Viscoplasticity Of Semicrystalline Polymers Research Articles

Modeling of multi‐cycle deformation of polymers with various deformation programs

PurposeThe purpose of this paper is to compare mechanical response of polypropylene in multi‐cycle tensile tests with strain‐controlled and mixed deformation programs and to develop constitutive equations that describe quantitatively the experimental data.Design/methodology/approachMulti‐cycle tensile tests are performed on isotactic polypropylene with strain‐controlled (oscillations between fixed maximum and minimum strains) and mixed (oscillations between a fixed maximum strain and the zero minimum stress) programs. A constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and its parameters are found by fitting observations. The effect of damage accumulation of material parameters is analyzed numerically.FindingsThe model predicts accurately mechanical behavior of polypropylene in tests with numbers of cycles strongly exceeding those used to determine its parameters. In the regime of developed damage, material constants in the stress‐strain relations are independent of deformation program.Originality/valueA novel constitutive model is derived in cyclic viscoelastoplasticity of semicrystalline polymers and comparison of its adjustable parameters is performed for different deformation programs.

Effect of crystalline structure on the mechanical response of polypropylene under cyclic deformation

Abstract To evaluate the influence of crystalline structure on the mechanical behavior of polypropylene (PP), uniaxial tensile cyclic tests with a mixed program (oscillations between fixed maximum strains and the zero minimum stress) were performed on isotactic PP (iPP) manufactured by the Ziegler-Natta catalysis method, metallocene catalyzed PP (mPP), and annealed mPP. Although the stress-strain diagrams of iPP and mPP under tension are quite similar, their responses under unloading differ markedly. The residual strain (measured as the strain under retraction down to the zero stress) of iPP strongly exceeds that of non-annealed mPP, and annealing of mPP increases this difference. To rationalize these findings, constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress-strain relations are found by fitting the observations. The ability of the model to describe the observed phenomenon and to predict the mechanical response in multi-cycle tensile tests, with various deformation programs, is demonstrated by numerical simulation.

Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling

Experimental data are reported on isotactic polypropylene in multi-cycle uniaxial tensile tests where a specimen is stretched up to some maximum strain and retracted down to the zero minimum stress, while maximum strains increase with number of cycles. Fading memory of deformation history is observed: when two samples are subjected to loading programs that differ along the first n−1 cycles only, their stress–strain diagrams coincide starting from the nth cycle. Constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress–strain relations are found by fitting the experimental data. Results of numerical simulation demonstrate that the model predicts the fading memory effect quantitatively. To confirm that the observed phenomenon is typical of semicrystalline polymers, experimental data are presented in tensile cyclic tests with large strains on low density polyethylene and compressive cyclic tests on poly(oxymethylene).

CYCLIC VISCOPLASTICITY OF SEMICRYSTALLINE POLYMERS WITH FINITE STRAINS: OBSERVATIONS AND CONSTITUTIVE MODELING

Observations are reported on low density polyethylene and isotactic polypropylene in uniaxial tensile cyclic tests (oscillations between maximum elongation ratios k max and the zero minimum stress σmin with k max increasing monotonically with number of cycles). Constitutive equations are developed in cyclic viscoplasticity of semicrystalline polymers with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Ability of the model to describe the characteristic features of the mechanical behavior and to predict the viscoplastic response in cyclic tests is confirmed by comparison of the results of numerical simulation with observations in additional tests.

