Contact around a Sharp Corner with Small Scale Plasticity
Advances in Materials
Volume 6, Issue 1-1, January 2017, Pages: 10-17
Received: Oct. 31, 2016; Accepted: Nov. 8, 2016; Published: Dec. 8, 2016
Views 3788      Downloads 144
Zupan Hu, Department of Mechanical Engineering, University of Michigan, Ann Arbor, USA; Stanley Black & Decker Inc, Towson, USA
Article Tools
Follow on us
Owing to elastic singularity, the contact stress around a sharp corner is highly sensitive to the boundary conditions and local geometrical details. Determination of such stress is critical in predicting failures such as wear, fretting fatigue and crack initiation. In this paper, the stress around such corner is analyzed based on linear elasticity and small scale plasticity. The stress on the contact interface is generalized in a way that the results can be easily converted to represent another corner with different dimensions or boundary conditions. An example is presented to show the determination of the stress scale and the formulation of a generalized solution. It is shown that the generalized macro stress field away from the corner dominates the contact behaviors around the corner.
Partial Slip, Stress Singularity, Plastic Yielding
To cite this article
Zupan Hu, Contact around a Sharp Corner with Small Scale Plasticity, Advances in Materials. Special Issue: Advances in Multiscale Modeling Approach. Vol. 6, No. 1-1, 2017, pp. 10-17. doi: 10.11648/
Copyright © 2016 Authors retain the copyright of this article.
This article 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.
Hoeppner, D. W., Fretting fatigue case studies of engineering components. Tribology International, 2006. 39(10): p. 1271-1276.
He, J. and F.-G. Yuan, Damage identification for composite structures using a cross-correlation reverse-time migration technique. Structural Health Monitoring, 2015.
He, J. and F.-G. Yuan. An enhanced CCRTM (E-CCRTM) damage imaging technique using a 2D areal scan for composite plates. 2016.
Cai, W., J. Chan, and D. Garmire, 3-Axes MEMS Hall-Effect Sensor, in 2011 IEEE Sensors Applications Symposium. 2011. p. 141-144.
Cai, W. and L. Gouveia, Modeling and simulation of Maximum power point tracker in Ptolemy. Journal of Clean Energy Technologies, 2013. 1(1): p. 4.
Cai, W., X. Cui, and X. Zhou, Optimization of a GPU Implementation of Multi-dimensional RF Pulse Design Algorithm, in International Conference on Bioinformatics and Biomedical Engineering 2011. 2011.
Cai, W., L. Huang, and N. Wu, Class E Power Amplifier for Wireless Medical Sensor Network. International Journal of Enhanced Research in Science, Technology & Engineering, 2016. 5(4): p. 6.
Wang, J., et al., An Innovative Two-Stage Reheating Process for Wrought Aluminum Alloy During Thixoforming. Metallurgical and Materials Transactions A, 2015. 46(9): p. 4191-4201.
Wang, J. J., et al., Alloy development and reheating process exploration of Al–Si casting alloys with globular grains for thixoforming. Journal of Materials Research, 2016. 31(16): p. 2482-2492.
Zhang, J., et al., An optimized cross-linked network model to simulate the linear elastic material response of a smart polymer. Journal of Intelligent Material Systems and Structures, 2015.
Zhang, J., et al., A novel statistical spring-bead based network model for self-sensing smart polymer materials. Smart Materials and Structures, 2015. 24(8): p. 085022.
Hu, Z., et al., Effect of plastic deformation on the evolution of wear and local stress fields in fretting. International Journal of Solids and Structures, 2016. 82: p. 1-8.
Hu, Z., M. D. Thouless, and W. Lu, Effects of gap size and excitation frequency on the vibrational behavior and wear rate of fuel rods. Nuclear Engineering and Design, 2016. 308: p. 261-268.
Hu, Z. and J. W. Pratt. The Environmental and Economic Impact of IGCC in China, With Comparison to Alternative Options. in Proceeding of ASME International Conference on Energy Sustainability, Volume 1. 2010. Phoenix, Arizona.
Banerjee, N. and D. A. Hills, Analysis of stick–slip and contact-edge behaviour in a simplified fretting fatigue test. The Journal of Strain Analysis for Engineering Design, 2006. 41: p. 183-192.
Tan, L., A. Acharya, and K. Dayal, Modeling of slow time-scale behavior of fast molecular dynamic systems. Journal of the Mechanics and Physics of Solids, 2014. 64: p. 24-43.
Tan, L. and K. Bhattacharya, Length scales and pinning of interfaces. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016. 374(2066).
Hu, Z., W. Lu, and M. D. Thouless, Slip and wear at a corner with Coulomb friction and an interfacial strength. Wear, 2015. 338–339: p. 242-251.
Hu, Z., et al., Simulation of wear evolution using fictitious eigenstrains. Tribology International, 2015. 82, Part A(0): p. 191-194.
He, J. and F.-G. Yuan, Lamb-wave-based two-dimensional areal scan damage imaging using reverse-time migration with a normalized zero-lag cross-correlation imaging condition. Structural Health Monitoring, 2016.
Lu, W., et al., CASL Structural Mechanics Modeling of Grid-to-Rod Fretting (GTRF). JOM, 2016. 68(11): p. 2922-2929.
Vingsbo, O. and S. Söderberg, On fretting maps. Wear, 1988. 126(2): p. 131-147.
He, J. and F.-G. Yuan, Lamb wave-based subwavelength damage imaging using the DORT-MUSIC technique in metallic plates. Structural Health Monitoring, 2016.
Tan, L., A. Acharya, and K. Dayal, Coarse variables of autonomous ODE systems and their evolution. Computer Methods in Applied Mechanics and Engineering, 2013. 253: p. 199-218.
