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Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II + III in niobium and titanium
Accepted Manuscript Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium Tomá š Vojtek, Anton Hohenwarter, Reinhard Pippan, Jaroslav Pokluda PII: DOI: Reference:
S0142-1123(16)30005-6 http://dx.doi.org/10.1016/j.ijfatigue.2016.02.042 JIJF 3879
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
18 December 2015 15 February 2016 29 February 2016
Please cite this article as: Vojtek, T., Hohenwarter, A., Pippan, R., Pokluda, J., Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium, International Journal of Fatigue (2016), doi: http://dx.doi.org/10.1016/j.ijfatigue.2016.02.042
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Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium Tomáš Vojtek1*, Anton Hohenwarter2, Reinhard Pippan3, Jaroslav Pokluda1,4
1
Central European Institute of Technology (CEITEC), Brno University of Technology, Technická 3058/10, CZ-61600 Brno, Czech Republic 2 Department of Materials Physics, Montanuniversität Leoben, Jahnstr. 12, A-8700 Leoben, Austria 3 Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstr. 12, A-8700 Leoben, Austria 4 Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, CZ-61669 Brno, Czech Republic *corresponding author: [email protected], tel.: +420 541 142 849
Key words shear loading modes, local mode II, growth mechanism, 3D crack path, coplanar growth
Abstract The paper is focused on an identification of the local mode II mechanism of fatigue cracks loaded under the remote mode III and the mixed mode II+III and presents a convincing experimental evidence of such a mechanism in materials with a nearly coplanar crack growth. Closure-free data were obtained by applying fatigue experiments in modes II, III and II+III in commercially pure titanium and niobium. The results revealed that the micromechanism of propagation of all kinds of shear-mode cracks can be described by a common model of advances of local mode II crack segments nearly in the direction of applied shear stress. These segments nucleated at spatial geometrical irregularities of the precrack front generating fibrous patterns at fracture surfaces.
Nomenclature ARMCO 3D bcc fcc hcp CTS MTS LMIIM SEM SIF
American Rolling Mills and Company three-dimensional body centred cubic face centred cubic hexagonal close packed compact-tension shear specimen maximum tangential stress local mode II mechanism scanning electron microscope stress intensity factor
a Δa/ΔN d
total crack length fatigue crack growth rate inner diameter of the cylindrical specimen
dmNb dmTi D F KII KIII ΔK ΔKth ΔKII ΔKIII l N R t T w YIII z ψ
mean grain size in niobium mean grain size in titanium outer diameter of the cylindrical specimen applied force mode II stress intensity factor mode III stress intensity factor stress intensity factor range crack growth threshold stress intensity factor range for mode II loading stress intensity factor range for mode III loading length coordinate of a fracture surface profile number of applied loading cycles cyclic stress ratio CTS specimen thickness applied torque CTS specimen width geometry function in the formula for mode III SIF height coordinate of a fracture surface profile orientation angle of the force applied to the CTS specimen loading device
1. Introduction In a majority of metallic materials, the mixed mode loaded cracks tend to bifurcate towards local opening mode according to the maximum tangential stress (MTS) criterion. Pure mode II cracks deflect by 70° and pure mode III cracks twist by 45° [1], i.e., they branch to a pure local mode I. This appears predominantly in materials with fcc structure or with secondary phases [2]. In both the ferritic-pearlitic and the JISS45C carbon steel (bcc metals), however, a rather extended (but limited) coplanar growth along the plane of maximum shear was reported [3, 4]. In single-phase bcc materials as niobium and ARMCO iron, moreover, the coplanar crack growth was observed in the whole near-threshold regime. The physical reason for the coplanar shear-mode crack growth in bcc metals is described in [5]. For a long time it was presumed that the fatigue damage ahead of mode II and mode III cracks loaded by the same ΔK-values (ΔKII = ΔKIII) in an isotropic material should be identical and, therefore, both the thresholds and the crack growth rates in these modes should also be equal. However, several authors measured slow crack growth rates in mode III with respect to those in mode I or mode II [6 – 8]. It should be noted that the sliding-mode crack closure has a significant influence on these crack growth rates in the near-threshold region. Loading of mode III cracks generates tortuous fractures surfaces (factory-roof morphology) which leads to a large friction and interlocking between the crack flanks and reduces the effective crack driving force significantly. On the other hand, sliding-mode crack closure of mode II loaded cracks vanishes when the crack deflects to the opening mode I. The friction stress component (also called extrinsic component) is much higher than the intrinsic one and is, therefore, responsible for the difference in crack growth rates of mode II and mode III cracks in materials with local mode I crack growth.
Coplanar shear-mode crack growth occurs in the low-cycle fatigue regime [9], however, in some metallic materials it was observed also in the near-threshold regime [5]. Here, the remote mode II and mode III crack growth thresholds and rates were comparable due to the same fracture morphology of both modes II and III and, consequently, the same level of friction between the crack flanks. The extrinsic component is usually several times higher than the intrinsic one and leads to a high scatter of mode II and mode III remote threshold data and to an apparent approximate identity of both remote thresholds (the sum of intrinsic and extrinsic resistance) [10]. Nevertheless, it was experimentally shown that the mode III crack growth rates are lower than those of mode II when effective (closure-free) stress intensities are taken into account [5]. This was explained by models of remote mode III growth based on Local Mode II Mechanisms (LMIIMs). In the last decade, experiments performed on bcc, hcp and fcc metals with suppressed friction effects in the crack wake revealed that all the measured effective thresholds in mode III were higher than those in mode II by the factor of approximately 1.7 [2, 5]. This result is in agreement with predictions of the LMIIM models. Some works devoted to measurement of the effective crack growth data for mode III cracks can be found in the literature. For example, in works [11 – 13] mode III fatigue experiments with superimposed static mode I loading were performed. However, these values were still higher than those obtained for shear-mode cracks propagating form closure-free precracks generated by cyclic compressive loading. Such experiments with suppressed friction stresses allow us not only to reveal the effective mode II and mode III thresholds but also the intrinsic growth mechanisms of shear-mode cracks. When clamping of asperities in the crack wake is present, it induces a local mode I at the crack front under the remote shear-mode loading [14] which disturbs the local pure shear mode by changing it to a more or less undefined mixed mode. Although a very small mode I component exists also in the case of coplanar cracks propagation (with crystallographic nature), this component is practically negligible in comparison with the shear mode one as commented in Discussion. The absence of friction is also important for the identification of the growth mechanism, since the friction contact leads to a fracture surface damage and does not allow observation of the related fractographical patterns. In some single-phase metals (ARMCO iron, niobium, titanium and nickel) the fractographical fibrous patterns revealed a crystallographic nature of the crack propagation which was explained by the model of cyclic plasticity based on emission of dislocations from the crack tip [15]. Detailed theoretical explanations of the micromechanisms and understanding of the intrinsic behaviour is the focus of another recent paper [16] which deals also with materials containing secondary phases. It should be emphasized, however, that the relation between the orientation of observed fibrous patterns and the local crack growth direction in the case of mode III loading could not be sufficiently elucidated until now. Indeed, the interpretation of these patterns on the coplanar fracture surfaces of the ARMCO iron was rather misleading since, due to the unusual behaviour of mode III loaded cracks, it was supposed that these cracks propagated in the direction perpendicular to the fibrous patterns. This paper revises the former idea by utilizing a clear experimental evidence of the LMIIM of fatigue cracks also in other materials with coplanar shear-mode growth, i.e., in niobium and titanium. Although the crack path in the latter material is not really coplanar, the mean deflection angle of the crack
path from the plane of maximum shear stress is rather small and the fracture surfaces of titanium also exhibit fibrous patterns. New findings about the origin of these patterns are also presented as discovered by observing three-dimensional (3D) pictures of fracture surface created by stereophotogrammetry in the scanning electron microscope (SEM). The fractographical data received for the ARMCO iron are not included in this paper due to their former publication in [15, 17]. They are, however, in agreement with those obtained for niobium (also a bcc metal) and can be interpreted using the LMIIM in an identical way.
