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Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones
Accepted Manuscript Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones Xiaofan He, Yinghao Dong, Yuhai Li, Xiangming Wang PII: DOI: Reference:
S0142-1123(17)30370-5 http://dx.doi.org/10.1016/j.ijfatigue.2017.09.003 JIJF 4456
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
12 July 2017 23 August 2017 4 September 2017
Please cite this article as: He, X., Dong, Y., Li, Y., Wang, X., Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue. 2017.09.003
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Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones Xiaofan Hea,∗, Yinghao Donga , Yuhai Lib , Xiangming Wangc a School
of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China b Aviation Industry Corporation of China, Beijing 100022, China c Shenyang Aircraft Design Institute, Shenyang 110035, China
Abstract Fatigue crack growth (FCG) tests were conducted to investigate the behavior and laws of crack growth in diffusion-bonded laminates of Ti-6Al-4V (2mm+2mm +2mm+2mm) with three unbonded zones, the initial crack being a semi-elliptical surface crack. Post-test fractographic analyses indicate the crack growth in the laminate characterized by four distinct stages. The crack initially propagates in the first layer as a semi-elliptical surface crack (Stage I). After the surface crack penetrates the first layer, the crack becomes a through crack, which continues propagating in the first layer (Stage II). When the through crack arrives at the boundary of the first unbonded zone, it evolves into a part-through crack, during which crack growth rate keeps decreasing (Stage III). After that, the crack propagates as a part-through crack until the laminate fractures (Stage IV). It also indicates that the crack-growth-deceleration effect of the first unbonded zone is of more significance compared with the other unbonded zones. With the marker bands on the fractography, FCG data was obtained. Then we used the finite element method to calculate stress intensity factors for the laminates and obtained the relationship between FCG rate (da/dN ) and stress intensity factor range (∆K). The analysis on the da/dN − ∆K curve shows that the decrease in ∆K is an important factor, although not the sole factor, contributing to the crack growth deceleration near the boundary of the unbonded zone. Keywords: fatigue crack growth, Ti-6Al-4V, diffusion bonding, laminate, unbonded zone
1. Introduction Ti-6Al-4V, as an α + β alloy, has good corrosion resistance, high specific strength and excellent weldability, justifying its wide utilization in aerospace, shipbuilding, petrochemical and automotive industry [1–3]. However, titanium ∗ Corresponding
author. Tel.: +86 01082315738. Email address: [email protected] (Xiaofan He)
Preprint submitted to Elsevier
August 23, 2017
Nomenclature a a1 a2 C m n N R ∆K ∆Kmin CA DB FCG FE FEM OM SEM
half-crack length distance of the outmost point on the left crack front from y-axis distance of the outmost point on the right crack front from y-axis coefficient in Paris-Erdogan law number of a vs. N pairs in a data set exponent in Paris-Erdogan law number of load cycles stress ratio stress intensity factor range the minimum of stress intensity factor range constant amplitude diffusion bonding fatigue crack growth finite element finite element method optical microscope scanning electron microscope
alloy is difficult to machine and expensive to use. To reduce the cost of processing, multiple forming processes have been developed since the 1950s, with diffusion bonding being a significant part of it. Diffusion bonding (DB) is a solid-state bonding process, during which bonds at atomic level are formed due to microscopic plastic deformation and diffusion of atoms between two solid surfaces in intimate contact under controlled conditions of time, temperature and pressure [4, 5]. There is no heat affected zone or macroscopic deformation associated with the bond, resulting in accurate dimensional control. This allows diffusion bonding to be successfully applied in titanium alloy forming. The diffusion-bonded laminate of Ti-6Al-4V (hereafter referred as Ti64) is a typical titanium-alloy structure, with the manufacturing process shown in Fig. 1. The large bond area associated with the laminate is likely to lead to interfacial defects, thus compromising bond strength. Many investigations have been conducted over the effect of interfacial defects on the strength of diffusion-bonded titanium alloy structures. Zhu [6] studied the influence of void ratio and maximum defect size on the joint strength, and produced the minimum void ratio and defect size that can adversely affect the fatigue strength of DB joints. CepedaJim´enez [7] examined the effect of interfacial defects on the shear strength and fracture toughness of DB laminates of Ti64. Wu [8] proposed that inclusions in the interface were responsible for the decrease in fatigue strength of DB joints. It also indicates that small single voids in the interface are insignifi-
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Fig. 1. Schematic of the manufacture of diffusion-bonded laminate of Ti-6Al-4V.
cant, but clusters of voids can remarkably reduce fatigue life [9, 10]. For a long time, researchers have been engaged in optimizing the diffusion bonding process to eliminate interfacial defects. However, interfacial defects are inevitable for diffusion-bonded laminates. Conventionally, interfacial defects can reduce structural strength. Experimental studies have shown that fatigue strength of DB laminates of titanium alloy can be adversely affected by the interfacial defects when out-of-plane loads (i.e. loads perpendicular to the interface) apply [6, 8, 10]. However, under the condition of in-plane loads (i.e. loads parallel to the interface), the effect of interfacial defects is insignificant [11–13]. Therefore, DB laminates of titanium alloy are suitable for applications sustaining in-plane loads, such as beam and flange. Damage tolerance of structures receives much attention due to its critical role in safeguarding structural safety and economy of aircraft. Titanium alloy is known for its good fatigue strength but unsatisfactory damage tolerance property [14, 15]. To improve the damage tolerance property of DB laminates of Ti64, Wang [16] developed a novel laminated structure, DB laminate with unbonded zones as shown in Fig. 2. Solder-resistant powder is placed between the mating surfaces prior to diffusion bonding, and laminates with localized unbonded zones can be made through diffusion bonding [17]. This concept abandons the zero-defect interface that has always been sought, and intentionally enlarges the interfacial defects. According to the design concept associated with the back-to-back structure [18], large interfacial defects are expected to retard crack growth under in-plane loading, and the fatigue crack growth (FCG) life can thus be extended. To verify the beneficial effect of the unbonded zone, fatigue tests were performed for the DB laminate of Ti64 with a centered hole and circular unbonded zones under in-plane cyclic loading [13, 19, 20]. The test results show that FCG rate decreases as the crack bypasses the boundary of the unbonded zone. FCG simulations were made for the DB laminate with unbonded zones [21–23]. The
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Fig. 2. Diffusion-bonded laminate with unbonded zones under in-plane loading.
