Viscoelastic effects related to residual thermal stresses in bismaleimide/carbon fiber composite laminates

This paper studies the effects of the residual stresses which originate in the laminates made of composite materials owing to the curing process, and on stresses affected by time and temperature. In order to sustain high operating temperatures, the polymer composites' laminates are made of high performance matrices that usually require processing cycles at high temperatures. The strong thermal variation due to the subsequent cooling process induces residual stresses, owing to the thermoelastic orthotropy of the material. For non-symmetrical stacking sequences, these stresses notably modify the shape of the laminate and reduce both its static strength and buckling load, as a consequence of the latent content of elastic energy stored by the pre-loading. The polymeric composites show a viscoelastic behavior, which implies a constitutive law dependent on both time and temperature. For this reason, the analysis of the phenomenon should account for the creep and the relaxation mechanisms. The configuration of asymmetric laminate is evaluated by both analytical and numerical finite element (FEM) methods. The actual shape of laminates of different geometries is also experimentally determined. On the basis of the analysis of the shape of laminates measured after different thermal cycles, the evolution of residual stresses with time and temperature is analyzed.     

Viscoelastic electrospun jets: Initial stresses and elongational rheometry

A novel method of characterization of viscoelastic longitudinal stresses in electrospun jets of semi-dilute and concentrated polymer solutions and melts is introduced. The measured longitudinal stresses at the beginning of the thin jet region in the jets of a 6 wt% aqueous solution of polyethylene oxide (M_w = 400 kDa) were of the order of 100 kPa, which is two orders of magnitude larger than in any other free viscoelastic jets issued from nozzles and orifices. This is attributed to elongation-driven stretching of polymeric liquids in the transition zone, between the preceding modified Taylor cone zone and the beginning of the thin jet region, where the stretching rates are of the order of 100-1000 s⁻¹. The Rouse relaxation times found were in the range of 3-8 ms, and the moduli of elasticity were of the order of 100 Pa. A novel explanation of the reasons for the formation of the straight sections in the electrospun jets is proposed. The straight sections are stabilized by the high initial longitudinal stresses in the jet generated due to strong electrically driven stretching in the transition zone. The further electrically driven stretching in the jet (after the transition zone) is relatively weak, and viscoelastic Rouse relaxation prevails. The relaxation distance of the longitudinal stresses along the jet increases with the applied voltage (which generates higher initial stresses in the transition zone) and thus the length of straight section of the jet should increase as the applied voltage increases.The results also point at an opportunity to develop an elongational rheometer for concentrated polymeric systems with stretching rates of the order of 100-1000 s⁻¹. The proposed rheometer employs excitation of electrically driven jets by single lateral pulses, and observation of the pulse propagation and widening along the jet. This reveals the level of the longitudinal stresses along the jet and allows evaluation of the viscoelastic Rouse relaxation time, modulus of elasticity and the elongational viscosity in the jet.     

The interfacial stresses in particulate composite systems

It is postulated that property gradients exist at the interface forming an “interphase” between the insert and the matrix. Such gradients might be caused by partial solubility and diffusivity of the two phases comprising a composite. For simplicity, the “interphase” is replaced by a shell exhibiting averaged properties (E_shell = 1/2 E_insert + 1/2 E_matrix, etc.). An exact linear elastic solution was employed to evaluate stress fields throughout all regions. The possible effect of the “interphase” and its thickness on several physical properties of the composite are evaluated in terms of the particular stress fields.     

A potential biodegradable rubber—Viscoelastic properties of a soybean oil-based composite

Scientists are more and more interested in biodegradable materials owing to their environmental advantage. We investigated viscoelastic properties of a newly developed biomaterial made from epoxidized soybean oil (ESO). ESO cross-linked by triethylene glycol diamine exhibited viscoelastic solid properties. The storage modulus (G′) was 2×10⁴ Pa over four frequency decades. The phase angles were 14–18°. Stress relaxation measurements showed that there was no relaxation up to 500 s. From the plateau modulus we estimated that the M.W. of this cross-linked soybean oil was on the order of 10⁵. The composites of cross-linked ESO with three different fibers had 50 times higher elasticity (G′) than those without fiber. Phase shifts were the same as those of cross-linked oil without fibers, but the linear range of rheological properties was much narrower than that of the material without fibers. All these results indicated that this new biopolymer made from soybean oil exhibited strong viscoelastic solid properties similar to synthetic rubbers. These rheological properties implied that this biomaterial has high potential to replace some of the synthetic rubber and/or plastics.     

