True Stress - True Strain Curve: Part One


During stress testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, obtained from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample. The nature of the curve varies from material to material.

A typical stress-strain curve is shown in Figure 1. If we begin from the origin and follow the graph a number of points are indicated.

Figure 1: A typical stress-strain curve

Point A: At origin, there is no initial stress or strain in the test piece. Up to point A Hooke's Law is obeyed according to which stress is directly proportional to strain. That's why the point A is also known as proportional limit. This straight line region is known as elastic region and the material can regain its original shape after removal of load.

Point B: The portion of the curve between AB is not a straight line and strain increases faster than stress at all points on the curve beyond point A. Point B is the point after which any continuous stress results in permanent, or inelastic deformation. Thus, point B is known as the elastic limit or yield point.

Point C & D: Beyond the point B, the material goes to the plastic stage till the point C is reached. At this point the cross- sectional area of the material starts decreasing and the stress decreases to point D. At point D the workpiece changes its length with a little or without any increase in stress up to point E.

Point E: Point E indicates the location of the value of the ultimate stress. The portion DE is called the yielding of the material at constant stress. From point E onwards, the strength of the material increases and requires more stress for deformation, until point F is reached.

Point F: A material is considered to have completely failed once it reaches the ultimate stress. The point of fracture, or the actual tearing of the material, does not occur until point F. The point F is also called ultimate point or fracture point.

If the instantaneous minimal cross-sectional area can be measured during a test along with P and L and if the constant-volume deformation assumption is valid while plastic deformation is occurring, then a true stress-strain diagram can be constructed.

The construction should consist of using the equation ε = log (L/L0) for true strain in the elastic and initial plastic regions and the equation ε= log (A0/A) once significant plastic deformation has begun. In practice, however, the equation ε= log (A0/A) is used for the entire strain range since the amount of error introduced is usually negligible. The equation σ = P/A for true stress is valid throughout the entire test.

Accurate construction of a true stress-strain diagram becomes exceedingly difficult if the plastic deformation cannot be assumed to occur at a constant volume.

Finally, it should be mentioned that the neither the true stress-strain diagram nor the engineering stress-strain diagram accounts for the fact that the state of stress within the necked-down region is multiaxial. There is no simple way to account for the effect of this multiaxial state of stress on the material’s response, so it is customarily ignored. A schematic representation of an engineering stress-strain diagram and the corresponding true stress-strain diagram can be found in Figure 2.

Figure 2: Material properties determined from stress-strain diagrams: (a) Engineering stress-strain diagram; (b) determination σ by the offset method; (c) true stress-strain diagram

기술 자료 검색

검색할 어구를 입력하십시오:

검색 범위



이 문서는 전체 문서 중 일부분입니다. 이 주제에 대해 더 읽고 싶으시면 아래 링크를 클릭하시면 됩니다.

Total Materia Extended Range는 수천개 재질의 탄성 영역 범위 내 계산용 응력-변형률 곡선, 열처리 및 공정 온도 정보를 포함하고 있습니다. 다양한 변형률 속도에 따른 진응력-진변형률 곡선 및 공칭응력-공칭변형률 곡선 또한 제공됩니다.

응력-변형률 곡선을 데이터베이스에서 검색하는 것은 매우 쉽습니다.

신속 검색에 검색할 재질명을 입력합니다. 원하신다면 국가/규격을 지정하신 후 검색 버튼을 클릭합니다.

관심 소재를 선택한 후, 선택된 소재에 대한 응력-변형률 곡선의 링크를 클릭하십시오. 가능한 응력 - 변형률 곡선 기록의 개수는 링크 옆 괄호 안에 표시됩니다.

Total Materia 응력-변형률 곡선은 규격 사양서와 무관하므로, 어떠한 소그룹 내의 링크를 클릭하셔도 응력-변형률 곡선을 검토하실 수 있습니다.

온도가 달라지면 응력-변형률 곡선도 변하기 때문에, 응력과 변형률 정보는 표로 주어져 있습니다. 이는 CAE 소프트웨어 등에 쉽게 응용하실 수 있습니다.

다른 작동 온도에서 응력-변형률 곡선을 검토하실 수도 있습니다.

이를 위해서는 간단히 범위 내 새로운 온도를 온도 입력 창에 입력하시면 됩니다.

계산 버튼을 누르시면 새로운 온도와 그에 대응하는 값이 출력됩니다. 250°C에서의 예를 보십시오.

Total Materia 데이터베이스를 사용해 보실 수 있는 기회가 있습니다. 저희는 Total Materia 무료 체험을 통해 150,000명 이상의 사용자가 이용하고 있는 커뮤니티로 귀하를 초대합니다.