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Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes
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Engineering Fracture Mechanics 75 (2008) 833–844 www.elsevier.com/locate/engfracmech
Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes Sami Heinila¨ *, Gary B. Marquis, Timo Bjo¨rk Lappeenranta University of Technology, Department of Mechanical Engineering, P.O. Box 20, FI-53851 Lappeenranta, Finland Received 30 November 2006; received in revised form 17 January 2007; accepted 18 January 2007 Available online 25 January 2007
Abstract Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and ‘‘S’’ shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens. 2007 Elsevier Ltd. All rights reserved. Keywords: Crack path; Multi-axial fatigue; Cold forming; Residual stresses
1. Introduction Cold forming is a widely used fabrication process for plate structures. The cold-forming process is known to introduce high levels of residual stresses which may be either beneficial of detrimental with respect to fatigue strength of the structure [1–4]. During plate bending or fabrication of a cold-formed rectangular hollow section (CFRHS), the concave inside corner surfaces experience significant compressive plastic strains. The resulting tensile residual stresses in the bent region enhance the crack propagation during cyclic loading. The forming process may also coarsen the initially smooth surface and enhance both micro-cracking and fatigue crack development on the surface [5]. If the tensile residual stresses in a fabricated component are sufficiently high, a crack can propagate even if the applied local stresses are cyclically compressive. Greasly and Naylor [6] showed that a mode I fatigue crack *
Corresponding author. Tel.: +358 5 621 2450; fax: +358 5 621 2499. E-mail address: sami.heinila@lut.fi (S. Heinila¨).
0013-7944/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2007.01.010
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Nomenclature a crack tip length, crack depth b width of a specimen c half width of a crack d carriage traveling distance h height of a specimen, effective height l strain gauge distance from the beam specimen end r inner radius of the corner t material thickness CFRHS cold-formed rectangular hollow section tube KI, KII, KIII stress intensity factors for crack growth modes I, II, and III L length of the beam specimen R stress ratio in fatigue testing SIF stress intensity factor rr local stress component in cylindrical coordinates rh local stress component, total tangential stress on inside surface rz local stress component in cylindrical coordinates rext local stress due to external loading rres local residual stress rm mean local stress ra amplitude of local stress rmax maximum local stress Dr local stress range DF applied load range srh local shear stress component in cylindrical coordinates shz local shear stress component in cylindrical coordinates szr local shear stress component in cylindrical coordinates
within a tensile welding residual stress field can grow when the cyclic external stresses are compressive. However, in this study the cracks arrested after a period of propagation. Hermann [7] tested compact tension aluminium alloy specimens that were pre-compressed in order to create a tensile residual stress field ahead of the notch tip. It was shown that the crack length at which a crack arrested increased with increasing levels of the pre-compression, i.e. an increasing large tensile residual stress field. The relaxation of manufacturing residual stresses during cyclic loading is of great importance in understanding the fatigue crack paths in cold-formed corners. It has been reported that the cyclic stress-strain properties of the material, rather than the static yield strength, are related to the relaxation and redistribution of residual stresses [8,9]. The implication is that residual stresses in cyclic softening materials would relax during the stabilization of the cyclic stress-strain curve. In cyclic hardening materials, any potential residual stress relaxation would occur within the few first cycles. It has also been observed that relaxation may even occur at stress levels below the cyclic yield stress [9]. Other factors affecting the relaxation include the initial magnitude and gradient of the residual stress field, the degree of cold working, the cyclic stress amplitude and the mean stress ratio [10,11]. It has been reported that higher strength materials are more resistant to residual stress relaxation than lower strength materials because the relaxation in some cases is associated with the rearrangement of dislocations which depends on the macro- and microplastic strain [12]. The mobility of the dislocations also depends on the initial dislocation density and the initial dislocation arrangement [8]. The current study was partially motivated by an observed in-service failure of a beam-type structure fabricated from high-strength steel CFRHS [5]. Numerous cracks were observed to have initiated along the inside corner of the structural tube. These were parallel to the longitudinal direction of the tube and had large aspect ratios, c/a. Several cracks propagated through the tube wall and the resulting fatigue crack had an ‘‘S’’ shaped
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Fig. 1. Observed crack path in a tube failed in service (a). Observed crack path in a large-scale laboratory test specimen (b).
path as seen in Fig. 1a. In this current study, bending fatigue loading was applied to long CFRHS tubes, CFRHS tube sections and simple bent plates. The combinations of alternating bending stress, alternating shear stress and static residual stresses produced complex multi-axial stress states that influenced the fatigue crack path behaviour. 2. Experimental program Experimental studies were planned to both reproduce the cracking behaviour observed during service and also to better understand the fatigue properties of the corners of cold-formed structural tubes. The experimental program included large- and small-scale specimens that were tested under cyclic constant amplitude loading. Details of the three alternate experimental set-ups are described in subsequent sections of this paper. 2.1. Large-scale specimens The CFRHS profile used in the large-scale laboratory specimens were identical to the profile used in the failed in-service structure, see Fig. 2a. The nominal dimensions of the profile are b = 155 mm, h = 250 mm,
Fig. 2. (a) CFRHS profile and the crack initiation location. (b) The large-scale specimen test arrangement. (c) Applied loading for one travel cycle of carriage.
