ProductsAbaqus/Standard Structural relaxationAt high temperatures glass behaves like a liquid, while at low temperatures glass behaves like a thermoelastic solid. In both temperature ranges the physical properties of glass depend only on the instantaneous value of the temperature. However, at temperatures in the vicinity of the glass transition temperature the behavior of glass is different. In this temperature range, the molecular structure of glass changes gradually with temperature and a noticeable delay is observed before the equilibrium state is reached. In this case the physical properties depend on both the temperature and the thermal history. Tool-Narayanaswamy-Moynihan modelIn Abaqus/Standard the Tool-Narayanaswamy-Moynihan (TNM) model can be used to predict structural relaxation in glass. It uses the fictive temperature, , originally proposed by Tool to describe the structure of the material. In the TNM model the thermal strains are obtained from the following relation: where
For a special case when the thermal expansion coefficients are not temperature- or field variable-dependent, it can be shown that the thermal strain increment can be expressed as In the TNM model we must specify the coefficients of thermal expansion for both glassy and liquid states. Input File Usage Use the following option to define the thermal expansion coefficient for the glassy state: EXPANSION Abaqus/CAE Usage Use the following option to define the thermal expansion coefficient for the glassy state: Property module: material editor: Input File Usage Use the following option to define the thermal expansion coefficient for the liquid state: EXPANSION, LIQUID Defining the reference temperatureIf the coefficients of thermal expansion are not functions of temperature or field variables, the value of the reference temperature, , is not needed. If or is a function of temperature or field variables, you can define . Input File Usage Use the following option to define the reference temperature value: EXPANSION, ZERO = Fictive temperatureThe fictive temperature is commonly expressed by introducing an equilibrium response function The response function, , is a decreasing function in time, such that and .In the Tool-Narayanaswamy-Moynihan model the response function is expressed with a series of exponential functions: where
In addition, the material parameters must satisfy the relation . Combining the equations above the expression for the fictive temperature has the form whereand is the reduced time, which is computed using the following shift function: where
Computation of fictive temperatureThe fictive temperature at time is computed using the algorithm proposed by Markovsky and Soules: andElementsThe structural relaxation model can be used with any stress/displacement element in Abaqus/Standard. ProceduresThe model can be used with all stress/displacement procedure types. However, the time effects are taken into account only in quasi-static (see Quasi-static analysis), coupled temperature-displacement (see Fully coupled thermal-stress analysis), and direct-integration implicit dynamic (see Implicit dynamic analysis using direct integration) analyses. In other stress/displacement procedure types the evolution of the fictive temperature is suppressed, so its value remains unchanged. OutputIn addition to the standard output identifiers available in Abaqus/Standard (Abaqus/Standard output variable identifiers), the following variable has special meaning for the TNM model:
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