Stress–strain behavior of SAN/glass bead composites above the glass transition temperature

Relaxation and stress–strain behavior of SAN–glass bead composites are studied above the glass transition temperature. The strain imposed on the polymeric matrix of the composite is defined as ?_p = ?_c/(1 ? ?^?). Stress relaxation data for the filled polymer which is independent of strain can be calculated by multiplying the relaxation modulus (at a certain strain) by (1 + ?_p). Stress–strain curves at constant strain rate and for different concentrations of the filler can be shifted to form a master curve independent of filler content if the tensile stress is plotted versus ?^p. The relaxation modulus increases with increasing the filler concentration and can be predicted by a modified Kerner equation at 110°C.     

Elastomeric and mechanical properties of poly-m-carboranylenesiloxanes

A new high-temperature elastomer, SiB-2, has been investigated by stress relaxation, modulus-temperature, and volume--temperature techniques. SiB-2 was found to be more stable than a related elastomer, radiation-cured silicone rubber, having about twice as long as a chemical relaxation time at 250°C. Possible mechanisms to account for this increased stability are discussed. At low temperatures, T_g for SiB-2 was estimated at –34°C., which compares well with T_i = ?30°C. for this polymer. By comparison, SiB-3 has T_i = ?60°C., while phenyl-modified SiB-4 was found to have T_i = ?25°C. T_m for SiB-2 was estimated to be + 56°C.     

Calculation of stress–strain curves from relaxation data in the rubbery flow region

Stress relaxation curves for polysulfone and Lexan polycarbonate are only time dependent at a constant temperature if strain is defined as ?_H = In (l/l₀) and the “true” cross-sectional area A = A₀/(1 + ?) is used. The strain-independent stress relaxation curves can be used to calculate stress–strain curves at different rates of strain according to the linear viscoelastic theory. The agreement between experimental and calculated stress–strain curves is good at least up to about 60% strain in the range of 0.01 to 0.2 in./min rate of extension if an average rate of strain defined by ?_H = 1/t ln(l/l₀) is used.     

Dynamic mechanical analysis of fibers. I. Effect of experimental variables and material type

Depending upon the fiber material, some of the experimental variables can have a profound effect on the dynamic tensile modulus vs. temperature data. With the use of an experimental fiber (25°C < T_g < 75°C; T_m > 220°C; hot stretched), the effect of several variables, e.g., moisture/volatiles, annealing/relaxation, frequency (strain rate), pretension, and % strain on the modulus retention term [(E_100°C/E_25°C) × 100] have been studied. Of these variables, pretension and especially % strain dramatically increase the modulus retention and this effect is attributed to the elastic orientation under force (EOF), i.e., it exists only in the presence of tensile forces and is reversible. Such an effect was insignificant for Kevlar (T_g ? 375°C) and absent for steel wire. Dynamic modulus measurements at 25°C using sonic techniques also support the EOF phenomenon in polyethylene yarns (T_g ～ ?30°C) but not in Kevlar polymide yarns (T_g ～ 375°C).     

Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. IV. States of ease and stress–strain behavior

Linear 1,2-polybutadiene, glass transition temperature (T_g) ?18°C, is crosslinked at ?10°C, to ?20°C by γ irradiation while strained in simple extension, with extension, ratios (λ₀) from 1.2 to 2.7. After release, the sample retracts to a state of ease (λ_s) at room temperature. From equilibrium stress–strain measurements up to a stretch ratio relative to the state of ease (Λ) of 1.2, together with λ₀ and λ_s, the concentration of network strands terminated by trapped entanglements (νN) is calculated. For this purpose, a three-constant Mooney–Rivlin formulation is used, in which the entanglement network is described by Mooney–Rivlin coefficients C_1N and C_2N, whereas the crosslink networks is described by the coefficient C_1x only. The ratio ψ_N = C_2N/(C_1N + C_2N) is estimated from parallel studies of nonlinear stress relaxation of the uncrosslinked polymer, taking into account the thermal history before and during irradiation. For substantial degrees of crosslinking, i.e., for R_0′ = ν_x/ν_N > 0.4 (where ν_N is the concentration of network strands terminated by crosslinks), and for λ₀ < 1.8, C_2N agrees rather well with the value obtained from stress relaxation of the uncrosslinked polymer in the range of time scale where it is nearly independent of time (1.87 X 10⁵ pascals). The corresponding value of ν_N is 2.3 × 10^?4 moles/cm³, in good agreement with that obtained from viscoelastic measurements of the uncrosslinked polymer in the plateau zone (2.5 × 10^?4). However, for R_0′ ? 0.2, smaller values of C_2N and ν_N are obtained, indicating that for low degrees of crosslinking the entanglements are not completely trapped. Also, for higher values of λ₀, C_2N and ν_N turn out to be somewhat smaller. Similar, less extensive results were obtained previously on a 1,2-polybutadiene with somewhat higher vinyl content and a higher T_g. Crosslinked samples of both these polymers were subjected to equilibrium stress–strain measurements in simple elongation from the state of ease at higher strains up to Λ = 1.7. The results agreed closely with calculations from the three-constant Mooney–Rivlin theory.     