simulations also illustrate the beneficial effect of the unbonded zone. Obviously, DB laminates of Ti64 with unbonded zones have good damage tolerance property. As design is allowed over the shape, size and position of the unbonded zone, the damage tolerance property is expected to be further improved through optimal design, which drives an urgent need for understanding the FCG behavior and FCG laws for the DB laminate with unbonded zones. To achieve this end, we first performed FCG tests for DB laminates of Ti64 with unbonded zones under in-plane tensile cyclic loading. With the aid of marker load, the whole process of crack growth was reconstructed. Second, quantitative fractographic analyses were conducted under the optical microscope and the scanning electron microscope, with the macroscopic and microscopic FCG behavior illustrated. Third, stress intensity factors were calculated for the crack fronts observed on the fractography, followed by an analysis of the variation of stress intensity factor range with crack length. The FCG laws were subsequently obtained, with the mechanism of crack growth deceleration near the boundary of the unbonded zone provided. This paper intends to shed light on the FCG property of the DB laminate with unbonded zones to further improve its optimal design. 2. Fatigue crack growth test 2.1. Specimen The DB laminate of Ti64 with three circular unbonded zones is illustrated in Fig. 3 (a), with compositions of Ti64 listed in Table 1. The material directions and processing technics are detailed below.
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(a)
(b)
Fig. 3. DB laminate with unbonded zones (a) specimen geometry, (b) initial defect.
Table 1. Compositions of Ti64.
Chemical compositions
Al
V
Mass fraction (wt%)
5.5–6.5
3.5–4.5
Fe
C
0.08 0.01
N
H
0.3
0.1
O
Ti
0.001 Bal.
The 2 mm-thickness Ti64 plate that had been annealed at 800 ℃ for 1 hour and then air-cooled to the ambient temperature was used to fabricate DB laminates following the procedures: (1) stacking four 2 mm-thickness plates in the same direction (L-T), with solder-resistant powder placed within a circular zone (diameter = 15 mm) between the mating surfaces, (2) keeping the combination in a vacuum chamber for 90 minutes under bonding temperature of 920 ℃ and pressure of 1.5 MPa, and (3) cooling to 580 ℃ in the chamber and then air cooling to the ambient temperature. Then, machine the DB laminate to the specimen shown in Fig. 3 (a).
(a)
(b)
Fig. 4. Metallography of the cross section of the DB laminate (a) metallography away from the interface, (b) metallography near the interface.
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Fig. 4 shows the metallography for the DB laminate. It is found that the metallography away from the interface and that near the interface show little differences and both include equiaxial primary α phase and intergranular β phase. Prior to the test, a semi-circular defect was made in the center of the specimen surface through electric spark discharge to facilitate precracking, the radius of the defect being 0.5 mm, as shown in Fig. 3 (b). Three laminate specimens were prepared, numbered as 1, 2 and 3. 2.2. Fatigue load Constant amplitude (CA) load was used in the FCG test, with the stress ratio (i.e. R) being 0.1 and peak stress 230 MPa. The stress level was the same for all the specimens. The size of the gauge section was measured to calculate fatigue load. Given the three-dimensional crack front, conventional methods for crack size measurement such as visual method, compliance method and electric potential difference method [24] were inapplicable to this case. To solve this problem, marker load was used in the test. By inserting marker load blocks into the CA load with R = 0.1 at a specific interval, marker bands, served as a tool for crack size determination, were expected to manifest on the fractography. The peak stress of marker load was set to be equal to that of the CA load with R = 0.1 to avoid load interaction, and the load ratio was elevated to 0.7. To produce legible marker bands on the fractography, a preliminary crack growth analysis was conducted to determine the number of marker loads in one load block, and the number was taken as 8,000 cycles. Moreover, visual measurements of crack surface length were conducted during the test to determine the interval between two neighboring marker load blocks. The interval determined are listed in Table A.1 to A.3 for each specimen (see Appendix A). 2.3. Test procedure The FCG test was performed on a 500kN-capacity servo-hydraulic MTS testing machine at room temperature. The testing machine was closed-loop controlled by an external controller, MTS TestStar IIs, in the load control mode with error within 1%. Axial load was applied in the form of sinusoidal wave with load frequency of 8 Hz. Firstly, fatigue load was stepped-down for precracking [24]; three levels of cyclic loads were involved, with R = 0.1 and peak stresses being 345 MPa, 276 MPa and 221 MPa respectively. During the application of fatigue load, the crack surface length was measured via a travelling microscope with grating scale. The number of load cycles was controlled to produce half-crack length increment of 0.5 mm at each load level. Fatigue precracking was completed when the halfcrack length reached 2 mm. After that, the fatigue load mentioned in Section 2.2 was applied until the specimen fractured. Finally, fractographic analyses were carried out under the optical microscope (OM) and the scanning electron microscope (SEM).
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3. Analysis on the fatigue crack growth behavior and laws 3.1. Macroscopic fatigue crack growth behavior Fig. 5 shows the fractography of the DB laminates. It can be seen that the fatigue propagation region is flat and bright, distinguishing it from the final fracture region characterized by coarse and dark morphology along with shear lips. Fine dark lines can be seen from the fatigue propagation region. The lines are the marker bands produced by the marker load. Each marker band is the crack front at a specific time, and the space between two neighboring marker bands is the crack size increment upon the application of one load block with R = 0.1. Compared with the crack size increment, the width of the marker band is negligible. All the information of crack growth can be retrieved through measurements of the marker band positions. As shown in Fig. 5, the crack growth in the DB laminate covers four stages:
(a)
(b)
(c) Fig. 5. Fractography of the DB laminates with unbonded zones, (a)–(c) correspond to Specimen 1–3. In (a), A represents the direction along x-axis, B along −x-axis and C along y-axis.