Viscoelastic properties of a pitch and coke-pitch disperse system

Viscoelastic properties of a pitch and a coke-pitch disperse system were studied by using a Weissenberg rheogoniometer and a simple compressive creep apparatus. Dynamic modulus and steady shear viscosity of the pitch, and creep compliance of the disperse system were determined. The pitch examined was found to be a Newtonian non-elastic fluid over a wide range of experimental conditions, whereas the coke-pitch disperse system showed a transition from non-elastic to viscoelastic fluid at about 50 wt% of coke content. It has also been shown that the time-temperature superposition principle is applicable to the disperse system, the temperature dependence of the shift factor being independent of coke content.     

Residual thermal stresses in bismaleimide/carbon fiber composite laminates

This is a study of residual thermal stresses in composite laminates, due to curing cycles. An extended formulation of Classical Lamination Theory (CLT) is adopted, which is able to take into account geometrical nonlinear effects owed to finite displacements. The approach is applied to square asymmetric laminates that have different dimensions and thicknesses. Final laminate shapes are evaluated after complete curing cycles; they can be cylindrical or saddle-like, and their equilibrium configuration stable or unstable depending on thickness vs. side length ratio. The same laminates are stacked, press-cured and the radii of curvature experimentally measured. In addition, they are modeled by means of finite element method (FEM) codes, using both linear and nonlinear techniques. Except for the thick laminates, the results obtained using nonlinear theoretical and numerical approaches show good agreement with experiment. Thermal residual strains are computed from non-mechanical strains by subtracting laminae free thermal deformations; the corresponding stresses are evaluated through layer stiffnesses. Residual stresses are evaluated both theoretically and experimentally. For thicker laminates the disagreement is mainly due to a mixed viscous phenomenon which takes place in resin interlaminar layers and matrix intralaminae. The share of relaxed stresses is evaluated and methods that include optimal cooling path techniques are suggested.     

Combustion of a composite solid propellant under conditions of static mechanical tensile stresses

Mechanical stresses have a progressive effect on the combustion characteristics of composite solid propellants. On the basis the kinetic theory for the durability of polymers within their composition the mechanism is studied for the effect of stress-strain state on steady combustion rate. Chemical bonds of the polymer matrix are activated as a result of an applied stress and there is an increase in the rate of their thermal destruction. It is shown that this is an important reason for an increase in combustion rate with uniaxial tension. An analytical equation is obtained which expresses the dependence of combustion rate on the magnitude of a prescribed stress or that measured by experiment.Novosibirsk. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 4, pp. 20–28, July–August, 1993.     

The influence of adhesive bondline thickness imperfections on stresses in composite joints

Adhesively-bonded joints can have spatial variations in bondline thickness with respect to their overlap length. Assumptions pertaining to shear-lag and adherend transverse shear deformation are used to compose a governing differential equation that permits any mathematical function to be used for representing the variation in bondline thickness, t a (x). Finite Difference solution techniques are employed to solve this equation, and it is shown by a series of case study example calculations that the adhesive shear stress changes significantly for deviations about a baseline, uniform thickness, configuration. It is also shown that for cases when the gradient in bondline thickness is small, simple closed-form solutions developed strictly for uniform thickness joints can provide reasonable accuracy. Numerical results are summarized as "stress concentration factor" curves, allowing quick estimation of the upper and lower bounds of normalized peak shear stress in joints having varying degrees of thickness imperfection.     

