Challenges associated with shear characterization of a cross-ply thermoplastic lamina using picture frame tests

The current research investigates characterization of soft composite materials used in the manufacture of combat helmets. The material system considered is a cross-ply unidirectional (UD) sheet comprised of ultrahigh molecular weight polyethylene (UHMWPE) fibers consolidated with a polyurethane (PUR) based matrix. This paper presents efforts toward characterization of the material’s shear behavior using the picture frame (a.k.a. trellis frame, shear frame, rhombus) test method and systematically investigates parameters influencing measurement of shear stiffness including sample arm geometry, forming temperature, strain rate, and mechanical conditioning. A specific emphasis is placed on the importance of arm geometry in the shear characterization. Overestimation of the force curve is found to result from interference of supporting arm material outside the central region of the test specimen. Removal of the excess arm material results in more accurate measurements of shear stiffness, which are subsequently available for input into FE models that simulate forming processes.     

Press forming a 0/90 cross-ply advanced thermoplastic composite using the double-dome benchmark geometry

A pre-consolidated thermoplastic advanced composite cross-ply sheet comprised of two uniaxial plies orientated at 0/90° has been thermoformed using tooling based on the double-dome bench-mark geometry. Mitigation of wrinkling was achieved using springs to apply tension to the forming sheet rather than using a friction-based blank-holder. The shear angle across the surface of the formed geometry has been measured and compared with data collected previously from experiments on woven engineering fabrics. The shear behaviour of the material has been characterised as a function of rate and temperature using the picture frame shear test technique. Multi-scale modelling predictions of the material’s shear behaviour have been incorporated in finite element forming predictions; the latter are compared against the experimental results.     

Elastic and initial flexural failure analysis of unsymmetrically laminated cross-ply strips

A finite difference version of the Dynamic Relaxation (DR) method is used to generate elastic solutions of the small and the large deflection Mindlin plate equations for unsymmetrically laminated cross-ply strips subjected to uniform lateral pressure. The Maximum Stress (Independent) and Tsai-Hill failure criteria are combined with these solutions to produce initial failure analyses. It is shown that coupling between bending and stretching due to the B₁₁ stiffness term can cause a considerable increase or decrease in the flexural stiffness of simply supported in-plane fixed strips relative to the equivalent orthotropic strips but not necessarily in the corresponding failure pressures. It is also found that the predictions of the two failure criteria are in close agreement.     

Time-dependence of the tensile stiffness and anisotropy of a reinforced thermoplastic

The stiffening in tension of injection-moulded polypropylene with the addition of glass fibres or spheres was found to depend on strain, time and the direction relative to that of the melt flow, as well as on the percentage and aspect ratio of the glass inclusions. Under loading of long duration this stiffening, expressed in terms of the stiffness factor, increased with time for fibre-filled material but varied little for the sphere-filled. In the latter case, the tensile creep could be predicted with some accuracy by a simple model. The anisotropy of the fibre-filled polypropylene was not time-dependent and conformed to the theory of orthotropic materials.     

Repetitive flow forming of wood impregnated with thermoplastic binder

A processing technique for applying plastic deformation to a solid wood has been developed. In the present study, the effects of repetitive flow forming on the fluidity of solid wood materials impregnated with thermoplastic binder and on the mechanical properties of the products were investigated. The results showed that the increase in the number of extrusions decreased the load of the starting point of the extrusion especially in the lower polymer content of the wood materials. The bending strengths of the products were decreased with the repetitive extrusion using the lower polymer content (less than approximately 50 %) of the materials. On the other hand, the strength with higher polymer content (more than approximately 50 %) increased with the repetitive extrusion. The wood particles were found to become smaller in size with the repetitive extrusion. The tangles of the wood particles were also observed in higher polymer content of the materials. It was speculated that these configuration changes during reprocessing strongly affect both the fluidity during the extrusion and the mechanical properties of the products.     

Reduction in tensile and flexural strength of unidirectional glass fibre-epoxy with increasing specimen size

Size effects in tensile failure were investigated by means of tensile and four-point bending tests. Tapered tensile specimens with plies dropped off internally showed a reduction in strain at failure with increasing gauge length. Scaled bending tests also showed a reduction in strain with increasing specimen size. These two effects and the relationship between the tensile and flexural results could all be fitted satisfactorily with a Weibull strength model.     

Analysis of tensile and flexural modulus in hemp strands/polypropylene composites

This research focuses on the behavior of the tensile and flexural modulus of polypropylene/hemps strands composites. The intrinsic tensile modulus of the hemp strands was computed using Hirsch model and experimental data of the tensile modulus of the polypropylene composites at the 20–50 wt.% hemp strands content. The modified rule of mixtures was used to evaluate the efficiency factor. Square packing distribution was assumed and the length factor was fixed by Cox–Krenchel’s model. The mean value of the orientation efficiency factor was found to be 0.55. Tensile and flexural modulus were compared concluding that its value was independent of the manner the composite was loaded. Finally the Tsai–Pagano model was applied to predict the behavior of the composite’s tensile modulus.     

