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In a linearly hardening plastic material, the true stress beyond initial yielding
[ME 2018,Set-1]
- a)increases linearly with the true strain
- b)decreases linearly with the true strain
- c)first increases linearly and then decreases linearly with the true strain
- d)remain constant
Correct answer is option 'A'. Can you explain this answer?
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In a linearly hardening plastic material, the true stress beyond initi...
Linearly hardening plastic material:
A linearly hardening plastic material is one in which the true stress increases linearly with the true strain beyond the initial yielding point. This means that as the material is subjected to increasing deformation, the true stress also increases in a linear manner.
Explanation:
When a plastic material is subjected to external forces, it undergoes plastic deformation. In the initial stage, the material undergoes elastic deformation up to a certain point called the yield point. Beyond this point, the material enters the plastic deformation region.
True stress and true strain:
True stress is defined as the ratio of the applied force to the actual cross-sectional area of the material, taking into account the change in area due to deformation. True strain is the natural logarithm of the ratio of the final length to the original length of the material.
Behavior of true stress in a linearly hardening plastic material:
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain. This means that as the material is deformed further, the true stress also increases in a linear manner.
Reasons for linear hardening:
There are several reasons why a material may exhibit linear hardening behavior:
1. Dislocation movement: The increase in true stress with true strain can be attributed to the movement of dislocations within the material. As the material is deformed, dislocations move and interact with each other, leading to an increase in resistance to deformation.
2. Strain hardening: Plastic deformation causes a redistribution of dislocations and an increase in dislocation density, which in turn leads to strain hardening. This strain hardening causes an increase in the material's resistance to further deformation.
3. Work hardening: As the material is deformed, energy is expended in the form of work, which leads to an increase in the material's strength and hardness. This work hardening effect contributes to the linear increase in true stress with true strain.
Conclusion:
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain. This behavior is due to the movement and interaction of dislocations, strain hardening, and work hardening within the material.
A linearly hardening plastic material is one in which the true stress increases linearly with the true strain beyond the initial yielding point. This means that as the material is subjected to increasing deformation, the true stress also increases in a linear manner.
Explanation:
When a plastic material is subjected to external forces, it undergoes plastic deformation. In the initial stage, the material undergoes elastic deformation up to a certain point called the yield point. Beyond this point, the material enters the plastic deformation region.
True stress and true strain:
True stress is defined as the ratio of the applied force to the actual cross-sectional area of the material, taking into account the change in area due to deformation. True strain is the natural logarithm of the ratio of the final length to the original length of the material.
Behavior of true stress in a linearly hardening plastic material:
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain. This means that as the material is deformed further, the true stress also increases in a linear manner.
Reasons for linear hardening:
There are several reasons why a material may exhibit linear hardening behavior:
1. Dislocation movement: The increase in true stress with true strain can be attributed to the movement of dislocations within the material. As the material is deformed, dislocations move and interact with each other, leading to an increase in resistance to deformation.
2. Strain hardening: Plastic deformation causes a redistribution of dislocations and an increase in dislocation density, which in turn leads to strain hardening. This strain hardening causes an increase in the material's resistance to further deformation.
3. Work hardening: As the material is deformed, energy is expended in the form of work, which leads to an increase in the material's strength and hardness. This work hardening effect contributes to the linear increase in true stress with true strain.
Conclusion:
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain. This behavior is due to the movement and interaction of dislocations, strain hardening, and work hardening within the material.
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In a linearly hardening plastic material, the true stress beyond initial yielding[ME 2018,Set-1]a)increases linearly with the true strainb)decreases linearly with the true strainc)first increases linearly and then decreases linearly with the true straind)remain constantCorrect answer is option 'A'. Can you explain this answer?
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