We use a lot of ductile materials in our day to day life. From the one’s we see to the ones we don’t see, ductile materials can be found everywhere. The electric poles we see is a good example; the steel rods that go into the construction of our homes is a good example of the usage of ductile material we don’t see.
Though it’s a property of ductile material to fracture if it is stresses beyond its ultimate tensile strength, there are many cases like in machine parts where they tend to yield due to static loading on them. Though several theories have been formulated to explain ductile material failure, only two of them are very prominent and widely used during the design of parts using ductile materials. They are
1. The Von-Mises Theory or The Distortion Energy theory: The theory is named after the contributor of this theory, Von Mises in 1913. The theory is basically formed on the shear strength value of a material and is very best suited for materials whose shear strengths are lesser than their tensile strengths and in which the compressive and tensile strengths are equal. Any material or component that fails due to shear stress can be best predicted using this theory. The theory states that “The Von-Mises Stress which can be determined using this theory is a uniaxial or one directional stress value that would tend to create the same distortion energy as created by a combination of various other applied stresses". For a component or material to be safe, we have to ensure that this Von Mises Stress value is below the yield stress limit of the material.
2. Maximum Shear Stress Theory: The theory was initially proposed by Coulomb and later formulated by Tresca in 1864. It was then later in the twentieth century J.Guest confirmed the theory. The theory is also called as the Tresca – Guest theory. This theory is also formulated on the basis of the shear strength of a material. The theory states that “Failure occurs in a part or component when the maximum shear stress exceeds the shear strength of the material at yield". The shear strength of the material is normally considered to be half of the yield strength of the material as per this theory. This is more of a conservative limit compared to the Von-Mises theory.
All the theories are formulated on the assumption that the material being considered is homogeneous and isotropic, free from any internal defects such as cracks, etc.