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• a semi-elliptical surface crack propagates along the width direction and the thickness direction in Layer 1 (Stage I); • the semi-elliptical surface crack penetrates Layer 1 and becomes a through crack that continues propagating along the width direction in Layer 1 (Stage II). The crack front is curved and lags behind in the free surface vicinity; • the through crack approaches the boundary of the first unbonded zone and evolves into a part-through crack with the shape of J (hereafter referred as J crack) due to the FCG rate variation along the crack front (Stage III); • J cracks propagate along three directions (Direction A, B and C in Fig. 5 (a)) and successively propagate into Layer 2, Layer 3 and Layer 4 (Stage IV). In this stage, J cracks propagate in Layer 1 and Layer 2 after the boundary of the first unbonded zone is bypassed. After J cracks bypass the boundary of the second unbonded zone, J cracks simultaneously propagate in Layer 1, Layer 2 and Layer 3, with the crack fronts in Layer 3 and Layer 2 propagating along the same direction with different FCG rates. The crack fronts propagate in Layer 2 until the left and the right crack front coalesce. After J cracks bypass the boundary of the third unbonded zone, crack growth becomes unstable and soon leads to specimen fracture. In addition, varying degrees of asymmetric crack growth can be observed from the fractography of the DB laminates. The degree of asymmetric crack growth increases from Specimen 1 to 3, which can be accounted for by the increasing eccentricity of the unbonded zone (Fig. 5 (c)). From the fractography, the crack growth near the boundary of the first unbonded zone is complicated. To resolve the marker bands in that area, we used the SEM to obtain the fractography shown in Fig. 6. Fig. 6 illustrates the crack growth in Specimen 1. We then plotted the evolution of crack fronts as shown in Fig. 7. It is noted that the crack front shape begins to change after its intersection with the boundary of the unbonded zone (Curve 1). Upon the application of fatigue load, the crack front becomes increasingly tortuous (see Curve 2), during which the intersection between the crack front and the unbonded zone remains stationary until the crack becomes a J crack (Curve 3). Afterwards, the J crack begins to simultaneously propagate in Layer 1 and Layer 2. During the crack front change from Curve 1 to Curve 3, 8,000 load cycles elapse, comparing with 33,335 load cycles from Curve 1 to final fracture.
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Fig. 6. Fractography near the boundary of the first unbonded zone. Bright lines are the marker bands, i.e. crack fronts at different time.
Fig. 7. Evolution of crack fronts with arrows indicating local FCG directions.
3.2. Microscopic fatigue crack growth behavior The fractography of the DB laminates at high magnification is shown in Fig. 8. Fig. 8 (a) and (b) respectively illustrate the fractography near the boundary of the first unbonded zone and that away from the interface. It can be found that the fracture surface is dominated by transgranular fracture. Plastic fatigue striations can also be identified. Relatively large steps and secondary cracks can be seen in Fig. 8 (a), and the fractography near the boundary of the first unbonded zone is coarser than that away from the interface. We used the SEM to examine all the fractography of the DB laminates and found such features commonly existing near the boundary of the first unbonded zone. The unbonded zone introduces free surfaces, leading to plane stress state near the free surfaces. As the plain strain state dominates in the material away from free surfaces, out-of-plane stress may arise in the free surface vicinity, which promotes the formation of secondary cracks. The formation of steps may be 9
associated with adjacent secondary cracks and the local stress state near the boundary of the unbonded zone.
(a)
(b) Fig. 8. Fractography of the DB laminate (a) fractography near the boundary of the first unbonded zone, (b) fractography away from the interface. Relatively large steps and secondary cracks can be seen in (a). Fatigue striations can be seen in (b).
3.3. Variation of crack length with number of load cycles An optical microscope with grating scale was employed in the measurement of marker band positions, with the error controlled within 0.01 mm. Crack length 2a is the sum of a1 and a2 , see Fig. 5 (a). It should be noted that a1 (a2 ) represents the distance of the outmost point on the left (right) crack front from y-axis, the left and the right crack front corresponding to the same number of load cycles.
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Fig. 9. Variation of half-crack length with number of load cycles.
To facilitate the comparison, initial half-crack length is taken as 2 mm. The variation of half-crack length with number of load cycles (i.e. a − N curve) is shown in Fig. 9. Small scatters can be observed from the a − N curves for the three specimens. It is indicated that crack growth deceleration occurs when the half-crack length ranges from 7.5 mm to 11 mm, corresponding to the crack growth near the boundary of the first unbonded zone. 3.4. Variation of fatigue crack growth rate with crack length This section will discuss the variation of FCG rate with crack length for the DB laminate. Considering the asymmetric crack growth in the DB laminate, we define the crack length as the distance of the outmost point on the left or the right crack front from y-axis (Fig. 5 (a)). The modified secant method (Eq. (1)) is used to calculate the FCG rate. In Eq. (1), m represents the number of a vs. N pairs in a data set. a i+1 − ai i=1 Ni+1 − Ni 1 a da ai − ai−1 i+1 − ai = + 1
Fig. 10. Variation of FCG rate with crack length and corresponding fractography for Specimen 2.
• Stage II: da/dN increases with a till the left crack reaches 7.45 mm and the right crack reaches 5.4 mm, the distance of the left (right) boundary of the first unbonded zone from y-axis being 8.609 mm (6.352 mm); • Stage III: da/dN decreases as the through crack approaches the boundary of the first unbonded zone and evolves into a J crack. When the J crack emerges, da/dN arrives at the minimum that is close to the da/dN of the initial through crack; the first unbonded zone effectively decelerates crack growth; • Stage IV: da/dN increases as the propagation of J cracks till the specimen fractures. It should be noted that the variation of da/dN with a is not synchronous for the left and the right crack. This can be justified by the eccentricity of the first unbonded zone, which leads to the crack closer to the boundary of the unbonded zone decelerating earlier. The reason for the decrease in da/dN will be discussed in the next section. 4. Mechanism of crack growth deceleration Fractographic analyses demonstrate that the evolution of crack fronts near the boundary of the first unbonded zone is a crack growth process. To identify the reason for the crack growth deceleration, we calculated the stress intensity factor for every marker band on the fractography.
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4.1. Stress intensity factor calculation The finite element method (FEM) was used to calculate the stress intensity factors for the DB laminate due to its complex geometry and crack front shapes. Regarding the material property, modulus of elasticity was defined as 110 GPa and Poisson’s ratio as 0.34 [25]. The finite element (FE) software ABAQUS (version 6.16) was employ to create FE models. The modeling methods are detailed below: (1) Modeling of crack fronts By using the OM and the SEM, the coordinates of a series of nodes were determined for each marker band on the fractography, with the distance between two neighboring nodes less than 0.2 mm. With the coordinates, cubic spline curves modeling virtual crack fronts were generated, as shown in Fig. 11. (2) Modeling of unbonded zones The thickness of the unbonded zone was measured under the SEM, the value being approximately 20 µm. Therefore, three disc cavities with the thickness of 20 µm were placed in the FE model, as shown in Fig. 11. (3) Element types The domain integral method [26] provided by ABAQUS was used to calculate stress intensity factors. A ring of quadratic wedge elements (C3D15) was used to define the crack front, for which the mid-side nodes on the sides connected to the crack front were moved to the 1/4 point nearest the crack front to create one over square root r singularity of the stress/strain field at the crack front. The remainder of the contour integral region was defined by several rings of quadratic hexahedral elements (C3D20) as paths for J integral calculation (see Fig. 12). In the other parts, quadratic tetrahedron elements (C3D10) or quadratic hexahedral elements (C3D20) were used, as shown in Fig. 12. (4) Boundary conditions In the FCG test, the specimen was gripped by the friction grips of the testing machine; one clamped end of the specimen was fixed and the other was only allowed to have displacements along the loading direction. Given the asymmetric rigidity of the cracked DB laminate, we modeled the virtual clamped end condition in ABAQUS. As the rigidity of the grips was much larger than that of specimens, the clamped ends could be rigidized, with all degrees of freedom restrained for one clamped end and displacements along the loading direction allowed for the other. Uniform tensile stress of 230 MPa was applied to the clamped end to allow displacements along the loading direction (see Fig. 13).
