Creep of Polymer Matrix Composites. II: Monkman-Grant Failure Relationship for Transverse Isotropy

This research concerns polymer matrix composite (PMC) materials having long or continuous reinforcement fibers embedded in a polymer matrix. The objective is to develop comparatively simple, designer friendly constitutive equations intended to serve as the basis of a structural design methodology for this class of PMC. Here (Part II), the focus is on extending the damage/failure model of an anisotropic deformation/damage theory presented earlier. A companion paper (Part I) by the writers deals with creep deformation of the same class of PMC. The extension of the damage model leads to a generalization of the well known Monkman/Grant relationship to transverse isotropy. The usefulness of this relationship is that it permits estimates of (long term) creep rupture life on (short term) estimates of creep deformation rate. The current extension also allows estimates of failure time for various fiber orientations. Supporting exploratory experiments are defined and conducted on thin-walled specimens fabricated from a model PMC. A primary assumption in the damage model is that the stress dependence of damage evolution is on the transverse tensile and longitudinal shear traction acting at the fiber/matrix interface. We conjecture that a supplemental mechanism of failure is the extensional strain in the fiber itself. The two postulated mechanisms used in conjunction suggest that an optimal fiber angle may exist in this class of PMC, maximizing the time to creep failure.     

Fiber-Reinforced Polymer Composites for Construction—State-of-the-Art Review

A concise state-of-the-art survey of fiber-reinforced polymer (also known as fiber-reinforced plastic) composites for construction applications in civil engineering is presented. The paper is organized into separate sections on structural shapes, bridge decks, internal reinforcements, externally bonded reinforcements, and standards and codes. Each section includes a historical review, the current state of the art, and future challenges.     

Failure Model for Rate-Dependent Polymer Matrix Composite Laminates under High-Velocity Impact

A modified Hashin failure model is developed to characterize different failure modes related to high-velocity impact of composite laminates. Hashin’s compressive fiber failure mode has been extended to consider the shear stress effect. Several micromechanics-based degradation rules are developed and applied to the stress and material property calculations according to different failure modes after the corresponding failure criterion is satisfied. This model has been implemented into a recently developed micromechanics model. Computational results show that this model is able to address shear failure, delamination, and tearing failure observed in the high-velocity impact of composite laminates.     

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of a representative polymer are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.     

Creep Effect in Structural Composite Lumber for Bridge Applications

Structural composite lumber (SCL) is a family of newly engineered wood products that are increasing in highway bridge applications. Advantages of SCL are its high strength, flexibility, stiffness, and excellent preservative treatability. A main concern in SCL bridge applications is serviceability performance. The long-term creep behavior of SCL flexural members is not presently determinable. In order to investigate creep effects, deflection monitoring of full-scale SCL T-beam bridge members was performed under ambient conditions and an accelerated aging process. Sixteen beams were monitored under exposed weather conditions with frequent wetting and drying. Variables in the experiment were: lumber type (Douglas fir and southern yellow pine), SCL type (LVL and PSL), preservative type (CCA and penta), and dead load intensity. It was found that creep behavior in SCL bridge members closely follows the Burger theoretical model. LVL, Douglas fir, and CCA treatment causes smaller creep deflections as compared to PSL, Southern Pine, and Penta treatment. NDS type creep multipliers for SCL vary between 2.2 and 2.67 for various subcategories. A single average creep multiplier of 2.3 may be used for treated SCL bridge beams.     

Deflection Creep of Pultruded Composite Sheet Piling

The time-dependent creep behavior of pultruded composite sheet piling was investigated. Two panels were tested under equally spaced third point bending at a span to depth ratio of 48; one was subject to a constant load of 50% of Pmax and the other 25% of Pmax. Tensile creep, shear creep, and deflection creep were recorded over 1 year. The time-dependent tensile and shear moduli were obtained using the simplified Findley’s model, and the deflection creeps were predicted based on both Findley’s model and Timoshenko’s equation. It was found that the time exponents in Findley’s model for tensile, shear and deflection creep were of close value and could therefore be averaged to provide a viscoelastic material constant for the composite sheet piling. With the averaged viscoelastic parameters, Timoshenko’s equation resembled the Findley’s power law model for the prediction of deflection creep and agreed well with experimental results up to 1 year. Over 30 years, it is estimated that the viscoelastic tensile and shear moduli will be reduced to 68 and 36% of their respective initial values and the creep deflection will reach 50% of its static deflection.     

