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완전접촉 상태의 프레팅피로 균열 진전조건 해석

Analysis of the Crack Advancement Conditions in Fretting Fatigue subject to Complete Contact

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초록

This study analytically studies the far-field tensile stress required to prevent intermediate arrest in fretting fatigue subject to a complete contact configuration. This concern is raised from the previous cracking behaviour analysis in the case of an incomplete contact configured fretting fatigue where a higher tensile stress is found to be necessary as the edge radius of a rounded punch decreases [4]. The Bückner principle is used to constitute governing equations for the crack stress intensity factors. The eigenvalue problem approach and dislocation density function method are utilized to analyze the complete contact and crack problems, respectively. The result is compared with the solutions acquired for the incomplete contact case. It is found that the far field tensile stress necessary to propel a continuous crack growth is a few times (2~6 times in the present example calculation) greater than the case of the incomplete contact. This shows that the tentative speculation, i.e. an infinite times of the tensile stress in an incomplete contact case might be necessary, is not true. Another achievement of this work is to establish a systematic analysis method to deal with a fretting fatigue cracking behaviour subject to the complete contact configuration in the sequel to the previous incomplete one.

Abstract

This study analytically studies the far-field tensile stress required to prevent intermediate arrest in fretting fatigue subject to a complete contact configuration. This concern is raised from the previous cracking behaviour analysis in the case of an incomplete contact configured fretting fatigue where a higher tensile stress is found to be necessary as the edge radius of a rounded punch decreases [4]. The Bückner principle is used to constitute governing equations for the crack stress intensity factors. The eigenvalue problem approach and dislocation density function method are utilized to analyze the complete contact and crack problems, respectively. The result is compared with the solutions acquired for the incomplete contact case. It is found that the far field tensile stress necessary to propel a continuous crack growth is a few times (2~6 times in the present example calculation) greater than the case of the incomplete contact. This shows that the tentative speculation, i.e. an infinite times of the tensile stress in an incomplete contact case might be necessary, is not true. Another achievement of this work is to establish a systematic analysis method to deal with a fretting fatigue cracking behaviour subject to the complete contact configuration in the sequel to the previous incomplete one.

참고문헌 (13)

  1. Tanaka, K., "Fretting Fatigue in 0.55C Spring Steel and 0.45C Carbon Steel", Fatigue Fract. Engng. Mater. Struct, 8, pp.129~142 (1985)
  2. Fenner, K. J., "Fretting Corrosion and its Influence on Fatigue Failure", Proc. Int. Conf. Fatigue of Metals, Institution of Mechanical Engineers (1956)
  3. Moobola R. D., "Designing against Fretting Fatigue : Crack Self-Arrest", J. Strain Anal, 33, pp.17~25 (1988)
  4. Kim. H. -K., "Analysis of Edge Crack Behaviour influenced by Non-symmetrical Contact Tractions and Bulk Tension", Fatigue Fract. Engng. Mater. Struct, 38, pp.551~562 (2015)
  5. Flamant, A., "Sur la Répartition des Pressions dans un Solide Rectangulaire chargé Transversalement", Compte. Rendu. Acad. Sci., 114, pp.1465~ (1892)
  6. Erdogan, F., "Methods of Analysis and Solutions of Crack Problems", pp.368~425 (1973), Noordhoff
  7. Williams, M. L., "Stress Singularities resulting from Various Boundary Conditions in Angular Corners of Plates in Extension", J. Appl. Mech., 19, pp.526~528 (1952)
  8. Kim, H.-K, "Asymptotic Analysis of an Adhered Complete Contact between Elastically Dissimilar Materials", J. Strain Analy. (2014)
  9. Dundurs, J., "Mathematical Theories of Dislocations", pp.70~115 (1969), ASME Pub
  10. Kim. H. -K., "Dislocation in a Semi-infinite Half Plane subject to an Adhesive Complete Contact with a Square Wedge : Part I-Derivation of the Corrective Functions", Tribol. Lubr, 38, pp.73~83 (2022)[DOI]
  11. Kim. H. -K., "Dislocation in a Semi-infinite Half Plane subject to an Adhesive Complete Contact with a Square Wedge : Part II-Approximation and Application of Corrective Functions", Tribol. Lubr, 38, pp.84~92 (2022)[DOI]
  12. Bueckner, H. F., "A Novel Principle for the Computation of Stress Intensity Factors", Z. Anew. Math. Mech., 50, pp.529~546 (1970)
  13. Krenk, S., "On the Use of the Interpolation Polynomial for Solutions of Singular Integral Equations", Q. Appl. Maths, 32, pp.479~484 (1975)

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