Fig. 11. Modeling of crack fronts and unbonded zones.
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(a)
(b) Fig. 12. Finite element model (a) global mesh, (b) mesh around the crack front and unbonded zones.
Fig. 13. Clamped end condition, w representing the displacement along z-axis.
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4.2. Variation of stress intensity factor with crack length The opening mode stress intensity factors were extracted for the outmost points used to determine crack length. Taking Specimen 2 as an instance, the variation of stress intensity factor range (∆K) and FCG rate (da/dN ) with crack length (a) is illustrated in Fig. 14. Apparently, the variation of ∆K with a is consistent with that of da/dN . When the through crack approaches the boundary of the first unbonded zone, both ∆K and da/dN decrease. ∆K keeps decreasing during the crack front change from the through crack to a J crack, which continues to the minimum, ∆Kmin . ∆Kmin corresponds to the initial J crack as is the case for da/dN . Given the fact that the variations of ∆K and da/dN show the same trend, it is concluded that the stress intensity factor range, ∆K, is responsible for the decrease in da/dN .
(a)
(b) Fig. 14. Variation of FCG rate and stress intensity factor range with crack length for the crack growth (a) on the left side and (b) the right side of Specimen 2.
15
(a)
(b)
(c) Fig. 15. da/dN − ∆K curves for (a) Specimen 1, (b) Specimen 2, and (c) Specimen 3.
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4.3. Analysis of fatigue crack growth rate To determine whether the decrease in da/dN is solely determined by the decrease in ∆K, we plotted the da/dN − ∆K curve in a log-log scale as shown in Fig. 15. It is illustrated that: • Stage II: when the through crack approaches the boundary of the first unbonded zone, the slope of da/dN − ∆K curve decreases to that of J cracks. da/dN then decreases with ∆K, and this segment of da/dN −∆K curve, however, falls below the da/dN − ∆K curve for the early through crack rather than coincides with the latter; • Stage III: da/dN decreases with ∆K till da/dN arrives at the minimum. This segment of da/dN − ∆K curve lies between those for the through crack and the J crack; • Stage IV: da/dN increases with ∆K, and good linear relationship can be found between da/dN and ∆K in the log-log scale. A zigzag is observed in the da/dN − ∆K curve, corresponding to the crack growth near the boundary of the first unbonded zone. The zigzag at the da/dN − ∆K curve indicates the reduction of crack growth rate larger than that resulting from the decrease in ∆K. Therefore, the decrease in ∆K may not be the sole factor contributing to the crack growth deceleration near the boundary of the first unbonded zone. The da/dN − ∆K curves for the three specimens are put together and linear fitted as shown in Fig. 16. The Paris parameters (i.e. C and n in da/dN = C(∆K)n ) are 5.61 × 10−9 and 3.26.
Fig. 16. da/dN − ∆K curves and regression line for the DB laminates.
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5. Discussion As shown in Fig. 14, da/dN and ∆K decrease as the crack approaches the boundary of the first unbonded zone. However, when the crack approaches the boundaries of the other unbonded zones, neither da/dN nor ∆K decreases. This phenomenon is assumed to be associated with the front shape and the FCG direction of the crack approaching the boundary of the unbonded zone. The crack bypassing the boundary of the unbonded zone shows the ongoing process of crack propagation along −x-axis and y-axis. When the crack approaches the boundary of the first unbonded zone, it simply propagates along x-axis as a through crack. It is difficult for such a crack to develop propagation along −x-axis and y-axis. As a result, the crack-growth-deceleration effect of the first unbonded zone is significant. The crack approaching the second or the third unbonded zone originally propagates along −x-axis and y-axis. It is therefore easier for such a crack to bypass the boundary of the unbonded zone. Thus, the second and the third unbonded zone cannot be depended on to decelerate crack growth. 6. Conclusions In this paper, fatigue crack growth tests have been conducted for diffusionbonded laminates of Ti64 with unbonded zones. The crack growth behavior and laws are investigated, with the mechanism of crack growth deceleration near the boundary of the unbonded zone illustrated. The conclusions are as follows: (1) The crack growth in the DB laminate covers four stages: 1) a semielliptical surface crack propagates in the first layer; 2) the semi-elliptical surface crack changes to a through crack that continues propagating in the first layer; 3) the through crack evolves into a J crack when bypassing the boundary of the first unbonded zone; 4) J cracks propagate until the laminate fractures. (2) The decrease in stress intensity factor ranges is an important factor, although not the sole factor, contributing to the crack growth deceleration near the boundary of the first unbonded zone. (3) The crack-growth-deceleration effect of the first unbonded zone is of more significance compared with the other unbonded zones. Acknowledgements The authors gratefully acknowledge the support from National Natural Science Foundation of China (No. 11772027), National Key Research and Development Program of China (No. 2017YFB 1104003) and Aeronautical Science Foundation of China (No. 28163701002).
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Appendix A. Details of the load blocks The following three tables list the number of load cycles in a load block with R = 0.1 along with the number of load blocks for each specimen. It should be noted that there is a load block containing 8,000 cycles of constant amplitude load with R = 0.7 between two neighboring load blocks with R = 0.1. Table A.1. Load blocks for Specimen 1.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3
5000 4000 1000
2 5 13
Table A.2. Load blocks for Specimen 2.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3 4
5000 3000 3500 1000
5 16 4 8
Table A.3. Load blocks for Specimen 3.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3 4
5000 3000 3500 1000
5 16 4 34
21
Graphical Abstract
da/dN - a
da/dN - a and ΔK - a
da/dN - ΔK
Highlights
Fatigue crack growth behavior and laws are illustrated.
The first unbonded zone can effectively decelerate fatigue crack growth.
The mechanism of crack growth deceleration is revealed.
