Experimental Mechanics

, Volume 51, Issue 1, pp 23–44 | Cite as

Experimental Energy Balance During the First Cycles of Cyclically Loaded Specimens Under the Conventional Yield Stress

  • N. Connesson
  • F. Maquin
  • F. Pierron


This paper, as an extension of Maquin and Pierron (Mech Mater 41(8):928–942, 2009), presents an experimental procedure developed to macroscopically estimate the energy balance during the very first cycles of a uniaxially loaded metallic specimen at low stress levels. This energy balance is performed by simultaneously measuring the plastic input energy using a load cell and a strain gauge, and the dissipative energy using the temperature field provided by an infrared camera. Some experimental limitations led to restrain the present procedure to positive stress ratios, and to complement this energy balance by a second measurement while the material plastic work per cycle is negligible compared to the dissipative energy. Some results obtained on a cold rolled low carbon steel specimen are presented. First, a sensitivity study is undertaken to precisely determine the detection threshold on both thermal and plastic energies. Then, after having verified the homogeneity of the dissipative source fields, energy balances have been performed at different stress levels. It was thus confirmed that the slow variations of the dissipative sources occurring during the first cycles are due to micro-plastic adaptation, and that the dissipative sources remaining after some hundreds of cycles are due to viscoelastic (internal friction) phenomena. This procedure provides a better understanding of dissipation based approaches to fatigue found in the literature and an advanced tool to study viscoelastic phenomena in uniaxial loading.


Dissipative sources Viscoelasticity Internal friction Microplasticity Cold work Energy balance Infrared thermography Transient-state 


