비틀림(Torsion) 시험

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"비틀림(Torsion) 시험"에 대한 내용입니다.

목차

1. 실험 목표 ·······················································2

2. 이론적 배경 ·····················································2
2.1. 전단 응력 ······················································2
2.2. 원형 봉의 비틀림 ··············································3
2.3. 사각 봉의 비틀림 ··············································4
2.4. 풀 브릿지(Full-Bridge) ········································4

3. 실험 방법 ·······················································5
3.1. 비틀림 시험 ···················································5
3.1.1. 실험 과정 ···················································5
3.1.2. 실험 원리 ···················································5
3.2. 데이터 처리 ····················································6
3.2.1. 원형 봉 ····················································6
3.2.2. 사각 봉 ····················································6

4. 결과 분석 ························································7
4.1. 원형 봉 ·······················································7
4.2. 사각 봉 ························································9
4.3. 종합 결과 분석 ················································10
4.4. 오차 원인 및 실험 개선 방안 ···································11

5. 결론 ·····························································11

6. 참고 문헌 ························································12

본문내용

1. 실험 목표
① 토크(T, Torque), 비틀림(Torsion), 전단응력(, Shear Stress), 전단변형률(, Shear Strain), 전단계수(G, Shear Modulus)를 이해한다.
② 비틀림 실험(Torsion Test)을 통해 전단응력에 의한 재료의 변형률을 계측하여 전단계수를 구하고, 실험에 사용된 재료를 확인한다.
2. 이론적 배경
2.1. 전단응력(Shear stress)
전단응력(τ, shear stress)은 재료의 표면에 접하는 방향으로 작용하는 응력을 말한다. 식 (1)에 전단응력의 정의가 있다. 여기서 V는 접선방향 힘은 전단력(shear force), A는 전단력이 작용하고 있는 면의 넓이이다.
   (1)
수직응력에서 수직변형률을 구헀듯이 전단응력에서도 전단변형율(shear strain) γ을 정의한다. 전단변형율은 전단응력에 의해 변형된 각도([rad단위])를 의미한다. 전단응력에서 또한 선형 탄성 구간에서 후크의 법칙이 성립하며 다음과 같다.
    (2)
위 식에서 G는 전단계수(shear modulus)라 한다. 전단계수 G와 선형탄성계수 E는 다음과 같은 관계가 성립한다.
       (3)
식(3)에서 ν 는 푸아송비(Poisson's ratio)이며, G, E, ν 3개의 물성치가 각각 독립적이기 않고 의존한다는 의미를 내포하고 있다. 즉 G, E, ν 3개 중 2개의 물성치를 알면 하나의 물성치를 자동으로 알 수 있다.
한편, 전단응력은 항상 쌍으로 작용한다. 하나의 전단응력은 마주 보는 전단응력과 헤어지는 전단응력과 각각 쌍을 이룬다. 전단응력만 작용하는 상태를 순수전단(pure shear)이라고 한다. 그러나 식(4)에서 볼 수 있듯이 순수전단이 작용하더라도 면을 기울인 상태에서 보면 수직응력이 작용한다.
       (4)
식(4)에서 순수 전단 상태에서 45° 기울어진 면에서 최대 수직응력이 작용함을 알 수 있다.
또한 [Fig1]에서 보이는바와 같이 45° 면에서는 인장력(또는 압축력)이 작용하지만 푸아송비의 존재로 인해 135°(-45°)면에서 작용하는 수직응력에 의해 압축력(또는 인장력)을 받을 수 있다. 이를 수직응력에 대한 후크의 법칙   과 식(3)을 연립하여 다음과 같은 결과를 얻는다.

참고 자료

“계측공학”(Thomas G.Beckwith 등 3인 저, 한철호 등 5인 공역, 도서출판YOUNG), 12.8.2.브리지상수 . 2020.11.10.
"Matweb:METERIAL PROPERTY DATA", Overview of materials for 2000 Series Aluminum Alloy
http://www.matweb.com/search/datasheettext.aspx?matguid=2076184469d740af9f86b0d69b2e42ff, 2020.11.10
“Wikipedia”, Aluminium alloy
https://en.wikipedia.org/wiki/Aluminium_alloy#2000_series, 2020.11.10