Numerical simulation of thermally induced stress and warpage in injection-molded thermoplastics

Abstract

Thermally induced stress and the relevant warpage caused by inappropriate mold design and processing conditions are problems that confound the overall success of injection molding. The numerical simulation with the finite element method is studied in this article to predict thermally induced warpage and residual stress of injection‐molded parts generated during the cooling stage of the injection‐molding cycle. A thermorheologically simple two‐dimensional thermoviscoelastic material model is used in the numerical computing. The initial temperature field of the analysis corresponds to the end of the filling stage. The fully time‐dependent algorithm is based on the calculation of the elastic response at every time step. Numerical results are discussed with respect to temperature and pressure, and compared with the experiment results in Santhanam and Wang.[14] © 2001 John Wiley & Sons, Inc. Adv Polym Techn 20: 14–21, 2001

A study on the distinguishing responses of shrinkage and warpage to processing conditions in injection molding

“…The final S&W of the injection molded product were simulated based on the shell theory as an assembly of flat elements. Deformation of a typical flat element can be presented by the in‐plane deformation of a membrane element combined with the bending deformation of a bending element 7, 10, 16, 17, 28, 29, 32, 33. Take a triangular flat element for example, with the commonly accepted linear thermal elastic model, the local equilibrium equation reads: where q e and r e are the integrated local nodal displacements and loads, and K e is the integrated stiffness matrix, which submatrix is where k and k are the corresponding elements of in‐plane stiffness matrix K and bending stiffness matrix K , respectively.…”

A study on the distinguishing responses of shrinkage and warpage to processing conditions in injection molding

“…The final S&W of the injection molded product were simulated based on the shell theory as an assembly of flat elements. Deformation of a typical flat element can be presented by the in‐plane deformation of a membrane element combined with the bending deformation of a bending element 7, 10, 16, 17, 28, 29, 32, 33. Take a triangular flat element for example, with the commonly accepted linear thermal elastic model, the local equilibrium equation reads: where q e and r e are the integrated local nodal displacements and loads, and K e is the integrated stiffness matrix, which submatrix is where k and k are the corresponding elements of in‐plane stiffness matrix K and bending stiffness matrix K , respectively.…”

Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content

“…As in the case of most substances, polymers decrease their volume during cooling and increase it when heated. Also filler content is changing of thermal properties of filler polymers [18,21]. The change in polymer specific volume during cooling is one of the main causes of processing shrinkage [14,22].…”

Stress Evolution of Amorphous Thermoplastic Plate during Forming Process

“…The volume shrinkage induces residual stress, while the viscoelasticity releases a portion of the formed stress. The empirical Tait equation, shown in Equation (4), is used to describe the specific volume, as a function of temperature and pressure [11,12]. The temperature-dependent density in Equation (1), and the coefficient of thermal expansion, can also be deduced from the specific volume:…”

“…Liu conducted a two-dimensional FEA of thermally-induced stress and warpage of an amorphous plastic, based on a viscoelastic phase transform model [ 3 ]. Gu et al conducted a similar two-dimensional analysis [ 4 ]. Li et al calculated the stress on the basis of the theory of shells [ 2 ].…”

A study on the distinguishing responses of shrinkage and warpage to processing conditions in injection molding

“…The final S&W of the injection molded product were simulated based on the shell theory as an assembly of flat elements. Deformation of a typical flat element can be presented by the in‐plane deformation of a membrane element combined with the bending deformation of a bending element 7, 10, 16, 17, 28, 29, 32, 33. Take a triangular flat element for example, with the commonly accepted linear thermal elastic model, the local equilibrium equation reads: where q e and r e are the integrated local nodal displacements and loads, and K e is the integrated stiffness matrix, which submatrix is where k and k are the corresponding elements of in‐plane stiffness matrix K and bending stiffness matrix K , respectively.…”

Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content

“…As in the case of most substances, polymers decrease their volume during cooling and increase it when heated. Also filler content is changing of thermal properties of filler polymers [18,21]. The change in polymer specific volume during cooling is one of the main causes of processing shrinkage [14,22].…”

Stress Evolution of Amorphous Thermoplastic Plate during Forming Process

“…The volume shrinkage induces residual stress, while the viscoelasticity releases a portion of the formed stress. The empirical Tait equation, shown in Equation (4), is used to describe the specific volume, as a function of temperature and pressure [11,12]. The temperature-dependent density in Equation (1), and the coefficient of thermal expansion, can also be deduced from the specific volume:…”

“…Liu conducted a two-dimensional FEA of thermally-induced stress and warpage of an amorphous plastic, based on a viscoelastic phase transform model [ 3 ]. Gu et al conducted a similar two-dimensional analysis [ 4 ]. Li et al calculated the stress on the basis of the theory of shells [ 2 ].…”

A study on the distinguishing responses of shrinkage and warpage to processing conditions in injection molding

“…The final S&W of the injection molded product were simulated based on the shell theory as an assembly of flat elements. Deformation of a typical flat element can be presented by the in‐plane deformation of a membrane element combined with the bending deformation of a bending element 7, 10, 16, 17, 28, 29, 32, 33. Take a triangular flat element for example, with the commonly accepted linear thermal elastic model, the local equilibrium equation reads: where q e and r e are the integrated local nodal displacements and loads, and K e is the integrated stiffness matrix, which submatrix is where k and k are the corresponding elements of in‐plane stiffness matrix K and bending stiffness matrix K , respectively.…”

Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content

“…As in the case of most substances, polymers decrease their volume during cooling and increase it when heated. Also filler content is changing of thermal properties of filler polymers [18,21]. The change in polymer specific volume during cooling is one of the main causes of processing shrinkage [14,22].…”

Stress Evolution of Amorphous Thermoplastic Plate during Forming Process

“…The volume shrinkage induces residual stress, while the viscoelasticity releases a portion of the formed stress. The empirical Tait equation, shown in Equation (4), is used to describe the specific volume, as a function of temperature and pressure [11,12]. The temperature-dependent density in Equation (1), and the coefficient of thermal expansion, can also be deduced from the specific volume:…”

“…Liu conducted a two-dimensional FEA of thermally-induced stress and warpage of an amorphous plastic, based on a viscoelastic phase transform model [ 3 ]. Gu et al conducted a similar two-dimensional analysis [ 4 ]. Li et al calculated the stress on the basis of the theory of shells [ 2 ].…”