Optimization Design of Unbonded Areas Layout in Titanium Alloy Laminates for Fatigue Performance

Abstract

This paper proposed a new type of unbonded areas which are preset in diffusion bonding titanium alloy laminates (DB-TAL). A group of DB-TAL specimens with symmetric striped unbonded areas were prepared, and the fatigue experiments under symmetric tension–tension cyclic loading were conducted. The fatigue crack growth behavior was studied from the fracture surface. The results show that this kind of unbonded area can toughen the DB-TAL based on a new mechanism. For the new toughening mechanism, we extracted the key factors in the DB-TAL specimens with symmetric striped unbonded areas and built a simplified model to analyze the key parameters. The results show that the size and location of the unbonded areas are the key factors for the toughening design, and the model we built can efficiently give the optimization design for the DB-TAL specimens with striped unbonded areas.

1. Introduction

Titanium alloy is one of the main structural materials of contemporary aircraft and engines due to its excellent material properties [1,2,3,4]. However, the damage tolerance performance of titanium alloy is its Achilles’ heel [5,6,7,8]. Titanium ally structures have a short residual crack growth life after a crack occurs. Therefore, it is important to research how to increase structural toughness through structural design.

It is an important way to prolong the life of the structure by controlling the crack growth path in the structure. Nowadays, a type of diffusion bonding laminates is receiving much attention because of the good controllability of crack growth. Diffusion bonding (DB) is a solid-state bonding technique without the presence of a liquid phase, which is a commonly used process in machining titanium alloys [9,10,11,12]. Titanium alloy laminates are made by diffusion welding several titanium sheets under a certain time, pressure, and temperature. This makes it more flexible to adapt to different structural requirements by using the thickness and number of layers of the diffusion bonding sheet as design parameters.

In Reference [13], it is found that some specimens with low bonding rate have longer crack growth life. Based on this discovery, they proposed the diffusion bonding titanium alloy laminates preset circular unbonded areas (DBTALCUA). For this kind of laminates, a series of studies were constructed. For instance, in Reference [14], the parameters affecting the crack growth life of DBTALCUA are analyzed numerically, and the proper design parameters can prolong the crack growth life by more than 100 percent. Reference [15] studied the surface crack growth process in the DBTALCUA based on an experimental method. Reference [16] studied the titanium alloy connector made of DBTALCUA using an experimental method, and that indicates that the structure works at the component level.

The research above showed that DBTALPCUA has well damage tolerance performance, but there is a noteworthy crack growth characteristic in DBTALPCUA to be observed. Although the circular unbonded areas can lead the crack growth path to prolong crack growth life, when the crack grows to the boundary of the unbonded areas, it will continue to penetrate the laminates and bypass the circular unbonded areas. Ideally, by keeping the integrality of the laminates, the fatigue crack grows in the sub-laminate, and the rest of the laminates can continue to carry the load even if the sub-laminate fails. In this situation, the unbonded areas lead the crack growth path and stop the crack from penetrating the thickness of laminates.

Based on the above considerations, one group of DB-TAL specimens with symmetric striped unbonded areas was prepared, and the fatigue experiments under symmetric tension-tension cyclic loading were conducted. The fatigue crack growth behavior was studied from the fracture surface. We extracted the key factors in the DB-TAL specimens with symmetric striped unbonded areas and built a simplified model to analyze the key parameters. The results show that the size and location of the unbonded areas are the key factors for the toughening design, and the model we built can efficiently give the optimization design for the DB-TAL specimens with symmetric striped unbonded areas.

2. Experimental Details

2.1. Specimens

Titanium alloy Ti-6Al-4V was employed, and

Table 1. The composition of the Ti-6Al-4V material.

Element	Al	V	Fe	C	O	N	Ti
Content (%)	5.5–6.75	3.5–4.5	≤0.5	≤0.1	≤0.2	≤0.05	Bal.

gives the composition.

The manufacturing process of the DB-TAL specimens with striped unbonded areas mainly includes the following steps:

(1)

The Ti-6Al-4V titanium alloy sheets were chosen to make the specimens. Two kinds of titanium alloy sheets were prepared with a thickness of 1 mm and 4 mm;

(2)

The solder-resistant was designed to be set between the sheets before the diffusion bonding process, which constituted the unbonded areas between sheets;

(3)

Five Ti-6Al-4V titanium alloy sheets were utilized to manufacture a titanium alloy laminate using diffusion bonding technology at 900 °C/1.5 MPa/1.5 h under protective gas. The laminates have a thickness of T = 8 mm with four 1 mm sheets and one 4 mm sheet, symmetric distribution in thickness direction;

(4)

Machining of the specimens was carried out according to design drawing. To easily study the crack growth process, a notch was made by electro-discharge machining, as shown in Figure 1.