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r = 20 mm and t = 8 mm. The laboratory test configuration included two beam-type specimens that were pinned at one end and cyclically loaded at the other end by a hydraulic cylinder. Roller bearing elements were used both for the pin connections and at the hydraulic cylinder attachments. The middle support consisted of a carriage with roller elements which was translated laterally by a second hydraulic cylinder. The bending and translation cylinders operated in-phase. A schematic diagram of the experimental set-up is shown in Fig. 2b–c. The dimensions of the beam specimen are l = 1500 mm and L = 3600 mm. Strain gauges were fixed to the outer surface of the tubes in the centre of the corner radius at distance l from the end of the beam. The gauges were on both corners of the two specimens nearest to the movable carriage. These are the corner areas where cracks were observed to initiate. The lateral carriage translation, d, was 700 mm and the strain gauges were approximately at the centre point of this translation. In total, eight specimens were tested. The CFRHS was fabricated of high-strength steel with nominal yield stress of 650 MPa. Fatigue cracking was observed within and slightly outside the region of travel of the carriage. Multiple cracks were found to initiate near the centre of the inner corner of the tube as shown in Fig. 3a. 2.1.1. Residual stress measurements Residual stresses on the inner and outer surface of one CFRHS were measured using the X-ray diffraction method. Measured tensile residual stresses in the middle of the corner on the inner surface were 313 ± 32 MPa and compressive residual stresses on the outer surface were 74 ± 44 MPa. Residual stresses along the inner corner at positions other than the centre were also measured. These stresses were also tensile, but the magnitudes were lower and are not here reported. 2.1.2. Crack paths Crack initiation was observed to occur in the centre of the corner on the inside of the tube. This corresponded well with the position of highest measured tensile residual stress. Numerous small cracks, longitudinal with respect to the beam-type specimen, propagated along the inner surface and eventually joined to form a single long large aspect ratio crack, see Fig. 3a. Crack growth was initially orthogonal to the inner surface of the tube corner. Near the neutral plane of the wall the crack appeared to turn 90 with respect to the original direction. Eventually the crack propagated transverse through the tube wall in a direction approximately parallel to the initial crack growth direction. An example of one such zig-zag crack is shown in Fig. 1b. A closer microscopic inspection revealed that the crack did not turn near the neutral plane but rather joined with other cracks that had initiated tangential to the tube corner radius near the neutral plane, see Fig. 4. Testing also included two beam-type specimens that were thermal treated so as to relieve or reduce the residual stresses in the beam corners. These specimens showed a completely different failure mode. No cracks were observed to initiate on the inner surfaces of these tubes but the cracks initiated on the outer surface of the tube due to contact fatigue with the moving carriage support rollers. The contact fatigue failure can be clearly
Fig. 3. (a) Multiple cracks initiated on the inner surface. Dark regions are cracks highlighted using a dye-penetrant solution. (b) Cracks observed in thermal treated large-scale test specimens. The dark region corresponds to contact fatigue failure on the outer surface of the specimen.
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Fig. 4. Closer inspection of kinked crack observed in large-scale laboratory specimen (Fig. 1b) shows secondary cracks initiated on neutral plane. Neutral plane is indicated as dash-dot line.
seen as a dark region in Fig. 3b. The fatigue strength was improved approximately 24% with respect to the non-heat treated beams. This observation clearly demonstrated that the residual stresses have a major effect on fatigue crack path and fatigue strength of the structure. 2.2. Small-scale specimens Two types of small-scale cold-formed specimens were tested. In some cases alternate material strengths were also investigated. The small-scale specimens allowed alternate load modes to be applied to the corner regions. 2.2.1. CFRHS specimens Short sections of CFRHS tubes made of structural steel with yield strength of 650 MPa were fatigue tested using external R = 0.1 compression–compression loading as shown in Fig. 5a. The external loading was applied by compressing the tube section between two parallel flat plates. The section dimensions are b = 200 mm, h = 200 mm, r = 25 mm and t = 12.5 mm. This distortional cyclic loading resulted in nearly pure bending loading in the corner region. The major principal stress in the corner was the tangential stress with respect to the corner radius. Crack propagation in this case is dominated by mode I loading. 2.2.1.1. Crack paths. Because the loading was compression–compression, the upper and lower inside corners of the tube were subject to cyclic tensile loading while the side corners were subject to cyclic compressive loading. The majority of specimens failed in the specimen corner subjected to cyclic tensile stresses, but crack initiation
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Fig. 5. Applied loading on (a) CFRHS specimen and (b) ‘‘L’’ specimen. Some ‘‘L’’ specimens were created by bending initially straight plate to meet the final angle of 90 and inner radius r.
in some specimens was observed in those corners subject to applied cyclic compressive stresses. This observation highlights again the critical role of high tensile residual stresses in the tube corners. In all these cases the cracks propagated relatively straight through the wall thickness as seen in Fig. 6c. Similar crack paths were previously reported by Ba¨ckstro¨m et al. [13]. 2.2.2. ‘‘L’’ specimens A pilot series of small-scale ‘‘L’’ shaped plate specimens were manufactured either by cold-forming small plate sections or by cutting corner sections from CFRHS tubes similar to large-scale laboratory test specimens. The ‘‘L’’ specimens were fatigue tested using R = 0.1 compressive loading using boundary conditions as shown in Fig. 5b. The load DF was applied at the intersection of the flat region of the specimen and the point where the corner radius starts. In the case of specimens produced by plate bending, the initially straight plates were bent in a single operation with special tools to achieve a final angle of 90 and an inner radius r = 30 mm, see Fig. 5b. Other dimensions were h = 40 mm, t = 6 mm (bent plates), t = 8 mm (cut sections) and r = 16 mm (cut sections). The loading fixture in Fig. 5b produced a bending stress in the corner region similar to that produced by the distortion compression loading of the CFRHS sections, Fig. 5a. However, a significant alternating shear stress
Fig. 6. Observed crack paths in small-scale specimens. (a) ‘‘L’’ specimen cut from CFRHS with yield strength of 650 MPa. (b) ‘‘L’’ specimen bent from a plate with yield strength higher than 650 MPa. (c) CFRHS specimen.