Prediction of long-term ABS relaxation behavior

The applicability of time–temperature superposition to tensile stress relaxation of ABS plastics has been verified at strains from 0.5 to 5% for temperatures in the range of 10–50°C. Master curves have been compiled to predict the long-term stress relaxation at 23°C. and a stress–strain–reduced time surface has been constructed. A comparison of relaxation times and activation energies has confirmed that a strain increase facilitates stress relaxation up to yield. The decay of relaxation modulus at linear viscoelastic strains was shown to be equivalent to that of tensile creep modulus. By normalizing the master curves to originate at yield stress and then converting them into multiaxial from the strain which gives the best data fit with long-term hydrostatic pipe-burst strength was shown to be at yield or beyond. The ABS yield-strain master curves at 23°C. were shown to match satisfactorily the long-term pipe-rupture data. Activation energies for ABS relaxation have been compared below and above the rigid matrix T_g, to assess the degree of stiffening of the polymer in the solid state.     

Motion mode of poly(lactic acid) chains in film during strain‐induced crystallization

How stress and temperature impact the movement of poly(lactic acid) (PLA) chains in the process of tensile film stretching was studied. The motion mode of chains was investigated through the study of the strain‐induced crystallization and orientation through changes in the draw temperature (T_d), draw ratio, and draw rate. The crystallinity and orientation degrees of the PLA films were measured by differential scanning calorimetry, Fourier transform infrared spectroscopy, and polarized optical microscopy. According to the competition between the orientation caused by the stretching and relaxation of chains under the temperature field, the motion modes of PLA chains during strain were divided into four types, modes I–IV. When T_d was 100°C, the PLA chains acted in mode I, in which the relaxation rate of chains was so fast that no crystallinity or orientation could be obtained. Beyond a draw rate of 20 mm/min at a T_d of 90°C, the type of chain movement changed from mode I to II. In mode II, only crystallites could be reserved after unloading. Chains in the PLA film moved in mode III at a T_d of 80°C; then, both the crystallization and orientation were enhanced monophonically with increasing draw rate. Beyond the draw rate of 10 mm/min at a T_d of 70°C, the orientation rate of chains was much faster than the relaxation one, and the motion mode transformed from mode III to IV. Then, obvious decreases in the crystallinity and orientation were observed with further increases in the draw rate; this resulted from the destruction of the crystallites. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42969.     

Relationships between mechanical properties and relaxation processes in polymers. Nylon 6

The dynamic-mechanical properties as a function of temperature and frequency were measured for five samples of polycaprolactam (nylon 6) containing different amounts of hydrosoluble products. Low- and high-speed tensile properties and Izod impact strength were determined between ?190° and 100°C for the same samples by using autographic methods. The influence of the mechanical relaxation processes on moduli, yield strength σ_y, yield strain ε_y, tough-brittle transition temperature, elongation at break ε_R, and tensile and Izod fracture energies was investigated. It has been found that some mechanical properties, such as modulus and yield properties, can be directly related to specific relaxation phenomena, whereas as far as other properties, such as the ultimate properties, are concerned, the existing correlation can be concealed by the interference of purely mechanical phenomena which depend on the testing technique used, the testing conditions, and the previous history of the material.     