2. Experiments and Methods The data analyzed in this work were obtained by applying mode II and mode III fatigue loading in the near-threshold regime of specimens made form commercially pure titanium and niobium (purity > 99.9%). In each specimen a precrack was introduced in the notch root by cyclic compressive loading [18]. This procedure resulted in an open precrack, which avoided a contact of the fracture surfaces and eliminated closure effects (friction). This method can only be used for specimens with notches. After precracking the specimens were annealed in order to eliminate the plastic zone in the vicinity of the crack tip, which resulted in the mean grain size dmNb = 400 μm in niobium and dmTi = 70 μm in titanium. The microstructure images taken by optical microscope are in Fig. 1. Annealing in vacuum enabled smoothing of the fracture surfaces at micro level and avoiding generation of an oxide layer which further ensured an absence of crack closure.
(b) (a) Fig. 1. Optical microscopy images of metallographic cuts showing the state of microstructure after heat treatment before the shear-mode experiments in (a) niobium and (b) titanium.
Three different experimental setups were used: (i) cylindrical specimen (Fig 2) with a circumferential notch with the inner diameter d = 12 mm and the outer diameter D = 25 mm loaded in torsion to generate a pure mode III loading, (ii) the same cylindrical specimen loaded by simple shear to load the crack in modes II and III, and (iii) the compact-tension shear (CTS) specimens for pure mode II loading. The effect of the notch can be neglected once the precrack reaches a certain length. If the precrack is longer that ρ/4, where ρ is the notch radius, the stress intensity factors can be calculated according to formulas for cracks of the length a, which represents the sum of the notch depth, the precrack length and the shear-
mode crack length [9, 19]. The notch root radius in all tested specimens was ρ = 150 μm (see Fig. 2) and the precrack lengths were in the range of 100 – 300 μm, which fulfils the above mentioned condition.
Fig. 2. Cylindrical specimen used for both the torsion test and the simple shear test with the notch detailed below. A typical precrack length of 0.15 mm is marked in the detail. The real precrack lengths were measured after the experiments and they ranged from 100 μm to 300 μm. Image adjusted according to [20]
2.1 Torsion Experiment The specimens (Fig. 2) were fixed into a device transforming force to torque loading of the specimen. The stress intensity factors (SIFs) were calculated according to Eq. (1) where a is the total crack length and YIII is the factor of geometry according to the asymptotic relationship Eq. (2) published in [21]: K III =
16T pa × YIII p D3
YIII = x
-
5 2
3 2 5 3 35 4 d æ 1 ö x + 0.208x 5 ÷ , x = ç1 + x + x + x + 8 16 128 D è 2 ø
(1) (2)
2.2 Simple- Shear Experiment A special device transforming tensile forces to a simple-shear was used to load the cylindrical specimens (Fig. 2). At the exact central point of the bar the bending moment was zero when considering ideal testing conditions and, therefore, no superposition of mode I was present. The circumferential crack was subjected to cyclic shear loading that resulted in various combinations of modes II and III as shown schematically in Fig. 3. The SIFs were determined using finite element analysis and the details of the calculation are published in [15, 22, 23].
(a)
(b)
Top mode III II mode
Left mode II mode III
j shear stress
Right mode II mode III
Bottom mode III mode II
Fig. 3. (a) Scheme of the device for simple shear loading of the cylindrical specimens. (b) Cross section of the cylindrical specimen in the notch showing the crack loading modes II and III resulting from the applied shear stress. Image adjusted according to [20].
2.3 Mode II experiment using CTS specimens Force was applied to the CTS specimen loading device (Fig. 4) in the orientation that resulted in a pure mode II crack loading. The notch root geometry wais the same as in Fig. 2 for the cylindrical specimen. The SIFs were calculated using the numerically determined formula Eq. (3) for the CTS specimens [24]
II
=
√
sin
.
.
.
.
,
(3)
where F is the applied force, w is the specimen width, t is the specimen thickness, ψ = 90° for pure mode II loading and a is the total crack length.
Fig. 4. Compact tension shear specimen used for mode II loading of the crack emanating from the notch root. The notch root geometry is the same as in Fig. 2 for the cylindrical specimen. The scheme on the right shows the loading device. Image adjusted according to [5, 15].
