Nonlinear Analysis Method of High-Strength Steel Based on Local Buckling Fiber Hinge

Abstract

Based on the analysis and summary of the research and application status of domestic and foreign high-strength steel local buckling fiber hinged rod stability and ordinary steel local buckling fiber hinged rod stability control, this paper proposes a fiber hinged rod suitable for spatial structures subject to local buckling. The new type is high-strength steel composite local buckling fiber hinged pressure rod. The influence of related parameters in the dislocation string model and the dislocation couple model on the ultrasonic nonlinear parameters is deeply analyzed. And, from the perspective of contact nonlinear acoustics, the mechanism of the ultrasonic nonlinear response of the crack is analyzed, and the finite element software ABAQUS is used to simulate it. The relationship between the nonlinear parameter and the internal crack shape of the material is simulated and analyzed, which proves the nonlinearity. A series of nonlinear ultrasonic testing was performed on three groups of FV520B high-strength steel fatigue specimens using a nonlinear testing system. Analyzing the results, it is found that the material has a good ultrasonic nonlinear cumulative effect, and the microcracks have a greater impact on the ultrasonic nonlinear response. The β-N curves under three sets of fatigue tests are obtained. The results show that the nonlinear parameters are very sensitive to the fatigue damage of FV520B high-strength steel, and the ultrasonic nonlinear parameters generally increase with the increase in the number of fatigue cycles.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

High-strength steel refers to steel with a standard value of yield strength between 460 and 690 MPa. With the development of new steel production processes, such as microalloying technology and thermomechanical treatment technology, high-strength steel, especially compared to earlier high-strength steels, has a higher cleanliness; Nb, V, and Ti are used as the elements. The representative microalloying replaces the traditional carbon element strengthening method, which not only improves the yield strength of steel, but also improves its plasticity and toughness [1]. The new high-strength steel developed by this new process has the characteristics of high strength, good toughness, and good processing and weldability and has been applied in many practical projects at home and abroad [2, 3].

For high-strength steel welded I-shaped section members, in order to make full use of the advantages of high strength, the section design can be more developed, but this can easily exceed the current specification limits, especially the height-to-thickness ratio of the web [4]. Under the load of the axial compression member with the web height-to-thickness ratio exceeding the limit, the web buckles first, but the bearing capacity of the entire member does not reach the maximum, and there is still a lot of room for ascent [5, 6]. Therefore, it is necessary to appropriately relax the height-to-thickness ratio limit of the web, so that it can give full play to its own strength advantages, and also improve the economics of welding I-shaped cross section members [7, 8]. However, there are relatively few studies on high-strength steels with a yield strength of 690 MPa, and there are even fewer design codes applicable to it. The existing specifications for high-strength steels simply apply design formulas suitable for ordinary-strength steels, which greatly restricts the promotion and application of high-strength steel structures [9].

This paper proposes a simplified calculation model of the composite local buckling fiber hinged compression rod (using the BEAM188 element node coupling method), and the correctness of the simplified calculation model is verified by comparison and analysis with solid elements. In the initial defect, the residual stress will have an unfavorable effect on the stable bearing capacity. In this paper, the analysis of the local buckling fiber hinged compression rod of high-strength steel with different slenderness ratios shows that the welding residual stress has little effect on the stable bearing capacity (when the residual stress is not considered, the maximum difference of the stable bearing capacity is only 3.02%). In this paper, the fabricated FV520B high-strength steel fatigue specimen was tested by a nonlinear ultrasonic testing system. Through the data collection and processing, the fundamental wave and the second harmonic amplitude were extracted. The relationship between the ultrasonic nonlinear parameters and the ultrasonic propagation distance in the material was studied. The ultrasonic nonlinear response was detected in the original plate specimen without fatigue damage, indicating the inherent nonlinear characteristics of the material itself. As the propagation distance increases, the ultrasonic nonlinear coefficient increases approximately linearly, indicating that the nonlinear response has a cumulative effect. Testing the notched samples that cycle for a certain number of cycles also found the cumulative effect of the ultrasonic nonlinear response. The β-N curves of FV520B material under three stress levels are obtained. The results show that the nonlinear parameters are very sensitive to the early fatigue damage of FV520B high-strength steel. The nonlinear parameters show an increasing trend with the increase of the number of fatigue cycles. The relationship between the ultrasonic nonlinear parameters of FV520B high-strength steel and the fatigue cycle cycles can be used to characterize the early fatigue damage degree of the material and reflect its fatigue life.

