Deformation (engineering)
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In engineering, deformation refers to the change in size or shape of an object.
Displacements are the absolute change in position of a point on the object.
Deflection is the relative change in external displacements on an object.
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. When there is a significant change in size, the true stress and true strain can be derived from the instantaneous size of the object.
In the figure it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the
The concept of a rigid body can be applied if the deformation is negligible.
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. The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel. Different deformation modes may occur under different conditions, as can be depicted using a
Permanent deformation is irreversible; the deformation stays even after removal of the applied forces, while the temporary deformation is recoverable as it disappears after the removal of applied forces. Temporary deformation is also called elastic deformation, while the permanent deformation is called plastic deformation.
Elastic deformation
The study of temporary or elastic deformation in the case of
For some materials, e.g.
Normal metals, ceramics and most crystals show linear elasticity and a smaller elastic range.
Linear elastic deformation is governed by Hooke's law, which states:
where
- σ is the applied stress;
- E is a material constant called Young's modulus or elastic modulus;
- ε is the resulting strain.
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). Engineers often use this calculation in tensile tests. The area under this elastic region is known as resilience.
Note that not all elastic materials undergo linear elastic deformation; some, such as
Plastic deformation
This type of deformation is not undone simply by removing the applied force. 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. Soft
Under tensile stress, plastic deformation is characterized by a
Compressive failure
Usually, compressive stress applied to bars, columns, etc. leads to shortening.
Loading a structural element or specimen will increase the compressive stress until it reaches its
In long, slender structural elements — such as columns or
Fracture
This type of deformation is also irreversible. A break occurs after the material has reached the end of the elastic, and then plastic, deformation ranges. At this point forces accumulate until they are sufficient to cause a fracture. All materials will eventually fracture, if sufficient forces are applied.
True stress and strain
Since we disregard the change of area during deformation above, the true stress and strain curve should be re-derived. For deriving the stress strain curve, we can assume that the volume change is 0 even if we deformed the materials. We can assume that:
Then, the true stress can be expressed as below:
Additionally, the true strain εT can be expressed as below:
Then, we can express the value as
Thus, we can induce the plot in terms of and as right figure.
Additionally, based on the true stress-strain curve, we can estimate the region where necking starts to happen. 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. 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. The relation can be expressed as below:
Where is stress coefficient and is strain-hardening coefficient. Usually, the value of has range around 0.02 to 0.5 at room temperature. If is 1, we can express this material as perfect elastic material.[3][4]
2) In reality, stress is also highly dependent on the rate of strain variation. Thus, we can induce the empirical equation based on the strain rate variation.
Where is constant related to the material flow stress. indicates the derivative of strain by the time, which is also known as strain rate. is the strain-rate sensitivity. Moreover, value of is related to the resistance toward the necking. Usually, the value of is at the range of 0-0.1 at room temperature and as high as 0.8 when the temperature is increased.
By combining the 1) and 2), we can create the ultimate relation as below:
Where is the global constant for relating strain, strain rate and stress.
3) Based on the true stress-strain curve and its derivative form, we can estimate the strain necessary to start necking. This can be calculated based on the intersection between true stress-strain curve as shown in right.
This figure also shows the dependency of the necking strain at different temperature. In case of FCC metals, both of the stress-strain curve at its derivative are highly dependent on temperature. Therefore, at higher temperature, necking starts to appear even under lower strain value.
All of these properties indicate the importance of calculating the true stress-strain curve for further analyzing the behavior of materials in sudden environment.
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 . By analyzing the shape of diagram and secant line, we can determine whether the materials show drawing or necking.
On the figure (a), there is only concave upward Considere plot. It indicates that there is no yield drop so the material will be suffered from fracture before it yields. On the figure (b), there is specific point where the tangent matches with secant line at point where . After this value, the slope becomes smaller than the secant line where necking starts to appear. On the figure (c), there is point where yielding starts to appear but when , the drawing happens. After drawing, all the material will stretch and eventually show fracture. Between and , the material itself does not stretch but rather, only the neck starts to stretch out.
Misconceptions
A popular misconception is that all materials that bend are "weak" and those that do not are "strong". 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.[6]
See also
- Artificial cranial deformation
- Buff strength
- Creep (deformation)
- Deflection (engineering)
- Deformation (mechanics)
- Deformation mechanism maps
- Deformation monitoring
- Deformation retract
- Deformation theory
- Elasticity
- Malleability
- Planar deformation features
- Plasticity (physics)
- Poisson's ratio
- Strain tensor
- Strength of materials
- Wood warping
References
- ISBN 0-7506-8025-3. Archivedfrom the original on 2017-12-22.
- ISBN 0-471-66081-7.
- ^ ISBN 9780073228242.
- ^ "True Stress and Strain" (PDF). Archived from the original (PDF) on 2018-01-27. Retrieved 2018-05-15.
- ^ Roland, David. "STRESS-STRAIN CURVES" (PDF). MIT.
- ISBN 0-419-19940-3.)
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