The simple-shear and CTS specimens were installed into the servo-hydraulic testing machine (Schenck) and loaded with a pulsating force with the cyclic ratio R = 0.1 and the frequency of 10 Hz. The experiments with torsion specimens had the same parameters except for the fact that the loading was applied at 100 Hz using the electromechanical resonant fatigue testing machine (Rumul). After applying N = 105 loading cycles, the shear-mode experiments were stopped and the specimens were fractured by fatigue in mode I. For each material and each experimental setup a few of specimens were tested (from 5 to 10) with different loading levels in the range from below threshold to the maximum load corresponding to approximately 3ΔKth. After some extension of the shear-mode crack the sliding-mode crack closure already emerged (and the crack was probably arrested). Due to this fact, the fractographical analysis was mostly done for specimens with a short shear-mode crack propagation. Other specimens with lower or higher loading were also observed and revealed analogical fractographical patterns. Therefore, only some of the analyzed specimens could be selected for presentation of the 3D data in this paper. Fracture surfaces were observed by stereophotogrammetry in SEM. This method measures spatial coordinates perpendicular to the fracture plane and reconstructs the fracture surfaces in three dimensions. The height profiles were measured and included in Figs. 6, 9 and 10. The coordinate l is defined by the white arrow in the fractography images and the coordinate z represents the height. The nature of crack propagation in 3D can also be visualized by tilted fracture surfaces in Figs. 5 and 8, where spatial orientations of the facets can be observed.
3. Results 3. 1. Mode II As already observed in the ARMCO iron [15], niobium (bcc) exhibited crystallographycontrolled crack growth. In each grain, conveniently oriented slip system with a highest Schmid factor was activated and dislocations were emitted from the crack tip. The local crack propagation direction and the orientation of the facet were pre-determined by the slip system. This behaviour is documented in Fig. 5 for a part of the fracture surface of a pure mode II loaded crack in niobium. The marked regions are the precrack, the pure mode II crack growth and the mode I final fracture. The direction of the shear stress, parallel to the mode II crack propagation direction, is marked by the arrow. One can see the lines parallel to the growth direction in the pure mode II crack growth area (hereafter called fibrous patterns). These lines are more clearly visible in Fig. 6 where the height profiles also show higher roughness is in the direction perpendicular to the lines than in the parallel one. These fibrous patterns possess different orientations in each grain as shown in Fig. 7. Note that the size of the facets nearly corresponds with that of the mean grain size dmNb = 400 μm.
shear stress precrack
mode II mode I final fracture
Fig. 5. Three-dimensional view of a fracture surface of the pure mode II loaded crack in niobium. The image was obtained by stereophotogrammetry in the SEM. The fracture surface was reconstructed in 3D and tilted to show the spatial relief. ΔKII = 2.2 MPa∙m1/2.
shear stress
profile 1
precrack
mode II
profile 2
10 5 0 -5 -10 -15 -20
z [μm]
Profile 1 0
10 5 0 -5 -10 -15 -20
l [μm] 10 20 30 40 50 60 70 80 90 100 110 120
z [μm]
Profile 2 0
l [μm] 10 20 30 40 50 60 70 80 90 100 110 120
Fig. 6. Three-dimensional data of a mode II fracture surface represented by the colour codes and the height Profiles 1 and 2. The data revealed that in the mode II area the roughness is higher in the direction perpendicular to the lines than in the direction parallel to the lines. ΔKII = 1.9 MPa∙m1/2.
precrack shear stress mode II
mode II
mode I final fracture
Fig. 7. SEM image of fracture surface of the mode II loaded crack in niobium. Fibrous patterns in the mode II area possess different orientations in each grain. ΔKII = 3.1 MPa∙m1/2.
shear stress
Fig. 8. Detailed 3D view of a facet on a mode II fracture surface in niobium (tilted image after 3D reconstruction by stereophotogrammetry in the SEM). It shows a higher roughness in the direction perpendicular to the lines than in the direction parallel to the lines. ΔKII = 3.1 MPa∙m1/2.
Further observation revealed that the lines started at the precrack front and then ran through the grain in the slip direction. Their orientation is parallel to or only slightly deviated from the applied shear stress direction and the local crack extension was generated by a cyclic slip along these lines. The particular direction in each grain was dictated by the slip system with the maximum resolved shear stress. This direction had usually a small deviation from the applied shear stress, which indicates that the lines originated by a mechanism depending on the crystal structure and that they could not originate by any contact mechanism. Indeed, the direction of lines produced by wear would be, in all grains, equal to that of the applied shear stress.
The spatial microgeometry of the precrack front caused that the lines (and emitted dislocations) started running at microscopically different heights with respect to the averaged (macroscopic) precrack plane. This means that the fibrous patterns exhibit a spatial microrelief depending on the precrack front microgeometry. This is evident from Fig. 6 where a rough profile corresponds to the direction perpendicular to the lines, while the profile parallel to the lines is rather smooth. The 3D image of a mode II facet in Fig. 8 offers even better demonstration of this kind of morphology.
3.2. Mode III The fractographical analysis of the morphology of mode II facets helped us to understand also the behaviour of mode III cracks. The crack growth mechanism as well as fracture morphology were more complicated in mode III which is illustrated by examples of fracture surface in Fig. 9. Some of the features observed on mode III fracture surfaces were equal to those identified on the mode II ones: coplanar growth along the shear plane, the crystallographical facets and lines oriented with a small deviation from the applied shear stress direction. In the case of mode III, however, the overall situation was much different from that of the mode II. The local crack extension along the parallel lines means that the crack propagated by local advances in the direction nearly parallel to the crack front. In the near-threshold regime, favourably oriented segments (local irregularities) of the precrack front, mostly associated with stress concentrations, were preferred for the crack nucleation and its further propagation as demonstrated in Fig. 9(a). When the crack passed through the first grain, it could continue growing in the adjacent grains with the preferred growth direction nearly parallel to that of the maximum shear. Therefore, the local crack growth direction was highly deviated from (almost perpendicular to) that of the macroscopic mode III crack propagation. This has two consequences: first, the cracks grew by a local mode II and second, the macroscopic mode III crack propagation was much more complicated and slower than that of the mode II cracks. These findings also revealed that, unlike for mode II cracks, there is no straightforward mode III crack growth (damage) mechanism. Indeed, a straightforward mechanism would not result in such a complicated way of crack propagation. The cracks grew in a direction deviated by a low angle from the applied shear stress, which corresponded to a high crack driving force. For example, Fig 9(b) shows that the lines of the facet A originated at microscopic precrack protrusions and followed them spatially in a direction highly deflected from that of the macroscopic mode III crack growth. The crack then continued growing into the neighbouring grain (segment B), where it deflected upwards and could be driven by even a higher shear stress component due to a different slip plane orientation. Meanwhile the crack segment C originated in another grain and, as soon as the fronts of cracks B and C met at different height levels, they joined by creating a step. Should the cracks A, B and C propagate perpendicular to the lines, such a step could not be created. Indeed, the unchanging colour at the precrack front near the B-C boundary means that there is no discontinuity in the spatial direction (z-axis). It supports the idea that the cracks grew along the crack front.
