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NASA NTRS1983

Elasticity solutions for a class of composite laminate problems with stress singularities

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Wang, S. S.↗

NASA NTRS1986

Fracture of thick laminated composites

The fracture of thick laminated graphite/epoxy composites has been the subject of an extensive research program. The program was divided into three major areas of investigation which included laminate thickness, laminate stacking sequence, and part-through surface flaws. The results from this program are reviewed with emphasis placed on their applicability to the design of thick laminated composite structures.

Harris, C. E.↗

NASA NTRS1985

Three-dimensional hybrid-stress finite element analysis of composite laminates with cracks and cutouts

A three-dimensional hybrid-stress finite element analysis of composite laminates containing cutouts and cracks is presented. Fully three-dimensional, hexahedral isoparametric elements of the hybrid-stress model are formulated on the basis of the Hellinger-Reissner variational principle. Traction-free edges, cutouts, and crack surfaces are modeled by imposition of exact traction boundary conditions along element surfaces. Special boundary and surface elements are constructed by introducing proper constraints on assumed stress functions. The Lagrangian multiplier technique is used to enforce ply-interface continuity conditions in hybrid bimaterial composite elements for modeling the interface region in a composite laminate. Two examples are given to illustrate the capability of the present method of approach: (1) the well-known delamination problem in an angle-ply laminate, and (2) the important problem of a composite laminate containing a circular hole. Results are presented in detail for each case. Implications of interlaminar and intralaminar crack initiation, growth and fracture in composites containing cracks and cutouts are discussed.

Wang, S. S.↗

NASA NTRS1986

A simple rectangular element for two-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two-dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.

Whitcomb, J. D.↗

NASA NTRS1980

Sound transmission into a laminated composite cylindrical shell

In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the transmission of an oblique plane sound wave into a laminated composite circular cylindrical shell. Numerical results are obtained for geometry typical of a narrow-bodied jet transport. Results indicate that from the viewpoint of noise attenuation on laminated composite shell does not appear to offer any significant advantage over an aluminum shell. However, the transmission loss of a laminated composite shell is sensitive to the orientation of the fibers and this suggests the possibility of using a laminated composite shell to tailor the noise attenuation characteristics to meet a specific need.

Koval, L. R.↗

NASA NTRS1975

Analytical displacements and vibrations of cantilevered unsymmetric fiber composite laminates

A fiber composite flat cantilever plate that has symmetric and nonsymmetric laminate configurations is theoretically investigated to determine its static and dynamic structural response. The finite element analysis method used includes a unique triangular finite element developed at Lewis for the analysis of fiber composite airfoils. The various responses investigated include tip displacements, natural frequencies, and fundamental mode shapes. The results show that laminate configurations may be selected for a cantilever such that when the tip at the leading edge is loaded normal to the plane of the plate, the tip at the trailing edge can (1) deflect in the opposite direction, (2) deflect about the same, or (3) deflect more than the tip at the leading edge. This variation in response can be utilized to provide built-in structural damping to resist flutter.

Minich, M. D.↗

NASA NTRS1993

Probabilistic simulation of stress concentration in composite laminates

A computational methodology is described to probabilistically simulate the stress concentration factors in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The probabilistic composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties while probabilistic finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate stress concentration factors such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using it to simulate the stress concentration factors in composite laminates made from three different composite systems. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the stress concentration factors are influenced by local stiffness variables, by load eccentricities and by initial stress fields.

Chamis, C. C.↗

NASA NTRS1997

A Higher-Order Bending Theory for Laminated Composite and Sandwich Beams

A higher-order bending theory is derived for laminated composite and sandwich beams. This is accomplished by assuming a special form for the axial and transverse displacement expansions. An independent expansion is also assumed for the transverse normal stress. Appropriate shear correction factors based on energy considerations are used to adjust the shear stiffness. A set of transverse normal correction factors is introduced, leading to significant improvements in the transverse normal strain and stress for laminated composite and sandwich beams. A closed-form solution to the cylindrical elasticity solutions for a wide range of beam aspect ratios and commonly used material systems. Accurate shear stresses for a wide range of laminates, including the challenging unsymmetric composite and sandwich laminates, are obtained using an original corrected integration scheme. For application of the theory to a wider range of problems, guidelines for finite element approximations are presented.

Cook, Geoffrey M.↗

NASA NTRS1992

Exact solutions for laminated composite cylindrical shells in cylindrical bending

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Yuan, F. G.↗

NASA NTRS1982

Fracture and crack growth in orthotropic laminates. Part 2: Experimental determination of internal damage growth in unidirectional boron/aluminum composite laminates

The fracture behavior of unidirectional boron/aluminum composite laminates is investigated in order to verify the results of mathematical models. These models predict the stresses and displacements of fibers and the amount of damage growth in a center-notched lamina as a function of the applied remote stress and the matrix and fiber material properties. The damage may take the form of longitudinal yielding and splitting in the matrix as well as stable transverse damage consisting of broken fibers and matrix yielding ahead of the notch. A brittle lacquer coating is used to detect the yielding in the matrix while X-ray techniques are used to detemine the number of broken fibers in the laminate. The notched strengths and the amounts of damage found in the experimental specimens agree well with those predicted by the mathematical model.

