R. E. Rowlands

Stress and failure analysis of a glass-epoxy composite plate with a circular hole

Experimental and finite-element analyses are presented for the anisotropic states of stress, strain and fracture of a glass-epoxy plate containing a circular hole and subjected to uniaxial tension. Strains were experimentally measured using foil gages, moiré and birefringent coating. Stresses are computed in the linear range from the measured strains. While the hole reduces the plate strength by a factor of two, the maximum tensile strain at fracture is greater than the ultimate strain in a plate without a hole. Fracture consists of crack initiation at the hole boundary but off the horizontal axis. Away from the hole, failure is accompanied by considerable delamination. Discontinuous crack propagation is present.

Higher-order numerical differentiation of experimental information

Cubic-spline and discrete-quadratic polynomial techniques are presented for reliably computing up to third-order derivatives of experimental information. The concept is demonstrated by stress analyzing from measured displacements a transversely loaded plate and a beam under four-point bending. The respective displacement fields were recorded using holography and moiré. The accuracy of the employed numerical-differentiation techniques is indicated.

Strain analysis of composites by moiré methods: Procedures and results using conventional and fringe-multiplication techniques are described and illustrated

Moiré techniques were developed, adapted and applied to the determination of strain fields in filamentary composite laminates. Conventional techniques, using 1000 line-per-inch (Ipi) arrays bonded or photoprinted onto the specimen, were applied to glass-epoxy and boron-epoxy specimens with holes and cracks. Techniques for tenfold fringe multiplication were also applied to glass-epoxy and boron-epoxy laminates with holes. A reflective surface of glass-like smoothness was produced on the specimen and a 500 dot-per-inch grid photoprinted on it. A rigid distortion-free camera was used for recording replicas of the specimen grid by projection photography. These replicas were analyzed with a 200 line-per-millimeter (5080 Ipi) grating for reconstruction of moiré-fringe patterns. These patterns were analyzed by graphical and mechanical differentiation using second-order moiré. Strain distributions and strain-concentration factors were in very good agreement with theoretical and other experimental results.

WAVE MOTION IN ANISOTROPIC MEDIA BY DYNAMIC PHOTOMECHANICS.

Photomechanical techniques are developed for studying wave propagation in anisotropic media such as fiber-reinforced composites and rocks. Moiré fringes in transparent and opaque materials, and isochromatic fringes in transparent composites, are photographed at rates up to over one-million frames/second. A Beckman and Whitley 189 framing camera is utilized with illumination provided by argon flashbombs or a special electronic flash.

Stress Analysis of Anisotropic Laminated Plates

Membrane and interlaminar stresses in statically loaded and vibrating composite structures are obtained by determining optically and numerically the respective partial derivatives of the holographically recorded transverse displacement field. A clamped, circular, orthotropic boron-epoxy plate under a uniformly applied static pressure and vibration are considered separately. Under uniform static pressure, yr0 = 0, while the anisotropy of the laminated composite results in ir9 ^ 0, which is unlike the corresponding isotropic case. The vibrating plate has complicated, unsymmetrical displacements producing both in-plane shearing strains and stresses. The higher order derivatives are obtained optically by holographic-moire and numerically by employing cubic-spline and discretequadratic differentiate functions.

Deformation and Failure of Boron-Epoxy Plate with Circular Hole

The behavior under uniaxial tension of a boron-epoxy composite plate with a circular hole was studied by means of experimental stress analysis and finite-element methods. The specimens were 10 by 26 in boron-epoxy panels of [0/′45/0/90] s layup. They were instrumented with strain gages, photoelastic coatings, and moire grids. The latter were analyzed using moire fringe multiplication techniques. Strain distributions as a function of applied nominal stress were obtained along the axes of symmetry and around the boundary of the hole. Youngs modulus and Poissons ratio were computed from the far-field strains. Tensile and compressive strain concentrations were computed for the linear range of strain response. Experimental results were compared with those obtained by homogeneous anisotropic elasticity and by finite-element analysis. The mode of failure was a combination of interlaminar shearing and tensile cracking starting at the hole boundary off the horizontal axis, at a point where the elastic shear stress and strain reach their maximum and where the tangential normal and shear strains increase rapidly and nonlinearly with load. The average applied stress at failure was 42 200 psi compared with a coupon strength of 94 000 psi. The average ultimate tensile strain at the hole boundary on the horizontal axis was 8 X 10 - 3 in./in. compared with a coupon ultimate strain of 6.8 X 10 - 3 in./in. At higher loads the peak of the tensile strain shifted, resulting in a higher ultimate strain away from the boundary.

