Thermomechanical Deformation Processes of Rate Sensitive Solids: Material Issues and Stability
Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Germany
Rate sensitivity becomes significant when metallic materials are processed at elevated temperature, and influences the deformation behaviour. Besides, rate effects may be activated under ambient conditions if deformation is fast. Accounting for rate sensitivity in the analysis of material deformation processes, implies considerations on the constitutive description of the material and the set up of a suitable algorithm for the numerical computer simulation. In addition, concurrent thermal phenomena that interact may be of importance. These are due to imposed boundary conditions and because of heat generation by the dissipation of mechanical work. The computer simulation of such thermomechanically coupled processes is a well developed subject [1]. An issue in the present account concerns the stability of the thermomechanical system along the deformation path. Thereby, conditions are explored which allow perturbations in the system to be augmented during the course of the process. For this purpose, the exposition in [2] is extended here to account for the thermal processes that interact with the deformation.
The pertinent equations for the thermomechanical deformation process are summarized, and a brief discussion on coupling effects refers to the continuum level; the equations governing a finite element representation of the system are listed. Subsequently, constitutive modelling of the material is reviewed from the mechanical aspect. The formalism for the viscous solid as a reference inelastic material, is extended to incorporate a yield limit, thus modelling viscoplastic response. The dynamic flow stress apertaining to this model increases with material viscosity and deformation rate. The impact of an elastic constituent is demonstrated, but the material model is ultimately restricted to inelastic behaviour. Specification of the viscosity coefficient accounts for the actual flow characteristic of the material which may depend on the strain, strain rate and temperature.
The considerations on stability start with uniaxial tension, distinguishing between stability of loading and stability of deformation. The thermal effect is investigated for adiabatic processes. The obtained stability criterion reproduces those known for inviscid and viscous solids under isothermal conditions. Rate sensitivity contributes to the stability of the deformation process while temperature dependence has the opposite effect. In the absence of strain hardening, stability requires the rate effect to be stronger than the thermal degradation. At higher strain the stress-strain dependence may exhibit a waved shape as a result of hardening and softening processes in the material structure. In regions with strain softening, the deformation process will be stable if the rate effect compensates both the thermal degradation and the strain softening. The stability conditions under more general situations involve the characteristics of the coupled thermomechanical system. Stability in more general situations regards the propagation of perturbations in the variables. Quantification for the finite element representation identifies the decisive characteristics of the system. Physical stability is seen to be of relevance for the sensitivity of the rate solution to fluctuations and for the numerical stability of the temporal integration of the process.
Applications of thermomechanical analysis are selected such that rate effects become apparent. The analysis of thermal shock for elastic-viscoplastic material demonstrates the transition from elastic to plastic behaviour while a process of emergency cooling progresses. The computer simulation of a forging operation at different speeds focuses on the development of the temperature field in the rate sensitive material. The splashing of ceramic droplets on a cold surface is associated with the manufacturing of protective coatings by plasma spraying. The originally liquid material solidifies while deforming upon impact. The shape of the splat is influenced by the material viscosity.
- [1]
- I. Doltsinis, "Large deformation processes of solids - From fundamentals to computer simulation and engineering applications", WIT Press, Southampton, 2003.
- [2]
- I. Doltsinis, "Critical states in deformation processes of inelastic solids", in: B.H.V. Topping and C.A. Mota Soares, (editors), Progress in Computational Structures Technology, Saxe-Coburg Publications, Stirling, Scotland, 2004.