Crack propagation mechanism and life prediction for very-high-cycle fatigue of a structural steel in different environmental medias

The influence of environmental medias on crack propagation of a structural steel at high and veryhigh-cycle fatigue (VHCF) regimes is investigated based on the fatigue tests performed in air, water and 3.5% NaCl aqueous solution. Crack propagation mechanisms due to different crack driving forces are investigated in terms of fracture mechanics. A model is proposed to study the relationship between fatigue life, applied stress and material property in different environmental medias, which reflects the variation of fatigue life with the applied stress, grain size, inclusion size and material yield stress in high cycle and VHCF regimes. The model prediction is in good agreement with experimental observations.


MATERIAL AND EXPERIMENTAL METHOD
our-glass shape specimens (Fig. 1) of a structural steel 40Cr (0.4% C, 1% Cr) were tested with a rotary bending machine operating at a frequency of 52.5 Hz and the testing environments were of three types, namely laboratory air, fresh water and 3.5% NaCl aqueous solution.The average size of original austenite grains is 11.2 m and the average yield stress is 1501 MPa.Vickers microhardness indentation on the heat-treated specimen gives the average value of 545 kgf/mm 2 with the uniform distribution over the specimen cross section.The pH values of fresh water and 3.5% NaCl aqueous solution are 7.70 and 7.47, respectively.Based on the fatigue test data and scanning electron microscopy (SEM) observations of fracture surfaces, the effect of environment on the fatigue behavior at high cycle and VHCF regimes was examined.

S-N CURVES
or specimens tested in laboratory air (triangles in Fig. 2), single crack originated from the surface of the specimens with fatigue life or the number of cycles to failure Nf less than 10 7 loading cycles and the corresponding stress levels are above 700 MPa, whereas the crack started from subsurface for the specimens with Nf beyond 10 7 loading cycles and the stress levels are below 700 MPa.For fatigue testing in fresh water, a similar stepwise S-N curve is presented (squares in Fig. 2), but the stress corresponds to the transition part of the S-N curve is dramatically decreased.For the fatigue tests in NaCl aqueous solution, the S-N curve (circles symbols in Fig. 2) displays a continuously descending shape.The fatigue strength is even lower than that tested in water from high cycle to VHCF regime, implying that the effect of NaCl aqueous solution on the degradation of fatigue strength for the structural steel is more remarkable than that of water media.

H F FRACTOGRAPHY AND FRACTURE MECHANICS ANALYSIS FOR SPECIMENS TESTED IN AIR
or the specimens tested in laboratory air, all the fatigue fracture surfaces of both surface initiation and subsurface initiation modes present the morphology of three regions as shown in Fig. 3(a).Region A [Fig. 3(a), (b)] is the crack initiation and early propagation zone, in which crack propagation velocity is very slow to produce a relatively smooth fracture surface with transgranular cleavage-like morphology and fatigue striations.This region is responsible for a substantially large part of the total fatigue life.As shown in Fig. 3 (b), crack initiated at the subsurface of specimen at VHCF regime, forming a fisheye pattern originated from a nonmetallic inclusion with the main chemical compositions examined as Al, Ca and O. Region B is the steady and relatively fast growth zone and Fig. 3(c) is a local micrograph of this zone showing quasi-cleavage morphology.Region C is the final fracture zone and the fracture surface presents the ordinary morphology of dimple pattern [Fig.3(d)].By considering the inner boundary as the crack tip for Regions A and B, the stress intensity factor (SIF) KI is calculated with the following formula where σ a is the applied stress, a is the crack radius and F is the geometry factor.In the calculation, Region A is assumed to be elliptical shape and Region B is regarded as circular shape where ΔK is the amplitude of K I , σ y is the yield stress of the material.The calculated plastic zone size for Region A is 32.6 μm, which approximately equals to the size of 2-3 grain sizes.In the crack initiation and early propagation stage (Region A), grain boundary serves as a microstructural obstacle.In Region B, the calculated plastic zone size is 1449 μm.As the increase of the plastic zone, the crack propagation rate increases significantly.In Region C, as the decrease of the ligament of the specimen, the specimen displays a plane stress state.Thus, the fracture morphology shows a shear fracture with an angle of 45 degree along the tension direction.For the tested specimens, the fracture is plane strain condition in the crack initiation stage and the crack tip has a high constraint effect as a result of the small plastic zone size and high stress triaxiality.With the decrease of ligament in Region C, the crack tip has a small constraint which causes large plastic deformation.However, the crack tip constraint effect during the crack propagation needs a further quantification by using a K-T or J-Q method.
The SIF ranges for inclusions and fisheye patterns are calculated by the following formula [2,6] where area is the square root of the area for inclusions or fisheyes.Fig. 4 (a) shows the relationship between ΔK and Nf.ΔK for inclusions is about 2.83 MPam 1/2 irrespective of the fatigue life, which is smaller than the threshold SIF range (ΔK th ) of the material.ΔK for fisheyes is about 10 MPam 1/2 , which is somewhat higher than ΔK th of the material.Therefore, it is understood that a crack that originates at an inclusion can propagate until it forms a fisheye pattern.
According to Murakami's model [2], fatigue strength at 10 8 cycles, denoted as σ w , is predicted by 1.56( 120) ( area) where HV is the Vickers hardness of the material.Fig. 4 (b) shows the relationship between σ max /σ w and number of cycles to failure.The ratio is between 1 and 1.2, indicating that the fatigue strength of the material in the present study is well predicted by the Murakami model.

