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I. S. Nikitin et al.
12.4 Calculation Results
Calculation of S-N curves and fatigue cracks propagation performed both in LCFHCF and VHCF modes are presented in Sect. 12.4.
To determine the parameters of the proposed model and verify its performance,
one of the fatigue experiments described in [29] was performed numerically. From the
condition of matching the experimental and calculated fatigue curve for a specimen
of certain geometry for a given loading amplitude and cycle asymmetry, the numerical coefficients were found. Using the obtained values, the experimental results on
specimens of a different geometry and asymmetry coefficients were reproduced, and
calculation algorithm operability was confirmed.
Hereinafter, the numerical results for LCH-HCF mode and VHCF mode are
discussed in Sects. 12.4.1 and 12.4.2, respectively.
12.4.1 Results for LCH-HCF Mode
Initial tests were conducted on a plate 100 × 25 × 1.57 mm in size with 1.56 mm
diameter through a hole in the center. Ratification tests were conducted on a Vnotched specimen that has 15 mm width w/o a notch, thickness of 1.7 mm, a notch
depth of 1.32 mm, a V-notch angle of 60 degrees, and a notch radius of 0.675 mm. The
cyclic loading of the upper and lower boundaries of the specimen with an amplitude
of 0.096 mm with the development of damage zones up to macroscopic destruction
was simulated and matched with the results from [29]. In the center of the plate,
there is a through-hole with diameter of 1.56 mm. Plate material is titanium alloy
with strength and fatigue parameters σ B = 1135 MPa, σ u = 30 MPa, β LH = 0.31.
Elasticity modulus of intact alloy are λ 0 = 77 GPa, μ 0 = 44 GPa. Figures 12.2
and 12.4 show the lines of the effective stress level σ LH for the specimen with a hole
(Fig. 12.2) and for the specimen with a notch (Fig. 12.4) in two states: before the
fatigue quasi-crack initiation and at the moment when it has passed approximately
halfway to macro-destruction.
In Figs. 12.3 and 12.5, the results of real and computational experiments on
constructing fatigue curves for specimens with a hole and a side notch are presented.
Both real and calculated points represent the moment of crack initiation. The curves
in the figures approximate the experimental points. The calculations presented in
Fig. 12.3b almost exactly fit the approximation curve for the values of the model
parameters γ = 0.1 and k = 0.5. Utilizing these parameters, the fatigue curves are
presented in Fig. 12.3a (specimen with a hole, R = −1) and in Fig. 12.5 (notched
specimen, R = −0.5 and R = 0.1). In Fig. 12.3b, the relative error equals 0 for the
calibration series. The average relative errors in Figs. 12.3a, 12.5a, b are 1%, 7%,
and 6%, respectively. The obtained satisfactory quality reproduction of real fatigue
experiments indicates the efficiency and prospects of the model and calculation algorithm. The considered model represents the development of the damage model in the
I. S. Nikitin et al.
12.4 Calculation Results
Calculation of S-N curves and fatigue cracks propagation performed both in LCFHCF and VHCF modes are presented in Sect. 12.4.
To determine the parameters of the proposed model and verify its performance,
one of the fatigue experiments described in [29] was performed numerically. From the
condition of matching the experimental and calculated fatigue curve for a specimen
of certain geometry for a given loading amplitude and cycle asymmetry, the numerical coefficients were found. Using the obtained values, the experimental results on
specimens of a different geometry and asymmetry coefficients were reproduced, and
calculation algorithm operability was confirmed.
Hereinafter, the numerical results for LCH-HCF mode and VHCF mode are
discussed in Sects. 12.4.1 and 12.4.2, respectively.
12.4.1 Results for LCH-HCF Mode
Initial tests were conducted on a plate 100 × 25 × 1.57 mm in size with 1.56 mm
diameter through a hole in the center. Ratification tests were conducted on a Vnotched specimen that has 15 mm width w/o a notch, thickness of 1.7 mm, a notch
depth of 1.32 mm, a V-notch angle of 60 degrees, and a notch radius of 0.675 mm. The
cyclic loading of the upper and lower boundaries of the specimen with an amplitude
of 0.096 mm with the development of damage zones up to macroscopic destruction
was simulated and matched with the results from [29]. In the center of the plate,
there is a through-hole with diameter of 1.56 mm. Plate material is titanium alloy
with strength and fatigue parameters σ B = 1135 MPa, σ u = 30 MPa, β LH = 0.31.
Elasticity modulus of intact alloy are λ 0 = 77 GPa, μ 0 = 44 GPa. Figures 12.2
and 12.4 show the lines of the effective stress level σ LH for the specimen with a hole
(Fig. 12.2) and for the specimen with a notch (Fig. 12.4) in two states: before the
fatigue quasi-crack initiation and at the moment when it has passed approximately
halfway to macro-destruction.
In Figs. 12.3 and 12.5, the results of real and computational experiments on
constructing fatigue curves for specimens with a hole and a side notch are presented.
Both real and calculated points represent the moment of crack initiation. The curves
in the figures approximate the experimental points. The calculations presented in
Fig. 12.3b almost exactly fit the approximation curve for the values of the model
parameters γ = 0.1 and k = 0.5. Utilizing these parameters, the fatigue curves are
presented in Fig. 12.3a (specimen with a hole, R = −1) and in Fig. 12.5 (notched
specimen, R = −0.5 and R = 0.1). In Fig. 12.3b, the relative error equals 0 for the
calibration series. The average relative errors in Figs. 12.3a, 12.5a, b are 1%, 7%,
and 6%, respectively. The obtained satisfactory quality reproduction of real fatigue
experiments indicates the efficiency and prospects of the model and calculation algorithm. The considered model represents the development of the damage model in the