Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954
This constant of proportionality describes the slope of the elastic region of the stress strain relationship. For many materials including viscoelastic materials, this relationship is not strictly linear. This results in the creation of a hysteresis loop between the loading and unloading curves of the stress-strain diagram. Referring back to our previous assertion that the energy required to impose this strain is the area under the stress-strain curve, it is obvious that this hysteresis loop dictates a loss in energy in the system. Given the law of conservation of energy, it is impossible for this energy to simply be lost. Instead, a large portion of this mechanical energy is converted into heat, approximately 70-80 with the remaining energy being converted into entropy within the atomic structure of the material. Such changes are manifested as changes in dislocation boundaries etc. By finding the difference in area under the loading, and unloading curves, and applying this to a heat transfer equation, the temperature at any point in a body can be predicted under cyclic load influences. Heat Explosion. When a material on which cyclic stress are imposed is sufficiently thermally insulated such that adiabatic or near adiabatic conditions are maintained, the results can be catastrophic. Since heat is not allowed to escape, the temperature will continue to rise with each successive stress cycle resulting in a massive temperature rise that ultimately results in catastrophic thermal failure known as heat explosion. When a material surface lacks sufficient thermal insulation to be considered adiabatic, the surface is said to be dissipative, or highly dissipative depending on the level of insulation. This will result in moderate temperature increases due to cyclic stress imposition compared to the model in which such self-heating effects are not considered. Consideration of these aforementioned effects prove to be of significant consequence when examining the mechanical behavior of the material. Analysis. While there are several different models for the propagation of heat through a material, the selection of such an equation will greatly affect the accuracy of your model. There are two classical approaches to modeling heat propagation, the Fourier equation and the Maxwell-Catteneo Equation. Each model can be used to produce accurate solutions; however the accuracy of the Fourier model has come into question and has the model itself has actually been broken in certain situations. However, the Fourier equation will prove to be much easier to solve, particularly when the nonhomogeneous case is considered (Fig. 1).
Fig. 1. Hysteresis loop in the stress-strain graph indicates a loss of energy from between the loading and unloading curves MMSE Journal. Open Access www.mmse.xyz
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