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component was also produced which caused the fatigue crack propagation to occur under mixed mode I and II loading. 2.2.2.1. Crack paths. Even though the cyclic normal stresses on the outside of the corner were tensile as compared to cyclic compression on the inside of the corner, fatigue cracking was always observed to initiate on the inside surface of the corner. Curvilinear crack paths similar to the service failure crack, Fig. 1a, were observed in specimens cut from CFRHS tubes, see Fig. 6a. Crack paths in specimens formed by simple bending of plates with nominal yield strengths greater than 650 MPa were observed to be straight, see Fig. 6b. 3. Numerical modelling 3.1. Large-scale specimen loading In order to better understand the complex loading conditions in the inside corners of the large-scale beam specimens, a finite element (FE) model was created. Boundary and loading conditions in the FE model were as close as possible to the large-scale laboratory test specimen. The moving load was simulated as a series of analyses with the carriage in different locations. The bending force was modified at each step so as to represent the force used in the laboratory tests, see Fig. 2c. Residual stresses were excluded from this global model but the contact between the carriage and the surface of the beam was included. Results from the multiple analyses were combined to create an influence line for the outer surface strain at the tube corner as a function of carriage position which could be compared with the measured strain data from the laboratory test. Additionally, the influence lines of the internal surface and through-thickness stresses were estimated. Fig. 7 shows the influence lines for rh and shz as the carriage passes the outer surface strain gauge. Stress components sz and shr are zero along the inside surface of the tube but increase through the wall thickness. 3.2. Crack growth in large-scale specimen The fatigue crack paths in the large-scale specimens were investigated using three dimensional (3D) FE models of the tube corner region. In these models different crack depths were assumed. Influence lines for the stress intensity factors (SIF) KI, KII and KIII on the bottom of the crack front due to external loading only were computed based on 3D models. Fig. 8 shows the mode I, II and III SIF’s influence lines for a = 0.1 mm deep crack. It is clearly seen that modes I and III are dominant in crack front. This figure includes only the external loading, i.e., the contribution of residual stresses was excluded. Modes I and III were found to be dominant regardless of the crack depth. It is worth noting that the crack growth through the thickness is driven by modes I and III but the growth in longitudinal direction is driven by mode II. The longitudinal mode II and transverse mode III are result of the shear stress component shz.
Fig. 7. Influence lines for stresses rh and shz on the inner surface at the location of the strain gauge on outer surface. The distance on horizontal axis is the position of the moving carriage with zero corresponding to the location of the strain gauge (see Fig. 2b).
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Fig. 8. Influence lines for SIF’s KI, KII, and KIII on crack front at the location of the strain gauge on the outer surface. The distance on horizontal axis is the position of the moving carriage with zero corresponding to the location of the strain gauge (see Fig. 2b).
A detailed evaluation of the stress inside of the tube revealed that a crack, once initiated, would be subject to a complex crack opening stress state dominated by out-of phase modes I and III. It is interesting to note that the local tangential normal stress due to external loading, rhext, is compressive. Therefore, cyclic mode I stress intensity range due to external load only is also compressive. This observation explains the absence of macroscopic fatigue cracking in the inside corners of tubes which had been stress relieved. The total stress state would include both a static stress component due to residual stresses, rhres, in additional to the cyclic rhext. Residual stresses change through the wall thickness and also redistribute with crack advance. However, near the inside surface rhres > rhext and the crack is expected to propagate. 3.3. Residual stresses In order to better understand the initial residual stress state, the FE method was used to simulate the elastic–plastic cold-forming operation for a structural tube [14]. The computed through-thickness distribution of tangential residual stresses rhres is shown in Fig. 9a. Numerous simplifying assumptions were made in this simulation and, as a result, the computed residual stresses did not quantitatively agree with the stresses measured by X-ray diffraction. The errors were mainly due to the overly simple material model implemented and the use of a two dimensional (2D) simulation. The true cold-forming process for a CFRHS is three dimensional and is difficult to simplify. Qualitatively the predicted residual stress state is useful in that the sign of the predicted residual stresses are correct and ratio of predicted residual stress between the inside and outside surface are in good agreement. Therefore, in computations involving residual stress, the computed residual stresses were multiplied by a constant in order to match the measured stresses on the inside corner. Through thickness residual stress measurements and a more refined FE analysis have been left for future work. During cyclic loading the residual stresses change both due to relaxation and due to redistribution as the crack advances. Residual stress relaxation has not been examined in the current study but residual stress redistribution during crack growth was assessed using the FE method. Methods which continuously assess the preferential direction for crack advance are available [15,16]. These methods include remeshing in the crack tip region which, in combination with residual stress redistribution, is a very complex problem and not fully solved. Therefore, a node releasing method with a pre-selected crack path was used. The method was applied using a 2D FE model where the crack path was pre-selected so as to be in agreement with either of the two crack paths that were physically observed. The first path was the ‘‘S’’ shaped path observed in the service failure, i.e. Fig. 1a, while the second path was a straight through-thickness path in the corner region, i.e. Fig. 6b. Residual stress redistribution was computed along these two paths by subsequently releasing nodes along the path. Fig. 9b and c show calculated KI and KII as a function of crack length due to the residual stress alone. Contact between the crack faces was excluded in this analysis so SIF values are physically meaningless when KI < 0. Some mesh simplifications were also used and therefore the SIF’s can contain errors. In general KI and
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Fig. 9. Computed profile of through thickness tangential residual stress rhres (a). SIF’s due to residual stresses computed for straight crack path (b) and for curvilinear crack path (c).
KII could be calculated based on the J-integral or its domain integral conversion [17,18] or from crack tip mesh local nodal displacements [18]. In Fig. 9b it is clearly seen that KI for the straight crack approaches zero at a crack depth of about 3 mm. On the other hand, KI remains positive in the case of a curvilinear crack path, Fig. 9c. If the external cyclic loading also produces only compressive stresses, it is clear that a straight crack path through the thickness is not expected. On the other hand, the curvilinear crack will remain open even at greater crack depths. The fact that KII becomes negative is not significant with respect to crack growth rate. 4. Discussion The local tangential stress on inside surface at the corner is the sum of the stress induced by the external loading and tensile residual stress. In general, the local tangential stress under alternating external loading can be stated as rhmin ¼ rhres þ rhext min rhmax h Dr
¼ r þ rhext max ¼ rhmax rhmin ¼ rhext max hext Drh rhext r max min
rha ¼
ð1aÞ
hres
2
¼
ð1bÞ
rhext min
ð3Þ
2
rhm ¼ rhmax rha ¼ rhmax
ð2Þ
hext rhext 1 max rmin ¼ rhres þ ðrhext þ rhext min Þ 2 max 2
ð4Þ
where rhres is the local tangential residual stress, rhext is the local tangential stress caused by remote external loading, Drh is the range of the local tangential stress caused by the external loading cycle, rhm and rha are the local mean stress and stress amplitude respectively. The range of local stress and the stress amplitude are clearly independent of the residual stress while the mean stress depends on both the residual stress and the applied external stress.