FRACTOGRAPHY FOR SPECIMENS TESTED IN ENVIRONMENTAL MEDIAS
or the case of fatigue tested in water and 3.5% NaCl aqueous solution, the crack origination observed by SEM is mainly the surface related initiation.Additionally, unlike the single crack origin for specimens tested in air, multiple fatigue crack origins were observed [8], and the fracture surface morphology for fatigue crack steady growth zone is predominantly intergranular, as shown in Fig. 5, where the secondary cracks along grain boundaries and cross section of the specimens are observed, which is the phenomenon of grain boundary embrittlement due to the aqueous environmental effect.The presence of widespread secondary cracks is the damage characteristics of the material subjected to aqueous environmental medias.

MODEL FOR S-N CURVE PREDICTION IN DIFFERENT ENVIRONMENTAL MEDIAS
t is known that crack initiation related to nonmetallic inclusions (subsurface crack initiation) is attributed to the weak cohesive state between inclusion and matrix.Under cyclic loading, a crack may easily form due to the interface debonding and grow into the matrix.In such a case, the subsurface crack initiation cycle Ni is [19] where W i is the surface energy related to subsurface crack initiation and ΔU i is the unit increment of energy for subsurface crack initiation.Wi and ΔUi are functions of grain radius l, inclusion radius r (ψ=r/l), stress amplitude Δσ and the resistance of dislocation movement k (φ=0.5Δσ/k).N  is defined to normalize i N , such that where with  being the shear modulus and ν being Poisson's ratio.Thus, the normalized N i is denoted as where   U is the dimensionless unit increment of energy for subsurface crack initiation.The variation of i n with φ and ψ are demonstrated in Fig. 6 by assuming φ to be 1.1, 1.2, 1.4, 2 and 4, and ψ varying from 0 to 2. It is shown that fatigue life i n increases with the decrease of φ, i.e. the decrease of fatigue loading Δσ or the increase of the resistance of dislocation movement k.For a given loading state (φ being constant), i n generally decreases with the increase of ψ, i.e. the increase of inclusion size r or the decrease of grain size l.The trends are in agreement with the experimental observations.Yang et al. [20] observed that the fatigue life increases with the decrease of inclusion size for an alloy steel.It is widely observed that the fatigue life increases with the decrease of the applied loading [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].Zhao et al. [10] found that the fatigue life increases with the resistance of the dislocation movement, i.e. the yield stress of material.For fatigue crack initiation at surface, by considering the surface crack factor and half cycling process [7,19], surface crack initiation cycle N s is where Ws is surface energy related to surface crack initiation.The normalized surface crack initiation cycle s n is where k w is the ratio of surface energy for crack formation at subsurface to that at surface (W i /W s ).Note that both i n and s n are functions of φ and ψ.In short, Eqs. ( 8) and ( 10) are used to calculate the fatigue life for crack initiation at surface or at subsurface in different environmental medias.
For the case tested in air, kw is taken as 3 in the calculation [8,21].For the case tested in 3.5 % NaCl solution, kw is taken as 25 times of that in air, i.e. 75, from the relationship of K Ic in air and the aqueous solution [8,22].The fatigue life for surface crack initiation s n and subsurface crack initiation i n in air as a function of φ and ψ is compared in Fig. 7 (a).It is seen that the subsurface crack initiation life is higher than the surface crack initiation life for a high φ (high loading or low material yield stress).Thus, surface crack initiation occurs much easier in this stage.With decreasing φ, the surface crack initiation life is higher than the subsurface crack initiation life at the same φ, which as a consequence leads to the subsurface crack initiation in this stage.At points A, B and C, the subsurface crack initiation life equals to the surface crack initiation.The three points correspond to the transition plateau in an S-N curve from the subsurface to the surface crack initiation.Fig. 7 (b) compares the surface crack initiation life with subsurface crack initiation life in 3.5% NaCl solution.A similar trend as that in air is found.However, the transition from surface to subsurface crack initiation in 3.5% NaCl solution is much lower than that in air.This is in agreement with the experimental observations that in aqueous environmental media, the crack initiation starts from the surface even in VHCF regime.It is also seen from Figs. 7 (a) and (b) that when subjected to the same loading, the fatigue life in air is much longer than that in aqueous medias.This explains the characteristics of the S-N curve in Fig. 2.

