• True stress-strain curve of FCC metal and its derivative form[3] Where is constant related to the material flow stress.

• The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.

• For deriving the stress strain curve, we can assume that the volume change is 0 even if we deformed the materials.

• [2] Difference in true and engineering stress-strain curves Plastic deformation[edit] Swebor-brand high-strength low alloy steel plate, showing both sides, after plastic deformation
  from bringing to rest projectiles in ballistics testing.

• Then the stress will be localized to specific area where the necking appears.Additionally, we can induce various relation based on true stress-strain curve.1) True strain
  and stress curve can be expressed by the approximate linear relationship by taking a log on true stress and strain.

• Since necking starts to appear after ultimate tensile stress where the maximum force applied, we can express this situation as below: so this form can be expressed as below:
  It indicates that the necking starts to appear where reduction of area becomes much significant compared to the stress change.

• An object in the plastic deformation range, however, will first have undergone elastic deformation, which is undone simply be removing the applied force, so the object will
  return part way to its original shape.

• 3) Based on the true stress-strain curve and its derivative form, we can estimate the strain necessary to start necking.

• Types of deformation Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result.

• True stress and strain Since we disregard the change of area during deformation above, the true stress and strain curve should be re-derived.

• Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion
  of the cube.

• 4) A graphical method, so-called “Considere construction”, can help determine the behavior of stress-strain curve whether necking or drawing happens on the sample.

• By setting as determinant, the true stress and strain can be expressed with engineering stress and strain as below: Therefore, the value of engineering stress can be expressed
  by the secant line from made by true stress and value where to .

• Engineering stress and engineering strain are approximations to the internal state that may be determined from the external forces and deformations of an object, provided
  that there is no significant change in size.

• See also: Plasticity (physics) This type of deformation is not undone simply by removing the applied force.

• This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young’s modulus (E).

• When there is a significant change in size, the true stress and true strain can be derived from the instantaneous size of the object.

• All of these properties indicate the importance of calculating the true stress-strain curve for further analyzing the behavior of materials in sudden environment.

• This can be calculated based on the intersection between true stress-strain curve as shown in right.

• The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel.

• Diagram of a stress–strain curve, showing the relationship between stress (force applied) and strain (deformation) of a ductile metal.

• [3][4] 2) In reality, stress is also highly dependent on the rate of strain variation.

• In reality, many materials that undergo large elastic and plastic deformations, such as steel, are able to absorb stresses that would cause brittle materials, such as glass,
  with minimal plastic deformation ranges, to break.

• This figure also shows the dependency of the necking strain at different temperature.

• Engineering strain is modeled by infinitesimal strain theory, also called small strain theory, small deformation theory, small displacement theory, or small displacement-gradient
  theory where strains and rotations are both small.

 

Works Cited

[‘Rees, David (2006). Basic Engineering Plasticity: An Introduction with Engineering and Manufacturing Applications. Butterworth-Heinemann. p. 41. ISBN 0-7506-8025-3. Archived from the original on 2017-12-22.
2. ^ Callister, William D. (2004) Fundamentals
of Materials Science and Engineering, John Wiley and Sons, 2nd ed. p. 184. ISBN 0-471-66081-7.
3. ^ Jump up to:a b Courtney, Thomas (2000). Mechanical Behavior of Materials. Illinois: Waveland Press. p. 165. ISBN 9780073228242.
4. ^ “True Stress
and Strain” (PDF). Archived from the original (PDF) on 2018-01-27. Retrieved 2018-05-15.
5. ^ Roland, David. “STRESS-STRAIN CURVES” (PDF). MIT.
6. ^ Rice, Peter and Dutton, Hugh (1995). Structural glass. Taylor & Francis. p. 33. ISBN 0-419-19940-3.

Photo credit: https://www.flickr.com/photos/60053822@N00/11768468623/’]