Yaoman stress rate

Introduction

The von Mises yield criterion, also known as the Maximum Distortion Energy Criterion, is a theory by Austrian engineer Richard Von Mises developed in 1913 for calculating the yield stress of ductile materials. It is simple yet powerful in its ability to determine the yield point of a variety of materials under different conditions. In other words, it is an effective way of predicting when a material will yield and is widely used in engineering today.

Background on Von Mises Yield Criterion

Richard Von Mises wanted to understand the stress behavior of certain materials and why certain materials yield under certain conditions. He proposed four key assumptions to explain this behavior, which are still used today:

1. The yield point of a material is related to its maximum shear stress.

2. Maximum shear stress is proportional to the strain energy of the material.

3. The strain energy of the material is related to its temperature at the time of loading.

4. Maximum shear stress is independent of the rotational stress.

Using these four assumptions, von Mises derived his famous yield criterion, which states:

“The yield point of a ductile material occurs when the maximum RPM (dynamic equivalent stress) exceeds a certain value, known as σv, which is determined by the material’s temperature at the time of loading.”

In other words, the material yields when the magnitude of the maximum shear stress exceeds a certain value, which is proportional to the temperature of the material. The equation Von Mises derived was:

σv = kT

Where σv is the von Mises yield stress (which gives the yield point for the particular material and loading condition), k is the temperature coefficient of the material and T is the temperature in Kelvin.

This equation is a simple yet powerful tool, as it can be used to calculate the exact yield point of a material based on its temperature and the temperature coefficient of that material. For example, if a material has a temperature coefficient of 400 and a temperature of 28 degrees Celsius, its von Mises yield stress (σv) is 400 x (28 + 273.15) = 281200 Pa.

Application of Von Mises Yield Criterion

The von Mises yield criterion has numerous applications in engineering, ranging from product design to structural integrity.

Product Design: When designing products, engineers often have to consider the yield point of their materials, as this will dictate the load bearing capacity of theproduct. The von Mises yield criterion is used to predict the yield point of different materials based on the temperature coefficient and temperature of the material. This helps engineers ensure that the product they are designing is able to withstand the load it was intended for.

Structural Integrity: The von Mises yield criterion is also used in structural integrity analysis to predict the load carrying capability of a metal structure. By calculating the von Mises yield stress of the likely materials used in the structure, engineers can ensure it is safe to operate under various conditions.

Conclusion

The von Mises yield criterion is an effective tool for predicting the yield stress of ductile materials. It is simple yet powerful, in its ability to determine the yield point of a wide variety of materials under different conditions. While it has many applications, it is most often used in product design and structural integrity analysis.

Von Mises Yield Criterion

The Von Mises yield criterion, also known as the maximum distortion energy criterion or the octahedral shear stress theory, is a method of failure analysis used to predict the yield of materials under different stress states. It was first developed by Gustav Ludwig Ferdinand von Mises in 1913 and is still widely used today in materials science and engineering.

The theory states that when a material is in a plane stress state, the principal strains must not exceed the yield strain, which is measured in terms of a required shear stress. In other words, the Von Mises yield criterion is a mathematical model of the maximum shear stress of a material that is required to reach plastic yielding.

The Von Mises yield criterion is based on two assumptions. The first is that all material deformations can be represented by shear components. The second is that the maximum shear stress in a solid is related to the maximum distortion energy of the material. By combining these two assumptions, the Von Mises yield criterion was able to establish a relationship between bulk strain and shear strain.

By looking at the relationship between bulk strain and shear strain, the Von Mises yield criterion can predict material yield under different stress states. It is primarily used for assessing the yield strength of ductile materials. Because of its ability to accurately predict material yield under varying stress states, the Von Mises yield criterion has become a standard for determining material performance.

Not only is the Von Mises yield criterion used for predicting yield strength, it is also used for predicting fracture strength or failure strength. By assessing the maximum distortion energy of a material, engineers can accurately predict the maximum load that a material can handle before it fails.

The Von Mises yield criterion has been used in materials science and engineering for more than a century and is still widely relied upon today. By accurately predicting material yield and failure strength, the Von Mises yield criterion has enabled engineers to assess the strength and durability of materials that have a complex stress state.