S0142-1123(17)30370-5 http://dx.doi.org/10.1016/j.ijfatigue.2017.09.003 JIJF 4456
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
12 July 2017 23 August 2017 4 September 2017
Please cite this article as: He, X., Dong, Y., Li, Y., Wang, X., Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue. 2017.09.003
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Fatigue crack growth in diffusion-bonded Ti-6Al-4V laminate with unbonded zones Xiaofan Hea,∗, Yinghao Donga , Yuhai Lib , Xiangming Wangc a School
of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China b Aviation Industry Corporation of China, Beijing 100022, China c Shenyang Aircraft Design Institute, Shenyang 110035, China
Abstract Fatigue crack growth (FCG) tests were conducted to investigate the behavior and laws of crack growth in diffusion-bonded laminates of Ti-6Al-4V (2mm+2mm +2mm+2mm) with three unbonded zones, the initial crack being a semi-elliptical surface crack. Post-test fractographic analyses indicate the crack growth in the laminate characterized by four distinct stages. The crack initially propagates in the first layer as a semi-elliptical surface crack (Stage I). After the surface crack penetrates the first layer, the crack becomes a through crack, which continues propagating in the first layer (Stage II). When the through crack arrives at the boundary of the first unbonded zone, it evolves into a part-through crack, during which crack growth rate keeps decreasing (Stage III). After that, the crack propagates as a part-through crack until the laminate fractures (Stage IV). It also indicates that the crack-growth-deceleration effect of the first unbonded zone is of more significance compared with the other unbonded zones. With the marker bands on the fractography, FCG data was obtained. Then we used the finite element method to calculate stress intensity factors for the laminates and obtained the relationship between FCG rate (da/dN ) and stress intensity factor range (∆K). The analysis on the da/dN − ∆K curve shows that the decrease in ∆K is an important factor, although not the sole factor, contributing to the crack growth deceleration near the boundary of the unbonded zone. Keywords: fatigue crack growth, Ti-6Al-4V, diffusion bonding, laminate, unbonded zone
1. Introduction Ti-6Al-4V, as an α + β alloy, has good corrosion resistance, high specific strength and excellent weldability, justifying its wide utilization in aerospace, shipbuilding, petrochemical and automotive industry [1–3]. However, titanium ∗ Corresponding
author. Tel.: +86 01082315738. Email address: [email protected] (Xiaofan He)
Preprint submitted to Elsevier
August 23, 2017
Nomenclature a a1 a2 C m n N R ∆K ∆Kmin CA DB FCG FE FEM OM SEM
half-crack length distance of the outmost point on the left crack front from y-axis distance of the outmost point on the right crack front from y-axis coefficient in Paris-Erdogan law number of a vs. N pairs in a data set exponent in Paris-Erdogan law number of load cycles stress ratio stress intensity factor range the minimum of stress intensity factor range constant amplitude diffusion bonding fatigue crack growth finite element finite element method optical microscope scanning electron microscope
alloy is difficult to machine and expensive to use. To reduce the cost of processing, multiple forming processes have been developed since the 1950s, with diffusion bonding being a significant part of it. Diffusion bonding (DB) is a solid-state bonding process, during which bonds at atomic level are formed due to microscopic plastic deformation and diffusion of atoms between two solid surfaces in intimate contact under controlled conditions of time, temperature and pressure [4, 5]. There is no heat affected zone or macroscopic deformation associated with the bond, resulting in accurate dimensional control. This allows diffusion bonding to be successfully applied in titanium alloy forming. The diffusion-bonded laminate of Ti-6Al-4V (hereafter referred as Ti64) is a typical titanium-alloy structure, with the manufacturing process shown in Fig. 1. The large bond area associated with the laminate is likely to lead to interfacial defects, thus compromising bond strength. Many investigations have been conducted over the effect of interfacial defects on the strength of diffusion-bonded titanium alloy structures. Zhu [6] studied the influence of void ratio and maximum defect size on the joint strength, and produced the minimum void ratio and defect size that can adversely affect the fatigue strength of DB joints. CepedaJim´enez [7] examined the effect of interfacial defects on the shear strength and fracture toughness of DB laminates of Ti64. Wu [8] proposed that inclusions in the interface were responsible for the decrease in fatigue strength of DB joints. It also indicates that small single voids in the interface are insignifi-
2
Fig. 1. Schematic of the manufacture of diffusion-bonded laminate of Ti-6Al-4V.
cant, but clusters of voids can remarkably reduce fatigue life [9, 10]. For a long time, researchers have been engaged in optimizing the diffusion bonding process to eliminate interfacial defects. However, interfacial defects are inevitable for diffusion-bonded laminates. Conventionally, interfacial defects can reduce structural strength. Experimental studies have shown that fatigue strength of DB laminates of titanium alloy can be adversely affected by the interfacial defects when out-of-plane loads (i.e. loads perpendicular to the interface) apply [6, 8, 10]. However, under the condition of in-plane loads (i.e. loads parallel to the interface), the effect of interfacial defects is insignificant [11–13]. Therefore, DB laminates of titanium alloy are suitable for applications sustaining in-plane loads, such as beam and flange. Damage tolerance of structures receives much attention due to its critical role in safeguarding structural safety and economy of aircraft. Titanium alloy is known for its good fatigue strength but unsatisfactory damage tolerance property [14, 15]. To improve the damage tolerance property of DB laminates of Ti64, Wang [16] developed a novel laminated structure, DB laminate with unbonded zones as shown in Fig. 2. Solder-resistant powder is placed between the mating surfaces prior to diffusion bonding, and laminates with localized unbonded zones can be made through diffusion bonding [17]. This concept abandons the zero-defect interface that has always been sought, and intentionally enlarges the interfacial defects. According to the design concept associated with the back-to-back structure [18], large interfacial defects are expected to retard crack growth under in-plane loading, and the fatigue crack growth (FCG) life can thus be extended. To verify the beneficial effect of the unbonded zone, fatigue tests were performed for the DB laminate of Ti64 with a centered hole and circular unbonded zones under in-plane cyclic loading [13, 19, 20]. The test results show that FCG rate decreases as the crack bypasses the boundary of the unbonded zone. FCG simulations were made for the DB laminate with unbonded zones [21–23]. The
3
Fig. 2. Diffusion-bonded laminate with unbonded zones under in-plane loading.
