連續衝擊(Consecutive Impact)行為經常出現在工程應用上，然而衝擊是一件相當複雜的過程，需考慮球的運動、基材表面形貌、過程中能量的轉換與溫度的影響。當基材考慮塑性時，衝擊後表面將產生凹痕與堆積的現象，而表面下層出現壓縮力使基材獲得表面硬化的效果，但是這也將造成表面的不平整現象。
本文使用有限元素法建立連續衝擊負載系統，探討連續衝擊次數對於彈塑性基材表面變形及能量吸收之影響。藉由運動方程式描述剛性球之運動，並利用彈塑性本構方程式及應變能方程式，計算衝擊過程中基材之變形與吸收之能量。
分析結果發現，隨著連續衝擊次數的增加，基材塑性區域、最大深度、殘留深度及堆積高度會先增加最終趨於穩定，然而初始衝擊速度與切線模數皆會影響達到穩定所需的連續衝擊次數，在具有較低之初始衝擊速度及較高之切線模數時，達到穩定所需的次數最少。在有限元素能量分析中，能量可分成，動能、位能、彈性應變能以及塑性消耗能等形式轉換，隨著衝擊次數的增加，基材所吸收的能量將會越來越少，最終如彈性碰撞，基材應變能將全部回傳至剛性球。此外透過剛性球在每次衝擊之回彈係數(e)與能量分析結果相比有相同之趨勢，隨著次數的增加回彈係數逐漸趨近於1，代表能量損失越來越小。

關鍵字: 表面硬化、連續衝擊負載、珠擊法

consecutive Impact behavior often appears in engineering applications. However, impact is a complicated process. It’s necessary to consider the ball motion, the surface morphology, the energy conversion, and the influence of temperature. When the plasticity of the substrate is considered, dents and pilled up will occur on the surface after impact, and the compression force on the lower surface will not only make the substrate obtain the effect of surface hardening, but also cause unevenness on the surface.
In this paper, the finite element method is used to establish a consecutive impact model to explore the influence of impact times on the surface deformation and energy absorption of the elasto-plastic substrate. The motion equation is used to describe the motion of the rigid ball, and the elastic-plastic constitutive equation and the strain energy equation are used to calculate the deformation and absorbed energy of the substrate during the impact process.
The plastic area, maximum depth, residual depth and stacking height of the substrate will be changed by the number of consecutive impacts.However, the initial impact velocity and tangent modulus will affect the impact times for stability. Therefore, the consecutive impact model from this research can be a reference for the impact surface treatment processes.
Keywords: surface hardening, consecutive impact load, shot peening