The specimen has a length L = 180 mm, width W = 40 mm, and thickness T = 8 mm. The specimen is shown in Figure 2.

The specimen is set in 5 layers with a total of 8 mm in the thickness direction, and the distribution is 1/1/4/1/1 mm, as shown in Figure 2. The current research showed that although the titanium alloy laminates with circular unbonded areas have longer fatigue crack growth life, the crack still can penetrate the laminates, bypassing the circular unbonded area. Ideally, the fatigue crack grows in the sub-laminate, and the rest of the laminates can continue to carry the load even if the sub-laminate fails. If there are no diffusion bonding interfaces between the sub-laminates, the failure of the sub-laminate cannot affect the rest of the laminates. However, the whole performance of the laminates will be degraded in that situation. Therefore, the key problem is how to design the unbonded areas’ distribution. Based on this idea the layout of the unbonded area was designed here. The total width of the unbonded area, which is between the two unbonded boundaries in Figure 2, is 24 mm, and the diffusion bonded connection areas with a width of 1 mm are preset in the unbonded area, which is shown in orange in Figure 2. In interfaces 1 and 4 in Figure 2, starting from the center line of the hole, a 1 mm wide bonding area is set every 8 mm until the edge. In interfaces 2 and 3 in Figure 2, starting from the center of the hole, a 1 mm wide bonding area is set every 6 mm to the edge. This design has a simple layout of the unbonded area and can focus on the influence of the crack on the lower layer when it passes through the interlayer bonding area, which is convenient for analyzing the conditions affecting the failure.

2.2. Test Conditions and Procedures

An Mts-810 1000 kN fatigue test machine was employed to finish the experiments at room temperature. In this paper, the crack growth process in the laminates is the main fatigue performance focused on. Therefore, a 2 mm pre-crack from the notch was made by tensile–tensile cyclic loading before the formal loading. Since the unbonded area is set inside the specimen, the benchmarking method was employed to study the crack growth process. TestStarIIs control system is employed to program the load spectrum which is shown in Figure 3. The loading part R = 0.1 with the frequency of 8 Hz is the formal load, and the loading part R = 0.7 with the frequency of 20 Hz is the marker load. The maximum tensile load of the cyclic loading was 73.6 kN.

3. Experimental Results

Figure 4 is the fracture surface of specimen 1 with striped unbonded areas. There are 4 DB interfaces and 5 layers in specimen 1, and the distribution is 1/1/4/1/1 mm. Only 3 layers can be seen on the fracture surface because the last two layers cannot be observed due to the deviation of the instantaneous fracture angle from the main fracture surface. Due to the complicated processing technology, the unbonded area size of the actual specimen does not fully meet the requirements of the drawings, so here, the dimensions of each interlayer unbonded area and bonding area are re-measured from the fracture surface of specimen 1, as shown in

Table 2. Parameters marking of striped unbonded areas for specimen 1. (Units: mm).

Unbonded	Bonded	Unbonded	Bonded	Unbonded	Bonded	Unbonded	Hole-Edge
1.04	0.86	4.25	1.00	8.03	0.82	0.69	Interface 1
——	——	——	——	9.98	0.73	5.57	Interface 2
——	——	——	——	——	——	Invalid	Interface 3
——	——	——	——	——	——	Invalid	Interface 4

. The data in the table correspond to Figure 4, and the rightmost column is the hole-edge location. It can be seen from the table that the design drawing of the bonding area is 1 mm, and the actual value measured from Figure 4 is about 0.6 ~ 1 mm, which is slightly different from the design, while the position of the unbonded area has a larger difference from the design.

Specimen 1 experienced a total of 278,525 cycles from loading to fracture. In each loading period, the stress radio R = 0.1 was loaded 1500 times, and R = 0.7 was loaded 5000 times, so a total of 42 complete loading periods were experienced. Analyzing the crack growth process from the fracture surface, first, the fatigue crack initiated and grew from the initial notch. When the crack front grew to the first bonding area, the crack began to grow in both the depth and width directions of the specimen. This double-direction growth process had a slow crack growth rate, and the trace lines on the fracture surface were very dense and difficult to distinguish accurately. The crack front can be divided into two parts, one part grew along the surface layer, and the other part grew towards the second layer through the bonding area. There was a total of 28 trace lines in the first sub-laminate of the specimen from the crack length of 1 mm, and the number of trace lines within 1 mm was estimated to be about 5 to 8 according to the previous test results. Therefore, when the first sub-laminate failed, the rest of the laminates also had some carrying capacity. There were 14 trace lines in the third layer of the specimen, and that means when the crack penetrated the first sub- laminate, the failure area of the specimen in the depth direction was already larger. From specimen 1, the designed local bonding laminates can produce a single-layer failure effect, but the interlayer bonding area will cause the crack to grow rapidly in the depth direction due to the excessive size.

