**4. Discussion**

Because the specimens that were subjected to PWHT were milled thereafter, we can assume that equality of surface roughness was provided, and we can exclude this factor from our further consideration. This allows us to consider microstructural changes as the main factor affecting the fatigue properties of the laser beam welded joints in the present work. The aim of this section is to link the results of mechanical testing with microstructural observations, microhardness measurements and fracture surface topography analysis. As described above, fatigue failure in the laser beam welded joints was always found in the FZ. Thus, the micro‐ structure in this region of the weldment is a crucial factor affecting the fatigue performance of the joints.

The HCF failure process comprises four stages: microcrack initiation, microcrack propagation, macrocrack propagation and final fracture [38]. The border between micro‐ and macrocrack propagation can be defined when the size of the crack is approximately one order of magnitude larger than the effective microstructural size [39], which is the average grain size (3–6 µm) in the case of an equiaxed microstructure and is the α colony size (10–40 µm, depending on the cooling rate) in the case of a lamellar structure. A number of researchers have shown that crack initiation and microcrack propagation take up to 95% of the high cycle fatigue life [28, 37, 40]. Macrocrack propagation is very fast relative to the first stages and does not play any significant role in unnotched HCF. In the presence of defects, the size and sharpness of notches are of great importance because they determine the size of the plastic zone at the tip of the notch. As already mentioned above, we can consider subsurface clusters of pores as single defects with approximate sizes of 150–250 µm. A sharp notch with a small crack at its tip may be regarded as a crack [37]. Because the transition short/long crack is on the order of 200 µm (10 times the microstructural size) for lamellar microstructures, a crack emanating from the pore in the FZ can already be assumed to be a long one after the initiation period. This brings us to an important conclusion that the HCF of the LBW joints primarily depends on crack initiation from the pore and near‐threshold macrocrack propagation.

A comprehensive study on the influence of microstructural variables on near‐threshold fatigue behaviour of macrocracks in titanium Ti‐6Al‐4V was conducted by Yoder et al. [41–43]. Bilinear crack growth rate behaviour was observed, with two distinct branches that independently obey the power law and join together in the transition point (∆*K*T). In the region ∆*K*th < ∆*K* < ∆*K*<sup>T</sup> (∆*K*th stands for the threshold stress intensity factor), the cyclic plastic zone is less than the effective grain size, and a microstructurally sensitive mode of crack growth occurs that involves crystallographic bifurcation in grains adjacent to the crack plane. In contrast, in the region ∆*K* > ∆*K*T, the grains within a larger plastic zone deform as a continuum, which results in a microstructurally insensitive, non‐bifurcated mode of crack growth. The observed values of ∆*K*T were in remarkable agreement with predictions according to the equation ∆*K*T = 5.5 *σ*y v*d*, where *σ*y is the yield strength of material, and *d* is the effective microstructural size. In the case of titanium alloys, the Hall–Petch relation is relatively weak [44], so the *d* term in the above‐ mentioned equation dominates, leading to the increase of ∆*K*T with increasing grain size. The inverse dependence of fatigue crack growth rates upon grain size was directly related to the microstructurally sensitive mode of crack growth because larger bifurcated cracks occur with increasing grain size.

**4. Discussion**

134 Study of Grain Boundary Character

the joints.

Because the specimens that were subjected to PWHT were milled thereafter, we can assume that equality of surface roughness was provided, and we can exclude this factor from our further consideration. This allows us to consider microstructural changes as the main factor affecting the fatigue properties of the laser beam welded joints in the present work. The aim of this section is to link the results of mechanical testing with microstructural observations, microhardness measurements and fracture surface topography analysis. As described above, fatigue failure in the laser beam welded joints was always found in the FZ. Thus, the micro‐ structure in this region of the weldment is a crucial factor affecting the fatigue performance of

The HCF failure process comprises four stages: microcrack initiation, microcrack propagation, macrocrack propagation and final fracture [38]. The border between micro‐ and macrocrack propagation can be defined when the size of the crack is approximately one order of magnitude larger than the effective microstructural size [39], which is the average grain size (3–6 µm) in the case of an equiaxed microstructure and is the α colony size (10–40 µm, depending on the cooling rate) in the case of a lamellar structure. A number of researchers have shown that crack initiation and microcrack propagation take up to 95% of the high cycle fatigue life [28, 37, 40]. Macrocrack propagation is very fast relative to the first stages and does not play any significant role in unnotched HCF. In the presence of defects, the size and sharpness of notches are of great importance because they determine the size of the plastic zone at the tip of the notch. As already mentioned above, we can consider subsurface clusters of pores as single defects with approximate sizes of 150–250 µm. A sharp notch with a small crack at its tip may be regarded as a crack [37]. Because the transition short/long crack is on the order of 200 µm (10 times the microstructural size) for lamellar microstructures, a crack emanating from the pore in the FZ can already be assumed to be a long one after the initiation period. This brings us to an important conclusion that the HCF of the LBW joints primarily depends on crack initiation

