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In a linearly hardening plastic material. The true stress beyond initial yielding
- a)increases linearly with the true strain
- b)decreases linearly with the true stain
- c)first increases linearly and then decreases linearly with the true stain
- d)remain constant
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a linearly hardening plastic material. The true stress beyond initi...
Given that the strain hardening is linear, the true stress will increase linearly after yield point.
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In a linearly hardening plastic material. The true stress beyond initi...
Linearly Hardening Plastic Material
A linearly hardening plastic material refers to a material that exhibits a linear relationship between stress and strain beyond the initial yielding point. This means that as the material undergoes deformation, the stress required to further deform the material increases linearly with the amount of deformation.
True Stress and True Strain
Before discussing the relationship between true stress and true strain in a linearly hardening plastic material, let's first understand what true stress and true strain are.
True stress is the stress calculated by considering the actual cross-sectional area of the material at any given point during deformation. It takes into account the change in the material's cross-sectional area as it undergoes deformation.
True strain is the logarithmic ratio of the final length of a material to its original length, taking into account the actual deformation that occurs. It represents the total amount of deformation experienced by the material.
Relationship between True Stress and True Strain
In a linearly hardening plastic material, the true stress beyond the initial yielding point increases linearly with the true strain. This can be understood by considering the behavior of the material during deformation.
Initially, when a plastic material is subjected to stress, it undergoes elastic deformation. During this stage, the material follows Hooke's law and exhibits a linear relationship between stress and strain. However, once the material reaches the yield point, it starts to undergo plastic deformation.
During plastic deformation, the material experiences a change in its microstructure, such as the rearrangement of dislocations. This results in an increased resistance to further deformation and an increase in the required stress to cause additional strain. As the material continues to deform, the true stress required to further deform the material increases linearly with the true strain.
Conclusion
In summary, in a linearly hardening plastic material, the true stress beyond the initial yielding point increases linearly with the true strain. This is due to the increased resistance to further deformation caused by the rearrangement of dislocations and other microstructural changes in the material. Understanding this relationship is essential in analyzing and predicting the behavior of linearly hardening plastic materials under different loading conditions.
A linearly hardening plastic material refers to a material that exhibits a linear relationship between stress and strain beyond the initial yielding point. This means that as the material undergoes deformation, the stress required to further deform the material increases linearly with the amount of deformation.
True Stress and True Strain
Before discussing the relationship between true stress and true strain in a linearly hardening plastic material, let's first understand what true stress and true strain are.
True stress is the stress calculated by considering the actual cross-sectional area of the material at any given point during deformation. It takes into account the change in the material's cross-sectional area as it undergoes deformation.
True strain is the logarithmic ratio of the final length of a material to its original length, taking into account the actual deformation that occurs. It represents the total amount of deformation experienced by the material.
Relationship between True Stress and True Strain
In a linearly hardening plastic material, the true stress beyond the initial yielding point increases linearly with the true strain. This can be understood by considering the behavior of the material during deformation.
Initially, when a plastic material is subjected to stress, it undergoes elastic deformation. During this stage, the material follows Hooke's law and exhibits a linear relationship between stress and strain. However, once the material reaches the yield point, it starts to undergo plastic deformation.
During plastic deformation, the material experiences a change in its microstructure, such as the rearrangement of dislocations. This results in an increased resistance to further deformation and an increase in the required stress to cause additional strain. As the material continues to deform, the true stress required to further deform the material increases linearly with the true strain.
Conclusion
In summary, in a linearly hardening plastic material, the true stress beyond the initial yielding point increases linearly with the true strain. This is due to the increased resistance to further deformation caused by the rearrangement of dislocations and other microstructural changes in the material. Understanding this relationship is essential in analyzing and predicting the behavior of linearly hardening plastic materials under different loading conditions.
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In a linearly hardening plastic material. The true stress beyond initial yieldinga)increases linearly with the true strainb)decreases linearly with the true stainc)first increases linearly and then decreases linearly with the true staind)remain constantCorrect answer is option 'A'. Can you explain this answer?
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