, ASTM STP 677, 1979, 106-124. [10] Cox, J.M., Pettit, D.E., Langenbeck, S.L., The Effect of Temperature on the Fatigue and Fracture Properties of 7475-T761 Aluminum, Fatigue at Low Temperature, ASTM STP 857, 1985, 241-256. [11] Abelkis, P.R., Harmon, M.B., Hayman, E.L., MacKay, T.L., Orlando, J., Low Temperature and and Loading Frequency Effects on Crack Growth and Fracture Toughness of 2024 and 7475 Aluminum, Fatigue at Low Temperature, ASTM STP 857, 1985, 257-273. [12] James, T.B., Vipul, K.G., Sean, R.A., Richard, P.G., Effect of low temperature on fatigue crack formation anf microstructure-scale propagation in legacy and modern Al-Zn-Cu alloys, Int. J. Fatigue, 55 (2013) 268-275. [13] Carey, L.W., The effect of low temperatures on the fatigue of high-strength structural grade steels, 20th European Conference on Fracture, Procedia Materials Science 3 (2014) 209–214. [14] Kamel, M., Jones, J.W., Effects of temperature and frequency on fatigue crack growth in 18% Cr ferritic stainless steel, Int. J. Fatigue, 15 No 3 (1993) 163-171. [15] Shlyannikov, V.N., Tumanov, A.V., Characterization of crack tip stress fields in test specimens using mode mixity parameters, Int. J. Fract., 185 (2014) 49-76. [16] Shlyannikov, V.N., Zakharov, A.P., Multiaxial crack growth rate under variable T-stress, Eng. Fract. Mech., 123 (2014) 86–99. [17] Shlyannikov, V.N., Tumanov, A.V., Zakharov, A.P., The mixed mode crack growth rate in cruciform specimens subject to biaxial loading, Theoret. Appl. Fract. Mech., 73 (2014) 68-81.
ScienceDirect Procedia Engineering 160 (2016) 199 – 206
XVIII International Colloquium on Mechanical Fatigue of Metals (ICMFM XVIII)
FATIGUE SURFACE CRACK GROWTH IN ALUMINUM ALLOYS UNDER DIFFERENT TEMPERATURES R. Yarullin, I. Ishtyryakov * Kazan Scientific Center of Russian Academy of Sciences, Kazan, Russia
Abstract The variation of crack growth behavior is studied under cyclic axial tension fatigue loading for the different temperatures conditions. The subject for studies is cylindrical hollow specimens of B95 and D16 aluminum alloys with semi-elliptical surface cracks. By experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, crack opening displacements (COD), crack growth rate and aspect ratio were obtained. These relationships are useful for automation of experimental studies of surface crack growth. For the same specimen configuration and the different crack front position as a function of cyclic tension loading and temperatures conditions, the following constraint parameters were analyzed, namely, the non-singular T-stress, Tz -factor and the stress triaxiality parameter h in the 3D series of elastic-plastic computations. The governing parameter of the elastic-plastic stress fields In-factor distributions along various crack fronts was also determined from numerical calculations. The plastic stress intensity factor (SIF) approach was applied to the fatigue crack growth on the free surface of the hollow specimens as well as the deepest point of the semi-elliptical surface crack front. As result principal particularities of the fatigue surface crack growth rate as a function of temperature conditions are established. ©2016 2016The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the University of Oviedo. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the University of Oviedo Keywords: surface crack; aluminum alloys; tension fatigue loading; crack growth; different temperatures
1. Introduction The circular cylindrical metallic components of aircraft structure, power engineering elements, pressure vessel and piping are subjected to temperature variations from -60°C (213K) to more than 250°C (523K). In most cases,
* Corresponding author. Tel.: +7-843-236-31-02; fax: +7-843-236-31-02. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the University of Oviedo
doi:10.1016/j.proeng.2016.08.881
200
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
part-through flaws appear on the free surface of the cylinder and defects are approximately considered as semielliptical cracks. The fatigue growth analysis of surface cracks under different environmental conditions is very important for many engineering applications in order to quantify the structural safety according to the so-called damage tolerant design. Therefore fracture mechanics properties and material data at such temperature extremes are needed for material selection and design. Some researches provides detailed plastic limit load solutions for cylinders containing part-through external and internal surface cracks under combined axial tension, internal pressure and global bending [1]. The numerical analysis has been carried out to calculate the aspect ratio changes for different values of the geometrical parameters for both cylinder and surface flow [2]. The fatigue failure of