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True Stress - True Strain Curve: Part One :: Total Materia Article
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True Stress - True Strain Curve: Part One
During stress testing of a material sample, te stress–strain curve is a graphical representation of te relationship between stress, obtained from measuring te load applied on te sample, and strain, derived from measuring te deformation of te sample. Te nature of te curve varies from material to material.
A typical stress-strain curve is shown in Figure 1. If we begin from te origin and follow te graph a number of point are indicated.
Figure 1: A typical stress-strain curve
Point A: At origin, there is no initial stress or strain in te test piece. Up to point A Hooke's Law is obeyed according to which stress is directly proportional to strain. That's why te point A is also known as proportional limit. This straight line region is known as elastic region and te material can regain its original shape after removal of load.
Point B: Te portion of te curve between AB is not a straight line and strain increases faster than stress at all point on te curve beyond point A. Point B is te point after which any continuous stress results in permanent, or inelastic deformation. Thus, point B is known as te elastic limit or yield point.
Point C & D: Beyond te point B, te material goes to te plastic stage till te point C is reached. At this point te cross- sectional area of te material starts decreasing and te stress decreases to point D. At point D te workpiece changes its length with a little or without any increase in stress up to point E.
Point E: Point E indicates te location of te value of te ultimate stress. Te portion DE is called te yielding of te material at constant stress. From point E onwards, te strength of te 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 te ultimate stress. Te point of fracture, or te actual tearing of te material, does not occur until point F. Te point F is also called ultimate point or fracture point.
If te instantaneous minimal cross-sectional area can be measured during a test along with P and L and if te constant-volume deformation assumption is valid while plastic deformation is occurring, then a true stress-strain diagram can be constructed.
Te construction should consist of using te equation e = log (L/L0) for true strain in te elastic and initial plastic regions and te equation e= log (A0/A) once significant plastic deformation has begun. In practice, however, te equation e= log (A0/A) is used for te entire strain range since te amount of error introduced is usually negligible. Te equation σ = P/A for true stress is valid throughout te entire test.
Accurate construction of a true stress-strain diagram becomes exceedingly difficult if te plastic deformation cannot be assumed to occur at a constant volume.
Finally, it should be mentioned that te neither te true stress-strain diagram nor te engineering stress-strain diagram accounts for te fact that te state of stress within te necked-down region is multiaxial. There is no simple way to account for te effect of this multiaxial state of stress on te material’s response, so it is customarily ignored. A schematic representation of an engineering stress-strain diagram and te 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 te offset method; (c) true stress-strain diagram
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True Stress - True Strain Curve: Part Two
True Stress - True Strain Curve: Part Three
True Stress - True Strain Curve: Part Four
Finding stress-strain diagrams in te Total Materia database
Te Total Materia Extended Range includes a unique collection of stress-strain curves and diagrams for calculations in te plastic range for thousands of metal alloys, heat treatments and working temperatures. Both true and engineering stress curves are given for various strain rates where applicable.
Finding a stress-strain graph in te database is simple and takes only seconds.
Enter te material of interest into te quick search field. You can optionally narrow your search by specifying te country/standard of choice in te designated field and click Search.
After selecting te material of interest to you, click on te Stress-Strain diagrams link to view data for te selected material. Te number of available stress-strain diagrams is displayed in brackets next to te link.
Because Total Materia stress-strain curves are neutral across standard specifications, you can review stress-strain diagrams by clicking te appropriate link for any of te subgroups.
Besides te stress-strain curves at different temperatures, stress and strain data are given in a tabular format which is convenient for copying to, for example, a CAE software.
It is also possible to view stress-strain curves and data for other working temperatures.
To do this, simply insert a new temperature into te ‘Enter temperature’ field within te defined range.
After clicking te Calculate button, a new curve is plotted and values in te table now correspond to te temperature you have defined. See example below for 250°C.
For you’re a chance to take a test drive of te Total Materia database, we invite you to join a community of over 150,000 registered users through te Total Materia Free Demo.
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