Shape‐memory behaviors of biodegradable poly(L‐lactide‐co‐ϵ‐caprolactone) copolymers

A series of biodegradable poly(L ‐lactide‐co‐?‐caprolactone) (PCLA) copolymers with different chemical compositions are synthesized and characterized. The mechanical properties and shape‐memory behaviors of PCLA copolymers are studied. The mechanical properties are significantly affected by the copolymer compositions. With the ?‐caprolactone (?‐CL) content increasing, the tensile strength of copolymers decreases linearly and the elongation at break increases gradually. By means of adjusting the compositions, the copolymers exhibit excellent shape‐memory effects with shape‐recovery and shape‐retention rate exceeding 95%. The effects of composition, deformation strain, and the stretching conditions on the recovery stress are also investigated systematically. A maximum recovery stress around 6.2 MPa can be obtained at stretching at T_g ? 15°C to 200% deformation strain for the PCLA70 copolymer. The degradation results show that the copolymers with higher ?‐CL content have faster degradation rates and shape‐recovery rates, meanwhile, the recovery stress can maintain a relative high value after 30 days in vitro degradation. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Effect of mean strain on the cyclic deformation and stress relaxation in polypropylene

The influence of mean strain Changes in the range from 0 to 4% on the cyclic deformation and stress-relaxation properties is investigated using rod specimens of polypropylene. An extensometer measures and controls the axial strain in a closed-loop, electrohydraulic, servocontrolled mechanical testing machine. The hysteresis loop at different numbers of cycles N of N = 35, 45, and 50 are irregular in shape, and the tensile portion decreases in size as the number of cycles was increased. The stress value of the tensile portion for three mean strains of ?_m = 1.0%, 2.0%, and 4.0% remains constant, but the value of the compressive portion decreases as the mean strain was increased. The stress level at a strain width of 3% changes little with mean strain. For the strain widths of 5% and 7%, however, the minimum stress levels at N = 35, 45, and 50 increase with increasing mean strain, in contrast to the behavior of maximum stress level. The stressrelaxation tests show that the drop of stress decreases with an increase in number of cycles. The discrepancy in the results of relaxation tests is due to the effect of the difference in strain rates.     

Effects of temperature and strain rate on the tensile behavior of short fiber reinforced polyamide-6

Tensile behavior of extruded short E-glass fiber reinforced polyamide-6 composite sheet has been determined at different temperatures (21.5°C, 50°C, 75°C, 100°C) and different strain rates (0.05/min, 0.5/min, 5/min). Experimental results show that this composite is a strain rate and temperature dependent material. Both elastic modulus and tensile strength of the composite increased with strain rate and decreased with temperature. Experimental results also show that strain rate sensitivity and temperature sensitivity of this composite change at a temperature between 25°C and 50°C as a result of the glass transition of the polyamide-6 matrix. Based on the experimental stress-strain curves, a two-parameter strain rate and temperature dependent constitutive model has been established to describe the tensile behavior of short fiber reinforced polyamide-6 composite. The parameters in this model are a stress exponent n and a stress coefficient σ*. It is shown that the stress exponent n, which controls the strain rate strengthening effect and the strain hardening effect of the composite, is not only strain rate independent but also temperature independent. The stress exponent σ*, on the other hand, varies with both strain rate and temperature.     

Effect of heat pretreatment and strain rate on tensile properties of polycarbonate sheet

The effects of heat pretreatment and ambient gas (air and vacuum) on selected properties of the polycarbonate sheet have been studied. Changes in tensile properties as functions of heat pretreatment temperature (up to 160°C) and strain rate (wide range of 1.7 × 10^?4 ? 13.1 m/sec = 0.29 ? 2.3 × 10⁴ %/sec) were determined and these are discussed in relation to changes in differential scanning calorimetry (DSC) and gel permeation chromatography (GPC) data. The performance characteristics of the present tensile testing are obtained over a wide range of extension rates without changing the mode of deformation and the shape of the test pieces. It was suggested from the experimental results that heat pretreatment below the glass transition temperature (T_g) causes ordered molecular domains to grow on the free surfaces of the sheet, consisting of thermally deteriorated macromolecules and possessing lower crazing stresses (exhibiting more brittle mechanical responses, leading to the decrease in breaking strain and energy). The effect of annealing above T_g on the tensile properties, and on the results of DSC and GPC, could not be precisely understood.     

