Titanium-alloy laminates fabricated by sheet materials using diffusion bonding process have drawn more and more attention in the recent years. Proper placement of nonwelded zones on the diffusion bonding (DB) interface within titanium-alloy laminates as crack arrest zones can improve damage tolerance. To achieve the optimal damage tolerance via designing non-welded zones, it is necessary to study fatigue crack growth characteristics for this type of laminates by adjusting all the relevant parameters such as geometrical sizes, locations, and the number of the nonwelded zones, which is highly time consuming. Therefore it is essential to develop a reliable and quick method to analyze the fatigue crack growth characteristics for titanium-alloy laminates with non-welded zones. In this paper, the extended finite element method (XFEM) which was employed to simulate the fatigue crack growth process and the applicability of this method to capture fatigue crack growth characteristics of titanium-alloy laminates with localized non-welded zones was also studied. The numerical results were compared with the experiment data, and the agreement on numerical and experimental results illustrated that the specific crack growth characteristics can be captured by using XFEM, thereby verifying the applicability of XFEM in the analysis of fatigue crack growth of the laminates with non-welded zones. The influence of non-welded zones on the fatigue crack growth was then discussed.
Titanium alloys have over the years proven themselves to be technically superior and cost effective materials for a wide range of applications spanning the industries of aerospace, marine, and even commercial products [
However, there is a disadvantage that the residual life is relatively short once the damage appears in the structure which is made of common titanium alloy. (Damage is inevitable actually.) Thus the common titanium alloys are ineffective in damage tolerance design [
Damage-tolerance-design strategy gets more and more attention in modern aircraft design. It takes the intrinsic/discrete damage, large area manufacturing flaws, or severe accidental damage into consideration and ensures that the remaining structure will withstand reasonable loads without failure or excessive structural deformation until the damage is detected. In order to improve the applicability of titanium alloys to damage-tolerance-design, one traditional method is through microstructural control, and another method is through the use of submacro laminated structures [
The recently proposed XFEM can describe the discontinuity and singularity by introducing the enrichment function to the shape function of the conventional finite element method (CFEM), and it exhibits a unique advantage in the analysis of discontinuous problem [
In this paper, the XFEM method based on the ABAQUS platform is employed for analyzing crack growth characteristics in the diffusion bonded laminates of TC4 titanium alloys, and the results obtained are compared with the experimental results given in [
The enrichment function in XFEM can accurately describe the crack or material interface’s discontinuity and singularity that exit inside the element. So the mesh in XFEM can be independent of the structure’s geometrical or physical interface, and that avoids the limit that there must be very fine grids near crack tip or material interface when using traditional finite element method, and it is more attractive that there needs no remeshing in analyzing the crack growth problem in XFEM. XFEM has all the advantages in CFEM. For this reason, the form of element stiffness matrix in XFEM is inline with that in CFEM, and the implementation of XFEM can make full use of the CFEM program that already exists.
The level set method is a numerical technique for tracking the evolution of interfaces. In this method, the interface is represented as the zero level set of a function
The level set function usually uses signal distance function to be constructed. Where
Level set method for interface described.
Consider
The description of crack growth can be got from the evolution of the level set, and the details refer to the literature [
The displacement field
Consider
The displacement mode in the crossed elements is
The junction between the enriched elements and the common elements will produce mixed elements, and the literature [
The weak form of XFEM discrete control equation can be described as follows in linear elasticity problems [
The form of equilibrium equation previously mentioned is inline with the CFEM.
The details of
The derivation of the discrete control equation refers to the literature [
We get the three energy release rate components at crack tip by virtual crack closure technique (VCCT) and calculate the equivalent energy release rate through (
The XFEM in ABAQUS lacks the description of crack tip inside element; therefore the crack tip has to grow to the boundary of element. So there are some differences in calculating the crack growth length from the traditional method. It calculates the needed cycles that the crack grows given length (the length of crossed element), which instead of calculating the length crack grows given cycles
Crack growth characteristics of diffusion bonded laminates of titanium alloys with localized nonwelded zone can be obtained by the XFEM based on the ABAQUS platform. In order to compare with the experimental data given in [
Model of the floor plan.
The boundary condition of two ends is clamp, and it is in keeping with the tensile experiment just like it was considered in [
Mechanical properties of TC4 [
Elastic |
Ultimate |
Fracture |
Poisson’s |
---|---|---|---|
|
|
|
|
110 | 913 | 78.3 | 0.34 |
The whole process of crack growth in the specimen is simulated by XFEM. The crack growth path is described in Figure
The path of crack growth.
Surface crack length varies with fatigue cycles (forecast results).
Crack growth rate varies with surface crack length.
Figure
The experimental data shown in Figure
The relationship between crack length and cycles in the experimental results [
Crack growth length needed for the fatigue cycles.
The surface crack growth is discussed in the above section. Actually, the internal growth of crack gets more worthy of attention. It is very difficult to observe the internal crack growth law by means of experiment. Fortunately, the numerical simulation is a good way to research the internal crack growth. There are another two performance indexes that are employed to analyze the law of the internal crack growth. One is the crack length along direction of the thickness, and the other is the projected crack area that is two-dimensional area measurement of the fracture by projecting its shape onto the plane perpendicular to the length direction.
Figure
Fatigue crack growth rate varies with the crack length in depth direction.
Crack length in depth direction varies with fatigue cycles.
Actually, the internal crack growth happens along the direction of radius and depth at the same time. The projected crack area as a new parameter is employed to describe the internal crack growth. Similar with definition of the crack length growth rate, the projected crack area growth rate
Projected crack area changes as fatigue cycles.
Fatigue crack growth rate changes as projected crack area.
Damage tolerance is a property of a structure which relates to its ability to sustain defects safely until the structure is repaired. In ensuring the continued safe operation of the damage tolerant structure, inspection schedules are devised. Thus, the objective of damage tolerance design is to maximize the crack growth life so that more inspection periods can be undergone or to maximize the crack length with the same residual life so that it is easier to be detected.
The residual life under the different surface crack length is shown in Figure
Structure of residual life changing with crack length along diameter direction.
This paper analyzes the crack that grows in the diffusion bonded laminates of TC4 titanium alloy using XFEM based on the ABAQUS platform and studies the crack growth law under the TC4 laminates. From the comparison between the predicted results and experiments, the XFEM can grasp the true crack growth law in the titanium-alloy laminates, and the XFEM is proved to be an efficient method to analyze the crack growth in the titanium-alloy laminates. In addition, through the analysis of the damage tolerance, the nonwelded zone set in the DB interface can significantly increase the fatigue life and improve the damage tolerance.
This research is supported by the National Basic Research Program (973Program) of China (Grant no. 2011CB610304), National Natural Science Foundation of China (11172052) and China Aviation Industry Research Project (CXY2011DG34).