Viscoelastic investigation of interfacial damage of glass and carbon fibers composite materials

Summary Glass/Epoxy and Carbon/Epoxy unidirectional composite materials have been subjected to cyclic ondulated loading of three points bending specimens. The viscoelastic properties of the new or damaged materials are recorded with a Polymer laboratories PL/DMTA viscoelasticimeter working at 10 Hz. The viscoelastic behavior of samples subjected to various dynamic shear strains has also been investigated with a computer driven Metravib viscoanalyser.The results show that under fatigue stresses, glass/epoxy interface has permanent damage leading to large damping while carbon/epoxy one seems to have only intermittent damage leading to lower damping and better fatigue properties.     

Correlation between viscoelastic behavior and cooling stresses in a cured epoxy resin system

This work deals with the study of the rheological behavior of an epoxy system subjected to three cooling processes referred to as the normal, air‐, and water‐cooling processes. The system was set up by a difunctional epoxy resin (DGEBA) mixed with a tetrafunctional diamine (mPDA) in stoichiometric proportions. Different samples of (1) neat and cured polymers and (2) alumina—epoxy composites were prepared. The first part of this work was devoted to optimizing the cure cycle of the neat samples using differential scanning calorimetry and rheometry. The best cure cycle is based on a first heat step at 110°C during 10 min followed by a crosslinking stage of 75 min at 180°C. In the second part of the study the influence of the cooling cycle on the thermomechanical behavior of polymer and composite samples was investigated. Measurement of loss modulus, G″, and loss factor, tan δ, versus temperature showed that an intermediate relaxation α′ peak arose between the main and secondary relaxations (resp. α and β). The position and amplitude of the α′ peak increased with the cooling rate. This rheological phenomenon is related to the presence of nonequilibrium stresses frozen in the sample during cooling. The effect of thermal aging on the α′ peak also is reported. Our work also showed the presence of an α′ peak for the composites. However, the amplitude of this peak was more pronounced in the composites because of additional stresses induced by the difference between the resin and the ceramic in thermal expansion coefficients. We showed that a calculation based on a thermoelastic model was useful for qualitative comparison of rheological data on the influence of the cooling process. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 679–690, 2006     

Viscoelastic breakup in a high velocity airstream

Viscoelastic fluids were injected into a high velocity airstream (200 m/s) to investigate how the addition of small polymer quantities to fluids significantly increase the resultant disseminated drop size. For each liquid tested several hundred resultant drops were sampled and measured using an automated image analyzer. The resultant mass median diameter (MMD) for a viscoelastic fluid was an order of magnitude larger than a comparable viscous Newtonian fluid. A relaxation time measured from a die swell experiment correlates the dissemination results suggesting, an elongational rather than shear breakup mechanism.     

Viscoelastic Effects in a Phosphate Glass-Metal Seal

A family of phosphate glasses has been developed with thermal expansion behavior in the elastic range that nearly matches the response of 304 stainless steel. Attempts to make concentric pin-shell seals consistently have yielded fractures between 400° and 300°C during cooling. Elastic stress analyses which neglect glass transitional behavior and utilize constant glassy ("elastic") thermal expansion coefficients predict a residual stress state that is compressive. However, viscoelastic computations which include the effects of structural relaxation during glass transtion show that tensile stresses sufficient to cause failure arise during cooldown of the seal.     

Experimental determination of the evolution of internal stresses in a composite material: Case of a circular bilayered laminate glass-resin

A nondestructive method is proposed to analyze the internal stresses of a circular bilayered laminate glassresin. It is based on the measurement by optical interferometry of small deformations of the laminate under the influence of temperature, time, or applied mechanical stresses of known value. For example, the stress induced by the curing of the thermosetting resin layer is determined and the postcuring relaxation of the stress is measured. Other possibilities or improvements of the method are indicated: The determination of the Young's modulus of the thermosetting resin as a function of time, the determination of the work-hardening rate, and the determination of the ultimate properties of the laminate are just a few of them.     

Design of a composite polymer plant using a simulation system

This paper describes the use of the General Purpose Simulation System (GPSS) to simulate the manufacture of a typical line of thermotropic liquid crystal polymer resins. Specifically considered were composite polymers based on parahydroxybenzoic acid with glass, graphite, or talc added as a filler or reinforcing agent. The process examined consists of a combination of batch and semicontinuous operations. Product campaigning and equipment cleaning requirements were also incorporated into the GPSS model. Different equipment configurations and manpower distributions were simulated to aid in the design of such a polymer plant. The simulation results were analyzed, and the calculated return on investment was used to select the final plant design.     