simulations also illustrate the beneficial effect of the unbonded zone. Obviously, DB laminates of Ti64 with unbonded zones have good damage tolerance property. As design is allowed over the shape, size and position of the unbonded zone, the damage tolerance property is expected to be further improved through optimal design, which drives an urgent need for understanding the FCG behavior and FCG laws for the DB laminate with unbonded zones. To achieve this end, we first performed FCG tests for DB laminates of Ti64 with unbonded zones under in-plane tensile cyclic loading. With the aid of marker load, the whole process of crack growth was reconstructed. Second, quantitative fractographic analyses were conducted under the optical microscope and the scanning electron microscope, with the macroscopic and microscopic FCG behavior illustrated. Third, stress intensity factors were calculated for the crack fronts observed on the fractography, followed by an analysis of the variation of stress intensity factor range with crack length. The FCG laws were subsequently obtained, with the mechanism of crack growth deceleration near the boundary of the unbonded zone provided. This paper intends to shed light on the FCG property of the DB laminate with unbonded zones to further improve its optimal design. 2. Fatigue crack growth test 2.1. Specimen The DB laminate of Ti64 with three circular unbonded zones is illustrated in Fig. 3 (a), with compositions of Ti64 listed in Table 1. The material directions and processing technics are detailed below.
4
(a)
(b)
Fig. 3. DB laminate with unbonded zones (a) specimen geometry, (b) initial defect.
Table 1. Compositions of Ti64.
Chemical compositions
Al
V
Mass fraction (wt%)
5.5–6.5
3.5–4.5
Fe
C
0.08 0.01
N
H
0.3
0.1
O
Ti
0.001 Bal.
The 2 mm-thickness Ti64 plate that had been annealed at 800 ℃ for 1 hour and then air-cooled to the ambient temperature was used to fabricate DB laminates following the procedures: (1) stacking four 2 mm-thickness plates in the same direction (L-T), with solder-resistant powder placed within a circular zone (diameter = 15 mm) between the mating surfaces, (2) keeping the combination in a vacuum chamber for 90 minutes under bonding temperature of 920 ℃ and pressure of 1.5 MPa, and (3) cooling to 580 ℃ in the chamber and then air cooling to the ambient temperature. Then, machine the DB laminate to the specimen shown in Fig. 3 (a).
(a)
(b)
Fig. 4. Metallography of the cross section of the DB laminate (a) metallography away from the interface, (b) metallography near the interface.
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Fig. 4 shows the metallography for the DB laminate. It is found that the metallography away from the interface and that near the interface show little differences and both include equiaxial primary α phase and intergranular β phase. Prior to the test, a semi-circular defect was made in the center of the specimen surface through electric spark discharge to facilitate precracking, the radius of the defect being 0.5 mm, as shown in Fig. 3 (b). Three laminate specimens were prepared, numbered as 1, 2 and 3. 2.2. Fatigue load Constant amplitude (CA) load was used in the FCG test, with the stress ratio (i.e. R) being 0.1 and peak stress 230 MPa. The stress level was the same for all the specimens. The size of the gauge section was measured to calculate fatigue load. Given the three-dimensional crack front, conventional methods for crack size measurement such as visual method, compliance method and electric potential difference method [24] were inapplicable to this case. To solve this problem, marker load was used in the test. By inserting marker load blocks into the CA load with R = 0.1 at a specific interval, marker bands, served as a tool for crack size determination, were expected to manifest on the fractography. The peak stress of marker load was set to be equal to that of the CA load with R = 0.1 to avoid load interaction, and the load ratio was elevated to 0.7. To produce legible marker bands on the fractography, a preliminary crack growth analysis was conducted to determine the number of marker loads in one load block, and the number was taken as 8,000 cycles. Moreover, visual measurements of crack surface length were conducted during the test to determine the interval between two neighboring marker load blocks. The interval determined are listed in Table A.1 to A.3 for each specimen (see Appendix A). 2.3. Test procedure The FCG test was performed on a 500kN-capacity servo-hydraulic MTS testing machine at room temperature. The testing machine was closed-loop controlled by an external controller, MTS TestStar IIs, in the load control mode with error within 1%. Axial load was applied in the form of sinusoidal wave with load frequency of 8 Hz. Firstly, fatigue load was stepped-down for precracking [24]; three levels of cyclic loads were involved, with R = 0.1 and peak stresses being 345 MPa, 276 MPa and 221 MPa respectively. During the application of fatigue load, the crack surface length was measured via a travelling microscope with grating scale. The number of load cycles was controlled to produce half-crack length increment of 0.5 mm at each load level. Fatigue precracking was completed when the halfcrack length reached 2 mm. After that, the fatigue load mentioned in Section 2.2 was applied until the specimen fractured. Finally, fractographic analyses were carried out under the optical microscope (OM) and the scanning electron microscope (SEM).
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3. Analysis on the fatigue crack growth behavior and laws 3.1. Macroscopic fatigue crack growth behavior Fig. 5 shows the fractography of the DB laminates. It can be seen that the fatigue propagation region is flat and bright, distinguishing it from the final fracture region characterized by coarse and dark morphology along with shear lips. Fine dark lines can be seen from the fatigue propagation region. The lines are the marker bands produced by the marker load. Each marker band is the crack front at a specific time, and the space between two neighboring marker bands is the crack size increment upon the application of one load block with R = 0.1. Compared with the crack size increment, the width of the marker band is negligible. All the information of crack growth can be retrieved through measurements of the marker band positions. As shown in Fig. 5, the crack growth in the DB laminate covers four stages:
(a)
(b)
(c) Fig. 5. Fractography of the DB laminates with unbonded zones, (a)–(c) correspond to Specimen 1–3. In (a), A represents the direction along x-axis, B along −x-axis and C along y-axis.
