Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Estimation and Application of Reliability Values for Strength of Material Following Gamma Distribution

감마분포를 따르는 재료강도의 신뢰도 예측과 응용

  • Park, Sung-Ho (Defence Systems Test Center, Agency for Defence Development) ;
  • Kim, Jae-Hoon (Dept. of Mechanical Design, Choongnam Nat'l Univ.)
  • 박성호 (국방과학연구소 종합시험단) ;
  • 김재훈 (충남대학교 기계설계공학과)
  • Received : 2011.06.07
  • Accepted : 2011.12.12
  • Published : 2012.02.01
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Abstract

The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

취성이 큰 재료의 강도는 일반적으로 정규분포 또는 와이블분포로 설명되어 왔으나 감마분포도적합할 수 있다. 재료의 파손이 가해진 응력의 연속된 값 중 가장 큰 값에 좌우된다면 극치분포를 적용하는 것이 합당하다. 본 논문에서는 재료강도가 감마분포를 따르며 극치분포하는 응력이 작용할 경우 응력-강도 간섭이론에 기반하여 신뢰도 계산식을 제시하였으며, 확률분포 파라미터별 신뢰도와 안전율 및 변동계수와의 관계를 통하여 신뢰도 계산식의 유효성을 입증하였다. 안전율과 변동계수에 기반한 신뢰도 예측방법으로 목표 신뢰도가 설정되었을 때 최소한 요구되는 안전율과 최대로 허용되는 응력의 변동계수를 예측할 수 있다.

Keywords

References

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