mode I final fracture
shear stress nucleation segment
mode III
precrack
A
B step
mode III mode I final fracture
100 50 0 -50 -100
l [μm] 100 200 300 400 500 600 700 800 900
precrack
shear stress
z [μm]
0
C
60 40 20 0 -20 -40
z [μm]
0
100
200
300
400
500
l [μm] 600
(b) (a) Fig. 9. Fracture surfaces of mode III loaded crack in niobium reconstructed in 3D by stereophotogrammetry with the corresponding height profiles below; (a) local irregularities of the precrack front, mostly associated with stress concentrations, were preferred for the crack nucleation. ΔKIII = 1.6 MPa∙m1/2; (b) lines of the facet A originated at microscopic precrack protrusions and followed them spatially in a direction highly deflected from that of the macroscopic mode III crack propagation, possessing a high shear stress component. The crack continued in the adjacent grain in segment B, where it deflected upwards due to a different slip plane orientation. Meanwhile the crack segment C originated in another grain and created a step by meeting the segment B at a different height level. ΔKIII = 2.2 MPa∙m1/2.
4. Discussion When analyzing the mode II and mode III crack growth, one should consider the effects of coupled modes II and III occurring in fracture specimens [e.g. 25, 26]. In the CTS specimen induction of mode III occurs which becomes significant close to the free surface. Therefore, the handbook formula for mode II stress intensity factor is not sufficiently precise and the quantitative data obtained using this specimen should be corrected. There are also other problems connected to the CTS specimen since its thickness is only 4 mm, which leads to parasitic out-of-plane loading and torque of the specimen. Despite this, the fractographical data presented in this work may still be useful for qualitative analysis of the mode II cracks. In the case of the round specimens (Fig. 2), however, no corner singularities are present and the geometry has symmetries that prevent from the occurrence of these effects. The simple shear specimen is symmetric with respect to the plane parallel to the shear stress perpendicular to the crack plane running through the centre of the specimen. The torsion specimen and its loading is axisymmetric. It should also be noted that despite the above mentioned arguments the micro geometry of a real precrack is always spatially tortuous which, to a certain extent, can lead to local mixedmode loading. The only way to produce ideal pure mode III crack front would be a precise cut using focused ion beam technique.
shear stress
precrack
mode III
Fig. 10(b)
mode III Fig. 10(d)
mode II+III
mode I final fracture
mode II Fig. 10(c)
shear stress direction
200 150 100 50 0 -50
z [μm]
l [μm] 0
200
400
600
(a)
800
1000
1200
(b)
shear stress
mode II+III
precrack
precrack mode II mode I final fracture
mode I final fracture
shear stress 30 20 10 0 -10 -20 -30
z [μm]
0
l [μm] 100 200 300 400 500 600 700 800 900
(c)
150 100 50 0 -50 -100
z [μm]
0
200
400
600
800
l [μm] 1000
(d)
Fig. 10. Fracture surfaces of shear-mode loaded cracks in titanium reconstructed in 3D by stereophotogrammetry in the SEM with the corresponding height profiles below. In all three modes the lines on facets are oriented close to the direction of applied shear stress; (a) overview of the fracture surface of the cylindrical specimen with the marked areas, where the SEM images were taken, with respect to the applied shear stress direction; (b) area of the mode III loading, ΔKIII = 4.8 MPa∙m1/2; (c) area of the mode II loading, ΔKII = 3.6 MPa∙m1/2; (d) area of the mixed mode II+III loading.
The results for mode II and mode III cracks can be compared with those of the mixed-mode II+III in niobium and titanium, which also revealed crystallographical facets with the fibrous patterns oriented nearly in the direction of the applied shear stress. This feature is, therefore, common for all loading modes II, III and II+III. A general overview of the fact that the LMIIM dominates in all kinds of shear-mode loading is illustrated in Fig. 10. Thus, for materials with coplanar shear-mode crack propagation, the LMIIM prevails among other possible mechanisms, e.g., the damage accumulation in the fracture process zone. The local mode II segments nucleate at microscopic irregularities of the crack front and extend to adjacent grains. Such a common micromechanism of crack nucleation and propagation under remote modes II, III and II+III can be described by the model of local mode II crack advances in agreement with the crack-growth model proposed by Pokluda and Pippan [8]. It also resembles the model of Nayeb-Hashemi et al. [7] for low-alloy steels in which, however, the mode II cracks originated at numerous inclusions ahead of the crack tip. Although it is very difficult to determine the local mode II stress intensity factors at the fronts of propagating crack segments, it is clear that the mode III crack propagation is not as straightforward as the mode II one. Thus, the complicated mechanism of mode III crack growth results in a higher resistance to crack propagation and, therefore, it can also explain the higher experimentally measured effective thresholds for mode III cracks than those for mode II ones.
5. Conclusions Fatigue experiments were conducted for modes II, III and II+III on commercially pure titanium and niobium. The procedure of cyclic compressive precracking resulted in an open precrack, which avoided contact of the fracture surfaces and eliminated friction. Observation of fracture surfaces generated by the loading in all the remote modes II, III and II+III revealed a nearly coplanar growth along the shear plane creating crystallographic facets with fibrous patterns oriented close to the direction of the applied shear stress. The shear-mode cracks grew by local mode II segments nucleated at spatially distributed microscopic irregularities of the crack front and extended to adjacent grains by forming fibrous patters in the direction nearly parallel to the applied shear stress. Macroscopic propagation of mode III cracks was much more complicated and slower than that of the mode II ones which means that no straightforward mode III crack growth mechanism exists. These findings give evidence that, in materials with nearly coplanar crack growth and for all kinds of shear-modes, a common mode II mechanism dominates other possible mechanisms as, e.g., the damage accumulation in the cyclic plastic zone.
Acknowledgements The authors acknowledge the financial support of this work by the Czech Science Foundation in the frame of the project No. GAP107/12/0800 and by the European Regional Development Fund (CEITEC CZ.1.05/1.1.00/02.0068).
