Mechanism of crack branching in the fatigue crack growth path of 2324-T 39 Aluminium alloy

The crack growth behavior in 2324-T39 aluminium alloy was experimentally investigated. Two types of crack branching were observed. The mechanism of an uncommon crack branching which results from the link up of secondary crack with the main crack was focused on. The crack paths were observed with optical microscope and in-situ SEM. Finite element crack tip simulation was performed to investigate the relationship between plastic zone size and the location of the secondary crack. Tests and analysis results indicate that the secondary crack initiates near the plastic zone boundary and from the subsurface. The mechanism of this kind crack branching relates to the interaction of grain size and plastic zone size.


INTRODUCTION
lloy 2324-T39 plate is a higher strength version of alloy 2024-T351, and is a high-purity controlled composition varient of alloy 2024.Both strength and fracture toughness properties are improved compared to 2024 plate via employing the T39 temper which was developed through special fabricating practices [1].Since this alloy was developed for tension-dominated, fatigue and fracture critical plate applications, most of the experimental investigations about it are most focused on the fatigue crack growth and fracture.William M. [2] and Dawicke D S [3] report the fracture test results of 2324-T39 plate with difference thicknesses.Stoychev S [4] investigates the effect of varying stress intensity factor range K on crack growth rate.Bao R et al. [5][6][7] present the macroscopic crack path branching observed during the crack growth tests of 2324-T39 middle crack tension (M (T)) specimen under spectrum loading.According to achievements in fatigue theory and fracture mechanics, a through thickness middle crack in an isotropic thin plate subjected to remote tension-dominated loading should propagate perpendicular to the load direction, i.e., Mode I.This is reasonable from a physical perspective because the tensile stress component, which opens the crack, will certainly promote the conversion of cyclic plastic deformation into crack extension [8].At the macro level, crack kinking, bifurcation and branching are influenced by micro-structural irregularities, load effects (global and local multiaxial stress state, spectrum loading), and environmental factors [9][10][11][12][13].Though, the T39 temper was said to account for the fracture toughness improvement, there is no evidence found in the literature that the T39 temper will contribute to the macroscopic crack path change with respect to those of other Al-Cu-Mg alloys, such as 2024-T351 and 2524-T3.

A
In the microscopic perspective, a series of investigations on crack branching, e.g.in-situ SEM tests of a nickel-based single crystal in Ref [14] and EBSD tests on crack propagation path of 7050 alloy in Ref [15], were carried out, which suggest that the crystallographic orientations and geometry of local microstructure, particularly the tilt and twist angle, differences of slip planes or crack planes, together with cooperation and competition between movement of slip systems and loading stress influence the crack propagation behavior.Patton's research indicated that crack bifurcation may be caused by plastic anisotropy and pre-existing defects in front of crack tip [16].Zhiyi Liu's research indicated that the extending potential decides the further extending of these bifurcated cracks [17].The potential of the propagation concerns the tilt angle, twist angle and Schmid factor differences between two neighboring grains.These factors, of commonsense, could result in kinking, bifurcation or branching in fatigue crack path, the appearance of which could be captured as soon as it arises [18].However, Ref. [6] reports that the crack branching observed in alloy 2324-T39 results from the linkup of secondary crack with the lead crack, the process of which is quite different from those common procedures found in the literatures, e.g.Ref. [14][15][16][17][18]. Ref. [7] presents the effect of overloads and K level on crack path change in alloy 2324-T39.For better understanding the mechanism of the uncommon macroscopic crack branching in 2324-T39 alloy, optical metallography analysis, in-situ SEM crack growth tests and numerical simulations on crack tip stress field were carried out in this paper, which will reveal the differences in macroscopic crack morphologies and metallographic fracture characteristics of the two types of crack branching, as well as the effect of the less common crack branching on crack growth rate and some relationship between the appearance of the less common crack branching with the crack tip plastic zone size.

EXPERIMENTS
hree kinds of crack growth tests were carried out to investigate the crack growth behavior in 2324-T39, i.e. tests with M(T) specimen of 4.5mm in thickness under spectrum loading (stated as test type I), tests with relatively small specimens of 1.5mm in thickness with single edge notch under constant amplitude loading(stated as test type II), and in-situ scanning electron microscope (SEM) crack growth tests under constant amplitude loading(stated as test type III).The details of the tests type I, such as specimen configuration, loading sequence, test procedures, etc., have been reported in Ref. [6,7].The aims of designing the other two kinds of tests are 1) to eliminate the potential effects of specimen thickness and loading sequence on crack branching; 2) to rule out the effect of crack configuration, i.e. middle crack and edge crack, on crack branching; 3) to observe the position where the secondary crack appears and the linkup via in-situ SEM test.The small specimens with single edge notch used in test type II and III were cut from the aforementioned M(T) specimen.The configurations of the specimens are designed to fit the loading facilities attached to test machines, which are given in Fig. 1 All the specimen was pre-cracked under constant amplitude load of R = 0.06 and  max = 120 MPa, which resulted in an initial crack whose length is about 0.3 mm from the notch tip.