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4.1. Mixed modes I and II Tensile or compressive mean stresses are known to have a strong influence on whether a crack grows predominantly by mode I or mode II [19,20]. Once a crack begins to branch, the mean stress does not influence the orientation of the back crack. Branch cracks initially propagate in the direction perpendicular to the local maximum tangential stress ðrhmax Þ and gradually changes to the direction perpendicular to the remote principal stresses [21,22]. Residual stresses would therefore be expected to have an influence on the dominant mode of crack growth but do not promote growth in arbitrary directions. The issue of residual stresses is of course further complicated by the fact that they are secondary stresses that continuously redistribute with crack advance. Residual stresses also frequently undergo cyclic relaxation and may have large gradients that change from tensile to compressive over very short distances. As mentioned previously, the loading configuration shown in Fig. 5b produces both tangential stresses and shear stresses in the corner region. A fatigue crack that initiates on the inner surface of the corner will initially propagate in the direction perpendicular to the local maximum tangential stress range. Even though the external load produces a local stress that is fully compressive, the crack will be open during the cycle due to the high tensile residual stresses. A crack propagating radially straight through the corner would eventually grow into a region of compressive residual stress due to residual stress redistribution and the mode I crack growth would arrest. The driving force for a straight crack is very small due to the significant compressive residual tangential stresses associated with this path. If the alternating shear stress was sufficiently small, the crack would arrest as was observed by previous researchers [6,7]. The large-scale CFRHS laboratory specimens showed straight radial crack paths in the tube corners to a depth of half the plate thickness (neutral plane). At this point the failure crack made a sudden 90 change of direction. The reason for the difference between this crack path and the more gradual change of direction observed for the in-service failed beam is not fully understood. The exact loading conditions of the in-service beam are not well documented but it is clearly a case of variable amplitude loading with possible under- and overloads and even with some beam torsion. By contrast, the cyclic loading of the laboratory test beam was nearly constant amplitude bending-only and the number of cycles to failure was in the range of 3 · 105 rather than the millions of cycles for the in-service structure. In case of the large-scale laboratory specimen the cyclic loading led to a network of tensile and shear cracks, see Fig. 4. The shear stress in the corner can be high enough to initiate a crack in the neutral plane after initiation and propagation of the primary crack. It is known that the multiple cracks can affect each other paths [23]. Of course the redistribution of the residual stresses is changed if two cracks are present and the crack tip plasticity must be greater due to potentially weaker structure. The greater magnitude of the external loading may lead to the initiation of the secondary crack. It is also suggested that the lower magnitudes simply leads to gradual turning of the crack to meet the direction perpendicular to the primary stress, i.e. to the direction of the maximum shear stress, and simply later initiation of the secondary crack. The turning is aided by the redistribution of the residual stresses in which the stresses tangential to the crack tip plane remain tensile. The alternating shear stresses near the neutral plane of the plate combined with a small tensile KI are sufficient to continue crack advance on the curved path. The increased stress amplitude may have some influence on the residual stress redistribution. Evidence on that was found e.g. Lee et al. [24], who stated that residual stress redistribution was affected also by the cyclic loading range. After a short period of crack extension along the neutral plane, mode I crack growth caused by the tensile external loading is again preferred to mode II and a branch crack develops that rapidly advances through the plate thickness. The ‘‘S’’ shaped crack path, Fig. 1a, is a result of lower applied loads and the zig-zag path, Fig. 1b, a result of higher applied loads. 4.2. Mixed mode I, II, and III It was computed that the external loading in the large beam-type specimen caused predominantly cyclic mixed mode I and III crack growth. Far fewer studies have been devoted to mixed mode I mode III loading as compared to mixed mode I mode II loading. Published experiments involving mixed mode I and III crack growth are normally limited to cases of tension–torsion loading of notched circular members with a torturous,
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factory-roof-like crack path [12,20] under low-amplitude loading and smooth crack paths for higher amplitudes of cyclic stress [12]. The geometrical constraint in a notched circular bar contribute significantly to the observed crack path. The cold-formed corners in the current investigation lack this geometrical constraint and the crack surfaces in the current study were very smooth. 4.3. Mode I loading The loading configuration shown in Fig. 5a produces predominantly tangential normal stresses and only negligible shear stresses. The resulting crack paths observed for the small-scale CFRHS specimens were nearly straight. In this case mode I crack propagation is assisted by the tensile residual stresses. The combination of external loading and redistributing residual stresses does not lead to a crack arrest condition but to a straight advancing crack. 5. Conclusions Fatigue crack paths in the corners of cold-formed high-strength structural tubes have been investigated both experimentally and numerically. Experiments have included full-scale beam fatigue tests and fatigue tests of cold-formed plate corners. Full scale beam tests were conducted in order to simulate the in-service failure and crack path. The simulation succeeded only partially and a new cracking behaviour, a zig-zag path involving two separately initiated cracks, was observed. The cold-formed corners have a complex residual stress state. The applied external loading combined with the residual stresses produce complex multi-axial cyclic stresses in the corner region. Depending on the exact loading conditions and material strength, straight, zig-zag and ‘‘S’’ shaped crack paths were observed. The tangential residual stresses due to cold-forming and the alternating shear stresses due to the external loading were found to have a dominating influence on the observed fatigue crack path. It was concluded: (1) The straight crack path was observed in loading cases where the external loading produced positive mode I SIF’s. (2) Fatigue crack initiated and propagated in the cold-formed corners even in those cases when the cyclic mode I SIF due to external loading was negative. The near-surface tensile residual stresses due to cold-forming were sufficient to open the crack so that cyclic compressive stresses resulted in crack growth. (3) For the zig-zag crack path observed in the laboratory beam tests, crack turning was enhanced by the initiation of transverse secondary cracks near the mid-point of the plate corner. The effects of the multiple cracks on the redistribution of residual stresses and the crack tip plasticity are complex and the subject of on-going investigations. (4) The crack growth in direction through the wall thickness in large-scale CFRHS beams was primarily due to cyclic mixed mode I and mode III. Mode II was also present but small compared to modes I and III. (5) FE analysis showed that the curved crack path in the CFRHS beams produced a tensile mode I SIF which would open an advancing crack and enhance cyclic mode I or mixed mode crack growth. The straight path was inhibited due to the negative mode I SIF associated with this path. (6) The final stage of crack growth from the plate mid-section to the outer surface for both zig-zag and ‘‘S’’ paths is due to external stresses that are locally tensile. References [1] [2] [3] [4] [5]
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Engineering Fracture Mechanics 75 (2008) 833–844 www.elsevier.com/locate/engfracmech
Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes Sami Heinila¨ *, Gary B. Marquis, Timo Bjo¨rk Lappeenranta University of Technology, Department of Mechanical Engineering, P.O. Box 20, FI-53851 Lappeenranta, Finland Received 30 November 2006; received in revised form 17 January 2007; accepted 18 January 2007 Available online 25 January 2007
Abstract Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and ‘‘S’’ shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens. 2007 Elsevier Ltd. All rights reserved. Keywords: Crack path; Multi-axial fatigue; Cold forming; Residual stresses
1. Introduction Cold forming is a widely used fabrication process for plate structures. The cold-forming process is known to introduce high levels of residual stresses which may be either beneficial of detrimental with respect to fatigue strength of the structure [1–4]. During plate bending or fabrication of a cold-formed rectangular hollow section (CFRHS), the concave inside corner surfaces experience significant compressive plastic strains. The resulting tensile residual stresses in the bent region enhance the crack propagation during cyclic loading. The forming process may also coarsen the initially smooth surface and enhance both micro-cracking and fatigue crack development on the surface [5]. If the tensile residual stresses in a fabricated component are sufficiently high, a crack can propagate even if the applied local stresses are cyclically compressive. Greasly and Naylor [6] showed that a mode I fatigue crack *
Corresponding author. Tel.: +358 5 621 2450; fax: +358 5 621 2499. E-mail address: sami.heinila@lut.fi (S. Heinila¨).
