Cutting force as an index to identify the ductile-brittle failure modes in rock cutting

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Abstract

Rock failure modes exist a transition from ductile to brittle with the increase of cutting depths. Further insight into the determination of critical transition depth is of great significance to optimize the design of cutting tools and operational parameters. In the present study, a novel method for identifying rock failure modes is proposed based on the evolution of cutting force. Furthermore, a series of experiments were conducted to validate this method and investigate the critical depth under different experimental conditions. Firstly, we calculate the cutting force difference (ΔF) from peak to valley and its variation rate (Ra). Then, Ra and ΔF are fitted linearly, and the slope of the fitting line (SlRa) is determined. According to the experimental results, rock breakage is a process involving continuous changes in failure modes. At shallow cutting depths, SlRa is close to zero, indicating the domination of ductile failure. Then SlRa rises with the increase of cutting depths, indicating that the proportion of brittle failure becomes higher. Such region is generally defined as a transition region. Once cutting depths exceed the critical depth, effects of ductile failure can be ignored and SlRa tends to be stable. The higher rock brittleness and smaller back rake angles result in a reduction of critical depth. In addition, the critical transition depth can be correlated with some parameters such as the distribution of cuttings and the number of valleys in cutting force. Our current study helps to identify rock failure modes and provides an in-depth understanding about the critical depth.

Introduction

Polycrystalline diamond compact (PDC) bits have gained increasing favor since their first application in oil fields in 1976.1 They have been used to drill more than 50% of the intermediate and production hole footage in some areas due to their long service life and effective rock-breaking ability.2 To further improve the performance of PDC bits, single PDC cutter tests are widely used to investigate the mechanism of rock breakage.3

It is well accepted that rock failure modes change from ductile to brittle with the increase of cutting depths.4, 5, 6, 7 This process is accompanied by the transition of rock failure characteristics, mainly including the morphology of cuttings, the mechanical specific energy (MSE) of rock breakage, and the fluctuation of cutting force. The determination of the critical transition depth is crucial to optimize cutting tools and drilling parameters.

The transition of failure modes was firstly proposed in the process of machining brittle materials such as porcelain, glass, and crystal. A relatively smooth surface can be obtained when the depth of cut is smaller than a few microns. While at large cutting depths, brittle failure dominates the cutting process and surfaces become relatively rough.8, 9, 10, 11 To accurately determine the critical transition depth, Bifano et al.12 developed a model based on the consumed energy in machining materials, which remains constant in ductile-regime grinding and begins to decrease beyond the critical transition depth.

The ductile-brittle failure of rocks has been one of the most active topics in the field of rock cutting. In the past few years, a series of evaluation models were proposed to determine the value of critical depth under different experimental conditions. Some researchers13, 14, 15 detected that the mean cutting force is proportional to depths of cut in the ductile regime, and the relationship between them gradually follows a non-linear pattern with the increase in cutting depths. That is, the critical depth can be determined based on the variation of mean cutting force at different cutting depths. Moreover, the cutting force in the ductile regime can be used to evaluate the strength of the rock. The same results were concluded by other scholars as well.6,7,16 But Zhou and Lin16 argued that there is an uncertain factor because we do not know from where the cutting force should be fitted by non-linear relations.

Meanwhile, the specific cutting energy, proposed by He and Xu, is an important index to identify the critical depth in single PDC cutter tests.6 When rocks are broken by the compression of PDC cutter at shallow cutting depths, the consumed energy remains relatively constant. However, rock failure modes will convert to brittle as depths of cut increase. And the corresponding energy is proportional to −4/3 power of cutting depths. A series of experiments were conducted and the results are consistent with the theoretical analysis. Despite this, He et al. 7argued that the reliability of this model should be further improved.

Furthermore, the size effect law was applied to determine the critical depth as well. Bazant et al. pointed out that large structures are more brittle than small structures, thereby resulting in the decrease in nominal strength of structures after their size exceeds a critical value.17, 18, 19 Depending on this theory, Zhou and Lin16 developed a model to calculate the nominal stress in rock cutting. The results indicate that the critical depth could be expressed in terms of the characteristic length and the uniaxial compressive strength (UCS) of rocks. A series of experiments have been conducted to verify the reliability of this model.7,16

In addition, some scholars employed numerical simulation to study the process of rock cutting. Rock failure modes can be directly determined based on the morphology of generated cuttings and induced cracks in rocks. Based on the simulation results in the discrete element code PFC,2D the number of cracks in rocks would intensely increase beyond the critical depth.20 The morphology of generated cuttings also varies obviously under different rock failure modes.4,21,22 Meanwhile, the rock cutting process can be revealed by the finite element method (FEM) as well. The results are in good agreement with experimental results and successfully present the transition of rock failure modes.16,23, 24, 25, 26

In conclusion, the critical transition depth has been a hot topic and attracted many researchers. However, this value is affected by many factors and cannot be determined with a general equation.27 In the present study, a novel method is proposed to determine the threshold depth based on the evolution of cutting force. Through the analysis of this paper, not only the value of critical depth is got, but also a clear understanding of the interaction between the rock and PDC cutter is obtained.

Section snippets

Determination of critical depth based on the evolution of cutting force

Previous studies found that the cutting force directly reflects the interaction between rocks and PDC cutter. As we can see in Fig. 1(a), the cutting force in single PDC cutter tests exist an obvious oscillatory behavior. When the PDC cutter squeezes the rock ahead of it, the cutting force increases and energy accumulates in this process. After the cutting force increases to a peak value, accumulated energy exceeds rock strength and then a sharp decrease in cutting force can be observed. In

Experiment setup

To validate the reliability of this method, a series of single PDC cutter tests were performed on a modified milling machine. This equipment can adjust the cutting depth with an accuracy of 0.01 mm. A sharp-edged PDC cutter is used in rock cutting tests, which has the dimension of Φ19 × 13 mm. This cutter is selected because PDC cutters with the same size as it are widely used in drilling process and previous research.31,32 Due to the short cutting distance in the present study, the wear and

The effects of rock failure modes on some parameters in rock cutting

In this section, we try to make a correlation between critical depth and some parameters in rock cutting, mainly including the distribution of cuttings, number of valleys and the frequency spectrum characteristics of the cutting force. The results are shown in section 4.1 The distribution of cuttings in different failure modes, 4.2 The variation of cutting force in different failure modes, 4.3 The frequency spectrum characteristics of cutting force respectively. Through the analysis of this

Conclusions

Based on the evolution of cutting force at different cutting depths, we proposed a novel method to determine the transition of rock failure modes. A series of single PDC cutter tests were conducted to validate this method and investigate the effects of rock properties and back rake angles on the critical transition depth. Then, we try to link critical depth and some experimental parameters, including the distribution of cuttings, the number of valleys and the frequency spectrum characteristics

Declaration of competing interest

All of authors declare that they have no conflict of interest.

Acknowledgments

Authors would like to acknowledge the financial support from the 111 Project of China (B17045) and the National Science Fund for Distinguished Young Scholars (51725404) and their approval of publishing this paper.

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