Prediction of Fatigue Crack Growth in Metallic Specimens under Constant Amplitude Loading Using Virtual Crack Closure and Forman Model
Abstract
:1. Introduction
2. Theoretical Background
2.1. Crack Propagation Model
2.2. Virtual Crack Closure Formulation for 4 and 8-Node Two-dimensional (2D) FEA
3. Computer Algorithm
4. Test Cases and FEA Details
5. Results
6. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
a0 | initial crack size |
ai | crack size for cycle i |
a | crack size |
a/w | relative crack size |
CF, mF | material constants for Forman model |
CVN | Charpy impact energy |
da/dN | crack propagation rate |
Δa | crack extension, length of the elements at the crack front |
ΔK | stress intensity factor range for a load cycle |
ΔKth0 | threshold stress intensity factor range for R = 0 |
ΔKthR | threshold stress intensity factor range for specific load asymmetry ratio R |
Δu | shear displacement at crack surface node |
Δv | opening displacement at crack surface node |
ΔW | work required to close the crack along one element side |
E | elasticity modulus |
F | specimen loading force |
Fmin | minimum loading force in a cycle |
Fmax | maximum loading force in a cycle |
Fx | shear force at the crack tip |
Fy | opening force at the crack tip |
G | strain energy release rate |
GI | strain energy release rate for crack opening mode I |
GII | strain energy release rate for crack opening mode II |
K | stress intensity factor |
KI | stress intensity factor for crack opening mode I |
KII | stress intensity factor for crack opening mode II |
Kmin | minimum stress intensity factor in a load cycle |
Kmax | maximum stress intensity factor in a load cycle |
KIc | critical stress intensity factor for plane-strain conditions, fracture toughness |
Kc | critical stress intensity factor |
Nef | experimental results for cycles to failure |
Npf | predicted cycles to failure |
R | load asymmetry ratio |
σ | normal stress |
σUTS | ultimate tensile strength |
σmin | minimum normal stress in a cycle |
σmax | maximum normal stress in a cycle |
σy, σ0.2 | yield stress |
t | specimen and element thickness |
u | x-coordinate of crack surface node after load |
v | y-coordinate of crack surface node after load |
w | specimen width |
ν | Poisson ratio |
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TEST CASE | 1 | 2 | 3 | |
---|---|---|---|---|
Material | 2024-T3 | 18G2A (1.0562) | A516 Gr70 (1.0473) 45% overmatch weld | |
Yield Strength σy, MPa | 324 | 398 | 511 | |
Ultimate Tensile strength σUTS, MPa | 469 | 540 | 580 | |
Young Modulus E, GPa | 73.1 | 210 | 210 | |
Poisson ratio ν | 0.33 | 0.3 | 0.3 | |
Plane-Strain Fracture Toughness KIc, MPa | 37 | 68 * | 91 * | |
Forman Constants | CF | 1 × 10−5 | 2.23 × 10−6 | 5.31 × 10−7 ** |
mF | 3.2094 | 3.073 | 3.256 ** |
TEST CASE | 1 | 2 | 3 | |
---|---|---|---|---|
Specimen Geometry | Single Edge Cracked Plate | M(T) | C(T) | |
Specimen Thickness t, mm | 6.5 | 4 | 12.5 | |
Initial Crack Size a0, mm | 17.75 | 10 | 12.7 | |
Maximum Load | Fmax. kN | 7.2 | - | 7.061 |
σmax. MPa | 21.3 | 137.5 | - | |
Minimum Load | Fmin. kN | 0.72 | - | 0.7061 |
σmin. MPa | 2.13 | 7.5 | - | |
Load Asymmetry Ratio R | 0.1 | 0.0545 | 0.1 |
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Krscanski, S.; Brnic, J. Prediction of Fatigue Crack Growth in Metallic Specimens under Constant Amplitude Loading Using Virtual Crack Closure and Forman Model. Metals 2020, 10, 977. https://doi.org/10.3390/met10070977
Krscanski S, Brnic J. Prediction of Fatigue Crack Growth in Metallic Specimens under Constant Amplitude Loading Using Virtual Crack Closure and Forman Model. Metals. 2020; 10(7):977. https://doi.org/10.3390/met10070977
Chicago/Turabian StyleKrscanski, Sanjin, and Josip Brnic. 2020. "Prediction of Fatigue Crack Growth in Metallic Specimens under Constant Amplitude Loading Using Virtual Crack Closure and Forman Model" Metals 10, no. 7: 977. https://doi.org/10.3390/met10070977