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• a semi-elliptical surface crack propagates along the width direction and the thickness direction in Layer 1 (Stage I); • the semi-elliptical surface crack penetrates Layer 1 and becomes a through crack that continues propagating along the width direction in Layer 1 (Stage II). The crack front is curved and lags behind in the free surface vicinity; • the through crack approaches the boundary of the first unbonded zone and evolves into a part-through crack with the shape of J (hereafter referred as J crack) due to the FCG rate variation along the crack front (Stage III); • J cracks propagate along three directions (Direction A, B and C in Fig. 5 (a)) and successively propagate into Layer 2, Layer 3 and Layer 4 (Stage IV). In this stage, J cracks propagate in Layer 1 and Layer 2 after the boundary of the first unbonded zone is bypassed. After J cracks bypass the boundary of the second unbonded zone, J cracks simultaneously propagate in Layer 1, Layer 2 and Layer 3, with the crack fronts in Layer 3 and Layer 2 propagating along the same direction with different FCG rates. The crack fronts propagate in Layer 2 until the left and the right crack front coalesce. After J cracks bypass the boundary of the third unbonded zone, crack growth becomes unstable and soon leads to specimen fracture. In addition, varying degrees of asymmetric crack growth can be observed from the fractography of the DB laminates. The degree of asymmetric crack growth increases from Specimen 1 to 3, which can be accounted for by the increasing eccentricity of the unbonded zone (Fig. 5 (c)). From the fractography, the crack growth near the boundary of the first unbonded zone is complicated. To resolve the marker bands in that area, we used the SEM to obtain the fractography shown in Fig. 6. Fig. 6 illustrates the crack growth in Specimen 1. We then plotted the evolution of crack fronts as shown in Fig. 7. It is noted that the crack front shape begins to change after its intersection with the boundary of the unbonded zone (Curve 1). Upon the application of fatigue load, the crack front becomes increasingly tortuous (see Curve 2), during which the intersection between the crack front and the unbonded zone remains stationary until the crack becomes a J crack (Curve 3). Afterwards, the J crack begins to simultaneously propagate in Layer 1 and Layer 2. During the crack front change from Curve 1 to Curve 3, 8,000 load cycles elapse, comparing with 33,335 load cycles from Curve 1 to final fracture.
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Fig. 6. Fractography near the boundary of the first unbonded zone. Bright lines are the marker bands, i.e. crack fronts at different time.
Fig. 7. Evolution of crack fronts with arrows indicating local FCG directions.
3.2. Microscopic fatigue crack growth behavior The fractography of the DB laminates at high magnification is shown in Fig. 8. Fig. 8 (a) and (b) respectively illustrate the fractography near the boundary of the first unbonded zone and that away from the interface. It can be found that the fracture surface is dominated by transgranular fracture. Plastic fatigue striations can also be identified. Relatively large steps and secondary cracks can be seen in Fig. 8 (a), and the fractography near the boundary of the first unbonded zone is coarser than that away from the interface. We used the SEM to examine all the fractography of the DB laminates and found such features commonly existing near the boundary of the first unbonded zone. The unbonded zone introduces free surfaces, leading to plane stress state near the free surfaces. As the plain strain state dominates in the material away from free surfaces, out-of-plane stress may arise in the free surface vicinity, which promotes the formation of secondary cracks. The formation of steps may be 9
associated with adjacent secondary cracks and the local stress state near the boundary of the unbonded zone.
(a)
(b) Fig. 8. Fractography of the DB laminate (a) fractography near the boundary of the first unbonded zone, (b) fractography away from the interface. Relatively large steps and secondary cracks can be seen in (a). Fatigue striations can be seen in (b).
3.3. Variation of crack length with number of load cycles An optical microscope with grating scale was employed in the measurement of marker band positions, with the error controlled within 0.01 mm. Crack length 2a is the sum of a1 and a2 , see Fig. 5 (a). It should be noted that a1 (a2 ) represents the distance of the outmost point on the left (right) crack front from y-axis, the left and the right crack front corresponding to the same number of load cycles.
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Fig. 9. Variation of half-crack length with number of load cycles.
To facilitate the comparison, initial half-crack length is taken as 2 mm. The variation of half-crack length with number of load cycles (i.e. a − N curve) is shown in Fig. 9. Small scatters can be observed from the a − N curves for the three specimens. It is indicated that crack growth deceleration occurs when the half-crack length ranges from 7.5 mm to 11 mm, corresponding to the crack growth near the boundary of the first unbonded zone. 3.4. Variation of fatigue crack growth rate with crack length This section will discuss the variation of FCG rate with crack length for the DB laminate. Considering the asymmetric crack growth in the DB laminate, we define the crack length as the distance of the outmost point on the left or the right crack front from y-axis (Fig. 5 (a)). The modified secant method (Eq. (1)) is used to calculate the FCG rate. In Eq. (1), m represents the number of a vs. N pairs in a data set. a i+1 − ai i=1 Ni+1 − Ni 1 a da ai − ai−1 i+1 − ai = + 1
Fig. 10. Variation of FCG rate with crack length and corresponding fractography for Specimen 2.
• Stage II: da/dN increases with a till the left crack reaches 7.45 mm and the right crack reaches 5.4 mm, the distance of the left (right) boundary of the first unbonded zone from y-axis being 8.609 mm (6.352 mm); • Stage III: da/dN decreases as the through crack approaches the boundary of the first unbonded zone and evolves into a J crack. When the J crack emerges, da/dN arrives at the minimum that is close to the da/dN of the initial through crack; the first unbonded zone effectively decelerates crack growth; • Stage IV: da/dN increases as the propagation of J cracks till the specimen fractures. It should be noted that the variation of da/dN with a is not synchronous for the left and the right crack. This can be justified by the eccentricity of the first unbonded zone, which leads to the crack closer to the boundary of the unbonded zone decelerating earlier. The reason for the decrease in da/dN will be discussed in the next section. 4. Mechanism of crack growth deceleration Fractographic analyses demonstrate that the evolution of crack fronts near the boundary of the first unbonded zone is a crack growth process. To identify the reason for the crack growth deceleration, we calculated the stress intensity factor for every marker band on the fractography.
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4.1. Stress intensity factor calculation The finite element method (FEM) was used to calculate the stress intensity factors for the DB laminate due to its complex geometry and crack front shapes. Regarding the material property, modulus of elasticity was defined as 110 GPa and Poisson’s ratio as 0.34 [25]. The finite element (FE) software ABAQUS (version 6.16) was employ to create FE models. The modeling methods are detailed below: (1) Modeling of crack fronts By using the OM and the SEM, the coordinates of a series of nodes were determined for each marker band on the fractography, with the distance between two neighboring nodes less than 0.2 mm. With the coordinates, cubic spline curves modeling virtual crack fronts were generated, as shown in Fig. 11. (2) Modeling of unbonded zones The thickness of the unbonded zone was measured under the SEM, the value being approximately 20 µm. Therefore, three disc cavities with the thickness of 20 µm were placed in the FE model, as shown in Fig. 11. (3) Element types The domain integral method [26] provided by ABAQUS was used to calculate stress intensity factors. A ring of quadratic wedge elements (C3D15) was used to define the crack front, for which the mid-side nodes on the sides connected to the crack front were moved to the 1/4 point nearest the crack front to create one over square root r singularity of the stress/strain field at the crack front. The remainder of the contour integral region was defined by several rings of quadratic hexahedral elements (C3D20) as paths for J integral calculation (see Fig. 12). In the other parts, quadratic tetrahedron elements (C3D10) or quadratic hexahedral elements (C3D20) were used, as shown in Fig. 12. (4) Boundary conditions In the FCG test, the specimen was gripped by the friction grips of the testing machine; one clamped end of the specimen was fixed and the other was only allowed to have displacements along the loading direction. Given the asymmetric rigidity of the cracked DB laminate, we modeled the virtual clamped end condition in ABAQUS. As the rigidity of the grips was much larger than that of specimens, the clamped ends could be rigidized, with all degrees of freedom restrained for one clamped end and displacements along the loading direction allowed for the other. Uniform tensile stress of 230 MPa was applied to the clamped end to allow displacements along the loading direction (see Fig. 13).