Determination of Strain Concentration in Composites by Moiré Techniques

composites. They include strain gages, photoelasticity, holography and moire. Surface strain gages are primarily used to obtain moduli, Poisson’s ratios and average stress-strain response to failure. A refinement of this method was developed recently whereby gages are embedded between the plies of a boron-epoxy composite. Photoelastic methods applicable to composites include two-dimensional anisotropic photoelasticity, birefringent coatings, and twoand three-dimensional model studies. Holographic methods are primarily suited for measuring out-ofplane deformations. One of the methods that have great potential for the macroscopic strain analysis of composites is the moire method and one of its most important applications is the determination of strain distributions and strain concentrations around holes. Two analytical approaches have been used to determine stress distributions around a hole in a composite plate. One is the classical anisotropic elasticity theory discussed by Lekhnitskii [1] and Savin [2]. This theory deals with a thin, infinite and homogeneous plate. The other approach is the finite element method which

Geometric and Loading Effects on Strength of Composite Plates with Cutouts

Stress concentration and strength of uniaxially loaded composite plates containing central circular, elliptical, and square holes are presented. Both smooth and rough holes are considered, as are the effects of relative plate width and thickness. The plates are subjected to static, cyclic, and controlled strain-rate loading. Fracture strength associated with rough holes is slightly lower than with smooth holes, while broad variations in loading history have minimal influence on strength. The tensile stress concentration factor increases and strength decreases as the hole-diameter to plate-width ratio increases. Strength decreases with decreasing ratio of laminate thickness to hole diameter.

A multiple-pulse ruby-laser system for dynamic photomechanics: Applications to transmitted- and scattered-light photoelasticity: Paper describes a new ultrahigh-speed multiple-frame recording system in which a ruby laser is sequentially modulated and the light pulses are synchronized with the camera and event

An ultrahigh-speed multiple-frame recording system for two- and three-dimensional dynamic photomechanics has been developed and is described here. The output from a ruby laser is modulated with a Pockels cell to produce a train of short, intense, monochromatic and polarized light pulses. Pulse widths of 50 nsec and repetition rates of up to 170,000 pulses/sec are obtained. These light pulses are synchronized with a “smear camera” and the event to produce a multiple-frame record of the phenomenon. The simplified camera requirements necessary for this purpose are indicated. The system is demonstrated by recording two-dimensional dynamic and scattered-light isochromatic fringe patterns. The capability of multiple recording of scattered-light fringe patterns, achieved here for the first time, has a tremendous potential for three-dimensional dynamic stress analysis. The developed system is also well suited for dynamic moiré, interferometry and holography.

EFFECTS OF MATERIAL AND STACKING SEQUENCE ON BEHAVIOR OF COMPOSITE PLATES WITH HOLES.

Strain distributions to failure, tensile and compressive strain-concentration factors, and strength-reduction factors were determined for glass-, boron-, and graphite-epoxy plates with holes loaded in tension. Strain gages, photoelastic coatings and moiré techniques were used. Ten variations of layup and stacking sequence were studied.The boron-epoxy composite was found to be the stiffest and strongest of the three. The graphite laminate with the highest stress concentration and the most linear strain response exhibited the highest strength-reduction factor. In all cases, the maximum strain at failure on the hole boundary was higher than the ultimate tensile-coupon strain.In general, it was found that, the higher the stress-concentration factor, the higher the strength-reduction factor. Thus, the [0/90/0/90]s layup with a stress-concentration factor of 4.82 had a strength-reduction factor of 3.18. At the other extreme, the most flexible layup [±45/±45]s with the lowest stress-concentration factor of 2.06 had the lowest strength-reduction factor of 1.10.Stacking sequences associated with the tensile interlaminar normal stress or high interlaminar shear stress near the boundary, resulted in laminates 10 to 20 percent weaker than corresponding alternate stacking sequences. Furthermore, it was found that stacking-sequence variations can alter the mode of failure from catastrophic to noncatastrophic.