Numerical Implementation of Polymer Viscoplastic Equations for High Strain-Rate Composite Models

For polymer matrix composites subjected to large strain rates, it is important to correctly characterize the nonlinear and strain-rate dependent response of polymers. Viscoplastic constitutive material models have been developed to account for the effects of hydrostatic effects and inelastic strains in polymer materials. The effective implementation of such viscoplastic models is important for development of composite models geared toward practical applications. Goldberg’s polymer model numerical implementation into a commercial finite-element code constitutes the main objective of this paper. Special attention is given to the use of effective algorithms for solving the model nonlinear rate dependent viscoplastic equations. Existent experimental data are used to verify the accuracy and robustness of the computational polymer model. A phenomenological fiber model and a simplified iso-strain mixture theory used to obtain the resultant stresses in the composite by averaging the stresses of the individual constituents are also defined. The validation of the simplified mixture theory for the composite model will be presented later on.     

Simplified Braiding through Integration Points Model for Triaxially Braided Composites

A simplified methodology has been developed for modeling two-dimensional triaxially braided composite plates impacted by a soft projectile using an explicit nonlinear finite-element analysis code LS-DYNA. The fiber preform architecture is modeled using shell elements by incorporating the fiber preform architecture at the level of integration points. The soft projectile was modeled by an equation of state. An arbitrary Lagrangian–Eulerian formulation is used to resolve numerical problems caused by large deformation of the projectile. The computed results indicate that this numerical model is able to simulate a triaxially braided composite undergoing a ballistic impact effectively and accurately, including the deformation and failure with a reasonable level of computational efficiency.     

Strengthening of Short Shear Span Reinforced Concrete T Joists with Fiber-Reinforced Plasic Composites

In this work, the results of an experimental study conducted in a 1964-vintage building are presented. Twelve reinforced concrete (RC) T-joists strengthened with fiber-reinforced plastic (FRP) composites were loaded until failure in a short shear span configuration. Different strengthening schemes, including different FRP materials and a new FRP anchorage system, were adopted in order to compare the performance of the different installations. Carbon FRP and aramid FRP sheets in an epoxy matrix were bonded to the RC joists using the wet layup technique. All of the joists were loaded close to one end support and showed similar cracking patterns at failure. The design calculations were based on experimental results. All of the unanchored FRP strengthened beams showed failure due to peeling, while the anchored FRP strengthened members showed failure due to anchor pullout at higher load values. It was found that an increase in the amount of FRP did not result in a proportional increase in the shear capacity, as expected by design equations, but all of the beams showed a considerable increase in stiffness. The experimental results are compared with the results expected by analytical models in order to discuss the structural behavior of FRP strengthened beams tested in a real building with a short shear span. It was found that theoretical calculations resulted in nonconservative results for the tested specimens.     

Delamination Analysis for Laminated Composites. I: Fundamentals

Analytical models for the delamination of a class of composite laminates are developed. Two approaches are used in deriving the governing equations. The first approach follows a refined engineering bending theory that stems from the premise that the statically equivalent stresses obtained from classical theory can be used to estimate the strains ignored in the classical theory. The second follows a modified Donnell approach in which the stresses obtained from the classical engineering theory are improved by adding a series of corrections. These corrections are determined by satisfying the stress equilibrium and compatibility conditions of two‐dimensional elasticity theory. A comparison of the derived governing equations is provided in order to assess the consistency and accuracy of the engineering approach. The deformation modes associated with each model are identified. Interlaminar stresses predicted by the developed models for a quasi‐isotropic double cracked‐lap‐shear laminate are compared with finite‐element results.     