Figure 5 is the fracture surface of specimen 2 with striped unbonded areas. The dimensions of the unbonded areas and the bonding areas between each layer are shown in

Table 3. Parameters marking of striped unbonded area for specimen 2. (Units: mm).

Unbonded	Bonded	Unbonded	Bonded	Unbonded	Hole-Edge
2.18	0.81	7.64	0.81	4.72	Interface 1
5.84	0.74	6.08	0.67	2.81	Interface 2
——	——	——	——	Invalid	Interface 3
——	——	——	——	Invalid	Interface 4

. The specimen experienced a total of 336,686 cycles from loading to fracture. In each loading period, R = 0.1 was loaded 1500 times, and R = 0.7 was loaded 5000 times, so it experienced a total of 51 complete loading periods. The fracture surface in Figure 5 shows that there were 40 trace lines in layer 1 of the specimen, 11 trace lines in layer 3, and the number of trace lines in layer 2 is too dense to directly obtain the number of trace lines. Layers 4 and 5 are in the transient fracture zone, which is not considered here. Fatigue cracks start to grow from layer 1, and an instantaneous break occurs after the failure of layer 3. The total number of trace lines in these two parts is the same as the total number of loading periods of the specimen, indicating that when layer 1 was penetrated by a fatigue crack, the fatigue crack just propagated to layer 3 of the specimen, and the last 11 loading periods were mainly the growth of fatigue crack in layer 3. It can be seen from the fracture surface that the trace lines are very dense when the fatigue crack front grows from layer 1 to the first bonding area, which indicates that the fatigue crack growth rate is very low at this time. Here, the number of trace lines in layer 2 can be obtained through the fatigue crack growth process and trace line information. There are 15 trace lines in the fatigue crack growth from the notch to the first bonding area. At this time, the crack front begins to move toward layer 2. There are 11 trace lines on layer 3 of final fatigue failure, which means that the number of trace lines in the second layer is 51 − (11 + 15) = 25. The existence of this bonding area greatly reduces the fatigue crack growth rate. When layer 1 of this specimen fails, the main bearing part inside the specimen has not yet failed; there is still a certain residual bearing capacity, and the failure of the surface layer is very easy to detect and remedy in time.

Figure 6 is the fracture surface of specimen 3 with striped unbonded areas. The dimensions of the unbonded areas and the bonded areas between each layer are shown in

Table 4. Parameters marking of striped unbonded area for specimen 3. (Units: mm).

Unbonded	Bonded	Unbonded	Bonded	Unbonded	Hole-Edge
4.17	0.68	7.68	0.83	2.86	Interface 1
7.55	0.81	5.73	0.83	0.99	Interface 2
——	——	——	——	Invalid	Interface 3
——	——	——	——	Invalid	Interface 4

. The specimen experienced a total of 284,734 cycles from loading to fracture. In each loading period, R = 0.1 was loaded 1500 times, and R = 0.7 was loaded 5000 times, so a total of 43 complete loading periods were experienced. The fatigue crack growth process of specimen 3 is consistent with that of specimen 2, but here it can be seen that specimen 3 is 8 periods less than specimen 2, which is mainly caused by the change in the position of the bonding areas. The width of the first unbonded area of layer 1 in the specimen is 2 about 4.72 mm, while the size of specimen 3 is only about 2.86 mm. From the three specimens, the toughening mechanism of the unbonded area can be seen clearly. The main area of fatigue crack growth is transferred from the high-stress area at the edge of the hole to the low-stress area far away from the edge of the hole, and the position of the first bonding area is crucial.