2. Related Work

At present, there are still few domestic studies on the overall stability and local stability of high-strength steel beams [10]. Relevant scholars have studied the stability of high-strength steel thin-walled box-section beams, mainly analyzing the effects of the slenderness ratio, flange width-to-thickness ratio, and section side-length ratio of the box beam on its overall stability [11]. The steel studied is 6 mm thick, 18Mn2Cr Mo BA high-strength steel with a yield strength of 745 MPa. This type of steel is generally used in bridge engineering. Relevant scholars pointed out that the slenderness ratio has little effect on the ultimate load of a box-shaped beam in a purely bending state [12]. After changing the slenderness ratio of the beam, the ultimate load changes within 5%. The flange width of the beam is relatively small. After the load-displacement curve appears at the highest point, the curve slowly and steadily declines; when the flange width-to-thickness ratio of the beam is increased, the flange or web has already experienced local instability after the load is added to the ultimate load [13]. The elastic section modulus of the beam decreases, so the slope of the descending section after the highest point of the load-displacement curve increases significantly. It can be seen that the width-to-thickness ratio of the flange affects the overall stability of the beam to a greater extent. When the cross-sectional side length ratio of the beam increases from 30 to 60, the web height-to-thickness ratio continues to increase, and local instability is prone to occur in the compression zone of the web, which leads to an acceleration of the overall stability of the ultimate load drop [14].

The research on the local-total related buckling of box-shaped cross section members has a long history. Domestic and foreign researches mainly focus on the local-total related buckling of ordinary steel members. The research on the local-total related buckling of high-strength steel members mainly focuses on the axis. Relevant scholars have used numerical analysis methods to study the relative buckling ultimate bearing capacity of ordinary steel members with thin-walled box-shaped sections under axial compression with hinged ends [15]. Research has found that when the ultimate bearing capacity of the component is reached, the bearing capacity of the component composed of weak panels will decrease sharply [16]. The researchers used the test results of four axial compression members with a nominal yield strength of 390 MPa to compare with the finite element model [17]. The research shows that residual stress and local overall geometric defects have a great influence on the ultimate bearing capacity of members. Researchers have proposed a formula for calculating the local-to-whole relative buckling ultimate bearing capacity of axial compression members with large width-to-thickness ratio based on the effective width method [18]. Relevant scholars have conducted experimental research on three S355 steel welded thin-walled box-shaped eccentric components, established a finite element model considering the effects of initial geometric defects and residual stress, and compared the experimental results, and they found that the two are in good agreement. Finally, the verified finite element model is used to study the influence of initial defects on the ultimate bearing capacity of the component [19].

Relevant scholars have, respectively, measured and analyzed the overall geometric initial defects of I-shaped section members with nominal yield strengths of 460 MPa and 960 MPa [20]. The results show that the measured amplitude of the overall geometric initial defects of most high-strength steels is less than 1/1000. The researchers measured and analyzed the overall geometric initial defects of the I-shaped section members with nominal yield strengths of 460 MPa, 550 MPa, and 690 MPa, and the results showed that the maximum amplitudes were 1/541, 1/339, and 1/702 [21]. Relevant scholars have studied the effect of geometric initial defects on the stability of ordinary steel and high-strength steel [22]. The results show that, compared with ordinary steel members, geometric initial defects have less effect on the stability coefficient of high-strength steel members; compared with the ultimate bearing capacity, the local buckling capacity is more sensitive to local geometric initial imperfections. Researchers have conducted experimental research and numerical analysis on the overall stability and local stability of high-strength steel axial compression members and have accumulated a wealth of experimental data and important research results [23]. In particular, the residual stress distribution of high-strength steel welded components is measured by the cutting method, and the residual stress distribution model suitable for different steel strength grades is summarized, which provides reliable residual stress treatment for the future finite element analysis of high-strength steel welded components method. Relevant scholars use ANSYS finite element software to simulate the axial compression components of hot-rolled high-strength equilateral angle steel. Studies have shown that the initial defects have a smaller effect on the local stability bearing capacity of high-strength hot-rolled equilateral angle steel axial compression members than ordinary steel axial compression members. The researchers analyzed and studied the ultimate bearing capacity of Q345, Q390, and Q420 steel welded box-section axial compression members whose aspect ratio exceeds the limit. The calculation results are compared with the direct strength method and the effective yield strength method. The study shows that the stability coefficient should be checked according to the type a section in the 03 specification; the direct strength method and the finite element calculation result are in good agreement, while the effective yield strength method is slightly conservative.