Analysis of the development of isotropic residual stresses in a bismaleimide/spiro orthocarbonate thermosetting resin for composite materials

In this article, we extend our model of isotropic residual stress development in thermosets to a novel thermosetting resin system: bismaleimide/spiro orthocarbonate. In this system, the cure shrinkage and resulting isotropic residual stresses are reduced through a ring‐opening reaction that occurs independently of the addition reaction. The modeling effort includes a parametric analysis of the effects of various parameters, including the volume changes involved in the reactions, the relative rates and orders of the reactions, the cure history, and the values of the bulk moduli and thermal expansion coefficients. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 227–244, 2003     

Elastic properties and structure of a composite elastomeric system

In the present paper the structural and mechanical properties of an elastomeric system, obtained by vulcanizing a mixture of nitrile rubber and magnesium methacrylate, have been analysed. The structural properties have been studied using the small angle X-ray technique. The mechanical data have been treated with the Mooney-Rivlin phenomenological equation. Experimental data clearly indicate that the examined system is a composite one. Phase separation plays an important role in the mechanical behaviour which is directly related to the morphological and topological properties. The results are discussed at the molecular level and give some critical evidence on the Gaussian theory of rubber elasticity.     

Effect of winding tension and cure schedule on residual stresses in radially-thick fiber composite rings

In filament winding, both the tension applied to the fiber strands and the subsequent cure schedule are important manufacturing variables that produce residual stresses and strains. A “radial cut method” was used to determine the circumferential and radial residual stress profiles in S2-glass fiber/epoxy and E/XA-A carbon fiber/epoxy circumferentially-wound composite rings. Of particular interest in this study were radially-thick composite rings in which the effect of cure schedules as well as constant and variable winding tension profiles on the radial residual stress profiles were evaluated. Several design-oriented relationships for estimating the maximum radial residual stress were developed.     

Effect of residual stresses on fatigue crack growth behavior of aluminum substrate repaired with a bonded composite patch

Composite patches bonded to cracked metallic aircraft structures have been shown to be a highly cost-effective method for extending the service life of the structures. The fatigue crack growth behavior of pre-cracked 7075-T6 aluminum substrate with the 12.7-mm V-notch crack repaired with boron/epoxy composite patches was investigated. 1-ply, 2-ply, 3-ply and 4-ply composite patches were studied. The residual stresses due to mismatch of the coefficients of thermal expansion between the aluminum plate and boron/epoxy composite patch were calculated based on the classical equation. The effects of the residual stresses and patch layers on fatigue lifetime, fatigue crack growth rate, and fatigue failure mode of the repaired plates were examined experimentally. A modified analytical model, based on Rose's analytical solution and Paris power law, was developed for this research. This model considered the residual stress effect and successfully predicted the fatigue lifetime of the patched plates. Results showed that the composite patch had two competing impacts on the structure. The composite patch could cause residual tensile stress in the aluminum substrate, which could consequently increase the crack growth rate. Moreover, reinforcement with the composite patch could also retard the crack propagation in the aluminum plate. If a 4-ply composite patch was used, it resulted in high residual stresses and effectively would not extend the fatigue lifetime of cracked aluminum plates.     

Viscoelastic Analysis of Thermal Stresses in a Composite Sphere

Viscoelastic analyses of thermal stresses are presented for composite spheres in which the viscous phase constitutes either the core or the cladding. These results should offer a better approximation to the stresses caused by spherical inclusions than the isolated sphere solution. The viscoelastic solution provides a means of finding the appropriate setting temperature for the composite, and its dependence on the volume fraction of the elastic material. The setting temperature of an elastic core composite is also shown to be predictable from that for a sandwich seal of the same materials. A "fluid core" analysis is shown to provide a good approximation when the elastic phase constitutes the cladding. This type of seal is sensitive to the dilatational relaxation behavior of the glass.