0013-7944/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2007.01.010
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Nomenclature a crack tip length, crack depth b width of a specimen c half width of a crack d carriage traveling distance h height of a specimen, effective height l strain gauge distance from the beam specimen end r inner radius of the corner t material thickness CFRHS cold-formed rectangular hollow section tube KI, KII, KIII stress intensity factors for crack growth modes I, II, and III L length of the beam specimen R stress ratio in fatigue testing SIF stress intensity factor rr local stress component in cylindrical coordinates rh local stress component, total tangential stress on inside surface rz local stress component in cylindrical coordinates rext local stress due to external loading rres local residual stress rm mean local stress ra amplitude of local stress rmax maximum local stress Dr local stress range DF applied load range srh local shear stress component in cylindrical coordinates shz local shear stress component in cylindrical coordinates szr local shear stress component in cylindrical coordinates
within a tensile welding residual stress field can grow when the cyclic external stresses are compressive. However, in this study the cracks arrested after a period of propagation. Hermann [7] tested compact tension aluminium alloy specimens that were pre-compressed in order to create a tensile residual stress field ahead of the notch tip. It was shown that the crack length at which a crack arrested increased with increasing levels of the pre-compression, i.e. an increasing large tensile residual stress field. The relaxation of manufacturing residual stresses during cyclic loading is of great importance in understanding the fatigue crack paths in cold-formed corners. It has been reported that the cyclic stress-strain properties of the material, rather than the static yield strength, are related to the relaxation and redistribution of residual stresses [8,9]. The implication is that residual stresses in cyclic softening materials would relax during the stabilization of the cyclic stress-strain curve. In cyclic hardening materials, any potential residual stress relaxation would occur within the few first cycles. It has also been observed that relaxation may even occur at stress levels below the cyclic yield stress [9]. Other factors affecting the relaxation include the initial magnitude and gradient of the residual stress field, the degree of cold working, the cyclic stress amplitude and the mean stress ratio [10,11]. It has been reported that higher strength materials are more resistant to residual stress relaxation than lower strength materials because the relaxation in some cases is associated with the rearrangement of dislocations which depends on the macro- and microplastic strain [12]. The mobility of the dislocations also depends on the initial dislocation density and the initial dislocation arrangement [8]. The current study was partially motivated by an observed in-service failure of a beam-type structure fabricated from high-strength steel CFRHS [5]. Numerous cracks were observed to have initiated along the inside corner of the structural tube. These were parallel to the longitudinal direction of the tube and had large aspect ratios, c/a. Several cracks propagated through the tube wall and the resulting fatigue crack had an ‘‘S’’ shaped
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Fig. 1. Observed crack path in a tube failed in service (a). Observed crack path in a large-scale laboratory test specimen (b).
path as seen in Fig. 1a. In this current study, bending fatigue loading was applied to long CFRHS tubes, CFRHS tube sections and simple bent plates. The combinations of alternating bending stress, alternating shear stress and static residual stresses produced complex multi-axial stress states that influenced the fatigue crack path behaviour. 2. Experimental program Experimental studies were planned to both reproduce the cracking behaviour observed during service and also to better understand the fatigue properties of the corners of cold-formed structural tubes. The experimental program included large- and small-scale specimens that were tested under cyclic constant amplitude loading. Details of the three alternate experimental set-ups are described in subsequent sections of this paper. 2.1. Large-scale specimens The CFRHS profile used in the large-scale laboratory specimens were identical to the profile used in the failed in-service structure, see Fig. 2a. The nominal dimensions of the profile are b = 155 mm, h = 250 mm,
Fig. 2. (a) CFRHS profile and the crack initiation location. (b) The large-scale specimen test arrangement. (c) Applied loading for one travel cycle of carriage.