3. Steel Tube Buckling Theory and Finite Element Simulation Method

3.1. The Basic Theory of Axial Buckling

According to the deformation state of the member during buckling, it can be divided into global buckling, local buckling, and global-local related buckling. When the component is only buckled as a whole, its parts will not be severely deformed, and only the whole body will undergo a huge change in configuration before and after buckling; local buckling means that, after buckling of the component, only the local elements will deform significantly; related buckling is a coupling of global buckling and local buckling; that is, when buckling occurs, both the overall and local elements of the member undergo a large configuration change. Due to the inevitable existence of local and overall defects, related buckling is very common in actual engineering and should be paid attention to.

As shown in Figure 1, a cylindrical shell subjected to axial pressure can only maintain a balanced state under conditions far below the critical buckling load after local buckling. Its load-displacement curve is shown in Figure 1. OAB’ belongs to unstable bifurcation instability, and this form of buckling is also called limited interference buckling. Under minimal external interference, the cylindrical shell may jump from the stable equilibrium state before buckling to the nonadjacent equilibrium state before reaching the critical load. The path is shown in the curve OA'CB in Figure 1. It should be noted that geometric defects have a great influence on this type of member, making its actual ultimate bearing capacity far less than the elastic critical buckling load Pcr.

[figure omitted; refer to PDF]

The relationship between the ultrasonic nonlinear parameter β and the propagation distance of the ultrasonic wave in the FV520B sample is shown in Figure 7. It can be concluded from Figure 7 that as the propagation distance increases, the ultrasonic nonlinear parameters have a cumulative effect, and the results of the original test on the undamaged plate shape show that the nondamaged FV520B high-strength steel medium itself has nonlinearity. According to the test results of notched specimens, it can be seen that the contribution of cracks to the ultrasonic nonlinear parameters is greater than the contribution of dislocations to the ultrasonic nonlinear parameters. The tested sample is a FV520B high-strength steel notched sample subjected to a certain fatigue cycle. After the fatigue test, cracks appear in the notch of the notched sample. Because the specimen is in a state of stress concentration at the notch, the stress it receives is much higher than the area far away from the notch. After the fatigue test, a large number of cracks appear near the notch, and no cracks are found in the area far away from the notch, which stays before the crack initiation. The dislocation stage is shown in Figure 8. This is consistent with the idea that the ultrasonic nonlinear response induced by cracks is greater than the ultrasonic nonlinear response induced by dislocations.

[figure omitted; refer to PDF]

Specimen No. 04 is a specimen of group B notch experiment (550 MPa) cycled for 105 cycles. The relationship between the ultrasonic nonlinear parameters of the specimen and the distance between the transmitting probe and the crack is shown in Figure 10. It can be seen from the figure that, unlike the test result of No. 03 specimen, the magnitude of the ultrasonic nonlinear parameter fluctuates greatly with the change of the position of the crack at the two ends between the two sensors.

[figure omitted; refer to PDF]

Comparing the nonlinear ultrasonic detection results of the above two experiments, it can be concluded that the change of the position of the crack between the two sensors has a greater impact on the ultrasonic nonlinear parameters. Comparing Figure 9 and Figure 10, it can be found that the ultrasonic nonlinear parameter of No. 04 sample in group B is larger than the value of the ultrasonic nonlinear parameter of No. 03 sample in group A. This is because the fatigue cycle cycles of these two specimens are both 10⁵ times, and the loading stress (660 MPa) of the No. 04 specimen in group B is greater than the loading stress of the No. 03 specimen in group A (550 MPa). This shows that the greater the loading stress of the fatigue experiment, the greater the value of the corresponding ultrasonic nonlinear parameter. There is a mapping relationship between the nonlinear coefficient and the degree of fatigue damage of FV520B high-strength steel.