Fig. 11. Modeling of crack fronts and unbonded zones.
13
(a)
(b) Fig. 12. Finite element model (a) global mesh, (b) mesh around the crack front and unbonded zones.
Fig. 13. Clamped end condition, w representing the displacement along z-axis.
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4.2. Variation of stress intensity factor with crack length The opening mode stress intensity factors were extracted for the outmost points used to determine crack length. Taking Specimen 2 as an instance, the variation of stress intensity factor range (∆K) and FCG rate (da/dN ) with crack length (a) is illustrated in Fig. 14. Apparently, the variation of ∆K with a is consistent with that of da/dN . When the through crack approaches the boundary of the first unbonded zone, both ∆K and da/dN decrease. ∆K keeps decreasing during the crack front change from the through crack to a J crack, which continues to the minimum, ∆Kmin . ∆Kmin corresponds to the initial J crack as is the case for da/dN . Given the fact that the variations of ∆K and da/dN show the same trend, it is concluded that the stress intensity factor range, ∆K, is responsible for the decrease in da/dN .
(a)
(b) Fig. 14. Variation of FCG rate and stress intensity factor range with crack length for the crack growth (a) on the left side and (b) the right side of Specimen 2.
15
(a)
(b)
(c) Fig. 15. da/dN − ∆K curves for (a) Specimen 1, (b) Specimen 2, and (c) Specimen 3.
16
4.3. Analysis of fatigue crack growth rate To determine whether the decrease in da/dN is solely determined by the decrease in ∆K, we plotted the da/dN − ∆K curve in a log-log scale as shown in Fig. 15. It is illustrated that: • Stage II: when the through crack approaches the boundary of the first unbonded zone, the slope of da/dN − ∆K curve decreases to that of J cracks. da/dN then decreases with ∆K, and this segment of da/dN −∆K curve, however, falls below the da/dN − ∆K curve for the early through crack rather than coincides with the latter; • Stage III: da/dN decreases with ∆K till da/dN arrives at the minimum. This segment of da/dN − ∆K curve lies between those for the through crack and the J crack; • Stage IV: da/dN increases with ∆K, and good linear relationship can be found between da/dN and ∆K in the log-log scale. A zigzag is observed in the da/dN − ∆K curve, corresponding to the crack growth near the boundary of the first unbonded zone. The zigzag at the da/dN − ∆K curve indicates the reduction of crack growth rate larger than that resulting from the decrease in ∆K. Therefore, the decrease in ∆K may not be the sole factor contributing to the crack growth deceleration near the boundary of the first unbonded zone. The da/dN − ∆K curves for the three specimens are put together and linear fitted as shown in Fig. 16. The Paris parameters (i.e. C and n in da/dN = C(∆K)n ) are 5.61 × 10−9 and 3.26.
Fig. 16. da/dN − ∆K curves and regression line for the DB laminates.
17
5. Discussion As shown in Fig. 14, da/dN and ∆K decrease as the crack approaches the boundary of the first unbonded zone. However, when the crack approaches the boundaries of the other unbonded zones, neither da/dN nor ∆K decreases. This phenomenon is assumed to be associated with the front shape and the FCG direction of the crack approaching the boundary of the unbonded zone. The crack bypassing the boundary of the unbonded zone shows the ongoing process of crack propagation along −x-axis and y-axis. When the crack approaches the boundary of the first unbonded zone, it simply propagates along x-axis as a through crack. It is difficult for such a crack to develop propagation along −x-axis and y-axis. As a result, the crack-growth-deceleration effect of the first unbonded zone is significant. The crack approaching the second or the third unbonded zone originally propagates along −x-axis and y-axis. It is therefore easier for such a crack to bypass the boundary of the unbonded zone. Thus, the second and the third unbonded zone cannot be depended on to decelerate crack growth. 6. Conclusions In this paper, fatigue crack growth tests have been conducted for diffusionbonded laminates of Ti64 with unbonded zones. The crack growth behavior and laws are investigated, with the mechanism of crack growth deceleration near the boundary of the unbonded zone illustrated. The conclusions are as follows: (1) The crack growth in the DB laminate covers four stages: 1) a semielliptical surface crack propagates in the first layer; 2) the semi-elliptical surface crack changes to a through crack that continues propagating in the first layer; 3) the through crack evolves into a J crack when bypassing the boundary of the first unbonded zone; 4) J cracks propagate until the laminate fractures. (2) The decrease in stress intensity factor ranges is an important factor, although not the sole factor, contributing to the crack growth deceleration near the boundary of the first unbonded zone. (3) The crack-growth-deceleration effect of the first unbonded zone is of more significance compared with the other unbonded zones. Acknowledgements The authors gratefully acknowledge the support from National Natural Science Foundation of China (No. 11772027), National Key Research and Development Program of China (No. 2017YFB 1104003) and Aeronautical Science Foundation of China (No. 28163701002).
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Appendix A. Details of the load blocks The following three tables list the number of load cycles in a load block with R = 0.1 along with the number of load blocks for each specimen. It should be noted that there is a load block containing 8,000 cycles of constant amplitude load with R = 0.7 between two neighboring load blocks with R = 0.1. Table A.1. Load blocks for Specimen 1.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3
5000 4000 1000
2 5 13
Table A.2. Load blocks for Specimen 2.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3 4
5000 3000 3500 1000
5 16 4 8
Table A.3. Load blocks for Specimen 3.
Sequence
Cycles in a load block with R = 0.1
Number of load blocks with R = 0.1
1 2 3 4
5000 3000 3500 1000
5 16 4 34
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Graphical Abstract
da/dN - a
da/dN - a and ΔK - a
da/dN - ΔK
Highlights
Fatigue crack growth behavior and laws are illustrated.
The first unbonded zone can effectively decelerate fatigue crack growth.
The mechanism of crack growth deceleration is revealed.