cylindrical specimens often develops from surface flaws, and thus several analyses have been carried out to determine the stress intensity factors along the front of an edge defects and crack growth rate study on this base [3-8]. The sensitivity of aluminium alloys to environment changes have begun to explore else in the mid-1970s. During that time some researchers reported a significant reduction in the toughness and crack growth of several 7000 series aluminium sheet materials at low temperature [9-11]. Other researchers [12] have reported that the temperature dependence of fatigue crack formation and microstructure-scale growth from constituent particles in 7075-T651 and 7050-T651 is quantified via load induced fracture surface marker bands. The Paris law constants and threshold stress intensity range (ΔKth) have been measured for S460 and S980 structural grade base plate material at room temperature and -70°C. These results support the conclusions found in the literature that the fatigue crack growth rate decreases with lower temperatures until the Fatigue Ductile-Brittle Transition (FDBT), and then it increases again [13]. The growth of fatigue cracks at elevated temperatures (25–800°C) was studied [14]. The fatigue crack growth behaviour of a ferrite stainless steel has been investigated as a function of test temperature, thermal exposure and frequency at intermediate growth rates. In general, fatigue crack growth rates increased with increasing temperature and in the temperature range 500-700 °C growth rates were described by a kinetic process with an activation energy of 48 kJ/mole. Furthermore, other environmental effects should be taken into account to assess the structural component safety: for example, the humidity and salt air content play an important role especially under fatigue loading. In this paper, only the temperature effects are considered and the fatigue crack propagation is examined. Firstly, experimental results of fatigue crack growth for a crack starting from a semi-elliptical edge notch in cylindrical hollow specimens under low/high and room temperature are given. The influence of different temperature conditions on fatigue life of cylindrical specimens is discussed. The relations of crack opening displacement and crack length on the free surface of specimens are obtained. Using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. Secondly, constrain parameters behaviour and governing parameter of elastic-plastic stress field distribution along the crack front was obtained using FEM analysis. Third, crack growth interpretation is performed using the traditional elastic and new plastic stress intensity factors [15-17]. Different crack growth rate is observed in the direction of the deepest point of the crack front with respect to the free surface of the hollow cylindrical specimen as a function of temperature conditions. 2. Experimental study The test materials are most popular in aircraft industry aluminum alloys D16T and B95AT (analogue of 2024 and 7075 aluminum). All tests were carried out at room (23°C or 296K), low (-60°C or 213K) and high (250°C or 523K) temperature. Low/high temperature tests were performed by using following equipment: Bi-00-101 UTM Test System with fatigue rated axial dynamic load cell (capacity +/- 50kN) and Bi-06-303 series axial extensometer; Climatic Chamber CM Envirosystems with temperature range: -60°C to 250°C (Fig.1). The first step of experimental study was determination the main mechanical properties of considered alloys. The tension testing was performed in accordance with ASTM E8. Obtained main mechanical properties are listed in Table 1, where E is the Young’s modulus, σs is the nominal ultimate tensile strength, σ0 is the monotonic tensile yield strength, σu is the true ultimate tensile strength, δ is the elongation, ψ is the reduction of area, n is the strain hardening exponent and α is the strain hardening coefficient. The distributions of this data for both materials are
201
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
presented in Fig. 2 as a function of test temperature. The results show that the D16T alloy is more sensitive to temperature changes. For both alloys the increasing of test temperature is leading to degradation in mechanical properties.
Fig. 1. Low/high temperature test equipment. Table 1. Main mechanical properties of aluminum alloys under different temperature. Material D16T B95AT
Temperature, K 213 296 523 213 296 523
σ0, MPa 406 438 294 506 520 415
σS, MPa 545 594 339 621 586 422
σu, MPa 633 665 371 694 775 436
α
n
E, GPa
δ, %
ψ, %
2.56 1.54 1.44 1.64 1.44 -
5.32 5.86 8.39 7.71 10.37 -
79.232 76.557 75.246 75.935 75.274 72.737
15 11 4 11 14 6
17 11 27 13 36 37
Fig. 2. Main mechanical properties distributions as a function of temperature for both aluminum alloys.
