## Transportation

Plastics and RPs offer a wide variety of benefits to the different transportation vehicles (automobiles, trucks, motorcycles, boats, airplanes, and so on). They range from assembling separate parts to providing safety (impact, etc.), aesthetics, lightweight, durability, corrosion resistance, recyclability, and fuel savings. Growth in the use of plastics tends to be a continuous process.

Structural analysis methods coupled with composite mechanics play a unique role during design in that they are used to formally evaluate alternative design concepts prior to committing some of these design concepts to costly testing or fabrication. Important material properties are not known during design in many cases. Frequently, some of these properties are assumed and structural analyses are performed to assess their effects on the design as well as their effects on the structural performance of the designed vehicle component. Also structural analysis methods are used to establish acceptable ranges of key factors (parameters) in a given design.

With BJ's there can be the intraply hybrid composites have two kinds of fibers embedded in the matrix in general with the same ply providing different orientation performances. They have evolved as a logical sequel to conventional composites and to interply hybrids. Intraply hybrid composites have unique features that can be used to meet diverse and competing design requirements in a more cost effective way than either advanced or conventional composites. Some of the specific advantages of intraply hybrids over other composites are balanced strength and stiffness, balanced bending and membrane mechanical properties, balanced thermal distortion stability, reduced weight and/or cost, improved fatigue resistance, reduced notch sensitivity, improved fracture toughness and/or crack-arresting properties, and improved impact resistance. With intraply hybrids, it is possible to obtain a viable compromise between mechanical properties and cost to meet specified design requirements.

Structural mechanics analyses are used to determined design variables such as displacements, forces, vibrations, buckling loads, and dynamic responses, including application of corresponding special areas of structural mechanics for simple structural elements. General purpose finite element programs such as NASTRAN are used for the structural analysis of complex structural shapes, large structures made from simple structural elements, And structural parts made from combinations of simple elements such as bars, rods and plates.

Composite mechanics in conjunction with structural mechanics can be used to derive explicit equations for the structural response of simple structural elements. These explicit expressions can then be used to perform parametric studies (sensitivity analyses) to assess the influence of the hybridization ratio on structural response. For example the

' - Loads related to flexural modulus structural response (behavior variables) equations for maximum deflection, buckling load and frequency of a simply supported beam made from intraply hybrids are summarized in Fig. 4.39 Flexural modulus is used to determine the maximum deflection, buckling load, and frequency of a simple supported beam made from intraply hybrids.

The notation in these equations and others that follow are as follows:

o,, o2 Correlation coefficients for longitudinal compressive strength.

8c1, k Buckling limit (buckling behavior constraint) due to loading condition k.

8'c2, k Strength limit (strength behavior constraint) due to loading condition k.

8'c3, k Interply delamintion limit (delamination constraint) due to loading condition k.

Ef Flexural modulus.

£fn. £f22 Longitudinal and transverse fibre moduli. £mii. £m22 s¡tu matrix longitudinal and transverse moduli.

FPC Modulus primary composite.

Esc Modulus secondary composite.

Gf12 Fibre shear modulus.

Gml2 Matrix shear modulus.

H¡ Matrix interply layer effect.

I Moment of inertia.

/C|12o[p Correlation coefficients in the combined-stress failure criterion; a, /3

= Tor Cdenoting stress direction.

kf Fiber volume ratio.

ky Void volume ratio.

k K = 1, 2, 3, denotes loading condition index.

N Number of plies.

WXk Wvk Inplane loads - xand y directions corresponding to k.

P Load.

Pc, Buckling load.

Pcr0 Buckling load of reference composite.

Sft Fiber tensile strength.

Spc Strength primary composite.

Ssc Strength secondary composite.

Vsc Volume fraction secondary composite..

IN Panel cost units per unit area.

/3, ¡3' Correlation coefficients in composite micromechanics to predict ply elastic behavior.

)3dei Interply delamination factor.

5 Displacement.

¿0 Displacement of reference composite

£mpC, S, T In situ allowable matrix strain for compression, shear and tension.