[1]C. LIJunsheng, Y. Baiyu, “Impact Damage on One Kind of Aero-engine Compressor Blade from Steel Sphere”, Journal of Air Force Engineering University: Natural Science Edition, pp. 14(6), 2013.
[2]E. Nordin, & B. Alfredsson, “Experimental investigation of shot peening on case hardened SS2506 gear steel”, Experimental Techniques, vol.41(4), pp. 433-451, 2017.
[3]S.A. Meguid, “Mechanics of shot-peening”, Ph.D. Thesis,, 1975.
[4]H.O. Fuchs, Mechanical Engineer's Handbook, Wiley, New York, 1986.
[5]J. Harrison, “Heat Treatment 19”, pp. 86-92, 1987.
[6]S. A. Meguid,”Fatigue and Fracture of Engineering Materials and Structures 14(5)”, pp. 332-343, 1991.
[7]H. Tresca, “Memoire sur l’ecoulement des corps soliders soumis a de fortes pressions”, C. R. Academie des Sciences de paris, vol. 59, pp. 754, 1864.
[8]H. Hencky, “Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen”, Zeitschrift fu ̈r angevandte Mathematik und Mechanik, vol. 4, pp. 323-335, 1924.
[9]李宏燁,莊新村與趙震,“材料常用流動應力模型研究”, 模具技術, vol. 5, pp. 1-4, 2009.
[10]K. L. Johnson, ” Contact mechanics”, Cambridge university press, 1987.
[11]S. Timoshenko, J. N. Goodier, “Theory of elastic”, 1951.
[12]C. Hardy, C. N. Baronct, and G. V. Tordion, “The Elasto Plastic indentation of a Half-space by a Rigid sphere”, Journal of Numerical Methods in Engineering, vol. 3, pp. 45, 1971.
[13]W. R. Chang, I. Etsion, and D. B. Bogy, ‘‘An Elastic-Plastic Model for the Contact of Rough Surfaces’’, ASME J. Tribol., vol. 109, pp. 257–263, 1987.
[14]L. Kogut, and I. Etsion, “Elastic-plastic contact analysis of a sphere and a rigid flat”, J. Appl. Mech, vol. 69, no. 5, pp. 657-662, 2002.
[15]R. L. Jackson, and I. Green, “A Finite Element Study of Elasto-PlasticHemispherical Contact Against a Rigid Flat”, ASME J. Tribol., vol. 127, no. 2, pp. 343–354, 2005.
[16]Z. Song, K. Komvopoulos, “Elastic-plastic spherical indentation: Deformation regimes, evolution of plasticity, and hardening effect”, Mechanics of Materials, vol. 61, pp. 91-100, 2013.
[17]Z. Chen, R. Goltsberg, I. Etison, “Yield modes in a coated spherical contact”, Tribology International, vol. 120, pp. 309-316, 2018.
[18]Z. Haibo, I. Etsion, “ A Coupled Eulerian–Lagrangian Model for Sliding Inception of Elastic–Plastic Spherical Contact”, J. Tribol., vol. 143, no. 1, pp. 014501, 2020.
[19]S. C. Hunter, “Energy absorbed by elastic waves during impact”, J Mech Phys Solids, vol. 5, no. 3, pp. 162–71, 1957.
[20]I. M. Hutchings. “Energy absorbed by elastic waves during plastic impact’’, J Phys D, vol. 12, no. 11, pp. 1819-24, 1979.
[21]C. Thornton, and Z. Ning, “Coefficients of restitution for elastoplastic Oblique Impact of Elasto-Plastic Spheres”, First International Particle Technology Forum, pp. 14–19, 1994.
[22]C. Thornton, “Coefficient of Restitution for Collinear Collisions ofElastic-Perfectly Plastic Spheres”, ASME J., vol. 64, no. 2, pp. 383–386, 1997.
[23]W. J. Stronge, “Impact mechanics”, Cambridge: Cambridge University Press, 2000.
[24]C.Y. Wu, L. Y. Li, and C. Thornton, “Energy dissipation during normal impact of elastic and elastic-plastic spheres”, International Journal of Impact Engineering, vol. 32, no. 1, pp. 593-604, 2006.
[25]N. Hirai, K. Tosha, and E. Rouhaud, “Finite element analysis of shot peening-on the form of a single dent”, Proceedings of the 9th International Conference on Shot Peening, Paris , 2005.
[26]H. Ghaednia, D. B. Marghitu, R. L. Jackson, “ Predicting the Permanent Deformation After the Impact of a Rod With a Flat Surface”, J. Tribol., vol. 137, no. 1, pp. 011403, 2014.
[27]P. Müller, R. Böttcher, A. Russell, M. Trüe, S. Aman, and J. Tomas, “Contact time at impact of spheres on large thin plates”, Adv Powder Technol, vol. 27, no. 4, pp. 1233–1243, 2016.
[28]F. Jebelisinaki, R. Boettcher, B. V. Wachem, and P. Müller, “Impact of dominant elastic to elastic-plastic millimeter-sized metal spheres with glass plates”, Powder Technology , vol. 356, pp. 208–221, 2019.
[29]J. D Beleran, Y. Y. Bo, H. G. Robles, A. Milanes, A. Yeo, & C. K. Chong, “ Copper wire bond analysis: Pad design effects and process considerations”, Electronic Components and Technology Conference , , vol. 13, pp. 1124-1129, 2012.
[30]A. Bolshakov, G. M. Pharr. “ Influences of pile up on the measurement of mechanical properties by load and depth sensing indentation techniques[J]”, Journal of materials research, vol. 13, pp. 4, 1998.
[31] 游至晨, 具彈性鍍膜/彈性基材系統之純擠壓彈液動潤滑分析, 2014.