# Fatigue-life curve-4130 Steel

From material science viewpoint, fatigue is caused by the application of repeated loads. Fatigue weakens the material. It is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading.[1] Generally, the nominal maximum stress that cause this kind of damage in a material may be much lower than the strength of the material normally known as the ultimate tensile stress limit or the yield stress limit. Fatigue happens when a material is under the influence of repeated loading and unloading conditions. If these loads are above a certain threshold, microscopic cracks will start to form at the stress concentrators like the surface, persistent slip bands (PSBs), and grain interfaces.[2] At some point a crack will reach a critical size, the crack will then propogate abruptly resulting in fracture.

## Introduction

Fatigue life $(N_f)$ is defined by the total number of stress cycles required to cause failure. Engineers have used any of three methods to determine the fatigue life of a material: the stress-life method, the strain-life method, and the linear-elastic fracture mechanics method.[3] Fatigue is a surface driven failure. This surface can be both internal as well as external, since defects are internal.[4]

## Fatigue life curve-4130 Steel

There is a wide application area of 4130 in the petroleum and gas industry. Owing to this use, it can be exposed to high temperatures and also severe cyclic loading conditions. The fatigue curve below show the influence of thermal treatment on high temperature behavior of this steel. These tests are carried out at a temperature of $450^{0}C$ with a strain range of 0.8% to 1.5%. Figures 1 and 2 below show the cyclic stress response of 4130 steel.

Figure 1: Cyclic stress response versus the number of cycles N and the life fraction.[5]

Figure 2: Cyclic stress response versus the number of cycles N for various strain range tests at $450^{0}C$ in air for the bainitic and the ferritic-pearlite 4130.[5]

An S-N curve, also known as a Wohler curve, is determined from the result of subjecting the material to a range of fatigue tests at variable stress levels. An example of such tests is shown in figure 3. In this test, $S_{m}=0$, and therefore the stress ratio $R=S_{min}/S_{max}=-1$. The variable in figure 3 is the stress amplitude $S_{a}$.

Figure 3: Fatigue test results of unnotched specimens of a low-alloy steel (SAE 4130).[6]

Figure 4 displays the predicted S-N curve for a mildly notched specimen of SAE 4130. The details of the test can be found in [6].

Figure 4: Predicted S-N curve for a mildly notched specimen, root radius $\rho = 8.1 mm$, material SAE 4130 steel.[6]

Figure 5 shows experimental S-N curve for tensile specimens made of AISI 4130 steel under fully reversed loading ($R = -1$). The specimens were prepared as per ASTM standard. Details can be found in the study by Singh et al[7].

Figure 5: Experimental S-N curve for AISI 4130 steel tensile specimen under fully reversed loading ($R = -1$).

Figure 6 shows the result of a cumulative fatigue damage in AISI steel. The details of the study can be found in the works of Jeelani and Musial [8]

Figure 6: S-N curve for AISI steel.(o) R=-1, m=-9.45638c/02, c-235610, p=10.57486, $\beta$ =6.459E+56:(filled o) R=0, M=-9.57304e/-02, c=313479, p=10.446,$\beta$ =2.590559E+57 .[8]

Figures 7, 8, and 9 show the rest of the X-ray diffraction study conducted in Shot-peened and fatigued 4130 steel by Esquivel and Evans [9]

Figure 7: Residual macrostresses variation in 4130 steel with fatigue cycling at numerous depths: at the surface (solid circles), near the surface (at depth, d=0.001 in.) at the stress profile minimum (d=0.007 in.), at the cross-over point (d=0.013 in.).[9]
Figure 8: Relaxation of residual macrostresses, (in ksi) at different depths with fatigue cycling.[9]
Figure 9: Changes in the residual stress gradient, in ksi.0.001 in. at different depths with fatigue cycling.[9]

## References

1. Kim, W.H; Laird, C. (1978). Crack Nucleation and State I Propagation in High Strain Fatigue- II Mechanism. Acta Metallurgica. pp. 789–799.
2. Joseph E. Shigley, Charles R. Mischke, and Richard G. Budynas.
3. ICME class lectures. Dr. Horstemeyer, Spring 2015
4. 5.0 5.1 Bultel, H., and Vogt, J-B., "Influence of heat treatment on fatigue behavior of 4130 AISI steel",Procedia Engineering 2(2010) 917-924.
5. 6.0 6.1 6.2 Fatigue of Structures and Materials, J. Schiive. [[1]]
6. Singh, K., Sadeghi, F., Correns, M., Blass, T. A microstructure based approach to model effects of surface roughness on tensile fatigue. Int. J. Fatiugue 129 (2019) 105229 [2]
7. 8.0 8.1 Jeelani, S., Musial, M., A study of cumulative fatigue damage in AISI 4130 steel. Jour. of Mat. Sci. 21 (1986) 2109-2113.
8. 9.0 9.1 9.2 9.3 Esquivel, A. L., Evans, K. R.,X-ray Diffraction Study of Residual Macrostresses in Shot-peened and Fatigued 4130 Steel,Experimental Mechanics, pp. 496-502