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Highlights · · · · ·
Experiments for closure-free shear-mode fatigue cracks in titanium and niobium Convincing fractographic evidence of a common local mode II mechanism Cracks in all shear modes II, III and II+III grew by local mode II advances All cracks grew nearly in the direction of the applied shear stress Cracks nucleated at geometrical irregularities of precrack fronts
S0142-1123(16)30005-6 http://dx.doi.org/10.1016/j.ijfatigue.2016.02.042 JIJF 3879
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
18 December 2015 15 February 2016 29 February 2016
Please cite this article as: Vojtek, T., Hohenwarter, A., Pippan, R., Pokluda, J., Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium, International Journal of Fatigue (2016), doi: http://dx.doi.org/10.1016/j.ijfatigue.2016.02.042
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Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II, III and II+III in niobium and titanium Tomáš Vojtek1*, Anton Hohenwarter2, Reinhard Pippan3, Jaroslav Pokluda1,4
1
Central European Institute of Technology (CEITEC), Brno University of Technology, Technická 3058/10, CZ-61600 Brno, Czech Republic 2 Department of Materials Physics, Montanuniversität Leoben, Jahnstr. 12, A-8700 Leoben, Austria 3 Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstr. 12, A-8700 Leoben, Austria 4 Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, CZ-61669 Brno, Czech Republic *corresponding author: [email protected], tel.: +420 541 142 849
Key words shear loading modes, local mode II, growth mechanism, 3D crack path, coplanar growth
Abstract The paper is focused on an identification of the local mode II mechanism of fatigue cracks loaded under the remote mode III and the mixed mode II+III and presents a convincing experimental evidence of such a mechanism in materials with a nearly coplanar crack growth. Closure-free data were obtained by applying fatigue experiments in modes II, III and II+III in commercially pure titanium and niobium. The results revealed that the micromechanism of propagation of all kinds of shear-mode cracks can be described by a common model of advances of local mode II crack segments nearly in the direction of applied shear stress. These segments nucleated at spatial geometrical irregularities of the precrack front generating fibrous patterns at fracture surfaces.
Nomenclature ARMCO 3D bcc fcc hcp CTS MTS LMIIM SEM SIF
American Rolling Mills and Company three-dimensional body centred cubic face centred cubic hexagonal close packed compact-tension shear specimen maximum tangential stress local mode II mechanism scanning electron microscope stress intensity factor
a Δa/ΔN d
total crack length fatigue crack growth rate inner diameter of the cylindrical specimen
dmNb dmTi D F KII KIII ΔK ΔKth ΔKII ΔKIII l N R t T w YIII z ψ
mean grain size in niobium mean grain size in titanium outer diameter of the cylindrical specimen applied force mode II stress intensity factor mode III stress intensity factor stress intensity factor range crack growth threshold stress intensity factor range for mode II loading stress intensity factor range for mode III loading length coordinate of a fracture surface profile number of applied loading cycles cyclic stress ratio CTS specimen thickness applied torque CTS specimen width geometry function in the formula for mode III SIF height coordinate of a fracture surface profile orientation angle of the force applied to the CTS specimen loading device
1. Introduction In a majority of metallic materials, the mixed mode loaded cracks tend to bifurcate towards local opening mode according to the maximum tangential stress (MTS) criterion. Pure mode II cracks deflect by 70° and pure mode III cracks twist by 45° [1], i.e., they branch to a pure local mode I. This appears predominantly in materials with fcc structure or with secondary phases [2]. In both the ferritic-pearlitic and the JISS45C carbon steel (bcc metals), however, a rather extended (but limited) coplanar growth along the plane of maximum shear was reported [3, 4]. In single-phase bcc materials as niobium and ARMCO iron, moreover, the coplanar crack growth was observed in the whole near-threshold regime. The physical reason for the coplanar shear-mode crack growth in bcc metals is described in [5]. For a long time it was presumed that the fatigue damage ahead of mode II and mode III cracks loaded by the same ΔK-values (ΔKII = ΔKIII) in an isotropic material should be identical and, therefore, both the thresholds and the crack growth rates in these modes should also be equal. However, several authors measured slow crack growth rates in mode III with respect to those in mode I or mode II [6 – 8]. It should be noted that the sliding-mode crack closure has a significant influence on these crack growth rates in the near-threshold region. Loading of mode III cracks generates tortuous fractures surfaces (factory-roof morphology) which leads to a large friction and interlocking between the crack flanks and reduces the effective crack driving force significantly. On the other hand, sliding-mode crack closure of mode II loaded cracks vanishes when the crack deflects to the opening mode I. The friction stress component (also called extrinsic component) is much higher than the intrinsic one and is, therefore, responsible for the difference in crack growth rates of mode II and mode III cracks in materials with local mode I crack growth.
Coplanar shear-mode crack growth occurs in the low-cycle fatigue regime [9], however, in some metallic materials it was observed also in the near-threshold regime [5]. Here, the remote mode II and mode III crack growth thresholds and rates were comparable due to the same fracture morphology of both modes II and III and, consequently, the same level of friction between the crack flanks. The extrinsic component is usually several times higher than the intrinsic one and leads to a high scatter of mode II and mode III remote threshold data and to an apparent approximate identity of both remote thresholds (the sum of intrinsic and extrinsic resistance) [10]. Nevertheless, it was experimentally shown that the mode III crack growth rates are lower than those of mode II when effective (closure-free) stress intensities are taken into account [5]. This was explained by models of remote mode III growth based on Local Mode II Mechanisms (LMIIMs). In the last decade, experiments performed on bcc, hcp and fcc metals with suppressed friction effects in the crack wake revealed that all the measured effective thresholds in mode III were higher than those in mode II by the factor of approximately 1.7 [2, 5]. This result is in agreement with predictions of the LMIIM models. Some works devoted to measurement of the effective crack growth data for mode III cracks can be found in the literature. For example, in works [11 – 13] mode III fatigue experiments with superimposed static mode I loading were performed. However, these values were still higher than those obtained for shear-mode cracks propagating form closure-free precracks generated by cyclic compressive loading. Such experiments with suppressed friction stresses allow us not only to reveal the effective mode II and mode III thresholds but also the intrinsic growth mechanisms of shear-mode cracks. When clamping of asperities in the crack wake is present, it induces a local mode I at the crack front under the remote shear-mode loading [14] which disturbs the local pure shear mode by changing it to a more or less undefined mixed mode. Although a very small mode I component exists also in the case of coplanar cracks propagation (with crystallographic nature), this component is practically negligible in comparison with the shear mode one as commented in Discussion. The absence of friction is also important for the identification of the growth mechanism, since the friction contact leads to a fracture surface damage and does not allow observation of the related fractographical patterns. In some single-phase metals (ARMCO iron, niobium, titanium and nickel) the fractographical fibrous patterns revealed a crystallographic nature of the crack propagation which was explained by the model of cyclic plasticity based on emission of dislocations from the crack tip [15]. Detailed theoretical explanations of the micromechanisms and understanding of the intrinsic behaviour is the focus of another recent paper [16] which deals also with materials containing secondary phases. It should be emphasized, however, that the relation between the orientation of observed fibrous patterns and the local crack growth direction in the case of mode III loading could not be sufficiently elucidated until now. Indeed, the interpretation of these patterns on the coplanar fracture surfaces of the ARMCO iron was rather misleading since, due to the unusual behaviour of mode III loaded cracks, it was supposed that these cracks propagated in the direction perpendicular to the fibrous patterns. This paper revises the former idea by utilizing a clear experimental evidence of the LMIIM of fatigue cracks also in other materials with coplanar shear-mode growth, i.e., in niobium and titanium. Although the crack path in the latter material is not really coplanar, the mean deflection angle of the crack
path from the plane of maximum shear stress is rather small and the fracture surfaces of titanium also exhibit fibrous patterns. New findings about the origin of these patterns are also presented as discovered by observing three-dimensional (3D) pictures of fracture surface created by stereophotogrammetry in the scanning electron microscope (SEM). The fractographical data received for the ARMCO iron are not included in this paper due to their former publication in [15, 17]. They are, however, in agreement with those obtained for niobium (also a bcc metal) and can be interpreted using the LMIIM in an identical way.