7.4. Research on the Variation Law of Nonlinear Parameters with Fatigue Cycles

In order to study the change law of ultrasonic nonlinear parameters of fatigue specimens in different cycles of fatigue cycles, a group of plate-shaped specimens and two groups of fatigue specimens with different loading stresses are used as the research objects, and the different cycle cycles of each group are analyzed. The second fatigue specimen is tested. The relationship between normalized nonlinear parameters and fatigue cycle is used to describe the nonlinear changes of materials due to fatigue damage.

In order to study the effect of fatigue crack growth on ultrasonic nonlinear parameters, we designed two sets of notched specimens. Figure 11 is the relationship curve between normalized ultrasonic nonlinear parameters and fatigue cycle cycles of the notched specimens in group A (550 MPa). Figure 12 shows the relationship between the normalized ultrasonic nonlinear coefficients of the notched specimens in group B (660 MPa) and fatigue cycle cycles. Ultrasonic nonlinear parameters are very sensitive to the fatigue damage of FV520B high-strength steel materials. The relationship between FV520B high-strength steel's nonlinear parameters and fatigue cycle cycles can be used to characterize its early fatigue.

[figure omitted; refer to PDF]

By studying the relationship between ultrasonic nonlinear parameters and fatigue cycle cycles, it can be found that there is a good correlation between the ultrasonic nonlinear parameters of FV520B high-strength steel and fatigue cycle cycles. Nonlinear parameters can be used to reflect the fatigue life of materials. In engineering practice, after obtaining enough sample data points, the nonlinear parameter curve of the engineering component of FV520B high-strength steel material is calibrated in advance. Comparing the nonlinear detection results with the calibration curve obtained in advance, the fatigue life can be evaluated.

8. Conclusion

The outer steel tube combined with the local buckling fiber hinged compression rod has a good restraint effect on the inner core tube, and the bearing capacity of the combined local buckling fiber hinged compression rod increases with the increase of the outer and inner stiffness ratio and the number of hoops. However, an excessively large ratio of external and internal stiffness will cause the instability mode of the composite locally buckled fiber hinged rod to change from common instability to the inner core alone, which will reduce the bearing capacity of the composite locally buckled fiber hinged rod. For the core tube of high-strength and ultra-high-strength steel, the stable bearing capacity of the composite local buckling fiber hinged compression rod becomes more obvious with the increase of the slenderness ratio of the core tube. The influence of related parameters in the dislocation string model and the dislocation couple model on the ultrasonic nonlinear parameters is analyzed. From the perspective of contact nonlinear acoustics, the influence of cracks on ultrasonic nonlinearity is analyzed, and the finite element software ABAQUS is used to simulate it. It is proved that the crack can produce nonlinear effects, and the relationship between nonlinear parameters and the internal crack shape of the material is analyzed. The effect of the relative position of the crack between the two transducers on the ultrasonic nonlinear coefficient is studied, and it can be concluded that the change of the position of the crack between the two transducers has little effect on the nonlinear coefficient, which can be approximated as no effect. By comparing two fatigue specimens with the same fatigue cycle but different fatigue loading stress, it is found that the larger the fatigue test loading stress, the larger the corresponding ultrasonic nonlinear parameter value. There is a mapping relationship between the nonlinear coefficient and the degree of fatigue damage. Lamb waves are used to perform a series of nonlinear tests on fatigue specimens of FV520B high-strength steel. Analyzing the results, it is found that the material has a good ultrasonic nonlinear cumulative effect. The experimental results show that the ultrasonic nonlinear parameters have high sensitivity to the early fatigue damage of FV520 B high-strength steel.

Consent

Informed consent was obtained from all individual participants included in the study references.

Acknowledgments

This work was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 19KJB560018) and by the Jiangsu Province Vocational Colleges Young Teacher Enterprise Practice Training Project (No. 2020QYSJ165).

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