The next step of experimental study was crack growth rate tests of cylindrical hollow specimens with semielliptical surface cracks. The hollow cylindrical specimen geometry configuration is shown in Fig. 3. The diameter is equal to 28 mm in the test section and the length is equal to 130 mm. Using electro spark method surface edge cracks were cut with initial flaw depths b0 3.0 mm for elliptical-arc initial edge notch. The geometric parameters of the specimen test section and of the growing crack are shown in Figs. 3. In this figure, b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2a. The crack length b is
202
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
obtained by measuring the distance between the advancing crack break through point and the notch break through point. The depth of the initial curvilinear edge notch is denoted by a and the initial notch length by h. Both the optical microscope measurements and the crack opening displacement (COD) method are used to monitor and calculate both crack depth and crack length during the tests. The COD is measured on the free hollow specimen cylindrical surface, in the central plane of symmetry as shown in Fig. 1. All tests are carried out with sinusoidal loading form with load control. For the cyclic tension fatigue tests, the specimens are tested with an applied maximum nominal stress equal to 65 MPa and with a frequency value 10 Hz.
Fig. 3. Details of the hollow specimen geometry and initial notch.
The stress ratio R=0.1 was periodically interspersed with marker loading R=0.5 to mark the fracture surface. In this manner the marker loading does not induce load history effects or overload retardation [8]. The typical fracture surface marks on the post mortem cross section of specimens are shown in Fig. 4 for different temperature conditions.
Fig. 4. Fracture surface of the hollow specimens at different temperatures: (a) 213K, (b) 296K, (c) 523K.
From the crack front shape obtained in this way, the relations between the relative crack depth a/D and the surface crack chord length b/D can be measured using a comparison microscope (Fig. 5). In addition, based on periodically measured increments of surface crack chord length 'b, the curve of surface crack propagation versus cycle numbers db/dN can be obtained. Afterwards, utilizing the relation of crack depth versus surface crack chord length, it is possible to obtain the crack growth rates da/dN in the depth direction. The evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using COD and the microscope. Fig. 6 shows relations between COD and crack length b on free surface for both alloys and three temperatures. It is found strong correlation between these two parameters which can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. It should be noted that the
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
measurements of crack length b by microscope on free surface of specimens for the test on climatic chamber are impossible. For these specimens crack length b was obtained on the base of experimental relations represented on Fig. 6.
Fig. 5. Aspect ratio versus crack depth (a) and crack length (b) for different temperature conditions.
Fig. 7 represents the surface crack growth rate db/dN versus COD on the hollow cylindrical specimens. It is found that the crack growth rate along the external surface direction as a function of COD described as a various curves with a small scatter band of the experimental results for both tested aluminum alloys. Also, looking at Fig.5b and considering changes in the general durability of the specimens in low/high temperature test, significant differences in the crack growth rate in the depth direction a and on the free surface b of hollow specimens under the above temperature conditions are expected.
Fig. 6. Relationship between COD and crack length on free surface of hollow specimen under different temperature conditions.
Fig. 7. Crack growth rate on the free surface of hollow specimen versus COD for different temperature conditions.
3. Numerical study FEM analysis was performed for semi-elliptical cracks in the cylindrical hollow specimens to determine the stress strain fields along the crack front. Typical finite element meshes for the cylindrical hollow specimens are illustrated in Fig. 8. Numerical analysis for the elastic constraint parameters in the form of the non-singular T-stress and TZ –factor, as well as the elastic-plastic constraint parameters, in the form of the local stress triaxiality h and In-factor along the experimental crack fronts in cylindrical hollow specimens for the cyclic tension testing at the room temperature conditions was performed in [8].
203
204
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
Fig. 8. Typical FEM-mesh for cylindrical hollow specimens with semi-elliptical surface crack.