4. The Optimization Design of the Striped Unbonded Areas

It can be seen from the experiments in the previous section that the position and size of the unbonded areas are important factors for the toughening design. Particularly, the position and size of the first bonding area crack passed is the key factor. To design this parameter, we simplified the model as shown in Figure 7. There is only one DB interface in the laminates, and we set one bonded area in this interface. The shape of the specimen is the same as that of the previous specimen. It is a tensile specimen with an open hole, and the tensile stress on the end face is σ. The width is W, the total thickness is T, and the radius of the open hole is R. The length of the specimen is not designed here, and only the section of the specimen is analyzed. Assuming that there is only one layer of unbonded area, the thickness of the surface layer is t, the size of the bonded area from the hole edge is L₁, the size of the bonded area is 2a, and the section width is W/2-R. It is assumed that the initial crack initiation position is located on the upper surface of the hole edge. When the crack front grows through the bonded area between layers, it is assumed that the shape of the crack front left in the lower layer is a semi-ellipse, the length of the short semi-axis of the ellipse is b, and the length of the major semi-axis is a. When the crack front passes through the bonded area in the surface layer, the lower part can be approximated as a three-dimensional surface crack growth problem on a uniformly stretched plate, and the stress intensity factor of the crack front can be calculated by following Reference [17].

To facilitate the investigation of the relationship between the position and size of the bonded area and the stress intensity factor of the crack front, the size and load of the specimen in the previous section are selected for the default analysis, and the specific values are shown in

Table 5. Parameter of single edge crack specimen.

W	T	R	σ
40 mm	8 mm	3 mm	230 MPa

.

According to the observation in the experiments in Section 3, the crack surface formed when the fatigue crack grew through the bonded area is a flat ellipse. In this case, at the lowest point of the crack, that is, the intersection of the short axis and the crack front, the stress intensity factor is the largest. The investigation of this crack front in this section aims to examine the stress intensity factor change at this point. Here, we first assume b/a = 1/4 to investigate the variation of the stress intensity factor at the crack front with L₁ under different sub-layer thicknesses, as shown in Figure 8. It can be seen from the figure that when L₁ < 5 mm, the stress intensity factor of the crack front is very high, and the intensity factor decreases sharply with the increase of L₁, which shows that the high-stress concentration at the hole edge has a great influence on the stress intensity factor of the crack front. As L₁ continues to increase, the stress intensity factor at the crack front starts to rise again. This is because as L₁ increases, the failure area of the structure increases when the crack grows through the bonded area, so the stress intensity factor increases. In the figure, it can be seen that the tendencies of the curves are consistent, and the positions of the turning points of the curves are nearly the same. Several curves are very close when L₁ < 3 mm, which indicates that the effect of stress concentration at the edge of the hole is dominant. It can be seen from the figure that there is a most suitable L₁ for different thicknesses of sub-layer to minimize the stress intensity factor.

When the crack grows through the bonded area, the size of the remaining crack surface is difficult to determine. Therefore, the variation law of the stress intensity factor with the size of the bonded area under different ratios of major and minor axes is investigated here. Here, t = 2 mm, and L₁ is the curve calculated before. The position of the inflection point is 4.7 mm, and the obtained variation law is shown in Figure 9. It can be seen from the figure that with the increase of the bonded size, the level of the stress intensity factor on the crack front increases sharply. Several curves are close when the bonded area is smaller than 0.2 mm. The smaller the value of b/a, the slower the change of the stress intensity factor.

The influence law of the position and size of the bonded area on the stress intensity factor of the crack front is obtained above. In the actual design process, we hope that the stress intensity factor of the crack front left in the bonded area is less than a specific value or threshold. By formula $\left|K_I^{}-K_{obj}\right|<\epsilon$, the arrangement curve of the size and position of the bonded area under different load conditions can be further obtained, as shown in Figure 10, where $\epsilon$ is a small amount of characterization accuracy and is taken as 0.001 here. K_I is the stress intensity factor at the crack front, and K_obj is the crack growth threshold. The curve in the figure is the layout curve of the bonded area when K_obj =5$\mathrm{MPa}\cdot {\mathrm{m}}^{1/2}$. Through this curve, the optimal relationship between the position and size of the connection area under different loads can be obtained, where t = 2 mm, b/a = 1/4.

5. Summary

In this paper, a new type of symmetric striped unbonded areas which preset in diffusion bonding titanium alloy laminates was proposed. Three specimens with symmetric striped unbonded areas were experimentally analyzed. Based on the experimental results, a simplified model was employed to analyze the key parameters of the toughening effect. Through the analysis of the experiment and the simplified model, several conclusions can be given as follows:

(1)

The symmetric striped unbonded areas preset in DB-TAL can effectively lead the crack growth path to prolong the crack growth life;

(2)

The size and location of the bonded areas between unbonded areas are the key parameters to the toughening effect. The crack growth life of Specimen 2 is about 20% longer than that of Specimen 1 because of the difference in the key parameters;

(3)

The simplified model proposed in this paper can effectively give the optimization layout of the striped unbonded areas preset in DB-TAL.