  1. 1.
    Maquin F, Pierron F (2009) Heat dissipation measurements in low stress cyclic loading of metallic materials: from internal friction to micro-plasticity. Mech Mater 41(8):928–942CrossRefGoogle Scholar
  2. 2.
    Magnin T (1991) Recent advances in low cycle fatigue from the physical metallurgy point of view. Mém Étud Sci Rev Métall 88(1):33–48 (in French)Google Scholar
  3. 3.
    Tanaka T, Hattori S (1978) Initial behavior of hysteresis loop of low carbon steels under repeated load (theoretical treatment on the multiplying model of dislocations). Bull JSME 21(161):1557–1564Google Scholar
  4. 4.
    Fatemi A, Yang L (1998) Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. Int J Fatigue 20(1):9–34CrossRefGoogle Scholar
  5. 5.
    Troshchenko VT (2006) Nonlocalized fatigue damage of metals and alloys. Part 3. Strain and energy criteria. Strength Mater 38(1):1–19CrossRefGoogle Scholar
  6. 6.
    Moore HF, Kommers JB (1921) Fatigue of metals under repeated stresses. Chem Metall Eng 25:1141–1144Google Scholar
  7. 7.
    Doudard C, Calloch S, Hild F, Cugy P, Galtier A (2004) Identification of the scatter in high cycle fatigue from temperature measurements. C R Mécanique 332(10):795–801Google Scholar
  8. 8.
    Fargione G, Geraci A, La Rosa G, Risitano A (2002) Rapid determination of the fatigue curve by the thermographic method. Int J Fatigue 24(1):11–19CrossRefGoogle Scholar
  9. 9.
    LaRosa G, Risitano A (2000) Thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components. Int J Fatigue 22(1):65–73CrossRefGoogle Scholar
  10. 10.
    Luong MP (1998) Fatigue limit evaluation of metals using an infrared thermographic technique. Mech Mater 28(1–4):155–163CrossRefGoogle Scholar
  11. 11.
    Starke P, Walther F, Eifler D (2007) Fatigue assessment and fatigue life calculation of quenched and tempered SAE 4140 steel based on stress–strain hysteresis, temperature and electrical resistance measurements. Fatigue Fract Eng Mater Struct 30(11):1044–1051CrossRefGoogle Scholar
  12. 12.
    Krapez JC, Pacou D (2002) Thermography detection of damage initiation during fatigue tests. Proc SPIE Int Soc Opt Eng 4710:435–449Google Scholar
  13. 13.
    Meneghetti G (2007) Analysis of the fatigue strength of a stainless steel based on the energy dissipation. Int J Fatigue 29(1):81–94CrossRefGoogle Scholar
  14. 14.
    Pastor ML, Balandraud X, Grédiac M, Robert JL (2008) Applying infrared thermography to study the heating of 2024-T3 aluminium specimens under fatigue loading. Infrared Phys Technol 51(6):505–515CrossRefGoogle Scholar
  15. 15.
    Galtier A, Bouaziz O, Lambert A (2002) Influence of steel microstructure on their mechanical properties. Méc Ind 3(5):457–462 (in French with English abstract)Google Scholar
  16. 16.
    Morabito AE, Chrysochoos A, Dattoma V, Galietti U (2007) Analysis of heat sources accompanying the fatigue of 2024 T3 aluminium alloys. Int J Fatigue 29(5):977–984CrossRefGoogle Scholar
  17. 17.
    Yang B, Liaw PK, Huang JY, Kuo RC, Huang JG, Fielden DE (2005) Stress analyses and geometry effects during cyclic loading using thermography. J Eng Mater Technol Trans ASME 127(1):75–82CrossRefGoogle Scholar
  18. 18.
    Charkaluk E, Constantinescu A (2009) Dissipative aspects in high cycle fatigue. Mech Mater 41(5):483–494CrossRefGoogle Scholar
  19. 19.
    Dang Van K, Papadopoulos IV (1999) High cycle metal fatigue: from theory to application, vol 392, CISM courses and lectures edn. CISM Courses and LecturesGoogle Scholar
  20. 20.
    Håkansson P, Wallin M, Ristinmaa M (2008) Prediction of stored energy in polycrystalline materials during cyclic loading. Int J Solids Struct 45(6):1570–1586zbMATHCrossRefGoogle Scholar
  21. 21.
    Kamlah M, Haupt P (1998) On the macroscopic description of stored energy and self heating during plastic deformation. Int J Plast 13(10):893–911CrossRefGoogle Scholar
  22. 22.
    Longère P, Dragon A (2008) Plastic work induced heating evaluation under dynamic conditions: critical assessment. Mech Res Commun 35(3):135–141CrossRefGoogle Scholar
  23. 23.
    Mollica F, Rajagopal KR, Srinivasa AR (2001) The inelastic behavior of metals subject to loading reversal. Int J Plast 17(8):1119–1146zbMATHCrossRefGoogle Scholar
  24. 24.
    Monchiet V, Charkaluk E, Kondo D (2006) Plasticity-damage based micromechanical modelling in high cycle fatigue. C R Mécanique 334(2):129–136zbMATHCrossRefGoogle Scholar
  25. 25.
    Rosakis P, Rosakis AJ, Ravichandran G, Hodowany J (2000) A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals. J Mech Phys Solids 48(3):581–607zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Vincent L (2008) On the ability of some cyclic plasticity models to predict the evolution of stored energy in a type 304L stainless steel submitted to high cycle fatigue. Eur J Mech A Solids 27(2):161–180zbMATHCrossRefGoogle Scholar