Zhou, Z. R., et al., Progress in fretting maps. Tribology International, 2006. 39(10): p. 1068-1073.
Gu, H., Molecular Dynamics Study on Mechanical Properties and Interfacial Morphology of an Aluminum Matrix Nanocomposite Reinforced by β–Silicon Carbide Nanoparticles. Journal of Computational and Theoretical Nanoscience, 2009. 6: p. 12.
Gu, H., A Technical Brief - Applications of Conductive Polymer Composites in Oil and Gas Industry, in Petroleum and Petrochemical Technical Symposium 2015: Huston, TX.
Peng, Y., et al., A comprehensive computational model of sound transmission through the porcine lung. The Journal of the Acoustical Society of America, 2013. 134(5): p. 4121-4121.
Peng, Y., et al. Experimental Study on Gastric Electrophysiology Signal by Electroacupuncture at Zusanli Point on Rabbits. in 2008 2nd International Conference on Bioinformatics and Biomedical Engineering. 2008.
Peng, Y., et al., Sound transmission in the chest under surface excitation: an experimental and computational study with diagnostic applications. Medical & Biological Engineering & Computing, 2014. 52(8): p. 695-706.
Peng, Y., et al., Sound transmission in porcine thorax through airway insonification. Medical & Biological Engineering & Computing, 2016. 54(4): p. 675-689.
Peng, Y., et al. Chest Response to Vibratory Excitation: Advances Beyond Percussion in ASME 2012 International Mechanical Engineering Congress and Exposition. 2012. Houston, TX.
Wang, J., A. B. Phillion, and G. Lu, Development of a visco-plastic constitutive modeling for thixoforming of AA6061 in semi-solid state. Journal of Alloys and Compounds, 2014. 609: p. 290-295.
Narayanunni, V., H. Gu, and C. Yu, Monte Carlo simulation for investigating influence of junction and nanofiber properties on electrical conductivity of segregated-network nanocomposites. Acta Materialia, 2011. 59(11): p. 4548-4555.
Wang, J., et al., Viscosity estimation of semi-solid alloys based on thermal simulation compression tests. International Journal of Materials Research, 2013. 104(3): p. 255-259.
Ma, X. and H.-J. Shi, On the fatigue small crack behaviors of directionally solidified superalloy DZ4 by in situ SEM observations. International Journal of Fatigue, 2012. 35(1): p. 91-98.
Ma, X. and H.-J. Shi, In situ SEM studies of the low cycle fatigue behavior of DZ4 superalloy at elevated temperature: Effect of partial recrystallization. International Journal of Fatigue, 2014. 61: p. 255-263.
Ma, X., et al., Influence of surface recrystallization on the low cycle fatigue behaviour of a single crystal superalloy. Fatigue & Fracture of Engineering Materials & Structures, 2015. 38(3): p. 340-351.
Gu Jiansheng, et al., Effect of Structural Relaxation on Hardness and Shear Band Features of Zr_(64.13)Cu_(15.75)Ni_(10.12)Al_(10) Bulk Metallic Glass During Indentation. Rare Metal Materials and Engineering, 2008. S4.
Zhang, J., et al., Bonding of alumina and metal using bulk metallic glass forming alloy. International Journal of Modern Physics B, 2009. 23(06n07): p. 1306-1312.
Churchman, C. M. and D. A. Hills, General results for complete contacts subject to oscillatory shear. Journal of the Mechanics and Physics of Solids, 2006. 54(6): p. 1186-1205.
Parmigiani, J. P. and M. D. Thouless, The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries. Engineering Fracture Mechanics, 2007. 74(17): p. 2675-2699.
Sills, R. B. and M. D. Thouless, The effect of cohesive-law parameters on mixed-mode fracture. Engineering Fracture Mechanics, (0).
Giannakopoulos, A. E., T. C. Lindley, and S. Suresh, Aspects of equivalence between contact mechanics and fracture mechanics: theoretical connections and a life-prediction methodology for fretting-fatigue. Acta Materialia, 1998. 46(9): p. 2955-2968.
Barber, J. R., Elasticity. 3rd ed. 2010, Dordrecht, NY: Springer.
Bogy, D. B., Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions. Journal of Applied Mechanics, 1971. 38(2): p. 377-386.
Kogut, L. and I. Etsion, A Semi-Analytical Solution for the Sliding Inception of a Spherical Contact. Journal of Tribology, 2003. 125(3): p. 499-506.
Zhang, J., et al., Crack initiation and fatigue life prediction on aluminum lug joints using statistical volume element–based multiscale modeling. Journal of Intelligent Material Systems and Structures, 2013. 24(17): p. 2097-2109.
Zhang, J., J. Johnston, and A. Chattopadhyay, Physics-based multiscale damage criterion for fatigue crack prediction in aluminium alloy. Fatigue & Fracture of Engineering Materials & Structures, 2014. 37(2): p. 13.
Bay, N. and T. Wanheim, Real area of contact and friction stress at high pressure sliding contact. Wear, 1976. 38(2): p. 201-209.
Flicek, R., D. A. Hills, and D. Dini, Progress in the application of notch asymptotics to the understanding of complete contacts subject to fretting fatigue. Fatigue & Fracture of Engineering Materials & Structures, 2013. 36(1): p. 56-64.
Hills, D. A. and D. Dini, Characteristics of the process zone at sharp notch roots. International Journal of Solids and Structures, 2011. 48(14–15): p. 2177-2183.
Williams, M. L., Stress singularities resulting from various boundary conditions in angular corners of plate in extension. ASME Journal of Applied Mechanics, 1952. 19: p. 526–528.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186