Mathematical Simulation of Plastic Deformation Process
Introduction
Plastic deformation is a process that affects the shape of a material by applying an external force. This process includes many subfields including tensile testing, bending, shearing, punching, and deep drawing. Among these subfields, tensile testing is the most often used method to characterize plastic deformation in materials. During tensile testing, a sample is loaded in tension until it breaks, and the response of the specimen is measured through strain gauges. This strain data can then be used to build a mathematical model of the plastic deformation process.
Theoretical Background
Plastic deformation is a process involving material yield, and the mathematical models used to predict the behavior of materials undergoing plastic deformation are referred to as yield models. A yield model is a mathematical equation which is used to predict the strain of a material under a certain load. The two most popular yield models are the Von Mises and Tresca models, both of which are based on the concept of equivalent or true stress-strain. The Von Mises model states that a material is assumed to yield once a certain equivalent or true stress is exceeded, and any load applied beyond this level will cause further plastic deformation. The Tresca model states that a material is assumed to yield at a certain true strain level, and any load applied beyond this will cause further plastic deformation. Both models appraise deformation behavior in terms of stress, strain, and strain rate.
Mathematical Modeling of Plastic Deformation
When using yield models for the mathematical simulation of plastic deformation, the true stress-strain data from the tensile test must be fitted to the model by using a curve fitting algorithm such as least squares or polynomial regression. This fitting is done by minimizing the sum of the squared errors between the predicted and measured values, and is used to identify a set of parameters which will be used to generate a mathematical approximation of the data. It is important to note that the parameters must be kept within the limits of the material being tested, and the model chosen must be able to relate the true stress and true strain values to the yield surfaces.
When the mathematical model has been established, simulations can be conducted to predict the behavior of future plastic deformation tests. This can be done by taking the parameters of the model and entering them into a simulator. The results of the simulations can be used to predict the ultimate strength of the material, the yield point, and any possible issues that could arise if the parameters are exceeded during the loading test.
Conclusion
In conclusion, plastic deformation can be studied through the use of yield models for the mathematical simulation of the process. When Tensile test data is used to set a set of parameters, a simulation is created which predicts the behavior of future plastic deformation tests. Using a simulation has been found to be an effective way of identifying the ultimate strength and yield point of the material.