CONCLUSIONS
ased on this study, the following conclusions are drawn: (1) During the crack propagation process for specimens tested in air, fracture surface displays three regions with different crack propagation mechanisms.The formation of different morphologies in these regions is attributed to different crack driving forces and different extents of crack tip constraint ahead of crack tip.
(2) The KI value of fisheye crack is close to the corresponding ΔKth.And there is an early crack steady growth zone named region A with constant K I value between ΔK th and fracture toughness.
(3) The fatigue strength for specimens tested in water and in 3.5% NaCl aqueous solution are significantly decreased compared to that tested in air.The fractography characteristics for specimens tested in aqueous solution are multiple crack origination and intergranular mode with widespread secondary cracks in crack steady propagation period.(4) A model is proposed to study the relationship between fatigue life, applied stress and material property in VHCF in different environmental medias.This model predicts that fatigue life decreases with the increase of applied loading and inclusion size, whereas it increases with the increase of material yield stress.In 3.5% NaCl solution, the fatigue life decreases significantly and surface crack initiation occurred even in VHCF regime.The model prediction is in good agreement with experimental observations.

Figure 1 :
Figure 1: Schematic drawing of hour-glass shape specimen for rotary bending fatigue test (dimensions in mm).

Figure 2 :
Figure2: S-N curves for specimens tested at laboratory air, fresh water and 3.5% NaCl aqueous solution, hollow symbols: crack origination at surface, solid symbols: crack origination at subsurface, semi-solid symbols: mixed crack origination.

Figure 3 :
Figure 3: Fracture surface of a specimen tested in laboratory air, at σmax = 610 MPa and Nf = 3.27×10 8 , (a) whole fracture surface (C.O.: crack origin), (b) enlargement of Region A, (c) enlargement of Region B and (d) enlargement of Region C.
. The values of K I almost keep constant at 16 MPam 1/2 from F VHCF regime for Region A. The values of KI for Region B are between 35 and 60 MPam 1/2 , which correspond to the material fracture toughness K Ic .K I for Region A and B is used to calculate the plastic zone size r p around the crack tip based on the expression

Figure 4 :
Figure 4: (a) ΔK for inclusions and fisheyes, (b) relationship between σ max /σ w and number of cycles to failure.

Figure 5 :
Figure 5: (a) Cracking surface for the specimen tested in water, at σ max =156 MPa and N f =8  10 7 , (b) secondary cracking (SC) in the cross section of the specimen tested in 3.5% NaCl, at σmax=41.3 MPa and Nf =9  10 7 .

Figure 6 :
Figure 6: Predicted ni of subsurface crack initiation for specimens tested in air, for different loading levels and material properties.

Figure 7 :
Figure 7: (a) Predicted results of fatigue life for surface and subsurface crack initiation in air, (b) predicted S-N curves for surface and subsurface crack initiation in 3.5% NaCl solution.