Analysis of temperature-dependent magnetization in Sm-Fe-Ccompounds using a two-sublattice model

The temperature dependence of magnetization in Sm₃Fe ₂₀C_x (x =0.3, 0.6, 0.8) and Sm₂Fe_16.5C_1.0 intermetallic compounds with rhombohedral structure has been analyzed using molecular field theory. On the basis of a two-sublattice model, the molecular field coefficients are calculated using a numerical fitting method. The Curie temperature and the Fe-Fe, Sm-Fe, Sm-Sm magnetic interaction energies for the compounds are determined from these coefficients. The results show that the increase of the Curie temperature (T_c) with the increase of carbon content x is attributed mainly to the enhancement of the Fe-Fe exchange interaction energy caused by carbon atoms added     

Correlation of tensile and flexural responses of strain softening and strain hardening cement composites

Closed form equations for generating moment–curvature response of a rectangular beam of fiber reinforced concrete are presented. These equations can be used in conjunction with crack localization rules to predict flexural response of a beam under four point bending test. Parametric studies simulated the behavior of two classes of fiber reinforced concrete: strain softening and strain hardening materials. The simulation revealed that the direct use of uniaxial tension and compression responses under-predicted the flexural response for strain softening material while a good prediction for strain hardening material was obtained. The importance of strain softening range on the flexural response is discussed using non-dimensional post-peak parameters. Results imply that the brittleness and size effect are more pronounced in the flexural response of brittle materials, while more accurate predictions are obtained with ductile materials. It is also demonstrated that correlations of tensile and flexural results can be established using normalized uniaxial tension and compression models with a single scaling factor.     

On the implementation of the EAS and ANS concept into a reduced integration continuum shell element and applications to sheet forming

This contribution deals with the application of a new solid-shell finite element based on reduced integration with hourglass stabilization in the field of sheet metal forming. The formulation includes the enhanced assumed strain (EAS) concept getting by with a minimum of enhanced degrees-of-freedom to overcome the volumetric locking and Pois- son’s thickness locking. To circumvent further the well-known effects of curvature thickness locking and transverse shear locking present in standard eight-node hexahedral finite elements the assumed natural strain (ANS) concept is applied. The implementation of the latter key feature is not straight-forward in reduced integration solid-shells. The second crucial point is a combined Taylor expansion of the compatible Green-Lagrange strain tensor with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization. Due to the three-dimensional modeling of the structure fully three-dimensional materials can be implemented without additional assumptions. Furthermore simulations of double-side contact problems (e.g. sheet metal forming) benefit from an exact modeling of the sheet thickness.     

The influence of hydrothermal conditioning on the Mode-I,thermal and flexural properties of Carbon/Benzoxazine composites with a thermoplastic toughening interlayer

Carbon/Benzoxazine laminates with and without non-woven thermoplastic fibrous polyamide (PA) veils at the interlaminar regions were manufactured using Vacuum Assisted Resin Transfer Moulding (VARTM). The effect of the interlaminar thermoplastic veils on the Mode-I strain energy release rate (G_IC), flexural stiffness, glass transition temperature (T_g) and water absorption behaviour was determined using two commercially available Benzoxazine resins. Despite an increase in the maximum moisture content, the veils greatly enhanced G_IC by an increase in fibre bridging of PA fibres, with concurrent reductions in flexural stiffness. Water ingress resulted in large reductions in the T_g, although no significant change was observed due to the PA interlayers. Fibre bridging and fibre pull-out were the main mechanisms by which the veils assisted in resisting delamination. The presence of the water was observed to degrade mechanical properties due to a reduction in fibre/matrix interfacial strength, molecular degradation and plasticisation of the matrix.     

Correlation of constitutive response of hybrid textile reinforced concrete from tensile and flexural tests

This papers addresses the disparities that exist in measuring the constitutive properties of thin section cement composites using a combination of tensile and flexural tests. It is shown that when the test results are analyzed using a simplified linear analysis, the variability between the results of tensile and flexural strength can be as high as 200–300%. Experimental results of tension and flexural tests of laminated Textile Reinforced Concrete (TRC) composites with alkali resistant (AR) glass, carbon, aramid, polypropylene textile fabrics, and a hybrid reinforcing system with aramid and polypropylene are presented. Correlation of material properties is studied analytically using a parametric model for simulation of flexural behavior using a closed form solution based on tensile stress–strain constitutive relation. The flexural load carrying capacity of TRC composites is computed using a back-calculation approach, and parameters for a strain hardening material model are obtained using the closed form equations. While the parametric model over predicts the simulated tensile response for carbon and polypropylene TRCs, predictions are however consistent with experimental trends for aramid and glass TRCs. Detailed discussion of the differences between backcalculated and experimental tensile properties is presented. Results can be implemented as average moment–curvature relationship in the structural design and analysis of cement composites.     