Durability Gap Analysis for Fiber-Reinforced Polymer Composites in Civil Infrastructure

The lack of a comprehensive, validated, and easily accessible data base for the durability of fiber-reinforced polymer (FRP) composites as related to civil infrastructure applications has been identified as a critical barrier to widespread acceptance of these materials by structural designers and civil engineers. This concern is emphasized since the structures of interest are primarily load bearing and are expected to remain in service over extended periods of time without significant inspection or maintenance. This paper presents a synopsis of a gap analysis study undertaken under the aegis of the Civil Engineering Research Foundation and the Federal Highway Administration to identify and prioritize critical gaps in durability data. The study focuses on the use of FRP in internal reinforcement, external strengthening, seismic retrofit, bridge decks, structural profiles, and panels. Environments of interest are moisture/solution, alkalinity, creep/relaxation, fatigue, fire, thermal effects (including freeze-thaw), and ultraviolet exposure.     

Fiber Reinforced Polymer Shear Strengthening of Reinforced Concrete Beams with Transverse Steel Reinforcement

The paper aims to contribute to a better understanding and modeling of the shear behavior of reinforced-concrete (RC) beams strengthened with carbon fiber reinforced polymer (FRP) sheets. The study is based on an experimental program carried out on 11 beams with and without transverse steel reinforcement, and with different amounts of FRP shear strengthening. The test results provide some new insights into the complex failure mechanisms that characterize the ultimate shear capacity of RC members with transverse steel reinforcement and FRP sheets. After the discussion of the above topics, a new upper bound of the shear strength is introduced. It should be capable of taking into account how the cracking pattern in the web failing under shear is modified by the presence of FRP sheets, and how such a modified cracking pattern actually modifies the anchorage conditions of the sheets and their effective contribution to the ultimate shear strength of the beams.     

Effect of Test Piece Size on Rheological Behavior of Wood Composites

The effect of size and the combined effect of the size and moisture sorption of test pieces on the long term creep behavior of wood composites were studied. Small-, wide-, and semisize test pieces from each of three commercial wood composites, particleboard (PB), oriented strand board (OSB), and medium density fiberboard (MDF) were tested. Three exposure regimes, constant 20°C/65%, a single change from 20°C/65% to 20°C/85%, and cyclic changes between 20°C/30% and 20°C/90% relative humidity (RH), were used. It was found that the width of test pieces had no effect while the length had a significant effect on long term behavior of wood composites, but the effect is in contrast to that of short term modulus of rupture (MOR) which ranged from 0.06 to 0.13 for the shape parameter and from 0.09 to 0.26 for the length parameter depending on the types of wood composites. The average ratio of the relative creep (kc) of small-:wide-:semisize was 1.14:1.13:1.00 for PB, 1.26:1.21:1.00 for MDF, and 1.24:1.24:1.00 for OSB, with the shape parameter ranging from 0.04 to 0.19 and the length parameter from 0.13 to 0.26. Change in RH significantly aggravated the size effect on kc with the most significant under cyclic RH, for which the ratio of kc small- to semisize was 1.45 for PB and 1.27 for OSB after 3 months’ exposure. Edge sealing on small test pieces efficiently prevented the effect of moisture sorption but the size effect on kc with a reduction of about 30 and 20%, respectively, for edge sealed PB and OSB in weekly changing climate between 20°C/30% and 20°C/90% RH compared to unsealed small-size test pieces. The findings elucidate the importance to take into account the size effects on short term strength, compensated size effect on long term creep, and the combined effects of size and moisture on long term behavior when predicting the long term load carrying capacity of wood composites in construction.     