6 Ply angle measured from x-axis.

Figure 4 4i Effects of hybridizing ratio and constituent composites or center deflection of intraply hybrid composite beams

Figure 4 4i Effects of hybridizing ratio and constituent composites or center deflection of intraply hybrid composite beams

Figure 4.41 Effects of hybridizing ratio and constituent composites on buckling load of intraply hybrid composite beams

Figure 4.41 Effects of hybridizing ratio and constituent composites on buckling load of intraply hybrid composite beams

HYBRIDIZING RATIO

vf Fiber Poisson's ratio, numerical subscripts denote direction.

vm Matrix Poisson's ratio, numerical subscripts denote direction.

(o„ Frequency of the nth vibration mode.

cOno Frequency of the nth vibration mode of the reference composite.

HYBRIDIZING RATIO

vf Fiber Poisson's ratio, numerical subscripts denote direction.

vm Matrix Poisson's ratio, numerical subscripts denote direction.

(o„ Frequency of the nth vibration mode.

cOno Frequency of the nth vibration mode of the reference composite.

The equations are first expressed in terms of E^ the equivalent flexural modulus, and then in terms of the moduli of the constituent composites (Epc and Esc) and die secondary composite volume ratio (Vsi). These equations were used to generate the parametric nondimensional plots shown in Figs 4.40 to 4.42.

The nondimensionalized structural response is plotted versus the rigure 4.42 Effects of hybridizing ratio and constituent composites on frequences of intraply hybrid composite beams

INTRAPLY

rigure 4.42 Effects of hybridizing ratio and constituent composites on frequences of intraply hybrid composite beams

INTRAPLY

HYBRIDIZING RATIO

Figure 4.4. Effects of hybridizing ratio and constituent composites on Izod-type energy density of intraply hybrids

HYBRIDIZING RATIO

Figure 4.4. Effects of hybridizing ratio and constituent composites on Izod-type energy density of intraply hybrids

IMPACT ENERGY DENSITY PARAMETER, IED E^/kS i

HYBRIDIZING RATIO cs-79-1:9

hybridizing rado Vsc for four different intraply hybrid systems. These figures show that small amounts of secondary composite (Vsc 0.2) have negligible effect on the structural response. However, small amounts of primary composite (Vsc 0.8) have a substantial effect on the structural response. A parametric plot of Izod-type, impact energy density is illustrated in Fig. 4.43. This parametric plot shows also negligible effects for small hybridizing ratios (Vsc 0.2) and substantial effects for hybridizing ratios (Vsc 0.2).

The parametric curves in Figs 4.40 to 4.43 can be used individually to select hybridization ratios to satisfy a particular design requirement or

IMPACT ENERGY DENSITY PARAMETER, IED E^/kS i

HYBRIDIZING RATIO cs-79-1:9

Figure 4 44 Schematic

### UNIDIRECTIONAL COMPOSITE STRIP

they may be used jointiy to satisfy two or more design requirements simultaneously, for example, frequency and impact resistance. Comparable plots can be generated for other structural components, such as plates or shells. Also plots can be developed for other behavior variables (local deformation, stress concentration, and stress intensity factors) and/or other design variables, (different composite systems). This procedure can be formalized and embedded within a structural synthesis capability to permit optimum designs of intraply hybrid composites based on constituent fibers and matrices.

Low-cost, stiff, lightweight structural panels can be made by embedding strips of advanced unidirectional composite (UDC) in selected locations in inexpensive random composites. For example, advanced composite strips from high modulus graphite/resin, intermediate graphite modulus/resin, and Keviar-49 resin can be embedded in planar random E-glass/resin composite. Schematics showing two possible locations of advanced UDC strips in a random composite are shown in Fig. 4.44 to illustrate the concept. It is important to note that the embedded strips do not increase either the thickness or the weight of the composite. However, the strips increase the cost.