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r = 20 mm and t = 8 mm. The laboratory test configuration included two beam-type specimens that were pinned at one end and cyclically loaded at the other end by a hydraulic cylinder. Roller bearing elements were used both for the pin connections and at the hydraulic cylinder attachments. The middle support consisted of a carriage with roller elements which was translated laterally by a second hydraulic cylinder. The bending and translation cylinders operated in-phase. A schematic diagram of the experimental set-up is shown in Fig. 2b–c. The dimensions of the beam specimen are l = 1500 mm and L = 3600 mm. Strain gauges were fixed to the outer surface of the tubes in the centre of the corner radius at distance l from the end of the beam. The gauges were on both corners of the two specimens nearest to the movable carriage. These are the corner areas where cracks were observed to initiate. The lateral carriage translation, d, was 700 mm and the strain gauges were approximately at the centre point of this translation. In total, eight specimens were tested. The CFRHS was fabricated of high-strength steel with nominal yield stress of 650 MPa. Fatigue cracking was observed within and slightly outside the region of travel of the carriage. Multiple cracks were found to initiate near the centre of the inner corner of the tube as shown in Fig. 3a. 2.1.1. Residual stress measurements Residual stresses on the inner and outer surface of one CFRHS were measured using the X-ray diffraction method. Measured tensile residual stresses in the middle of the corner on the inner surface were 313 ± 32 MPa and compressive residual stresses on the outer surface were 74 ± 44 MPa. Residual stresses along the inner corner at positions other than the centre were also measured. These stresses were also tensile, but the magnitudes were lower and are not here reported. 2.1.2. Crack paths Crack initiation was observed to occur in the centre of the corner on the inside of the tube. This corresponded well with the position of highest measured tensile residual stress. Numerous small cracks, longitudinal with respect to the beam-type specimen, propagated along the inner surface and eventually joined to form a single long large aspect ratio crack, see Fig. 3a. Crack growth was initially orthogonal to the inner surface of the tube corner. Near the neutral plane of the wall the crack appeared to turn 90 with respect to the original direction. Eventually the crack propagated transverse through the tube wall in a direction approximately parallel to the initial crack growth direction. An example of one such zig-zag crack is shown in Fig. 1b. A closer microscopic inspection revealed that the crack did not turn near the neutral plane but rather joined with other cracks that had initiated tangential to the tube corner radius near the neutral plane, see Fig. 4. Testing also included two beam-type specimens that were thermal treated so as to relieve or reduce the residual stresses in the beam corners. These specimens showed a completely different failure mode. No cracks were observed to initiate on the inner surfaces of these tubes but the cracks initiated on the outer surface of the tube due to contact fatigue with the moving carriage support rollers. The contact fatigue failure can be clearly
Fig. 3. (a) Multiple cracks initiated on the inner surface. Dark regions are cracks highlighted using a dye-penetrant solution. (b) Cracks observed in thermal treated large-scale test specimens. The dark region corresponds to contact fatigue failure on the outer surface of the specimen.
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Fig. 4. Closer inspection of kinked crack observed in large-scale laboratory specimen (Fig. 1b) shows secondary cracks initiated on neutral plane. Neutral plane is indicated as dash-dot line.
seen as a dark region in Fig. 3b. The fatigue strength was improved approximately 24% with respect to the non-heat treated beams. This observation clearly demonstrated that the residual stresses have a major effect on fatigue crack path and fatigue strength of the structure. 2.2. Small-scale specimens Two types of small-scale cold-formed specimens were tested. In some cases alternate material strengths were also investigated. The small-scale specimens allowed alternate load modes to be applied to the corner regions. 2.2.1. CFRHS specimens Short sections of CFRHS tubes made of structural steel with yield strength of 650 MPa were fatigue tested using external R = 0.1 compression–compression loading as shown in Fig. 5a. The external loading was applied by compressing the tube section between two parallel flat plates. The section dimensions are b = 200 mm, h = 200 mm, r = 25 mm and t = 12.5 mm. This distortional cyclic loading resulted in nearly pure bending loading in the corner region. The major principal stress in the corner was the tangential stress with respect to the corner radius. Crack propagation in this case is dominated by mode I loading. 2.2.1.1. Crack paths. Because the loading was compression–compression, the upper and lower inside corners of the tube were subject to cyclic tensile loading while the side corners were subject to cyclic compressive loading. The majority of specimens failed in the specimen corner subjected to cyclic tensile stresses, but crack initiation
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Fig. 5. Applied loading on (a) CFRHS specimen and (b) ‘‘L’’ specimen. Some ‘‘L’’ specimens were created by bending initially straight plate to meet the final angle of 90 and inner radius r.
in some specimens was observed in those corners subject to applied cyclic compressive stresses. This observation highlights again the critical role of high tensile residual stresses in the tube corners. In all these cases the cracks propagated relatively straight through the wall thickness as seen in Fig. 6c. Similar crack paths were previously reported by Ba¨ckstro¨m et al. [13]. 2.2.2. ‘‘L’’ specimens A pilot series of small-scale ‘‘L’’ shaped plate specimens were manufactured either by cold-forming small plate sections or by cutting corner sections from CFRHS tubes similar to large-scale laboratory test specimens. The ‘‘L’’ specimens were fatigue tested using R = 0.1 compressive loading using boundary conditions as shown in Fig. 5b. The load DF was applied at the intersection of the flat region of the specimen and the point where the corner radius starts. In the case of specimens produced by plate bending, the initially straight plates were bent in a single operation with special tools to achieve a final angle of 90 and an inner radius r = 30 mm, see Fig. 5b. Other dimensions were h = 40 mm, t = 6 mm (bent plates), t = 8 mm (cut sections) and r = 16 mm (cut sections). The loading fixture in Fig. 5b produced a bending stress in the corner region similar to that produced by the distortion compression loading of the CFRHS sections, Fig. 5a. However, a significant alternating shear stress
Fig. 6. Observed crack paths in small-scale specimens. (a) ‘‘L’’ specimen cut from CFRHS with yield strength of 650 MPa. (b) ‘‘L’’ specimen bent from a plate with yield strength higher than 650 MPa. (c) CFRHS specimen.
