What is the variation of stress with strain ?

Question

Answer

A particular material displays is known as that particular materials stress - strain curve . it is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of the variety of lodgings (stress)

Answer

Stress is applied force upon area

strain is ratio of change in dimensions upon original dimensions

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Answer

STRAIN IS DIRECTLY PROPORTIONAL TO STRESS.AFTER ULTIMATE TENSILE STRENGTH STRAIN INCREASE EVEN IF STRESS IS ZERO

Answer

Variation of Stress with Strain

Introduction:
The variation of stress with strain is a fundamental concept in the study of material behavior under external forces. Stress is defined as the force per unit area, while strain is the measure of deformation or change in shape. The relationship between stress and strain helps us understand how materials respond to applied forces and can be represented graphically by a stress-strain curve.

Stress-Strain Curve:
The stress-strain curve is a graphical representation of the relationship between stress and strain for a given material. It provides valuable information about the material's mechanical behavior and its ability to withstand external loads. The curve typically consists of several distinct regions, each indicating a different response of the material to applied stress.

Elastic Region:
In the initial portion of the stress-strain curve, the material behaves elastically, which means it can deform under stress and return to its original shape once the stress is removed. This region is characterized by a linear relationship between stress and strain, and the material follows Hooke's Law. The slope of the curve in this region represents the material's elastic modulus, which describes its stiffness.

Yield Point and Plastic Deformation:
Beyond the elastic region, the stress-strain curve exhibits a deviation from linearity, indicating the material has reached its yield point. At this point, the material undergoes plastic deformation, meaning it deforms permanently even after the applied stress is removed. The strain continues to increase with only a slight increase in stress. The yield strength is the stress required to produce a specific amount of plastic deformation.

Plastic Region:
After the yield point, the stress-strain curve enters the plastic region. In this region, the material experiences significant plastic deformation, and the strain increases rapidly with a relatively constant stress. The material's ability to withstand further deformation decreases, and its strength gradually decreases as well.

Ultimate Tensile Strength and Fracture:
The stress-strain curve reaches its maximum point at the ultimate tensile strength, which represents the maximum stress the material can withstand before failure. Beyond this point, the material undergoes necking, a localized reduction in cross-sectional area, and eventually fractures. The strain at fracture is a measure of the material's ductility, with more ductile materials exhibiting higher values.

Conclusion:
The variation of stress with strain is a crucial concept in understanding the mechanical behavior of materials. The stress-strain curve provides valuable information about a material's elastic and plastic properties, including its stiffness, yield strength, ultimate tensile strength, and ductility. By analyzing the curve, engineers and scientists can determine the suitability of materials for specific applications and design structures that can withstand the expected loads.

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