Fracture Toughness Prediction under Compressive Residual Stress by Using a Stress-Distribution T-Scaling Method
Abstract
:1. Introduction
2. T-Scaling Method
3. Application of T-Scaling Method to 780-MPa-Class High-Strength Steel without and with CRS
3.1. Outline of Tests to Be Reproduced
3.2. EP-FEA to Reproduce Test Results for HT780
3.3. Proposed Method to Predict Fracture Load for Cases with CRS
4. Validation of Application of T-Scaling Method to Predict Fracture Load of Specimens with CRS
4.1. Material Selection
4.2. Fracture Toughness Tests for S45C without CRS
4.3. Selection of Load Ppre to Apply CRS
4.4. Prediction of Fracture Load with CRS
4.5. Validation of Predicted Fracture Load for Specimens with CRS
5. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
B | Test specimen thickness |
E | Young’s modulus |
J | J-integral |
Jc | Fracture toughness obtained from experimental results |
Kc | Stress intensity factor corresponding to fracture load Pc |
Ke | Elastic stress intensity factor |
KJc | Fracture toughness expressed in terms of K (=(EJc/(1 − ν2))1/2) |
Pc | Fracture load |
Ppre | Preload for applying compressive residual stress |
Vg | Crack-mouth opening displacement |
W | Specimen width |
α, n | Parameters of Ramberg–Osgood power law |
a | Crack depth |
ε0 | Reference strain for Ramberg–Osgood power law |
In, | Parameters depending on n and θ for HRR stress solution |
ν | Poisson’s ratio |
rT | Intersection point between K and HRR stress distributions (T-point) |
δt | Crack-tip opening displacement |
σij | Stress components (i, j = 1, 2, 3) |
σ0 | Reference stress for Ramberg–Osgood power law |
σ22HRR | Stress of J-dominated region described as HRR stress distribution |
σ22K | Stress of K-dominated region described as K stress distribution |
σ22T | Crack-opening stress σ22 at r = rT |
Abbreviations
ASTM | American Society for Testing and Materials |
BS | British Standard |
CRS | Compressive residual stress |
CTOD | Crack-tip opening displacement |
DBTT | Ductile-to-brittle transition temperature |
EP-FEA | Elastic–plastic finite element analysis |
HRR | Hutchinson–Rice–Rosengren |
HT780 | 780-MPa-class high-strength steel |
JIS | Japan Industrial Standard |
SE(B) | Single-edge notched bend bar |
SIF | Stress-intensity factor |
SSY | Small-scale yielding |
T-point | Location where σ22HRR and σ22K intersect on x1-axis |
Appendix A
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Model | ρ (μm) | Rs (mm) | Na | Nnotch | Nlig | Ns | Nθ | Nrings |
---|---|---|---|---|---|---|---|---|
Without CRS | 2.5 | 2.56 | 18 | 18 | 18 | 20 | 24 | 50 |
With CRS | 3.5 | 2.56 | 18 | 18 | 18 | 20 | 24 | 50 |
T (°C) | σ0 (MPa) | α | n | In | |
---|---|---|---|---|---|
20 | 838 | 2.56 | 19.5 | 4.40 | 2.62 |
−75 | 938 | 2.56 | 39.8 | 4.40 | 2.62 |
JIS S45C | C | Si | Mn | P | S | Cu | Ni | Cr |
---|---|---|---|---|---|---|---|---|
Specified | 0.42–0.48 | 0.15–0.35 | 0.60–0.90 | ≤0.030 | ≤0.035 | ≤0.30 | ≤0.20 | ≤0.20 |
Check analysis | 0.47 | 0.17 | 0.64 | 0.009 | 0.004 | 0.02 | 0.02 | 0.02 |
T (°C) | σYS0 (MPa) | σB0 (MPa) | Elongation (%) | σ0 (MPa) | α | n | In | |
---|---|---|---|---|---|---|---|---|
20 | 467 | 738 | 22 | 468 | 2.71 | 4.73 | 5.07 | 2.21 |
−10 | 492 | 770 | 22 | 493 | 2.59 | 4.83 | 5.04 | 2.22 |
Specimen ID | 1 | 2 | 3 | 4 | 5 | μ | ∑ |
---|---|---|---|---|---|---|---|
a/W | 0.50 | 0.51 | 0.50 | 0.50 | 0.50 | 0.50 | 0.00 |
Pc (kN) | 32.9 | 37.1 | 38.5 | 39.1 | 42.6 | 38.0 | 3.50 |
Kc (MPam1/2) | 71.9 | 81.9 | 83.3 | 85.0 | 91.6 | 82.7 | 7.09 |
Jc (N/mm) | 24.8 | 36.0 | 39.3 | 42.0 | 52.1 | 38.8 | 9.87 |
KJc (MPam1/2) | 77.4 | 92.8 | 97.0 | 101 | 111 | 95.8 | 12.3 |
M | 453 | 310 | 287 | 269 | 218 | 307 | 88.1 |
Model | ρ (μm) | Rs (mm) | Na | Nnotch | Nlig | Ns | Nθ | Nrings |
---|---|---|---|---|---|---|---|---|
Without CRS | 1.0 | 2.3 | 18 | 18 | 18 | 20 | 24 | 50 |
With CRS | 1.0 | 2.3 | 18 | 18 | 18 | 20 | 24 | 50 |
Specimen ID | Predicted | 1 | 2 | 3 | 4 | 5 | μ | ∑ |
---|---|---|---|---|---|---|---|---|
a/W | 0.50 | 0.51 | 0.50 | 0.50 | 0.50 | 0.50 | 0.00 | |
Pc (kN) | 39.3 | 39.5 | 42.2 | 43.9 | 43.4 | 43.8 | 42.6 | 1.83 |
Kc (MPam1/2) | 84.8 | 85.6 | 93.1 | 94.3 | 94.9 | 95.1 | 92.6 | 3.97 |
Jc (N/mm) | 38.1 | 41.5 | 51.6 | 52.1 | 66.6 | 69.3 | 56.2 | 11.6 |
KJc (MPam1/2) | 93.6 | 98.2 | 110 | 110 | 125 | 127 | 114 | 12.0 |
M | 272 | 217 | 218 | 169 | 163 | 208 | 44.5 |
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Meshii, T.; Ishihara, K. Fracture Toughness Prediction under Compressive Residual Stress by Using a Stress-Distribution T-Scaling Method. Metals 2018, 8, 6. https://doi.org/10.3390/met8010006
Meshii T, Ishihara K. Fracture Toughness Prediction under Compressive Residual Stress by Using a Stress-Distribution T-Scaling Method. Metals. 2018; 8(1):6. https://doi.org/10.3390/met8010006
Chicago/Turabian StyleMeshii, Toshiyuki, and Kenichi Ishihara. 2018. "Fracture Toughness Prediction under Compressive Residual Stress by Using a Stress-Distribution T-Scaling Method" Metals 8, no. 1: 6. https://doi.org/10.3390/met8010006