Viscoelastic properties of suspensions with weakly interacting particles

Rheological characterization of a model suspension containing hydroxyl-terminated polybutadiene and glass beads with filler concentration up to 30% by volume was performed by using a Haake parallel disk rheometer. The rheological tests conducted were the measurement of the storage modulus, G′, loss modulus, G′, and complex viscosity, η*, as functions of the frequency and the steady shear viscosity as a function of the shear rate. The linear viscoelastic region was determined to extend up to 50% strain by measuring G′, G′, and η* as functions of strain amplitude. By using multiple gap separations between the disks, it was found that the suspension did not exhibit slip at the walls of the rheometer. G′ and G′ were used to determine the relaxation times distribution, G_i(λ_i, ⊘) as functions of the relaxation time, λ_i, and the filler content, ⊘. The relaxation moduli, G_i(λ_i, ⊘), decreased with the relaxation time, but increased with the filler content. The Cox–Merz rule was also observed to be valid for these suspensions. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 507–514, 1998     

Effect of zinc stearate on properties of melt processable ionomer based on sodium salt of sulphonated maleated EPDM rubber

Abstract

Sulphonation of maleated copoly (ethylen/propylen/diene), followed by its neutralisation by sodium hydroxide produces an ionomer containing both carboxylate and sulphonate anions on the backbone. Addition of zinc stearate lowers the melt viscosity of the ionomer, which is higher than the corresponding non-ionomer. Dynamic mechanical thermal analysis shows that zinc stearate acts as a low reinforcing filler under ambient conditions and as a plasticiser above 100°C (i.e. above the melting point of zinc stearate). For example, incorporation of zinc stearate causes an increase in storage modulus E′ at 25°C, but a sharp decrease in E′ at 110°C. Furthermore, the plot of tan δ v. temperature reveals that tan δ at the low glass–rubber transition temperature T _g decreases, while tan δ at the high temperature ionic relaxation temperature T _i increases in the presence of zinc stearate. Incorporation of carbon black lowers tan δat T _g and increases tan δ at T _i, thus strengthening the biphasic structure of the ionomer. The ionomer shows higher tensile strength and modulus than the corresponding non-ionomer. Addition of zinc stearate increases the tensile strength and elongation at break, with marginal decrease in modulus. Carbon black increases the stress–strain properties of the zinc stearate filled ionomer. Reprocessability studies of the ionomer filled with zinc stearate and carbon black show that the material can be recycled without a decrease in properties.     

Studies on the stretching of polypropylene film. I. Two-step biaxial stretching

A polypropylene film was stretched at 100–160°C., quenched to room temperature, and then restretched at the same temperature perpendicularly to the first stretching. The reorientation behavior was investigated by using optical and x-ray methods. During the restretching the monoaxial orientation caused by the stretching is converted into a new monoaxial orientation through a balanced state, where n_pp = n_ps < n_ss. The more or less parallel orientation to the film surface of the polypropylene molecules, brought about by the first stretching, proceeds further on restretching. n_ss is a linear function of the degree of stretching in area v_A. The inclination of this line is independent of the type of deformation, stretching, or restretching, provided the temperature is kept constant. At 160°C. the plot of n_ss versus thickness is less steep than it is at 100 or 130°C. The overall reorientation apparently proceeds according to Kratky's first deformation law. The x-ray pattern of a res?tretched film is a four-point diagram which indicates the existence of a pair of reorientation axes inclined symmetrically against the stretching axis. The inclination grows larger with restretching, and the axes merge into the restretching axis at extreme restretching. This phenomenon is less pronounced when the restretching is carried out at higher temperatures. The density of the restretched film is determined mainly by the stretching temperature, but extreme restretching has a tendency to lower it very slightly.     

Studies on the stretching of polypropylene film. II. Polyaxial stretching

Polypropylene film was stretched polyaxially at 100–160°C., and the orientation behavior was studied by means of optical and x-ray method. The molecular chains oriented progressively to the film surface with an increase in stretching area v_A in the range 1–16, and the (040) selective uniplanar orientation developed at the extreme stretching. The plot of orientation versus v_A was less steep when the stretching was carried out at higher temperature, but the final degree of orientation was independent of the temperature, because the final v_A increased with temperature. At 160°C. premelting occured to such a degree that the high stretching and, consequently, the high orientation could not be obtained. The orientation of the amorphous chains was always behind that of the crystalline region. In the initial stage the polyaxial stretching was not as effective in attaining high biaxial orientation as the two-step biaxial stretching, but the final orientation was the same in both types of stretching because v_A reached a value of 16 in the polyaxial stretching while it was only 2 in biaxial stretching.     