2. Experiments and Methods The data analyzed in this work were obtained by applying mode II and mode III fatigue loading in the near-threshold regime of specimens made form commercially pure titanium and niobium (purity > 99.9%). In each specimen a precrack was introduced in the notch root by cyclic compressive loading [18]. This procedure resulted in an open precrack, which avoided a contact of the fracture surfaces and eliminated closure effects (friction). This method can only be used for specimens with notches. After precracking the specimens were annealed in order to eliminate the plastic zone in the vicinity of the crack tip, which resulted in the mean grain size dmNb = 400 μm in niobium and dmTi = 70 μm in titanium. The microstructure images taken by optical microscope are in Fig. 1. Annealing in vacuum enabled smoothing of the fracture surfaces at micro level and avoiding generation of an oxide layer which further ensured an absence of crack closure.
(b) (a) Fig. 1. Optical microscopy images of metallographic cuts showing the state of microstructure after heat treatment before the shear-mode experiments in (a) niobium and (b) titanium.
Three different experimental setups were used: (i) cylindrical specimen (Fig 2) with a circumferential notch with the inner diameter d = 12 mm and the outer diameter D = 25 mm loaded in torsion to generate a pure mode III loading, (ii) the same cylindrical specimen loaded by simple shear to load the crack in modes II and III, and (iii) the compact-tension shear (CTS) specimens for pure mode II loading. The effect of the notch can be neglected once the precrack reaches a certain length. If the precrack is longer that ρ/4, where ρ is the notch radius, the stress intensity factors can be calculated according to formulas for cracks of the length a, which represents the sum of the notch depth, the precrack length and the shear-
mode crack length [9, 19]. The notch root radius in all tested specimens was ρ = 150 μm (see Fig. 2) and the precrack lengths were in the range of 100 – 300 μm, which fulfils the above mentioned condition.
Fig. 2. Cylindrical specimen used for both the torsion test and the simple shear test with the notch detailed below. A typical precrack length of 0.15 mm is marked in the detail. The real precrack lengths were measured after the experiments and they ranged from 100 μm to 300 μm. Image adjusted according to [20]
2.1 Torsion Experiment The specimens (Fig. 2) were fixed into a device transforming force to torque loading of the specimen. The stress intensity factors (SIFs) were calculated according to Eq. (1) where a is the total crack length and YIII is the factor of geometry according to the asymptotic relationship Eq. (2) published in [21]: K III =
16T pa × YIII p D3
YIII = x
-
5 2
3 2 5 3 35 4 d æ 1 ö x + 0.208x 5 ÷ , x = ç1 + x + x + x + 8 16 128 D è 2 ø
(1) (2)
2.2 Simple- Shear Experiment A special device transforming tensile forces to a simple-shear was used to load the cylindrical specimens (Fig. 2). At the exact central point of the bar the bending moment was zero when considering ideal testing conditions and, therefore, no superposition of mode I was present. The circumferential crack was subjected to cyclic shear loading that resulted in various combinations of modes II and III as shown schematically in Fig. 3. The SIFs were determined using finite element analysis and the details of the calculation are published in [15, 22, 23].
(a)
(b)
Top mode III II mode
Left mode II mode III
j shear stress
Right mode II mode III
Bottom mode III mode II
Fig. 3. (a) Scheme of the device for simple shear loading of the cylindrical specimens. (b) Cross section of the cylindrical specimen in the notch showing the crack loading modes II and III resulting from the applied shear stress. Image adjusted according to [20].
2.3 Mode II experiment using CTS specimens Force was applied to the CTS specimen loading device (Fig. 4) in the orientation that resulted in a pure mode II crack loading. The notch root geometry wais the same as in Fig. 2 for the cylindrical specimen. The SIFs were calculated using the numerically determined formula Eq. (3) for the CTS specimens [24]
II
=
√
sin
.
.
.
.
,
(3)
where F is the applied force, w is the specimen width, t is the specimen thickness, ψ = 90° for pure mode II loading and a is the total crack length.
Fig. 4. Compact tension shear specimen used for mode II loading of the crack emanating from the notch root. The notch root geometry is the same as in Fig. 2 for the cylindrical specimen. The scheme on the right shows the loading device. Image adjusted according to [5, 15].