It is important that the amount, type and location of the strip reinforcement be used judiciously. The determination of all of these is part of the design and analysis procedures. These procedures would require composite mechanics and advanced analyses methods such as finite element. The reason is that these components are designed to meet several adverse design requirements simultaneously. Henceforth, planar random composites reinforced with advanced composite strips will be called strip hybrids. Chamis and Sinclair give a detailed description of strip hybrids. Here, the discussion is limited to some design guidelines inferred from several structural responses obtained by using finite element structural analysis. Structural responses of panels structural components can be used to provide design guidelines for sizing and designing strip hybrids for aircraft engine nacelle, windmill ip hybrids

RANDOM

RANDOM

RANDOM

ONE WAY STRIPS

-4-1---- | |

---m |
-I-+--- |

---4- 4- |
—1- +--- |

-—J.+. i i i i — i. i |
TWO WAY STRIPS Structural responses of strip hybrid plates with fixed edges DISPLACEMENT, DISPLACEMENT, in. CONCENTRATED LOAD AT CENTER. 10 lb BUCKLING LOAD, lb/in. CONCENTRATED LOAD AT CENTER. 10 lb BUCKLING LOAD, lb/in. REINFORCING STRIP MODULUS, msi REINFORCING STRIP MODULUS, msi BUCKLING LOAD LOWEST FREO blades and auto body applications. Several examples are described below to illustrate the procedure. The displacement and base material stress of the strip hybrids for the concentrated load, the buckling load, and the lowest natural frequency are plotted versus reinforcing strip modulus in Fig. 4.45. As can be seen die displacement and stress and the lowest natural frequency vary nonlinearly with reinforcing strip modulus while the buckling load varies linearly. These figures can be used to select reinforcing strip moduli for sizing strip hybrids to meet several specific design requirements. These figures are restricted to square fixed-end panels with 20% strip reinforcement by volume. For designing more general panels, suitable graphical data has to be generated. The maximum vibratory stress in the base material of the strip hybrids due to periodic excitations with three different frequencies is plotted versus reinforcing strip modulus in Fig. 4.46. The maximum vibratory stress in the base material varies nonlinearly and decreases rapidly with reinforcing strip modulus to about 103 GPa (15 x 106 psi). It decreases mildly beyond this modulus. The significant point here is that the modulus of the reinforcing strips should be about 103 GPa (15 x 106 psi) to minimize vibratory stresses (since they may cause fatigue failures) for the strip hybrids considered. For more general strip hybrids, graphical data with different percentage reinforcement and different boundary condidons are required. The maximum dynamic stress in the base material of the strip hybrids : Maximum stress in base material die to periodic vibrations : Maximum stress in base material die to periodic vibrations due to an impulsive load is plotted in Fig. 4.47 versus reinforcing strip modulus for two cases: (1) undamped and (2) with 0.009% of critical damping. The points to be noted from this figure are: (a) the dynamic displacement varies nonlinearly with reinforcing strip modulus and (b) the damping is much more effective in strip hybrids with reinforcing strip moduli less than 103 GPa (15 X 106 psi). Corresponding displacements are shown in Fig. 4.48. The behavior of the dynamic displacements is similar to that of the stress as would be expected. Curves comparable to those in Figs 4.46 and 4.47 are needed to size : Maximum impulse displacement DISPLACEMENTS, in. 0 5 10 15 20 25 30 35 REINFORCING STRIP MODULUS, msi and design strip hybrid panels so that impulsive loads will not induce displacements or stresses in the base material greater than those specified in the design requirements or are incompatible with the material operational capabilities. The previous discussion and the conclusions derived therefrom were based on panels of equal thickness. Structural responses for panels with different thicknesses can be obtained from the corresponding responses in Fig. 4.47 as follows (let t= panel thickness): 1 The displacement due to a concentrated static load varies inversely with t3 and the stress varies inversely with t2. 2. The buckling load varies direcdy with t3. 