Abstract
To improve the accuracy of erosion prediction, the effect of subsequent particles impacting the same area while the first single particle rebounds from the substrate must be considered. This issue has rarely been considered in studies pertaining to erosion damage. In the present study, the ABAQUS software is used to investigate the erosion crater morphology and stress distribution on a target material subjected to overlapping impacts of spherical particles. Subsequently, the validated model is applied to investigate the effect of the overlapping impacts of particles on the target. Accordingly, the correlation between erosion severity and the impact locations of the two incident particles is quantified. The results show that the horizontal distance between two solid particle impact locations can significantly affect the erosion magnitude and pattern. The interactions of the resulting craters diminish when the horizontal distance exceeds 0.6 times the particle diameter. When the horizontal distance is approximately 0.06 times the particle diameter, the energy loss originating from collisions reaches the maximum, which modifies the crater morphology. The present study is expected to provide in-depth insights into erosion mechanisms and erosion modeling.
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Abbreviations
- A, B, n :
-
Train hardening at reference strain rate
- A 0 :
-
Contact area between particle and material
- a :
-
Radius of smallest cross-section of pattern
- BH :
-
Brinell hardness of material
- C :
-
Strain rate of material
- D :
-
Particle diameter
- D m :
-
Middle diameter, which is equal to the outer diameter minus the wire diameter
- D 1−D 5 :
-
Damage constants
- d :
-
Damage parameter
- d t :
-
Damage parameters at time t
- d w :
-
Wire diameter
- d 0 :
-
Initial diameter
- d 1 :
-
Final diameter after deformation
- E C :
-
Energy dissipated by time-dependent deformation (creep, swelling, and viscoelasticity) at EC = 0
- E FD :
-
Energy dissipated by friction
- E I :
-
Remaining energy, which is known as the internal energy
- E K :
-
Kinetic energy
- E P :
-
Energy dissipated by plasticity
- E QB :
-
Energy dissipated by damping effect of solid medium infinite elements
- E S :
-
Applied elastic strain energy
- E total :
-
Total energy
- E U :
-
Dissipated portion of internal energy
- E V :
-
Energy dissipated by viscous effects, EV = 0
- E W :
-
Work performed by external forces on body
- ER :
-
Ratio of mass loss of target material to mass of erosion particles
- F :
-
Applied force
- F s :
-
Coefficient related to shape of particles
- F(α):
-
Function of impact angle
- H 1 :
-
Penetration depth of first single particle
- H 2 :
-
Penetration depth of second particle
- G :
-
Rigidity modulus of wire
- K :
-
Stiffness coefficient representing attribute of spring
- K B :
-
Constant related to velocity of particle before collision
- K 0 :
-
Empirical constant related to material properties
- m :
-
Thermal softening of material
- m p :
-
Quality of abrasive particle
- N c :
-
Effective number of turns, which is equal to the total number of turns minus two
- n 1 :
-
Empirical constant related to material properties
- n 2 :
-
Empirical constant related to impact velocity
- P :
-
Pressure on surface of material
- Q p :
-
Formation of permanent indentation, which requires a certain amount of energy
- R :
-
Notch radius of smallest cross-section of pattern
- T m :
-
Melting temperature
- T r :
-
Reference temperature
- T* :
-
Normalized temperature
- t :
-
Duration of impact process
- u :
-
Horizontal distance between the two impact events
- υ p :
-
Average impact velocity of particles
- υ 0 :
-
Impact velocity
- υ′:
-
Velocity of particle after impact
- W D :
-
Wear due to repeated deformation
- W t :
-
Initial kinetic energy of particles
- W u :
-
Increased internal energy of target material
- α :
-
Impact angle of particles
- ε :
-
Equivalent plastic strain rate
- ε B :
-
Deformation wear factor
- ε el :
-
Elastic stress
- ε f :
-
Fracture strain
- ε pl :
-
Equivalent plastic strain
- ε 0 :
-
Reference strain rate
- η :
-
Energy conversion rate
- σ :
-
Static yield stress
- σ c :
-
Total elastic stress
- σ u :
-
Elastic stress
- σ* :
-
Stress triaxiality
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Acknowledgements
The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51874340), the Natural Science Foundation of Shandong Province (Grant No. ZR2018MEE004), the National Key R&D Program of China (Grant No. 2016YFC0802301) and the Graduate Innovation Foundation of China University of Petroleum (East China) (Grant No. CXJJ-2022-44). The authors would like to thank all the member companies who have supported E/CRC research for many years.
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Xuerui ZANG. He obtained his Bachelor’s degree from the Petroleum Engineering College of Yangtze University in 2020. Now he works with Prof. Xuewen CAO as a student of Ph.D. in the College of Pipeline and Civil Engineering, China University of Petroleum (East China). His interested research area includes erosion wear, pipe-soil interaction, and multi-phase flow.
Xuewen CAO. He obtained his Bachelor’s degree of Engineering and Ph.D. degree in 1989 and 2006 from East China Petroleum Institute and Xi’an Jiaotong University, respectively. Now he is a professor and tutor of Ph.D. students in major oil and gas storage and transportation engineering. His interested research areas include multi-phase flow, erosion, offshore oil, supersonic nozzle, gas pipeline integrity management, and natural gas treatment and processing. He successively presided and participated in many research projects like “the National Science and Technology Major Project” and “the National Natural Science Foundation of China”. He has published more than 150 papers in leading journals.
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Zang, X., Cao, X., Xie, Z. et al. Surface deformation under overlapping impacts of solid particles. Friction 11, 280–301 (2023). https://doi.org/10.1007/s40544-021-0600-2
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DOI: https://doi.org/10.1007/s40544-021-0600-2