The simple-shear and CTS specimens were installed into the servo-hydraulic testing machine (Schenck) and loaded with a pulsating force with the cyclic ratio R = 0.1 and the frequency of 10 Hz. The experiments with torsion specimens had the same parameters except for the fact that the loading was applied at 100 Hz using the electromechanical resonant fatigue testing machine (Rumul). After applying N = 105 loading cycles, the shear-mode experiments were stopped and the specimens were fractured by fatigue in mode I. For each material and each experimental setup a few of specimens were tested (from 5 to 10) with different loading levels in the range from below threshold to the maximum load corresponding to approximately 3ΔKth. After some extension of the shear-mode crack the sliding-mode crack closure already emerged (and the crack was probably arrested). Due to this fact, the fractographical analysis was mostly done for specimens with a short shear-mode crack propagation. Other specimens with lower or higher loading were also observed and revealed analogical fractographical patterns. Therefore, only some of the analyzed specimens could be selected for presentation of the 3D data in this paper. Fracture surfaces were observed by stereophotogrammetry in SEM. This method measures spatial coordinates perpendicular to the fracture plane and reconstructs the fracture surfaces in three dimensions. The height profiles were measured and included in Figs. 6, 9 and 10. The coordinate l is defined by the white arrow in the fractography images and the coordinate z represents the height. The nature of crack propagation in 3D can also be visualized by tilted fracture surfaces in Figs. 5 and 8, where spatial orientations of the facets can be observed.
3. Results 3. 1. Mode II As already observed in the ARMCO iron [15], niobium (bcc) exhibited crystallographycontrolled crack growth. In each grain, conveniently oriented slip system with a highest Schmid factor was activated and dislocations were emitted from the crack tip. The local crack propagation direction and the orientation of the facet were pre-determined by the slip system. This behaviour is documented in Fig. 5 for a part of the fracture surface of a pure mode II loaded crack in niobium. The marked regions are the precrack, the pure mode II crack growth and the mode I final fracture. The direction of the shear stress, parallel to the mode II crack propagation direction, is marked by the arrow. One can see the lines parallel to the growth direction in the pure mode II crack growth area (hereafter called fibrous patterns). These lines are more clearly visible in Fig. 6 where the height profiles also show higher roughness is in the direction perpendicular to the lines than in the parallel one. These fibrous patterns possess different orientations in each grain as shown in Fig. 7. Note that the size of the facets nearly corresponds with that of the mean grain size dmNb = 400 μm.
shear stress precrack
mode II mode I final fracture
Fig. 5. Three-dimensional view of a fracture surface of the pure mode II loaded crack in niobium. The image was obtained by stereophotogrammetry in the SEM. The fracture surface was reconstructed in 3D and tilted to show the spatial relief. ΔKII = 2.2 MPa∙m1/2.
shear stress
profile 1
precrack
mode II
profile 2
10 5 0 -5 -10 -15 -20
z [μm]
Profile 1 0
10 5 0 -5 -10 -15 -20
l [μm] 10 20 30 40 50 60 70 80 90 100 110 120
z [μm]
Profile 2 0
l [μm] 10 20 30 40 50 60 70 80 90 100 110 120
Fig. 6. Three-dimensional data of a mode II fracture surface represented by the colour codes and the height Profiles 1 and 2. The data revealed that in the mode II area the roughness is higher in the direction perpendicular to the lines than in the direction parallel to the lines. ΔKII = 1.9 MPa∙m1/2.
precrack shear stress mode II
mode II
mode I final fracture
Fig. 7. SEM image of fracture surface of the mode II loaded crack in niobium. Fibrous patterns in the mode II area possess different orientations in each grain. ΔKII = 3.1 MPa∙m1/2.
shear stress
Fig. 8. Detailed 3D view of a facet on a mode II fracture surface in niobium (tilted image after 3D reconstruction by stereophotogrammetry in the SEM). It shows a higher roughness in the direction perpendicular to the lines than in the direction parallel to the lines. ΔKII = 3.1 MPa∙m1/2.
Further observation revealed that the lines started at the precrack front and then ran through the grain in the slip direction. Their orientation is parallel to or only slightly deviated from the applied shear stress direction and the local crack extension was generated by a cyclic slip along these lines. The particular direction in each grain was dictated by the slip system with the maximum resolved shear stress. This direction had usually a small deviation from the applied shear stress, which indicates that the lines originated by a mechanism depending on the crystal structure and that they could not originate by any contact mechanism. Indeed, the direction of lines produced by wear would be, in all grains, equal to that of the applied shear stress.
The spatial microgeometry of the precrack front caused that the lines (and emitted dislocations) started running at microscopically different heights with respect to the averaged (macroscopic) precrack plane. This means that the fibrous patterns exhibit a spatial microrelief depending on the precrack front microgeometry. This is evident from Fig. 6 where a rough profile corresponds to the direction perpendicular to the lines, while the profile parallel to the lines is rather smooth. The 3D image of a mode II facet in Fig. 8 offers even better demonstration of this kind of morphology.
3.2. Mode III The fractographical analysis of the morphology of mode II facets helped us to understand also the behaviour of mode III cracks. The crack growth mechanism as well as fracture morphology were more complicated in mode III which is illustrated by examples of fracture surface in Fig. 9. Some of the features observed on mode III fracture surfaces were equal to those identified on the mode II ones: coplanar growth along the shear plane, the crystallographical facets and lines oriented with a small deviation from the applied shear stress direction. In the case of mode III, however, the overall situation was much different from that of the mode II. The local crack extension along the parallel lines means that the crack propagated by local advances in the direction nearly parallel to the crack front. In the near-threshold regime, favourably oriented segments (local irregularities) of the precrack front, mostly associated with stress concentrations, were preferred for the crack nucleation and its further propagation as demonstrated in Fig. 9(a). When the crack passed through the first grain, it could continue growing in the adjacent grains with the preferred growth direction nearly parallel to that of the maximum shear. Therefore, the local crack growth direction was highly deviated from (almost perpendicular to) that of the macroscopic mode III crack propagation. This has two consequences: first, the cracks grew by a local mode II and second, the macroscopic mode III crack propagation was much more complicated and slower than that of the mode II cracks. These findings also revealed that, unlike for mode II cracks, there is no straightforward mode III crack growth (damage) mechanism. Indeed, a straightforward mechanism would not result in such a complicated way of crack propagation. The cracks grew in a direction deviated by a low angle from the applied shear stress, which corresponded to a high crack driving force. For example, Fig 9(b) shows that the lines of the facet A originated at microscopic precrack protrusions and followed them spatially in a direction highly deflected from that of the macroscopic mode III crack growth. The crack then continued growing into the neighbouring grain (segment B), where it deflected upwards and could be driven by even a higher shear stress component due to a different slip plane orientation. Meanwhile the crack segment C originated in another grain and, as soon as the fronts of cracks B and C met at different height levels, they joined by creating a step. Should the cracks A, B and C propagate perpendicular to the lines, such a step could not be created. Indeed, the unchanging colour at the precrack front near the B-C boundary means that there is no discontinuity in the spatial direction (z-axis). It supports the idea that the cracks grew along the crack front.