Micromechanical model of 3D cross-ply copper matrix composite reinforced with SiC fibres

A 3D cross-ply micromechanical model is used to analyse the thermomechanical behaviour of copper matrix composite reinforced with SiC fibres, when subjected to cyclic loadings at high temperature. The copper matrix composite is reinforced with 45% fibre volume fraction. A cohesive model is employed to capture the influence of the debonding interface in the composite, during the consolidation and subsequent thermal and mechanical loading.     

Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

Scanning electron microscopy studies on tensile,tear and abrasion failure of thermoplastic elastomers

The tensile strength, tear resistance and abrasion resistance of four different types of commercial thermoplastic elastomers have been studied and their fracture surfaces examined by scanning electron microscopy. Thermoplastic polyurethane (TPU) showed elastic deformation under tensile fracture, whereas in 1,2 polybutadiene (1,2 PB) the fracture was initiated by craze formation and propagated by tear failure. Styrene-isoprene-styrene block copolymer (K1107) showed ductile type failure whereas in styrene-butadiene-styrene block copolymer containing a higher proportion of styrene and silica filler (K5152), the fracture occurred by shearing action. The tear failure surfaces of the thermoplastic elastomers showed different fracture patterns which could be correlated with the tear strength of the materials. The tear fracture surface of 1,2 PB showed stick-slip tear lines and that of TPU had a broad tear path with vertical striations. The fracture surfaces of K5152 and K1107 had the characteristics of laminar tearing and uninterrupted continuous tearing processes, respectively. The abrasion resistance of the samples was in the order TPU>1,2 PB>K5152, which was manifested through the type of ridge patterns formed on the abraded surfaces. Abraded surfaces of TPU, 1,2 PB and K5152 showed closely spaced stable ridges, widely spaced ridges bridged by elongated fibrils and highly deformed ridges, respectively.     

Transverse vibration of a two-segment cross-ply composite shafts with a lumped mass

The advantages of having higher stiffness to weight ratio and strength to weigh ratio that composite materials have resulted in an increasing interest in them. In automotive engineering, weight savings has positive impacts on other attributes like fuel economy, performance and possibly noise, vibration and harshness (NVH). The driveline of an automotive system can be a target for possible weight reduction. This can be done through the use of composite materials. The design of the driveshaft of an automotive system is primarily driven by its natural frequency. This paper presents an exact solution for the vibration of a cross-ply laminated composite driveshaft with an intermediate joint. The joint is modeled as a frictionless internal hinge. The Euler–Bernoulli beam theory is used. Lumped masses are placed on each side of the joint to represent the joint mass. Equations of motion are developed using the appropriate boundary conditions and then solved exactly.     

Design of plates with given rigidities from a minimum number of layers and materials

The problem of designing a plate with a given set of rigidities using a minimum number of layers, which, as it has been established, is equal to four, has been considered. We consider the cases where flexural rigidities, rigidities in the plate plane, and asymmetric rigidities and where only longitudinal and flexural rigidities, which are the physical characteristics of the plane, are given. It has been proved that in both cases the ranges of longitudinal and flexural rigidities are equal (thus the question of the role of asymmetric rigidities is solved). __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 5, pp. 165–174, September–October, 2006.     

Dislocation model of the interaction between a tensile crack and a hole

The representation of a crack by discrete dislocations and that of a hole by surface dislocations is used to study the interaction between a tensile crack and a hole. It is shown that for a given size and shape of a pre-existing hole in a homogeneous material, a crack of only one size can exist in equilibrium. This equilibrium size of the crack depends on the size and shape of the hole and also on the distance between the crack and the hole. All cracks whose size is greater than or lesser than the equilibrium size are unstable. The effect of the size and shape of the hole on the equilibrium size of the crack is illustrated. The asymmetry in the dislocation configuration of the crack and the hole is useful in understanding the stress concentration that exists around the crack tip and the corners of the hole and to further study the mechanism of the growth of the crack and the hole.

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Résumé La représentation d'une fissure par des dislocation discrètes et d'un trou par des dislocations de surface est utilisée pour l'étude de l'interaction entre une fissure résultant d'un état de tension et un trou. On montre que pour une dimension et une forme données d'un trou préexistant dans un matériau homogène il ne peut exister une fissure que d'une seule dimension pour maintenir l'équilibre. Cette dimension d'équilibre de la fissure dépend de la dimension et de la forme du trou ainsi que de la distance entre la fissure et le trou. Toutes les fissures dont les dimensions sont supérieures ou inférieures à la dimension d'équilibre sont instables. L'effet de la dimension de la forme du trou sur la dimension d'équilibre de la fissure est illustré. L'assymétrie de la configuration des dislocations associée à la fissure et au trou est utile pour comprendre la concentration de contrainte qui existe au voisinage de l'extrémité d'une fissure et au bord d'un trou, ainsi que pour étudier d'une manière plus approfondie le mécanisme de croissance de la fissure et du trou.