Citation: Zhou, Z.; Guan, D.
Considering the Effect of
Non-Propagating Cracks on Fatigue
Limit Prediction in the Critical
Distance Method Framework. Appl.
Sci. 2022, 12, 10994. https://
doi.org/10.3390/app122110994
Academic Editors: Alberto
Campagnolo and Alberto Sapora
Received: 5 October 2022
Accepted: 27 October 2022
Published: 30 October 2022
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Article
Considering the Effect of Non-Propagating Cracks on Fatigue
Limit Prediction in the Critical Distance Method Framework
Zhuo Zhou and Deqing Guan *
Department of Civil Engineering, The Changsha University of Science &Technology, Changsha 410114, China
* Correspondence: gdeqing491596452@163.com
Abstract:
Although the material has developed micro-scale cracks, the micro-cracks stop propagating
and transform into non-propagating cracks (NPCs) under fatigue limit loading. The movement of
the crack tip position caused by the non-propagating crack will generate a small change in the notch
geometry, which easily triggers the geometric size effect. Since the critical distance method focuses
on evaluating the limit of fatigue in terms of the material’s cracking conditions, the present study
attempted to develop a notched fatigue analysis model to consider the effect of non-propagating
cracks on fatigue limit prediction in the critical distance method framework. The effectiveness and
capability of the proposed model were demonstrated by the fatigue experimental data of Q345qD
low carbon steel.
Keywords: notch fatigue; critical distance method; non-propagating crack; size effect
1. Introduction
Due to the limitations of construction technology and design, engineering structures
will inevitably form some notch features (such as holes, grooves, corners, welding, etc.)
on components or structures. The complicated stress characteristics of the notch position
will significantly weaken the fatigue resistance of the components [
1
–
5
]. Therefore, how to
accurately evaluate the fatigue performance of the notch position under cyclic loading has
become an important research project, especially for the long-term operation of mechanical
and civil engineering.
The theory of critical distance (TCD) has been a popular fatigue analysis method in
the last two decades [
6
–
12
]. TCD was proposed by Taylor [
13
–
15
] in the late 1990s by sum-
marizing the views of Neuber [
3
] and Peterson [
16
]. Since the critical distance theory takes
into account the effect of the stress gradient at the notch root on fatigue damage, the critical
distance method has better predictive power than the relatively conservative peak stress
method in notch fatigue analysis. However, the expected effect of critical distance theory
is not ideal in some small notches and low/medium cycle fatigue.
Lanning et al.
[
17
,
18
]
pointed out that the size effect exists in some very small notches, showing the critical dis-
tance theory to be inapplicable to very small notches. Yamashita et al. [
19
] have illustrated
that due to the volume effect of the notch, the conventional critical distance method does
not work well for small notch fatigue problems. In view of this, some researchers have
also carried out research on the critical distance size effect and proposed a corresponding
correction model. Among these, Wang et al. [
20
] considered that the fatigue process region
depends on the severity of stress concentration and put forward the idea of superimposing
the Kt coefficient on the critical length to deal with the critical distance size effect. From
the perspective of fracture mechanics, Hertel et al. [21] provided a rigorous interpretation
of the geometric size effect and corrected the critical distance length.
Wang et al.
[
22
] and
Li et al
. [
23
] suggested that the size effect of the notch can be analyzed by combining TCD
and highly-stressed-volume (HSV) methods. Zhu et al. [
11
] proposed a specific mathemati-
cal quantification of the relationship between hole radius and critical distance to account
Appl. Sci. 2022, 12, 10994. https://doi.org/10.3390/app122110994 https://www.mdpi.com/journal/applsci
