Viscoplastic deformation processes

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

As discussed in Sect. 3.2, once a mature fibril is created, further thickening occurs by a viscoplastic drawing mechanism which involves intense plastic deformation at the craze/bulk interface [32], Instead of using a non-Newtonian formulation as in [32] or a formulation based on Eyring s model [45], but on the basis of a preliminary study of the process [36], the craze thickening is described with a similar expression as the viscoplastic strain rate for the bulk in Eq. 3 as [20]... 

In general, SMPF is perceived as a two-phase composite material with a crystalline phase mixed with an amorphous phase. A multiscale viscoplasticity theory is developed. The amorphous phase is modeled using the Boyce model, while the crystalline phase is modeled using the Hutchinson model. Under an isostrain assumption, the micromechanics approach is used to assemble the microscale RVE. The kinematic relation is used to link the micro-mechanics constitutive relation to the macroscopic constitutive law. The proposed theory takes into account the stress induced crystallization process and the initial morphological texture, while the polymeric texture is updated based on the apphed stresses. The related computational issue is discussed. The predictabihty of the model is vahdated by comparison wifli test results. It is expected that more accurate measurement of the stress and strain in the SMPF with large deformation may further enhance the predictability of the developed model. It is also desired to reduce the number of material parameters in the model. In other words, a deeper understanding and physics based theoretical modeling are needed. 

Both the elastic and the plastic behaviour of polymers are time-dependent even at room temperature polymers are thus viscoelastic and viscoplastic. In this section, we discuss the time-dependent deformation behaviour phenomenologically and explain how thermal activation of relaxation processes causes the time-dependence of deformation. 

Creep is the time-dependent, plastic deformation of a material. According to the definition from section 2.1, creep processes are viscoplastic processes. The time-dependent plastic deformation of polymers has already been covered in chapter 8. Here we discuss creep of metals and ceramics. 

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