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component was also produced which caused the fatigue crack propagation to occur under mixed mode I and II loading. 2.2.2.1. Crack paths. Even though the cyclic normal stresses on the outside of the corner were tensile as compared to cyclic compression on the inside of the corner, fatigue cracking was always observed to initiate on the inside surface of the corner. Curvilinear crack paths similar to the service failure crack, Fig. 1a, were observed in specimens cut from CFRHS tubes, see Fig. 6a. Crack paths in specimens formed by simple bending of plates with nominal yield strengths greater than 650 MPa were observed to be straight, see Fig. 6b. 3. Numerical modelling 3.1. Large-scale specimen loading In order to better understand the complex loading conditions in the inside corners of the large-scale beam specimens, a finite element (FE) model was created. Boundary and loading conditions in the FE model were as close as possible to the large-scale laboratory test specimen. The moving load was simulated as a series of analyses with the carriage in different locations. The bending force was modified at each step so as to represent the force used in the laboratory tests, see Fig. 2c. Residual stresses were excluded from this global model but the contact between the carriage and the surface of the beam was included. Results from the multiple analyses were combined to create an influence line for the outer surface strain at the tube corner as a function of carriage position which could be compared with the measured strain data from the laboratory test. Additionally, the influence lines of the internal surface and through-thickness stresses were estimated. Fig. 7 shows the influence lines for rh and shz as the carriage passes the outer surface strain gauge. Stress components sz and shr are zero along the inside surface of the tube but increase through the wall thickness. 3.2. Crack growth in large-scale specimen The fatigue crack paths in the large-scale specimens were investigated using three dimensional (3D) FE models of the tube corner region. In these models different crack depths were assumed. Influence lines for the stress intensity factors (SIF) KI, KII and KIII on the bottom of the crack front due to external loading only were computed based on 3D models. Fig. 8 shows the mode I, II and III SIF’s influence lines for a = 0.1 mm deep crack. It is clearly seen that modes I and III are dominant in crack front. This figure includes only the external loading, i.e., the contribution of residual stresses was excluded. Modes I and III were found to be dominant regardless of the crack depth. It is worth noting that the crack growth through the thickness is driven by modes I and III but the growth in longitudinal direction is driven by mode II. The longitudinal mode II and transverse mode III are result of the shear stress component shz.
Fig. 7. Influence lines for stresses rh and shz on the inner surface at the location of the strain gauge on outer surface. The distance on horizontal axis is the position of the moving carriage with zero corresponding to the location of the strain gauge (see Fig. 2b).
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Fig. 8. Influence lines for SIF’s KI, KII, and KIII on crack front at the location of the strain gauge on the outer surface. The distance on horizontal axis is the position of the moving carriage with zero corresponding to the location of the strain gauge (see Fig. 2b).
A detailed evaluation of the stress inside of the tube revealed that a crack, once initiated, would be subject to a complex crack opening stress state dominated by out-of phase modes I and III. It is interesting to note that the local tangential normal stress due to external loading, rhext, is compressive. Therefore, cyclic mode I stress intensity range due to external load only is also compressive. This observation explains the absence of macroscopic fatigue cracking in the inside corners of tubes which had been stress relieved. The total stress state would include both a static stress component due to residual stresses, rhres, in additional to the cyclic rhext. Residual stresses change through the wall thickness and also redistribute with crack advance. However, near the inside surface rhres > rhext and the crack is expected to propagate. 3.3. Residual stresses In order to better understand the initial residual stress state, the FE method was used to simulate the elastic–plastic cold-forming operation for a structural tube [14]. The computed through-thickness distribution of tangential residual stresses rhres is shown in Fig. 9a. Numerous simplifying assumptions were made in this simulation and, as a result, the computed residual stresses did not quantitatively agree with the stresses measured by X-ray diffraction. The errors were mainly due to the overly simple material model implemented and the use of a two dimensional (2D) simulation. The true cold-forming process for a CFRHS is three dimensional and is difficult to simplify. Qualitatively the predicted residual stress state is useful in that the sign of the predicted residual stresses are correct and ratio of predicted residual stress between the inside and outside surface are in good agreement. Therefore, in computations involving residual stress, the computed residual stresses were multiplied by a constant in order to match the measured stresses on the inside corner. Through thickness residual stress measurements and a more refined FE analysis have been left for future work. During cyclic loading the residual stresses change both due to relaxation and due to redistribution as the crack advances. Residual stress relaxation has not been examined in the current study but residual stress redistribution during crack growth was assessed using the FE method. Methods which continuously assess the preferential direction for crack advance are available [15,16]. These methods include remeshing in the crack tip region which, in combination with residual stress redistribution, is a very complex problem and not fully solved. Therefore, a node releasing method with a pre-selected crack path was used. The method was applied using a 2D FE model where the crack path was pre-selected so as to be in agreement with either of the two crack paths that were physically observed. The first path was the ‘‘S’’ shaped path observed in the service failure, i.e. Fig. 1a, while the second path was a straight through-thickness path in the corner region, i.e. Fig. 6b. Residual stress redistribution was computed along these two paths by subsequently releasing nodes along the path. Fig. 9b and c show calculated KI and KII as a function of crack length due to the residual stress alone. Contact between the crack faces was excluded in this analysis so SIF values are physically meaningless when KI < 0. Some mesh simplifications were also used and therefore the SIF’s can contain errors. In general KI and
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Fig. 9. Computed profile of through thickness tangential residual stress rhres (a). SIF’s due to residual stresses computed for straight crack path (b) and for curvilinear crack path (c).
KII could be calculated based on the J-integral or its domain integral conversion [17,18] or from crack tip mesh local nodal displacements [18]. In Fig. 9b it is clearly seen that KI for the straight crack approaches zero at a crack depth of about 3 mm. On the other hand, KI remains positive in the case of a curvilinear crack path, Fig. 9c. If the external cyclic loading also produces only compressive stresses, it is clear that a straight crack path through the thickness is not expected. On the other hand, the curvilinear crack will remain open even at greater crack depths. The fact that KII becomes negative is not significant with respect to crack growth rate. 4. Discussion The local tangential stress on inside surface at the corner is the sum of the stress induced by the external loading and tensile residual stress. In general, the local tangential stress under alternating external loading can be stated as rhmin ¼ rhres þ rhext min rhmax h Dr
¼ r þ rhext max ¼ rhmax rhmin ¼ rhext max hext Drh rhext r max min
rha ¼
ð1aÞ
hres
2
¼
ð1bÞ
rhext min
ð3Þ
2
rhm ¼ rhmax rha ¼ rhmax
ð2Þ
hext rhext 1 max rmin ¼ rhres þ ðrhext þ rhext min Þ 2 max 2
ð4Þ
where rhres is the local tangential residual stress, rhext is the local tangential stress caused by remote external loading, Drh is the range of the local tangential stress caused by the external loading cycle, rhm and rha are the local mean stress and stress amplitude respectively. The range of local stress and the stress amplitude are clearly independent of the residual stress while the mean stress depends on both the residual stress and the applied external stress.
