A unified K‐BKZ model for residual stress analysis of injection molded three‐dimensional thin shapes

Abstract

The flow‐induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post‐filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K‐BKZ viscoelastic constitutive model, capable of modeling both the fluid‐rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow‐induced residual stress predictions of the filling stage, a quasi‐steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post‐filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post‐filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post‐filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow‐induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow‐induced residual stress by one to two orders of magnitude.

Accurate predictions of fiber orientation and mechanical properties in long‐fiber‐reinforced composite with experimental validation

“…The basic governing equations of fluid mechanics which describe the transient and non‐isothermal flow behaviors are: where is the density; u the velocity vector; t the time; the total stress tensor; g the acceleration vector of gravity; P the pressure; η the viscosity; C p the specific heat; T the temperature; k the thermal conductivity; and the shear rate. Tait's pVT model is used to express a thermodynamic state relationship, namely, the volume of the material as a function of the temperature and pressure . The Cross–William–Landel–Ferry (Cross‐WLF) model is used to describe complex viscosity behaviors, including the variation in viscosity with shear rate for the Cross and the dependence upon temperature and pressure for the WLF.…”

Industrial thermoforming simulation of automotive fuel tanks

“…However, during the reheat stage (of order 300 s) the prediction of the resulting sag due to gravity requires suitable viscoelastic models since the rate of deformation is slow under such circumstances. In the present approach, the sheet sag as well as the sheet forming is modelled by the K-BKZ viscoelastic constitutive model [18][19][20]. The K-BKZ model relates the stress tensor r to the strain history as follows…”

“…Furthermore, c is the Cauchy deformation tensor, c À1 is the Finger deformation tensor, h is a damping function based on the Cauchy strain invariants I 1 and I 2 , and h refers to the second normal stress difference in the deformation [18][19][20].…”

Approximate Model of Thermal Residual Stress in an Injection Molded Part

“…Injection molding introduces residual stresses, a stress state that exists in the bulk of a material without application of any external load, in the ®nal product [1,2]. It is important to know the residual stress state of the part to predict its performance under load.…”

“…In the injection-molding process, molten polymer is injected into a mold and then is packed under pressure, solidi®ed, and then cooled to a uniform temperature. Figure 1 schematically illustrates the solidi®cation stage of a``platelike'' part.Injection molding introduces residual stresses, a stress state that exists in the bulk of a material without application of any external load, in the ®nal product [1,2]. It is important to know the residual stress state of the part to predict its performance under load.…”