  27. 27.
    Wong AK, Kirby GC (1990) A hybrid numerical/experimental technique for determining the heat dissipated during low cycle fatigue. Eng Fract Mech 37(3):493–504CrossRefGoogle Scholar
  28. 28.
    Scholz F, Woldt E (2001) The release of stored energy during recovery and recrystallization of cold rolled ultra high purity iron. J Therm Anal Calorim 64(3):895–903CrossRefGoogle Scholar
  29. 29.
    Chrysochoos A, Maisonneuve O, Martin G, Caumon H, Chezeaux JC (1989) Plastic and dissipated work and stored energy. Nucl Eng Des 114(3):323–333CrossRefGoogle Scholar
  30. 30.
    Hodowany J, Ravichandran G, Rosakis AJ, Rosakis P (2000) Partition of plastic work into heat and stored energy in metals. Exp Mech 40(2):113–123CrossRefGoogle Scholar
  31. 31.
    Macdougall D (2000) Determination of the plastic work converted to heat using radiometry. Exp Mech 40(3):298–306CrossRefGoogle Scholar
  32. 32.
    Meyer LW, Herzig N, Halle T, Hahnb F, Krueger L, Staudhammer KP (2007) A basic approach for strain rate dependent energy conversion including heat transfer effects: an experimental and numerical study. J Mater Process Technol 182(1–3):319–326CrossRefGoogle Scholar
  33. 33.
    Oliferuk W, Maj M, Raniecki B (2004) Experimental analysis of energy storage rate components during tensile deformation of polycrystals. Mater Sci Eng Abstr 374(1–2):77–81CrossRefGoogle Scholar
  34. 34.
    Zehnder AT, Babinsky E, Palmer T (1998) Hybrid method for determining the fraction of plastic work converted to heat. Exp Mech 38(4):295–302CrossRefGoogle Scholar
  35. 35.
    Harvey DP, Bonenberger RJ, Wolla JM (1998) Effects of sequential cyclic and monotonic loadings on damage accumulation in nickel 270. Int J Fatigue 20(4):291–300CrossRefGoogle Scholar
  36. 36.
    Kaleta J, Blotny R, Harig H (1991) Energy stored in a specimen under fatigue limit loading conditions. J Test Eval 19(4):326–333CrossRefGoogle Scholar
  37. 37.
    Bodelot L, Sabatier L, Charkaluk E, Dufrénoy P (2009) Experimental setup for fully coupled kinematic and thermal measurements at the microstructure scale of an AISI 316L steel. Mater Sci Eng Abstr 501(1–2):52–60CrossRefGoogle Scholar
  38. 38.
    Chrysochoos A, Berthel B, Latourte F, Galtier A, Pagano S, Wattrisse B (2008) Local energy analysis of high-cycle fatigue using digital image correlation and infrared thermography. J Strain Anal Eng Des 43(6):411–421CrossRefGoogle Scholar
  39. 39.
    Lebedev AB (1999) Amplitude-dependent elastic-modulus defect in the main dislocation-hysteresis models. Phys Solid State 41(7):1105–1111CrossRefGoogle Scholar
  40. 40.
    Audenino AL, Calderale PM (1996) Measurement of non-linear internal damping in metals: Processing of decay signals in a uniaxial stress field. J Sound Vib 198(4):395–409CrossRefGoogle Scholar
  41. 41.
    Bovsunovsky AP (1996) Application of the strain-phase-shift method for the determination of damping in metals. Exp Mech 36(3):243–250CrossRefGoogle Scholar
  42. 42.
    Foster CG, Meimaris C, Hooker RJ (1992) Transverse strain behaviour in no. 2011 aluminium alloy subjected to cyclic loading. J Sound Vib 158(2):245–256CrossRefGoogle Scholar
  43. 43.
    Wren GG, Kinra VK (1992) Axial damping in metal-matrix composites. II: a theoretical model and its experimental verification. Exp Mech 32(2):172–178CrossRefGoogle Scholar
  44. 44.
    Kinra VK, Wren GG (1992) Axial damping in metal-matrix composites. I: a new technique for measuring phase difference to 10 − 4 radians. Exp Mech 32(2):163–171CrossRefGoogle Scholar
  45. 45.
    Chrysochoos A, Berthel B, Latourte F, Pagano S, Wattrisse B, Weber B (2008) Local energy approach to steel fatigue. Strain 44(4):327–334CrossRefGoogle Scholar
  46. 46.
    Louche H, Chrysochoos A (2001) Thermal and dissipative effects of accompanying Lüders band propagation. Mater Sci Eng Abstr 307(1–2):15–22CrossRefGoogle Scholar
  47. 47.
    Boulanger T, Chrysochoos A, Mabru C, Galtier A (2004) Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels. Int J Fatigue 26(3):221–229CrossRefGoogle Scholar
  48. 48.
    Chrysochoos A, Louche H (2000) Infrared image processing to analyze the calorific effects accompanying strain localization. Int J Eng Sci 38(16):1759–1788CrossRefGoogle Scholar
  49. 49.
    Berthel B, Chrysochoos A, Wattrisse B, Galtier A (2008) Infrared image processing for the calorimetric analysis of fatigue phenomena. Exp Mech 48(1):79–90CrossRefGoogle Scholar
  50. 50.
    Brown N, McMahon CJ, Jr (1968) Observation of microplasticity. Microplasticity 2:45–73Google Scholar

Copyright information

© Society for Experimental Mechanics 2010

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Procédés de Fabrication (LMPF)Arts et Metiers ParisTechChâlons-en-Champagne cedexFrance

Personalised recommendations