A comprehensive study on the influence of microstructural variables on near‐threshold fatigue behaviour of macrocracks in titanium Ti‐6Al‐4V was conducted by Yoder et al. [41–43]. Bilinear crack growth rate behaviour was observed, with two distinct branches that independently obey the power law and join together in the transition point (∆*K*T). In the region ∆*K*th < ∆*K* < ∆*K*<sup>T</sup> (∆*K*th stands for the threshold stress intensity factor), the cyclic plastic zone is less than the effective grain size, and a microstructurally sensitive mode of crack growth occurs that involves crystallographic bifurcation in grains adjacent to the crack plane. In contrast, in the region ∆*K* > ∆*K*T, the grains within a larger plastic zone deform as a continuum, which results in a microstructurally insensitive, non‐bifurcated mode of crack growth. The observed values of ∆*K*T were in remarkable agreement with predictions according to the equation ∆*K*T = 5.5 *σ*y v*d*, where *σ*y is the yield strength of material, and *d* is the effective microstructural size. In the case of titanium alloys, the Hall–Petch relation is relatively weak [44], so the *d* term in the above‐ mentioned equation dominates, leading to the increase of ∆*K*T with increasing grain size. The inverse dependence of fatigue crack growth rates upon grain size was directly related to the

from the pore and near‐threshold macrocrack propagation.

The most influential microstructural parameter on the mechanical properties of lamellar (platelet) microstructures is the α colony size (packet size) because it determines the effective slip length in lamellar structures [28, 41]. This parameter should be considered as the effective microstructural size for lamellar morphology in the FZ. With increasing α colony size, the unnotched fatigue strength and yield stress decrease because smooth HCF strength depends primarily on the resistance to crack nucleation and microcrack propagation. However, if macrocracks or sharp notches already exist in the material, a coarse lamellar microstructure is more beneficial for fatigue performance because increased effective slip length retards fatigue crack propagation due to increased crack front roughness. The trade‐off between decreased strength and increased fracture toughness makes the coarse lamellar microstructure less sensitive to notches and more advantageous for usage in applications, in which notched fatigue performance is the crucial factor.

Annealing of the laser beam welded Ti‐6Al‐4V butt joints at temperatures up to 650°C is insufficient for full martensite decomposition into an equilibrium lamellar α + β structure in the FZ and recrystallization in the BM. The width of individual α lamellae and the average α colony size remained almost the same after heat treatments at low temperatures. Hence, mechanical properties also should have remained approximately the same. We can conclude that the low‐temperature annealing does not affect the HCF performance of the laser beam welded Ti‐6Al‐4V butt joints.

As described above, starting from the temperature of 750°C, the metastable martensitic structure in the FZ transforms to equilibrium platelet α + β morphology, as shown in **Figure 8**. With increasing temperature during PWHT, the width of individual lamellae and α colony size increases with a commensurate increase in the effective slip length and a corresponding decrease in the yield stress. A coarse lamellar structure with lower density of defects after annealing at high temperatures has lower strength and higher ductility than martensitic morphology [6, 45, 46]. This was indirectly confirmed by the decreased microhardness in the FZ after PWHT at high temperatures. Although the static strength of the joint decreased slightly, more ductile and softer material in the FZ was more beneficial for the HCF of laser beam welded joints than a hard martensitic structure. High‐temperature annealing reduced the notch sensitivity of the FZ, and internal defects were less detrimental for fatigue properties than in a martensitic structure. Increased α colony size and consequently larger effective slip length leads to a more bifurcated crack growth profile and increased crack propagation resistance of the material. This result is consistent with the works of Yoder et al. [41–43] and Lütjering and Williams [28].

To verify our assumptions, transverse cross sections of fractured specimens were made. Grinding and polishing was performed to the plane containing the pore to compare the crack front roughness in different conditions. As shown in **Figure 19**, the coarser lamellar micro‐ structure displayed a more tortuous and deflected crack path than the finer‐scale martensitic microstructure in the region adjacent to the pore, where the crack growth is sensitive to the microstructure. The effective slip length in the case of annealed material is the α colony size,

but in case of martensitic morphology, it is the width of individual α plates. Increased crack path tortuosity leads to enhanced crack deflection and a resulting increase in the FCP resistance and the overall fatigue performance.

**Figure 19.** Comparison of crack front roughness profiles in the zone adjacent to the pore. (a) As welded condition and (b) annealed at 850°C for 1 h.

The effect of grain size on the notch sensitivity is well known for steels. Murakami [37] investigated microcrack propagation starting from artificial holes with diameters of 35–500 µm in steels. They concluded that defects smaller than a critical size are non‐damaging (not detrimental) to fatigue strength, and the critical size is smaller for materials having higher static strength. Harder material is more sensitive to notches and defects. A larger decrease in fatigue strength for materials of higher static strength was found. This trend is generally in reasonable agreement with our findings, although we investigated different materials. Based on the results for steels, we can also assume the existence of non‐damaging permissible defects for titanium alloys because micromechanisms and models for the behaviour of cracks ema‐ nating from sharp notches do not depend on the material. However, further investigations must be carried out to prove this assumption. If the dependence of critical size on the micro‐ structure of the FZ is obtained, an obvious way to exclude the detrimental effect of pores on fatigue is to provide a welding technique leading to smaller pores than the critical size. However, it should be kept in mind that in the absence of pores or if the size of defects is lower than the critical size, PWHT will have an opposite effect on fatigue; that is, fatigue strength will be reduced after high‐temperature annealing. This was shown in the work of Babu et al. [7] for electron beam welded joints. The fatigue cracks in their work originated at the surface, implying that internal defects were insignificant. PWHT at temperatures of approximately 900°C reduced the fatigue strength of the joints at 2·× 106 cycles compared to that of the as‐ welded condition and those annealed at lower temperatures.
