The computation of properties of injection-moulded products

Injection moulding is a flexible production technique for the manufacture of complex shaped, thin walled polymer products that require minimal finishing. During processing, the polymer experiences a complex deformation and temperature history that affects the final properties of the product. In a growing number of applications, injection-moulded products must meet high demands concerning their properties and dimensional stability. As a consequence, the ultimate aim of numerical simulations of the injection-moulding process is not only to analyse the processing stage but also to calculate the mechanical (and optical) properties of the product, starting from the material properties and the processing conditions. This also requires measurement techniques that can determine molecular orientation, residual stresses and density distributions. In all recent models of the injection-moulding process, the so-called approach is employed, referring to limitations of the mould geometry to narrow, weakly curved channels. Thus the ratio of the cavity thickness h and a characteristic length l in the mid-plane of the cavity must be much less than unity. In this paper an attempt is made to model all the stages of the production process, using this approach. The analysis is restricted to amorphous thermoplastics. Residual stresses in injection-moulded products stem from two main sources: first, the frozen-in flow-induced stresses, caused by viscoelastic flow of the polymer during the filling and post-filling stage of the injection-moulding process. These stresses correspond with the orientation of macromolecules; second, the thermally- and pressure-induced stresses, which are caused by differential shrinkage. In absolute value, the thermally-induced stresses are usually substantially larger than the frozen-in flow-induced stresses. However, the molecular orientation, as reflected in the frozen-in flow-induced stresses, determines the anisotropy of mechanical, thermal and optical properties and influences the long-term dimensional stability of an injection-moulded product. A decoupled method is proposed to calculate flow-induced stresses. Firstly, the kinematics of the flow field are determined, employing a viscous, generalized Newtonian constitutive law for the Cauchy stress tensor in combination with the balance laws. This is realized for all stages of the process: injection, packing, holding and cooling. The flow kinematics are subsequently substituted in a viscoelastic constitutive equation to calculate the transient stresses. Two constitutive models are used: a compressible version of the Leonov model (differential formulation) and a compressible version of the Wagner model (integral formulation). In the decoupled method, the flow kinematics are, consequently, supposed not to be influenced by the viscoelastic character of the flowing polymer melt. This decoupled method has a number of advantages compared to a coupled viscoelastic computation: the computation time is reduced considerably, an arbitrary viscoelastic constitutive equation can be employed easily, and no restrictions on the complexity of the flow field are imposed. In the case of 2D geometries, the validity of this approach is investigated by comparison of the results with those of a fully coupled viscoelastic calculation. These calculations show that the results obtained by the decoupled method are in acceptable agreement with the results of a fully coupled viscoelastic calculation. For the calculation of thermally-induced stresses a thermo-viscoelastic constitutive law, a linearized form of both viscoelastic constitutive models mentioned above, is employed. In order to attain realistic results, special attention must be paid to the boundary conditions. In particular, it is shown that not only the temperature history, but also the pressure history has a marked influence on the residual stress state of an injection-moulded product. The theories, derived in this paper, are illustrated by a number of examples. Computed results are compared with well documented experimental results from literature. A fair prediction of the properties of injection-moulded products is obtained. It is concluded that for more precise predictions, future attention should be focused on a more accurate and extended determination of the material properties. In particular, non-equilibrium/wT-data, the pressure dependence of the stationary shear viscosity, and the shear rate dependent first normal stress difference should be measured with great accuracy