Large Strain Four-Point Bending of Thin Unidirectional Composites

Abstract

A large deformation four-point bending fixture was used to test thin unidirectional composite laminas primarily used in strain energy deployable space structures. The tests allowed investigation of the large strain elastic constitutive behavior of two aerospace-grade intermediate modulus carbon fibers, a high modulus carbon fiber, and a structural glass fiber. Thermoset plastic coupons reinforced with these fibers and ranging in thickness from 0.1 to 0.5 mm were tested. A nonlinear empirical constitutive model was used to represent fiber axial tensile and compressive behavior and through a structural model, predict coupon flexural response and estimate constitutive model parameters. Intermediate modulus carbon fibers were found to be significantly nonlinear with modulus linearly increasing with strain. At failure, the fiber tangent modulus in tension was 2 to 3.1 times higher than in compression. The modulus of glass fibers was essentially constant. High modulus carbon fibers exhibited a more complex response with flexural stiffness initially slightly increasing followed by a moderate reduction in stiffness and finally, a sharp reduction in stiffness and failure. Nomenclature a = perpendicular distance between bearing axles of a cart, m b = coupon width, m β = initial angle from vertical of the plane defined by the cart bearing axles, rad D = coupon flexural rigidity, Nm ε = fiber or composite strain ε b = bending strain E c = composite tangent modulus in the fiber direction, Pa E f = fiber tangent modulus in the fiber direction, Pa E m = matrix Young's modulus, Pa E cC = composite tangent modulus in the fiber direction in compression, Pa E cT = composite tangent modulus in the fiber direction in tension, Pa E fC = fiber tangent modulus in the fiber direction in compression, Pa E fT = fiber tangent modulus in the fiber direction in tension, Pa ε f C = coupon surface strain at failure on compression side ε f T = coupon surface strain at failure on tension side E f fC = fiber tangent modulus at failure in the fiber direction in compression, Pa E f fT = fiber tangent modulus at failure in the fiber direction in tension, Pa E o = fiber initial tangent modulus at zero strain, Pa E 1 = composite Young's modulus in the fiber direction, Pa E 2 = composite Young's modulus in the transverse direction, Pa F = crosshead load, N γ 1 = fiber first-order nonlinear parameter γ 1C = fiber first-order nonlinear parameter in compression γ 1T = fiber first-order nonlinear parameter in tension h = vertical distance between bearing axles of a cart, m κ x = coupon curvature, 1∕m κ y = coupon transverse curvature, 1∕m κ f x = coupon curvature at failure, 1∕m M x = coupon moment per width, N M f x = coupon moment per width at failure, N M y = coupon transverse moment per width, N N c = composite normal force resultant, N∕m ν 12= composite Poisson's ratio R 2 = coefficient of determination s = coupon gage length, m σ c = composite stress, Pa σ cC = composite stress in compression, Pa σ cT = composite stress in tension, Pa t = coupon thick...

Stiff Composite Cylinders for Extremely Expandable Structures

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Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

“…The solution found in conjunction with experimental research can be used for identifying constitutive models. Various bending tests have already been employed for this purpose [ 2 , 3 , 4 , 5 , 6 , 7 ]. An advantage of the present solution is that it is given in closed form, except simple numerical techniques for calculating the bending moment and solving transcendental equations, for arbitrary function involved in Equation (2).…”

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