Primarily, the numerical calculations of the present study are concerned with the determination of the elastic and elastic-plastic constraint parameters along the crack front in the cylindrical hollow specimens under different temperature conditions. All the stress-strain state and constraint parameters at the crack tip for each type of the tested specimens were calculated by using the corresponding static material properties listed in Table 1 and ranges of the testing loads. These distributions correspond to the crack front positions at the accumulated number of loading cycles: initial front, intermediate front and final failure front (Fig. 9).
Fig. 9. FEM crack front geometry: initial (a), intermediate (b, c), final (d).
The distributions of the elastic and elastic-plastic constraint parameters along the crack front in the hollow specimen for both alloys and three temperatures are plotted in Fig. 10, 11.
Fig. 10. Constraint parameter distributions along crack front (1-initial, 2-intermediate, 3-final) for different temperature conditions.
205
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
The constraint parameter is plotted against the normalized coordinate R. In this plot R = 0.0 is the crack border (the specimen free surface) while R = 1.0 is the mid-plane of the hollow specimen thickness. It can be observed that all constraint parameters essentially changed along the crack front from the free surface toward the mid-plane. It should be noted that the front with the number three in Fig. 10 corresponds to condition when the surface crack becomes completely through-thickness and intersects the cylinder wall. 1.2
1.2
D16T
B95AT 213K
1.1
296K 523K
In-factor
In-factor
1 1 0.9
0.8
213K
0.8
0.6
296K
0.7
523K
0.6
0.4 0
0.2
0.4
0.6
R
0.8
1
1.2
0
0.2
0.4
R
0.6
0.8
1
Fig. 11. In-factor distributions along crack front for different temperature conditions.
The distributions along the crack front of the governing parameter for the elastic-plastic solution in the form of an In-integral measured above used to determination the plastic stress intensity factor (SIF) Kp in pure Mode I for cylindrical hollow specimens as follows:
ª K12 º « » 2 ¬D V 0 I n T ¼
KP
1 n 1
ª§ V · 2 SO Y 2 a w º 1 «¨¨ ¸¸ » «¬© V 0 ¹ D I n T »¼
1 n 1
;
V SO Y1 a w
K1
(1)
where K1 K1 / w is normalized by a characteristic size of cracked body elastic stress intensity factor and E' E for plane stress and E' E 1 Q 2 for plane strain. In the above equations, D and n are the hardening parameters, O a w is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen diameter), V is the nominal stress, and V0 is the yield stress. The procedure for calculating the governing parameter of the elastic–plastic stress–strain fields in the form of In for the different specimen geometries by means of the elastic–plastic FE-analysis of the near crack-tip stress-strain fields suggested by [15-17].
0.8
0.8
6
B95AT
D16T
0.7
plastic SIF
elastic SIF [MPa*m^0.5]
8
296K
0.6
296K
0.5
4
523K
0.7
523K
plastic SIF
0.6
213K
0.5
213K 0.4
0.4
0.3
0.3
2 0
0.2
0.4
R
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
0
0.2
R
Fig. 12. Elastic and plastic stress intensity factor distributions for initial crack front.