Preflex Beams: A Method of Calculation of Creep and Shrinkage Effects

This paper presents a method of calculation of creep and shrinkage effects for composite beams. It is particularly applicable to Preflex and Flexstress beams, which are composed of a steel I-girder with the bottom flange encased by concrete. The concrete is prestressed by predeflection of the steel beam and the subsequent release after hardening of the concrete flange or by means of prestressing cables. The presented approach using concrete age-adjusted modular ratios allows the calculation of time-dependent stresses in the concrete flange due to creep and shrinkage, with sufficient accuracy for practical applications and without carrying out cumbersome numerical computations. The results can be extended directly to the analysis of ordinary steel–concrete composite beams. The main goal of the present paper is the calibration of the parameters which must be introduced to simplify the equations describing the system. This calibration is discussed and its sensitivity to some calculation inputs is presented. The conclusions are very encouraging and the simplified approach seems to agree very well with the results of the numerical approach.     

Upgrading Torsional Resistance of Reinforced Concrete Beams Using Fiber-Reinforced Polymer

An experimental investigation is conducted on the improvement of the torsional resistance of reinforced concrete beams using fiber-reinforced polymer (FRP) fabric. A total of 11 beams were tested. Three beams were designated as control specimens and eight beams were strengthened by FRP wrapping of different configuration and then tested. Both glass and carbon fibers were used in the torsional resistance upgrade. Different wrapping designs were evaluated. The reinforced concrete beams were subjected to pure torsional moments. The load, twist angle of the beam, and strains were recorded. Improving the torsional resistance of reinforced concrete beams using FRP was demonstrated to be viable. The effectiveness of various wrapping configurations indicated that the fully wrapped beams performed better than using strips. The 45° orientation of the fibers ensures that the material is efficiently utilized.     

Development of a Specification for Bridge Seismic Retrofit with Carbon Fiber Reinforced Polymer Composites

The U.S. Interstate 80 bridge over State Street in Salt Lake City is very near the Wasatch fault, which is active and capable of producing large earthquakes. The bridge was designed and built in 1965 according to the 1961 American Association of State Highway Officials specifications, which did not consider earthquake-induced forces or displacements. The bridge consists of reinforced concrete bents supporting steel plate welded girders. The bents are supported on cast-in-place concrete piles and pile caps. A seismic retrofit design was developed using carbon fiber reinforced polymer (CFRP) composites, which was implemented in the summer of 2000 and the summer of 2001, to improve the displacement ductility of the bridge. The seismic retrofit included column jacketing, as well as wrapping of the bent cap and bent cap-column joints for confinement, flexural, and shear strength increase. This paper describes the specifications developed for the CFRP composite column jackets and composite bent wrap. The specifications included provisions for materials, constructed thickness based on strength capacity, and an environmental durability reduction factor. Surface preparation, finish coat requirements, quality assurance provisions, which included sampling and testing, and constructability issues regarding the application of fiber composite materials in the retrofit of concrete bridges are also described.     

Bond between Carbon Fiber Reinforced Polymer Bars and Concrete. I: Experimental Study

The bond characteristics of four different types of carbon fiber reinforced polymer (CFRP) rebars (or tendons) with different surface deformations embedded in lightweight concrete were analyzed experimentally. In a first series of tests, local bond stress-slip data, as well as bond stress-radial deformation data, needed for interface modeling of the bond mechanics, were obtained for varying levels of confining pressure. In addition to bond stress and slip, radial stress and radial deformation were considered fundamental variables needed to provide for configuration-independent relationships. Each test specimen consisted of a CFRP rebar embedded in a 76-mm-(3 in.)-diam, 102-mm-(4 in.)-long, precracked lightweight concrete cylinder subjected to a constant level of pressure on the outer surface. Only 76 mm (3 in.) of contact were allowed between the rebar and the concrete. For each rebar type, bond stress-slip and bond stress-radial deformation relationships were obtained for four levels of confining axisymmetric radial pressure. It was found that small surface indentations were sufficient to yield bond strengths comparable to that of steel bars. It was also shown that radial pressure is an important parameter that can increase the bond strength almost threefold for the range studied. In a second series of tests, the rebars were pulled out from 152-mm-(6 in.)-diam, 610-mm-(24 in.)-long lightweight concrete specimens. These tests were conduced to provide preliminary data for development length assessment and model validation (Part II).     