CRACK BRANCHING PROCESS AND MECHANISM
ig. 2(a), (b) and (c) show the crack morphologies observed in test type I, II and III, respectively.Two types of crack branching were observed in the crack paths corresponding to all the three test types.The ones marked by circle in Fig. 2 are the familiar type of crack branching which were captured once they appeared.The intersection angles are usually less than 90 degree.However, the branches marked by square in Fig. 2 are obviously different with those marked by circles.The following on discussion will centre on this type of crack branching.It can be seen from Fig. 2, for the less familiar type of crack branching (marked by squares), the turning angles are almost 90 degree.The procedure of the appearance of such branches is also different to the common ones.The growth of the leading crack slowed down firstly, and a surface secondary crack was observed away from the leading crack tip, both of the leading crack and the secondary crack kept growing for several loading cycles and finally they linked up to each other.Fig. 3 and Fig. 4 give the observed crack branching procedures in test type I and III, respectively, which indicate exactly the same manner.

F
The surface secondary crack cannot be observed immediately after it initiates even in the in-situ tests.Once it appears on the specimen surfaces, it is already in a certain length as shown in Fig. 4(b).The crack growth of the secondary crack was transgranular, while the link up path was long the grain boundary.The omen of the appearance of surface secondary crack is the slowing down in the growth rate of the previously dominated crack, as shown in Fig. 5.It can be seen from Fig. 5 that there is a remarkable crack growth rate drop at about 3467 loading however, there was no abnormal observed around the crack tip in the picture corresponding to 5969 cycles in Fig. 4(a).Compare Fig. 4(a) and (b), it can be found that there is little growth of previously dominated crack during the 2598 cycles.There is a sudden increase in crack length in Fig. 5(a) at about 8567 cycles that is because of the appearance of the surface secondary crack of about 150m in Fig. 4(b).From these clues, it can be deduce that the secondary crack initiates from subsurface at about 3467 cycles, which dissipates the energy and in consequence decreases the growth rate of the main crack.After the link up of secondary crack and the main crack, the crack growth rate recovers.

THE POSITION WHERE THE SECONDARY CRACK APPEARS
t can be seen from Fig. 2, 3, 4, 7 and 8 that the secondary cracks, on the L-T plane, located a certain distance away from the main cracks.Analysis with empirical equations and finite element (FE) simulation were performed to investigate the relationship between the value of this distance and the crack tip plastic zone size.In the condition of small scale yielding, the curve equation of the crack tip plasticity boundaries, as shown in Fig. 9, under Mises criterion is as follows [18]: where θ is defined as the upward inclination from the horizontal and ν is Poisson's ratio.

I
The FE calculated plastic zone sizes at θ =90° for the three specimens are listed in Tab. 1, together with the results calculated by Eq. (1).The distances from the surface secondary cracks to the main crack tips are also measured from the optical photographs and listed in Tab. 1.The comparison in Tab. 1 indicates that: 1) the FE simulation results are about 10% higher than the results obtained by empirical equation, that is because the elastic-plastic material model is used in the FE model; 2) the calculated plastic zone sizes at θ =90° by both Eq.(1) and FE model match the measured distances from the surface secondary cracks to the main crack tips.That is to say, the secondary cracks initiation positions are near the plastic zone boundaries of the main crack.

CONCLUSIONS
he following conclusions can be drawn from the experimental investigations and crack tip analysis: 1) The macroscopic crack branching in AA 2324-T39 results from two different types of mechanism.The uncommon kind of branching is resulted from the linking up of the secondary crack with the main crack, which is different from the intergranular crack branching.
2) The secondary cracks usually locate near the plastic zone boundaries of the main cracks and show transgranular growth characteristics.The initiation sites of the secondary cracks were deduced at the sub-surfaces of the specimen.
3) The grain shapes characteristics in different orientations of this alloy and their interaction with the plastic zone size contribute to the appearance of the second type of crack branching.

Figure 9 :Figure 10 :
Figure 9: Sketch map of crack tip plastic zone.It is acceptable that the crack tip is in small scale yielding state for case of the edge notch specimens used in this study when the secondary cracks initiate on the surface.Since the secondary cracks usually initiate above or below the main crack tip, θ in Eq. (1) is set to be 90 degree in the calculation.The calculation results are listed in Tab. 1 for specimen L-T-2-1, L-T-2-2 and L-T-3-1.Since the specimens are thin sheet, the calculation is based on the equation for plain stress.Although the specimen configurations and the clapping mode were slightly different in test type II and III, the section as shown in Fig.10(a) could be regarded as an edge cracked plane subjected to uniaxial stress state.Finite element simulation was performed for this section.Considering the symmetry, a 1/2 plane model was used here and the boundary conditions and the meshing was illustrated in Fig.10(b) and (c).Line AB is the crack surface.Symmetry constraint was applied to line BC.Constraint in x direction and uniformly distributed load in y direction are applied to line DE.The three specimens, i.e.L-T-2-1, L-T-2-2 and L-T-3-1, are all simulated.The widths and crack lengths of the FE models and the applied stress levels are in accord with those in the corresponding tests.The material behavior is assumed to be elastic-plastic isotropic to acquire the crack tip stress field.The trilinear constitutive mode is adopted with  e = 450 MPa,  0.2 = 481 MPa,  b = 532 MPa, which were obtained from the - curve of the mechanical property test.(a)(b) (c)

Table 1 :
Comparison of the plastic zone size of plane stress state at θ =90° with the measuring distance from the secondary crack to the main crack (mm).