Crack tip fields at crack initiation and growth under monotonic and large amplitude cyclic loading: Experimental and FE analyses
Introduction
Prediction of crack behaviour under large-amplitude cyclic loading is important to ensure structural integrity under seismic loading. Existing experimental data given in Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] have shown that, for a given displacement, crack growth under large-amplitude cyclic loading can be much faster than that under monotonic loading, and resulting crack resistance curves are lower under large-amplitude cyclic loading. It has been claimed that re-sharpening of the crack tip due to cyclic compressive loading could give different crack growth behaviour from that under monotonic loading [1], [2], [3]. Different fracture surfaces were also observed depending on the loading type (monotonic vs cyclic) [1], [2]. Although many factors such as the load ratio, incremental displacement magnitude and others have been shown to affect the crack growth resistance under cyclic loading [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], there has been no study to quantify the effect of the loading type (monotonic or large-amplitude cyclic loading) on crack tip deformation and stress fields.
One possible difficulty for the lack of systematic quantitative analysis is that such work firstly requires determination of a proper material hardening model under large-amplitude cyclic loading. Many works on the cyclic hardening model have been mostly experimental and numerical ones have been only for uncracked specimens [11], [12], [13], [14], [15]. The majority of the existing works has been focused, for instance, on efficient determination of the parameters in complex cyclic hardening models [11], [12], on ratcheting simulating [11], [13], [14], or on analysis under non-proportional loading conditions [15]. For uncracked specimens, the strain range can be relatively easily obtained from the applied load, and thus an appropriate material hardening model can be characterized by experimental hysteresis loops under relevant strain ranges. However, for cracked specimens, determination of a suitable cyclic hardening model is quite difficult due to the high stress triaxiality and strain gradient ahead of the crack tip. Although some works have been reported on crack growth simulation under large-amplitude cyclic loading [7], [16], investigation of the suitable cyclic hardening model was not the main purpose. Hojo et al. [17], [18] discussed how to determine various material hardening models from the monotonic and cyclic stress-strain curves, and applied for fracture mechanics analysis of the C(T) specimen under large-amplitude cyclic loading.
Crack tip stress and strain fields under cyclic loading have been performed by many researchers [19], [20], [21], [22], [23], [24], [25], [26], [27]. However, in most of works, material hardening models under cyclic loading were simply assumed to be ideal ones [19], [20], [21]. Furthermore, the crack tip deformation and stress fields have been investigated under the small-scale yielding condition [19], [20], [21], [22], [23], [24], [25], [26], but not under large-scale yielding one. The extent of yielding under cyclic loading can cause significant differences in crack tip deformation and stress fields, due to different crack closure behaviors. For instance, Wang et al. [27] observed that crack closure and crack tip opening displacement under the large-scale cyclic yielding condition were different from those under small-scale yielding one, but analysis was again based on an ideal hardening model.
Review of existing works show that there has been no work on investigating the effect of loading type (monotonic vs cyclic) on crack tip deformation and stress fields under monotonic and large-amplitude cyclic loading. It is partly because a suitable material hardening model must be chosen for a cracked specimen for the investigation. A systematic analysis thus requires combination of experiment using a cracked specimen and numerical analysis; (1) firstly to determine a suitable material hardening model depending on the loading type (monotonic vs cyclic), and (2) then to investigate crack tip deformation and stress fields. As a suitable material hardening model depends on the material as well, different materials should be considered.
The objective of this work is to present the effect of the loading type (monotonic vs cyclic) on crack tip deformation (plastic zone size) and stress fields under monotonic and cyclic loading. For systematic analysis, combined experimental and numerical work is performed, of which the process is schematically shown in Fig. 1. The process consists of three steps. The first step is to perform tensile test and cyclic C(T) tests with two different cyclic loading ratios. To see the effect of cyclic hardening behaviour, two materials were chosen; SA508 Gr. 1a low-alloy steel showing almost cyclic non-hardening behaviour and TP316 stainless steel showing cyclic hardening. This is explained in Section 2. The second step is to determine a suitable hardening model depending on the loading type (monotonic vs cyclic) by simulating the cyclic C(T) tests using the debond option in ABAQUS [28]. The simulation method is explained in Section 3 and Section 4 describes how to determine a suitable hardening model using FE simulation. The third and final step is to present the effect of the loading type (monotonic vs cyclic) on crack tip deformation in Section 5 and crack tip stress fields in Section 6. The presented work is concluded in Section 7.
Section snippets
Uniaxial tensile and cyclic test
Two materials are considered in this paper; SA508 Gr.1a low-alloy steel and SA312 TP316 stainless steel. Standard tensile test was performed at room temperature using the round bar specimen in Fig. 2(a) according to the ASTM standard [29]. Resulting tensile properties are summarized in Table 1 and engineering stress-strain curves are shown in Fig. 2(b).
To determine the material behaviour under cyclic loading, cyclic tensile tests were conducted using the round bar specimen (Fig. 3(a)) under the
FE mesh
The two-dimensional (2-D) plane strain FE mesh for the C(T) specimen is shown in Fig. 5. Note that the debond option in ABAQUS [28] can be used only for 2-D analysis not for 3-D one. The mesh consists of 2-D eight-noded plane strain quadrilateral element with reduced integrations (CPE8R) with the 0.1 mm element size. The contact surface was applied to the elements along the crack path to consider for crack closure under compressive cyclic loading. The 0.5 T FE mesh of TP316 consists of 9720
Hardening models for monotonic and cyclic loading
Materials show changes in the size and position of the initial yield surface (σy0) under plastic deformation. The change in yield surface is expressed as the isotropic hardening [32], [33], [34], [35], generally expressed as followwhere Q and b are the material constants.
The kinematic hardening model simulates the movement of the initial yield surface using the back-stress term (α) [32], [33], [34], [35]. The Chaboche kinematic hardening model consists of three non-linear
Contours for plastic zone and opening stress
In this section, contours of the plastic zone size and high hoop stress will be presented at crack initiation (Δa = 0) and during steady state crack growth (Δa = 2.5 mm for SA508 Gr.1a and Δa = 1.5 mm for TP316). Fig. 14 depicts the contour location in the C(T) FE mesh. For the plastic zone (where the von Mises stress σe is larger than the yield strength σ0), the region covers up to the free surface. On the other hand, for the high hoop stress (where the crack opening hoop stress σθθ is larger
Effective and hoop stresses
The effect of the loading type (monotonic and cyclic) on radial variations of the von Mises effective stress (σe) and hoop stress (σθθ) ahead of the crack tip is shown in Fig. 20. The stresses are normalized with respect to the yield strength σ0. At the crack initiation (Δa = 0), the hoop stress variation is almost similar, regardless of the loading type (monotonic vs cyclic) and material. The effective stress is the largest under monotonic loading possibly due to more crack-tip blunting (shown
Conclusion
This paper investigates crack tip deformation and stress fields at crack initiation and growth under monotonic and large-amplitude cyclic loading conditions. The approach is to combine series of experimental data and FE crack initiation and growth simulation using the ABAQUS debonding option. To achieve the goal of this paper, three steps are taken as follows.
As the first step, tests are performed for two materials under monotonic and cyclic loadings; SA508 Gr.1a low-alloy steel and TP316
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This research was supported by National Research Foundation (NRF) funded by Ministry of Science and ICT (NRF-2018M2A8A4084016).
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