Upsetting Tests of Fresh Cementitious Composites for Extrusion

Upsetting tests were conducted on cylindrical specimens made of a typical fresh short fiber-reinforced cementitious composite (SFRCC) paste for extrusion at various boundary conditions to derive the paste’s constitutive behavior. Due to friction present at the specimen and the equipment platens interfaces, stress was not uniformly distributed in the specimen and had to be corrected. In this study, two analytical methods were utilized to derive the true flow stress of the fresh SFRCC paste through correcting the nominal yield stress obtained from the upsetting test. One of them was the stress extrapolation method, which required a large number of experimental data and predetermined boundary friction. It was found that the results corrected by this method from experiments at the lubricated boundary were more reliable than those at the dry boundary and this method could also give an approximate estimation of the boundary friction coefficient. As comparison, the flow stress correction method required only a small amount of experimental data and no predetermined boundary friction. It was found that this method provided better results at the dry boundary than at the lubricated boundary. The fresh SFRCC paste exhibited both strain and strain rate hardening characteristics whereas strain rate hardening effect was more significant and dominated.     

E-Glass/Vinylester Composites in Aqueous Environments: Effects on Short-Beam Shear Strength

The paper present the results of extended (225 weeks) aqueous immersion of E-glass/vinylester composites, fabricated by the resin infusion process. Two different architectures (unidirectional and bidirectional) are tested to assess effects of temperature levels between 5 and 60°C on the short-beam shear strength. Tests show the competing effects of plasticization and postcuring balanced by hydrolytic degradation. The maximum reduction in performance is seen through immersion in deionized water at 60°C wherein pronounced interface and fiber level degradation is noted. Cycling between the two extremes of 5 and 60°C is also seen to cause acceleration of some interface and bulk resin related degradation phenomena. Experimental results obtained from hygrothermal aging at 23°C are compared with predictions based on an Arrhenius type model, and it is shown that good correlation can be obtained in sets where degradation mechanisms remain the same. Shortcomings of this type of model for life predictions are discussed to emphasize viability of use in design.     

Characterization of Damage in Triaxial Braided Composites under Tensile Loading

Carbon fiber composites that utilize flattened, large tow yarns in woven or braided forms are being used in many aerospace applications. The complex fiber architecture and large unit cell size in these materials present challenges for both understanding the deformation process and measuring reliable material properties. In this paper composites made using flattened 12k and 24k (referring to the number of fibers in the fiber tow) standard modulus carbon fiber yarns in a 0°/+60°/?60° triaxial braided architecture are examined. Standard straight-sided tensile coupons were tested with the 0° axial braid fibers either parallel to (axial tensile test) or perpendicular to (transverse tensile test) the applied tensile load. The nonuniform surface strain resulting from the triaxial braided architecture was examined using photogrammetry. Local regions of high strain concentration were examined to identify where failure initiates and to determine the local strain at the time of failure initiation. Splitting within fiber bundles was the first failure mode observed at low to intermediate strains. For axial tensile tests the splitting was primarily in the ±60° bias fibers, which were oriented 60° to the applied load. At higher strains in the axial tensile test, out-of-plane deformation associated with localized delamination between fiber bundles or damage within fiber bundles was observed. For transverse tensile tests, the splitting was primarily in the 0° axial fibers, which were oriented transverse to the applied load. The initiation and accumulation of local damage caused the global transverse stress-strain curves to become nonlinear and caused failure to occur at a reduced ultimate strain for both the axial and transverse tensile tests. Extensive delamination at the specimen edges was also observed. Modifications to the standard straight-sided coupon geometry are needed to minimize these edge effects when testing the large unit cell type of material examined in this work.