how to convert load vs displacement curve to stress-strain curve

Stress-strain curve and load vs displacement curve are two useful tools in materials testing. The former provides the relationship between a material's stress and strain, while the latter records the applied load against the corresponding displacement. Although both can provide information on a material's mechanical properties, stress-strain curve is more informative, but it is often more challenging to obtain than load vs displacement curve. In this article, we will show you how to convert load vs displacement curve to stress-strain curve.

What is Load vs Displacement Curve?

A load vs displacement curve is a graph that shows the relationship between the applied load and the displacement of a material under a particular testing setup. The test setup often involves a specimen being compressed, stretched, or bent while being subjected to an increasing load. The resulting load vs displacement curve can be used to determine several mechanical properties of the material, such as the elastic modulus, yield strength, ultimate tensile strength, and fracture strength.

What is Stress-Strain Curve?

Stress-strain curve is a graph that shows the relationship between a material's stress and strain under varying loading conditions. Stress is the force applied per unit area of the original cross-sectional area of the specimen, and strain is the deformation per unit length. The curve obtained from the test gives information on the material's stiffness, elasticity, plasticity, ductility, toughness, and resilience. The shape, position, and magnitude of the stress-strain curve provide valuable information on the material's strength, deformation capacity, and failure behavior.

Converting Load vs Displacement Curve to Stress-Strain Curve

To convert a load vs displacement curve to a stress-strain curve, we need to use the following steps:1. Calculate the cross-sectional area of the specimen.2. Convert displacement in millimeters to elongation in meters.3. Calculate the true stress.4. Calculate the true strain.5. Plot the true stress and true strain on a graph to obtain the stress-strain curve.

Calculating the Cross-sectional Area of the Specimen

To calculate the cross-sectional area of the specimen, measure its diameter or thickness using standard techniques such as using a caliper or micrometer. If the specimen has an irregular shape, use an optical microscope or image analysis software to obtain its cross-sectional area. Once the cross-sectional area has been obtained, it can be used to calculate the true stress.

Calculating the True Stress and True Strain

The true stress is calculated as the applied load divided by the cross-sectional area of the specimen at any point during the test. The true stress takes into account the reduction in cross-sectional area that occurs during the test due to necking or other deformation. The true strain is calculated as the natural logarithm of the ratio of the final length to the original length of the specimen. The true strain provides a measure of the deformation directly proportional to the stress.

Conclusion

In conclusion, we have shown you how to convert load vs displacement curve to stress-strain curve. The stress-strain curve is more informative than the load vs displacement curve as it provides more information on the material's mechanical properties. Converting from one curve to the other is possible using the steps outlined above. Knowing the mechanical properties of materials are important in engineering and materials science fields as it is essential in designing and selecting components for various applications.