Sealing glass‐ceramics with near‐linear thermal strain,part III: Stress modeling of strain and strain rate matched glass‐ceramic to metal seals

Thermal mechanical stresses of glass‐ceramic to stainless steel (GCtSS) seals are analyzed using finite element modeling over a temperature cycle from a set temperature (T_set) 500°C to ?55°C, and then back to 600°C. Two glass‐ceramics having an identical coefficient of thermal expansion (CTE) at ~16 ppm/°C but very different linearity of thermal strains, designated as near‐linear NL16 and step‐like SL16, were formed from the same parent glass using different crystallization processes. Stress modeling reveals much higher plastic strain in the stainless steel using SL16 glass‐ceramic when the GCtSS seal cools from T_set. Upon heating tensile stresses start to develop at the GC‐SS interface before the temperature reaches T_set. On the other hand, the much lower plastic deformation in stainless steel accumulated during cooling using NL16 glass‐ceramic allows for radially compressive stress at the GC‐SS interface to remain present when the seal is heated back to T_set. The qualitative stress comparison suggests that with a better match of thermal strain rate to that of stainless steel, the NL16 glass‐ceramic not only improves the hermeticity of the GCtSS seals, but would also improve the reliability of the seals exposed to high‐temperature and/or high‐pressure abnormal environments.     

Orientation and relaxation in uniaxially stretched atactic polystyrene

Infra-red measurements of the dichroic ratio of atactic polystyrene absorption bands provide a valuable method of determination of orientation as well as relaxation of chains during stretching. Different strain rates and temperatures of stretching were used. Orientation relaxation was analysed using Lodge's constitutive equation and a master curve was obtained at a reference temperature T₀ = 115°C. Orientation relaxation behaves similarly to mechanical relaxation and a scaling factor of 3.6 × 10^?8 m² N^?1 holds between the two sets of results.     

Enhanced polycarbonate toughness. II: Mechanisms

Glassy shell-rubbery core polymer particles, 0.1 to 0.2 μm in diameter, increase the plane strain J_IC values of 3.175 mm thick polycarbonate from 3.05 kJ/m² (no particles) to 9.5 kJ/m² (7.5 phr particles) at 23°C. Some modest decreases in these values are caused by tests at ?20°C in samples 9.525 and 3.175 mm thick. If only the particle concentration is varied, J_IC increases monotonically to 7.5 phr (by wt), then levels off or decreases slightly at 10.0 phr. The total volume of 1 to 2 μm diameter cavities formed in the matrix by the apparently unbonded particles behaves similarly; cavity volume and J_IC are directly related. With increasing particle concentration the tensile modulus is unchanged, the yield stress and strain decrease modestly, the strain at fracture decreases appreciably, and the heat recoverable orientation in the fractured samples decreases. Few cavities are formed. The particles reduce the extent of shear deformation in the tensile samples.     

Optimizing maximum equivalent strain on solder balls in flip‐chip packages

Flip‐chip packaging provides a high‐performance low‐cost approach for development of electronic packages. A three‐dimensional (3D) viscoelastic‐plastic finite element analysis using the commercial software ANSYS has been performed to study the thermo‐mechanical behavior in flip‐chips assemblies, i.e., the four components: chip, solder ball, underfill, and substrate. The viscoelastic behavior of underfill is modeled by a Maxwell constitutive equation, while the viscoplastic behavior of solder balls is modeled by an Anand model. Both chip and substrate are assumed to elastic materials modeled by Hooke's law. As in standard industry practice, temperature cycling from 125 to −40°C is used. Thermo‐mechanical behavior of solder balls is presented, and the effects of underfill material properties are investigated. Further, Taguchi methods are used to optimize flip‐chip package performance. The design goal is to minimize the maximum equivalent strain on the solder balls. The eight flip‐chip assembly factors chip‐thickness/substrate‐thickness ratio, underfill modulus (G_i), underfill relaxation time (λ_i), solder height‐to‐diameter ratio, chip coefficient of thermal expansion (CTE), underfill CTE, solder CTE, and substrate CTE are chosen for optimization. POLYM. COMPOS., 2008. © 2007 Society of Plastics Engineers