mode I final fracture
shear stress nucleation segment
mode III
precrack
A
B step
mode III mode I final fracture
100 50 0 -50 -100
l [μm] 100 200 300 400 500 600 700 800 900
precrack
shear stress
z [μm]
0
C
60 40 20 0 -20 -40
z [μm]
0
100
200
300
400
500
l [μm] 600
(b) (a) Fig. 9. Fracture surfaces of mode III loaded crack in niobium reconstructed in 3D by stereophotogrammetry with the corresponding height profiles below; (a) local irregularities of the precrack front, mostly associated with stress concentrations, were preferred for the crack nucleation. ΔKIII = 1.6 MPa∙m1/2; (b) lines of the facet A originated at microscopic precrack protrusions and followed them spatially in a direction highly deflected from that of the macroscopic mode III crack propagation, possessing a high shear stress component. The crack continued in the adjacent grain in segment B, where it deflected upwards due to a different slip plane orientation. Meanwhile the crack segment C originated in another grain and created a step by meeting the segment B at a different height level. ΔKIII = 2.2 MPa∙m1/2.
4. Discussion When analyzing the mode II and mode III crack growth, one should consider the effects of coupled modes II and III occurring in fracture specimens [e.g. 25, 26]. In the CTS specimen induction of mode III occurs which becomes significant close to the free surface. Therefore, the handbook formula for mode II stress intensity factor is not sufficiently precise and the quantitative data obtained using this specimen should be corrected. There are also other problems connected to the CTS specimen since its thickness is only 4 mm, which leads to parasitic out-of-plane loading and torque of the specimen. Despite this, the fractographical data presented in this work may still be useful for qualitative analysis of the mode II cracks. In the case of the round specimens (Fig. 2), however, no corner singularities are present and the geometry has symmetries that prevent from the occurrence of these effects. The simple shear specimen is symmetric with respect to the plane parallel to the shear stress perpendicular to the crack plane running through the centre of the specimen. The torsion specimen and its loading is axisymmetric. It should also be noted that despite the above mentioned arguments the micro geometry of a real precrack is always spatially tortuous which, to a certain extent, can lead to local mixedmode loading. The only way to produce ideal pure mode III crack front would be a precise cut using focused ion beam technique.
shear stress
precrack
mode III
Fig. 10(b)
mode III Fig. 10(d)
mode II+III
mode I final fracture
mode II Fig. 10(c)
shear stress direction
200 150 100 50 0 -50
z [μm]
l [μm] 0
200
400
600
(a)
800
1000
1200
(b)
shear stress
mode II+III
precrack
precrack mode II mode I final fracture
mode I final fracture
shear stress 30 20 10 0 -10 -20 -30
z [μm]
0
l [μm] 100 200 300 400 500 600 700 800 900
(c)
150 100 50 0 -50 -100
z [μm]
0
200
400
600
800
l [μm] 1000
(d)
Fig. 10. Fracture surfaces of shear-mode loaded cracks in titanium reconstructed in 3D by stereophotogrammetry in the SEM with the corresponding height profiles below. In all three modes the lines on facets are oriented close to the direction of applied shear stress; (a) overview of the fracture surface of the cylindrical specimen with the marked areas, where the SEM images were taken, with respect to the applied shear stress direction; (b) area of the mode III loading, ΔKIII = 4.8 MPa∙m1/2; (c) area of the mode II loading, ΔKII = 3.6 MPa∙m1/2; (d) area of the mixed mode II+III loading.
The results for mode II and mode III cracks can be compared with those of the mixed-mode II+III in niobium and titanium, which also revealed crystallographical facets with the fibrous patterns oriented nearly in the direction of the applied shear stress. This feature is, therefore, common for all loading modes II, III and II+III. A general overview of the fact that the LMIIM dominates in all kinds of shear-mode loading is illustrated in Fig. 10. Thus, for materials with coplanar shear-mode crack propagation, the LMIIM prevails among other possible mechanisms, e.g., the damage accumulation in the fracture process zone. The local mode II segments nucleate at microscopic irregularities of the crack front and extend to adjacent grains. Such a common micromechanism of crack nucleation and propagation under remote modes II, III and II+III can be described by the model of local mode II crack advances in agreement with the crack-growth model proposed by Pokluda and Pippan [8]. It also resembles the model of Nayeb-Hashemi et al. [7] for low-alloy steels in which, however, the mode II cracks originated at numerous inclusions ahead of the crack tip. Although it is very difficult to determine the local mode II stress intensity factors at the fronts of propagating crack segments, it is clear that the mode III crack propagation is not as straightforward as the mode II one. Thus, the complicated mechanism of mode III crack growth results in a higher resistance to crack propagation and, therefore, it can also explain the higher experimentally measured effective thresholds for mode III cracks than those for mode II ones.
5. Conclusions Fatigue experiments were conducted for modes II, III and II+III on commercially pure titanium and niobium. The procedure of cyclic compressive precracking resulted in an open precrack, which avoided contact of the fracture surfaces and eliminated friction. Observation of fracture surfaces generated by the loading in all the remote modes II, III and II+III revealed a nearly coplanar growth along the shear plane creating crystallographic facets with fibrous patterns oriented close to the direction of the applied shear stress. The shear-mode cracks grew by local mode II segments nucleated at spatially distributed microscopic irregularities of the crack front and extended to adjacent grains by forming fibrous patters in the direction nearly parallel to the applied shear stress. Macroscopic propagation of mode III cracks was much more complicated and slower than that of the mode II ones which means that no straightforward mode III crack growth mechanism exists. These findings give evidence that, in materials with nearly coplanar crack growth and for all kinds of shear-modes, a common mode II mechanism dominates other possible mechanisms as, e.g., the damage accumulation in the cyclic plastic zone.
Acknowledgements The authors acknowledge the financial support of this work by the Czech Science Foundation in the frame of the project No. GAP107/12/0800 and by the European Regional Development Fund (CEITEC CZ.1.05/1.1.00/02.0068).
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Highlights · · · · ·
Experiments for closure-free shear-mode fatigue cracks in titanium and niobium Convincing fractographic evidence of a common local mode II mechanism Cracks in all shear modes II, III and II+III grew by local mode II advances All cracks grew nearly in the direction of the applied shear stress Cracks nucleated at geometrical irregularities of precrack fronts