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4.1. Mixed modes I and II Tensile or compressive mean stresses are known to have a strong influence on whether a crack grows predominantly by mode I or mode II [19,20]. Once a crack begins to branch, the mean stress does not influence the orientation of the back crack. Branch cracks initially propagate in the direction perpendicular to the local maximum tangential stress ðrhmax Þ and gradually changes to the direction perpendicular to the remote principal stresses [21,22]. Residual stresses would therefore be expected to have an influence on the dominant mode of crack growth but do not promote growth in arbitrary directions. The issue of residual stresses is of course further complicated by the fact that they are secondary stresses that continuously redistribute with crack advance. Residual stresses also frequently undergo cyclic relaxation and may have large gradients that change from tensile to compressive over very short distances. As mentioned previously, the loading configuration shown in Fig. 5b produces both tangential stresses and shear stresses in the corner region. A fatigue crack that initiates on the inner surface of the corner will initially propagate in the direction perpendicular to the local maximum tangential stress range. Even though the external load produces a local stress that is fully compressive, the crack will be open during the cycle due to the high tensile residual stresses. A crack propagating radially straight through the corner would eventually grow into a region of compressive residual stress due to residual stress redistribution and the mode I crack growth would arrest. The driving force for a straight crack is very small due to the significant compressive residual tangential stresses associated with this path. If the alternating shear stress was sufficiently small, the crack would arrest as was observed by previous researchers [6,7]. The large-scale CFRHS laboratory specimens showed straight radial crack paths in the tube corners to a depth of half the plate thickness (neutral plane). At this point the failure crack made a sudden 90 change of direction. The reason for the difference between this crack path and the more gradual change of direction observed for the in-service failed beam is not fully understood. The exact loading conditions of the in-service beam are not well documented but it is clearly a case of variable amplitude loading with possible under- and overloads and even with some beam torsion. By contrast, the cyclic loading of the laboratory test beam was nearly constant amplitude bending-only and the number of cycles to failure was in the range of 3 · 105 rather than the millions of cycles for the in-service structure. In case of the large-scale laboratory specimen the cyclic loading led to a network of tensile and shear cracks, see Fig. 4. The shear stress in the corner can be high enough to initiate a crack in the neutral plane after initiation and propagation of the primary crack. It is known that the multiple cracks can affect each other paths [23]. Of course the redistribution of the residual stresses is changed if two cracks are present and the crack tip plasticity must be greater due to potentially weaker structure. The greater magnitude of the external loading may lead to the initiation of the secondary crack. It is also suggested that the lower magnitudes simply leads to gradual turning of the crack to meet the direction perpendicular to the primary stress, i.e. to the direction of the maximum shear stress, and simply later initiation of the secondary crack. The turning is aided by the redistribution of the residual stresses in which the stresses tangential to the crack tip plane remain tensile. The alternating shear stresses near the neutral plane of the plate combined with a small tensile KI are sufficient to continue crack advance on the curved path. The increased stress amplitude may have some influence on the residual stress redistribution. Evidence on that was found e.g. Lee et al. [24], who stated that residual stress redistribution was affected also by the cyclic loading range. After a short period of crack extension along the neutral plane, mode I crack growth caused by the tensile external loading is again preferred to mode II and a branch crack develops that rapidly advances through the plate thickness. The ‘‘S’’ shaped crack path, Fig. 1a, is a result of lower applied loads and the zig-zag path, Fig. 1b, a result of higher applied loads. 4.2. Mixed mode I, II, and III It was computed that the external loading in the large beam-type specimen caused predominantly cyclic mixed mode I and III crack growth. Far fewer studies have been devoted to mixed mode I mode III loading as compared to mixed mode I mode II loading. Published experiments involving mixed mode I and III crack growth are normally limited to cases of tension–torsion loading of notched circular members with a torturous,
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factory-roof-like crack path [12,20] under low-amplitude loading and smooth crack paths for higher amplitudes of cyclic stress [12]. The geometrical constraint in a notched circular bar contribute significantly to the observed crack path. The cold-formed corners in the current investigation lack this geometrical constraint and the crack surfaces in the current study were very smooth. 4.3. Mode I loading The loading configuration shown in Fig. 5a produces predominantly tangential normal stresses and only negligible shear stresses. The resulting crack paths observed for the small-scale CFRHS specimens were nearly straight. In this case mode I crack propagation is assisted by the tensile residual stresses. The combination of external loading and redistributing residual stresses does not lead to a crack arrest condition but to a straight advancing crack. 5. Conclusions Fatigue crack paths in the corners of cold-formed high-strength structural tubes have been investigated both experimentally and numerically. Experiments have included full-scale beam fatigue tests and fatigue tests of cold-formed plate corners. Full scale beam tests were conducted in order to simulate the in-service failure and crack path. The simulation succeeded only partially and a new cracking behaviour, a zig-zag path involving two separately initiated cracks, was observed. The cold-formed corners have a complex residual stress state. The applied external loading combined with the residual stresses produce complex multi-axial cyclic stresses in the corner region. Depending on the exact loading conditions and material strength, straight, zig-zag and ‘‘S’’ shaped crack paths were observed. The tangential residual stresses due to cold-forming and the alternating shear stresses due to the external loading were found to have a dominating influence on the observed fatigue crack path. It was concluded: (1) The straight crack path was observed in loading cases where the external loading produced positive mode I SIF’s. (2) Fatigue crack initiated and propagated in the cold-formed corners even in those cases when the cyclic mode I SIF due to external loading was negative. The near-surface tensile residual stresses due to cold-forming were sufficient to open the crack so that cyclic compressive stresses resulted in crack growth. (3) For the zig-zag crack path observed in the laboratory beam tests, crack turning was enhanced by the initiation of transverse secondary cracks near the mid-point of the plate corner. The effects of the multiple cracks on the redistribution of residual stresses and the crack tip plasticity are complex and the subject of on-going investigations. (4) The crack growth in direction through the wall thickness in large-scale CFRHS beams was primarily due to cyclic mixed mode I and mode III. Mode II was also present but small compared to modes I and III. (5) FE analysis showed that the curved crack path in the CFRHS beams produced a tensile mode I SIF which would open an advancing crack and enhance cyclic mode I or mixed mode crack growth. The straight path was inhibited due to the negative mode I SIF associated with this path. (6) The final stage of crack growth from the plate mid-section to the outer surface for both zig-zag and ‘‘S’’ paths is due to external stresses that are locally tensile. References [1] [2] [3] [4] [5]
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