Cyclic deformations of polypropylene with a strain-controlled program

Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain-controlled program (oscillations between fixed minimum and maximum strains). The following characteristic features of stress–strain diagrams are observed: (i) logarithmic decay in maximum and minimum stresses with number of cycles (cyclic softening), (ii) more pronounced reduction in minimum stress than in maximum stress (cyclic strengthening), (iii) independence of rates of decrease in maximum and minimum stresses of strain rate, (iv) decrease in hysteresis energy with number of cycles. To rationalize these observations, a constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers. Numerical simulation demonstrates that the model correctly describes experimental stress–strain curves and quantitatively predicts evolution of maximum and minimum stresses with number of cycles. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers

Universal mechanical response of polypropylene under cyclic deformation

Abstract Experimental data are reported on isotactic polypropylene in uniaxial tensile (i) cyclic tests (oscillations between maximum strain 0.15 and the zero minimum stress) with various cross-head speeds and (ii) relaxation tests at temperatures ranging from room temperature to 100°C. Observations in cyclic tests show that maximum stresses decrease, while minimum strains grow with the number of cycles. A universal character is revealed of the dependence of minimum strain on the number of cycles: this function is independent of temperature and weakly affected by strain rate. To rationalize this observation, constitutive equations are proposed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers and a scenario is suggested for damage accumulation. Two types of damage are distinguished which are induced by (i) lamellar fragmentation in the crystalline phase and (ii) nucleation and growth of micro-voids in the amorphous matrix. The stress–strain relations involve five adjustable parameters that are found by fitting observations (50 cycles of loading–retraction) at room temperature and α-transition point. Numerical simulation demonstrates that the model correctly describes experimental data and can predict observations in tests with a large number of cycles.

Cyclic viscoplasticity of semicrystalline polymers

Abstract Observations are reported on three grades of isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains. Constitutive equations are derived for the viscoplastic behavior of a semicrystalline polymer. A characteristic feature of the model is that the rate-of-strain tensor for plastic flow is split into the sum of two components, one of which is proportional to the deviator of the stress tensor, while the other is proportional to the rate-of-strain tensor. The stress–strain relations involve four adjustable parameters that are found by fitting the experimental data. Numerical simulation demonstrates that the model correctly predicts the mechanical response of semicrystalline polymers in cyclic tests.

Viscoelasticity and viscoplasticity of semicrystalline polymers: Structure–property relations for high-density polyethylene

Observations are reported on two commercial grades of high-density polyethylene (HDPE) in uniaxial tensile tests, relaxation tests, creep tests and cyclic tests with a strain-controlled deformation program. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformation with small strains. A polymer is modeled as a two-phase continuum consisting of a crystalline skeleton and an amorphous phase treated as a transient network of chains. Its viscoelastic response is associated with thermally activated rearrangement of strands in the temporary network. The viscoplastic behavior reflects fine and coarse slip of lamellar stacks and sliding of junctions between chains in the network. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The study focuses on the effect of molecular weight of HDPE on its mechanical properties.

Cyclic viscoplasticity of high-density polyethylene: Experiments and modeling

Observations are reported on high-density polyethylene in uniaxial cyclic tensile tests. Two deformation programs are considered. In tests with a strain-controlled program, each cycle of deformation involves tension up to a maximum engineering strain ϵ max and retraction down to the zero stress. In tests with a stress-controlled program, any cycle of deformation consists of tension up to a maximum engineering stress σ max and retraction down to some minimum engineering stress σ min. The study focuses on low-cycle programs with a constant cross-head speed and small strains. A constitutive model is derived in viscoplasticity of semicrystalline polymers at isothermal three-dimensional cyclic deformations. Material constants in the stress–strain relations are found by fitting the experimental data. Good agreement is demonstrated between the observations and the results of numerical analysis. Some interesting phenomena are revealed by means of numerical simulation of cyclic deformations.

Finite viscoplasticity of semicrystalline polymers

A series of uniaxial tensile tests is performed on isotactic polypropylene at room temperature with cross-head speeds ranging from 5 to 100 mm/min. Prior to mechanical testing, injection-molded samples are annealed for 24 h at the temperature 160 °C that ensures that the specimens can be drawn up to the Hencky strain of 0.6 without necking. A constitutive model is derived for the viscoplastic behavior of a semicrystalline polymer at finite strains. The stress–strain relations are determined by five adjustable parameters that are found by matching the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. It is shown that the material parameters in the constitutive equations are strongly affected by the strain rate.