3. The natural vibration frequencies vary directly with t. No simple relationships exist for scaling the displacement and stress due to periodic excitation or impulsive loading. Also, all of the above responses vary inversely with the square of the panel edge dimension. Responses for square panels with different edge dimensions but with all edges fixed can be scaled from the corresponding curve in Fig. 4.45. The significance of the scaling discussed above is that the curves in Fig. 4.45 can be used directly to size square strip hybrids for preliminary design purposes. The effects of a multitude of parameters, inherent in composites, on the structural response and/or performance of composite structures, and/or structural components are difficult to assess in general. These parameters include several fiber properdes (transverse and shear moduli), in situ matrix properties, empirical or correlation factors used in the micromechanical. equations, stress allowables (strengths), processing variables, and perturbations of applied loading conditions. The difficulty in assessing the effects of these parameters on composite structural response arises from the fact that each parameter cannot be isolated and its effects measured independendy of the others. Of course, the effects of single loading conditions can be measured independendy. However, small perturbations of several sets of combined design loading conditions are not easily assessed by measurement. An alternate approach to assess the effects of this multitude of parameters is the use of optimum design (structural synthesis) concepts and procedures. In this approach the design of a composite structure is cast as a mathematical programming problem. The weight or cost of the structure is the objective (merit) function that is minimized subject to a given set of conditions. These conditions may include loading conditions, design variables that are allowed to vary during the design (such as fiber type, ply angle and number of plies), constraints on response (behavior) variables (such as allowable stress, displacements, buckling loads, frequencies, etc.) and variables that are assumed to remain constant (preassigned parameters) during the design. The preassigned parameters may include fiber volume ratio, void ratio, transverse and shear fiber properties, in situ matrix properties, empirical or correlation factors, structure size and design loads. Once the optimum design for a given structural component has been obtained, the effects of the various preassigned design parameters on the optimum design are determined using sensitivity analyses. Each parameter is perturbed about its preassigned value and the structural component is re-optimized. Any changes in the optimum design are a direct measure of the effects of the parameter being perturbed. This provides a formal approach to quantitatively assess the effects of the numerous parameters mentioned previously on the optimum design of a structural component and to identify which of the parameters studied have significant effects on the optimum design of the structural component of interest. The sensitivity analysis results to be described subsequendy were obtained using the angle plied composite panel and loading conditions as shown in Fig. 4.49. Sensitivity analyses are carried out to answer, for example, the following questions: 1. What is the influence of the preassigned filament elastic properties on the composite optimum design? Figure 4 49 Schematic of composite panel used in structural synthesis Figure 4 49 Schematic of composite panel used in structural synthesis HMOS ft ft. ft HMOS ft ft. ft 2. What is the influence of the various empirical factors/correlation coefficients on the composite optimum design? 3. Which of the preassigned parameters should be treated with care or as design variables for the multilayered-filamentary composite? 4. What is the influence of applied load perturbations on the composite optimum design? The load system for the standard case consisted of three distinct load conditions as specified in Fig. 4.49. The panel used is 20 in. x 16 in. made from an [(+6)n]s. angle plied laminate. The influence of the various preassigned parameters and the applied loads on optimum designs is assessed by sensitivity analyses. The sensitivity analyses consist of perturbing the preassigned parameters individually by some fixed percentage of that value which was used in a reference (standard) case. The results obtained were compared to the standard case for comparison and assessment of their effects. Introductory approaches have been described to formally evaluate design concepts for select structural components made from composites including intraply hybrid composites and strip hybrids. These approaches consist of structural analysis methods coupled with composite micro-mechanics, finite element analysis in conjunction with composite mechanics, and sensitivity analyses using structural optimization. Specific cases described include: 1. Hybridizing ratio effects on the structural response (displacement, buckling, periodic excitation and impact) of a simply supported beam made from intraply hybrid composite. 2. Strip modulus effects on the structural response of a panel made Graphite fiber RP automobile (Courtesy of Ford Co.) Graphite fiber RP automobile (Courtesy of Ford Co.) from strip hybrid composite and stibjected to stadc and dynamic loading conditions. 3. Variotis constituent material properties, fabrication processes and loading conditions effects on the optimum design of a panel subject to three different sets of biaxial in-plane loading condidons. |

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