0.4
0.6
R
0.8
1
206
R. Yarullin and I. Ishtyryakov / Procedia Engineering 160 (2016) 199 – 206
In Fig.12 shown the distributions of the elastic and plastic SIF's for the same tensile loading conditions along the same crack front. Fig. 12 gives a clear illustration of the necessity to take into account the plastic properties of the material in the interpretation of the characteristics of the material resistance to crack propagation. In contrast to the elastic SIF K1, the plastic SIF Kp shows very useful effect of the sensitivity to the plastic properties of the tested materials. It can be seen from Fig. 12 that the plastic SIF gradually increases by increasing the test temperature conditions. The data presented very obvious advantages of using the plastic stress intensity factors to characterize the material's resistance to cyclic crack growth. 4. Conclusions The main mechanical properties of aluminum alloys at different temperature conditions were obtained. It is found, that for both alloys the increasing of test temperature is leading to degradation in mechanical properties. The variation of crack growth behavior in cylindrical hollow specimens for the different temperatures conditions was studied. By experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, crack opening displacements (COD), crack growth rate and aspect ratio were obtained. For the same specimen configuration and the different crack front position as a function of cyclic tension loading and temperatures conditions the elastic and elastic-plastic constraint parameters were analyzed. The distributions of governing parameter of the elastic-plastic stress fields - In-factor and plastic stress intensity factors - Kp along various crack fronts was determined. It is stated that the elastic-plastic stress intensity factor, which is sensitive to the constraint effects and elastic-plastic material properties, is attractive as the self-dependent unified parameter for characterization of the material fracture resistance properties. References [1] Kim, Y.J., Shim, D.J., Nikbin, K., Kim, Y.Jin, Hwang, S.S., Kim, J.S., Finite element based plastic limit loads for cylinders with part-through surface cracks under combined loading, Int. J. of Pressure Vessels and Piping, 80 (2003) 527-540. [2] Shlyannikov, V.N., Fatigue shape analysis for internal surface flow in a pressurized hollow cylinder, Int. J. of Pressure Vessels and Piping, 77 (2000) 227-234. [3] Newman, J.C., Raju, I.S., An empirical stress-intensity factor equation for the surface crack, Eng. Fract. Mech., 15 (1-2) (1981) 185-192. [4] Carpinteri, A., Brighenti, R., Part-through cracks in round bars under cyclic combined axial and bending loading, Int. J. Fatigue, 18 (1) (1996) 33-39. [5] Yang, F.P., Kuang, Z.B., Shlyannikov, V.N., Fatigue crack growth for straight-fronted edge crack in a round bar, Int. J. Fatigue, 28 (2006) 431–437. [6] Predan, J., Mocilnic, V., Gubeljak, N., Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion, Eng. Fract. Mech., 105 (2013) 152-168. [7] Citarella, R., Lepore, M., Slyannikov, V., Yarullin, R., Fatigue surface crack growth in cylindrical specimen under combined loading, Eng. Fract. Mech., 131 (2014) 439-453. [8] Slyannikov, V., Yarullin, R., Ishtyryakov, I., Surface crack growth in cylindrical hollow specimen subject to tension and torsion, Frattura ed Integrita Structurale, 33 (2015) 335-344. [9] Pettit, D.E., Van Orden, J.M., Evaluation of Temperature Effects on Crack Growth in Aluminum Sheet Material, Fracture Mechanics, ASTM STP 677, 1979, 106-124. [10] Cox, J.M., Pettit, D.E., Langenbeck, S.L., The Effect of Temperature on the Fatigue and Fracture Properties of 7475-T761 Aluminum, Fatigue at Low Temperature, ASTM STP 857, 1985, 241-256. [11] Abelkis, P.R., Harmon, M.B., Hayman, E.L., MacKay, T.L., Orlando, J., Low Temperature and and Loading Frequency Effects on Crack Growth and Fracture Toughness of 2024 and 7475 Aluminum, Fatigue at Low Temperature, ASTM STP 857, 1985, 257-273. [12] James, T.B., Vipul, K.G., Sean, R.A., Richard, P.G., Effect of low temperature on fatigue crack formation anf microstructure-scale propagation in legacy and modern Al-Zn-Cu alloys, Int. J. Fatigue, 55 (2013) 268-275. [13] Carey, L.W., The effect of low temperatures on the fatigue of high-strength structural grade steels, 20th European Conference on Fracture, Procedia Materials Science 3 (2014) 209–214. [14] Kamel, M., Jones, J.W., Effects of temperature and frequency on fatigue crack growth in 18% Cr ferritic stainless steel, Int. J. Fatigue, 15 No 3 (1993) 163-171. [15] Shlyannikov, V.N., Tumanov, A.V., Characterization of crack tip stress fields in test specimens using mode mixity parameters, Int. J. Fract., 185 (2014) 49-76. [16] Shlyannikov, V.N., Zakharov, A.P., Multiaxial crack growth rate under variable T-stress, Eng. Fract. Mech., 123 (2014) 86–99. [17] Shlyannikov, V.N., Tumanov, A.V., Zakharov, A.P., The mixed mode crack growth rate in cruciform specimens subject to biaxial loading, Theoret. Appl. Fract. Mech., 73 (2014) 68-81.