Goree, J. G.↗

NASA NTRS2012

Microcracking in Composite Laminates: Simulation of Crack-Induced Ultrasound Attenuation

Microcracking in composite laminates is a known precursor to the growth of inter-ply delaminations and larger scale damage. Microcracking can lead to the attenuation of ultrasonic waves due to the crack-induced scattering. 3D elastodynamic finite integration technique (EFIT) has been implemented to explore the scattering of ultrasonic waves due to microcracks in anisotropic composite laminates. X-ray microfocus computed tomography data was directly input into the EFIT simulation for these purposes. The validated anisotropic 3D EFIT code is shown to be a useful tool for exploring the complex multiple-scattering which arises from extensive microcracking.

Leckey, C. A. C.↗

NASA NTRS1990

Plasticity analysis of fibrous composite laminates under thermomechanical loads

Elastic-plastic behavior of fibrous composite laminates is analyzed for coupled in-plane mechanical loads and uniform thermal changes. Constitutive equations of the individual fibrous layers are derived from a vanishing fiber diameter model that represents the essential axial constraint between the phases. This permits derivation of closed form equations for the overall yield condition, stress concentration factors, and instantaneous compliance. Thermoelastic properties of the phases and yield stress of the matrix phase are functions of temperature. The effect of the model assumptions on the predicted behavior of composite laminates is examined by comparing the calculated response under cyclic thermal changes to available theoretical results and experimental measurements.

Bahei-El-din, Yehia A.↗

NASA NTRS1989

A detailed investigation of the micromechanisms of compressive failure in open hole composite laminates

Micromechanisms responsible for compressive failure in open-hole composite laminates were investigated. Specimens containing circular center holes were loaded in compression to failure at a slow rate, and the surface damage development during loading was monitored. Several coupon compression tests were interrupted prior to catastrophic failure to allow for the assessment of fiber shear crippling and/or fiber microbuckling by NDE techniques. From these sectioning studies, the extent and mode of failure were determined, and a three-dimensional schematic of the shear crippling zone was developed. Results show that the majority of the damage in compression-loaded open-hole composite laminates is shear crippled or microbuckled 0-deg fibers; in many cases, however, the shear crippling damage within the 0-deg plies produced shear strains and damage in the adjacent off-axis plies.

Guynn, E. Gail↗

NASA NTRS1990

Composite laminate tailoring with probabilistic constraints and loads

A reliability-based structural synthesis procedure was developed to tailor laminates to meet reliability-based (ply) strength requirements and achieve desirable laminate responses. The main thrust is to demonstrate how to integrate the optimization technique in the composite laminate tailoring process to meet reliability design requirements. The question of reliability arises in fiber composite analysis and design because of the inherent scatter that is observed in the constituent (fiber and matrix) material properties during experimentation. Symmetric and asymmetric composite laminates subject to mechanical loadings are considered as application examples. These application examples illustrate the effectiveness and ease with which reliability considerations can be integrated in the design optimization model for composite laminate tailoring.

Thanedar, P. B.↗

NASA NTRS1990

Composite laminate tailoring with probabilistic constraints and loads

Thanedar, P. B.↗

NASA NTRS1991

A continuum model for damage evolution in laminated composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Lo, D. C.↗

NASA NTRS1989

A review of failure models for ceramic matrix composite laminates under monotonic loads

Ceramic matrix composites offer significant potential for improving the performance of turbine engines. In order to achieve their potential, however, improvements in design methodology are needed. In the past most components using structural ceramic matrix composites were designed by trial and error since the emphasis of feasibility demonstration minimized the development of mathematical models. To understand the key parameters controlling response and the mechanics of failure, the development of structural failure models is required. A review of short term failure models with potential for ceramic matrix composite laminates under monotonic loads is presented. Phenomenological, semi-empirical, shear-lag, fracture mechanics, damage mechanics, and statistical models for the fast fracture analysis of continuous fiber unidirectional ceramic matrix composites under monotonic loads are surveyed.

Tripp, David E.↗

NASA NTRS2002

Micro-Cracking Detection in Laminated Composites

Porosity and fatigue cracking are two critical factors that affect the performance and safety of cryogenic fuel tanks and feedlines made from unlined laminated or weaved carbon/epoxy materials. This paper presents the experiments to induce fatigue cracking of laminated composites through thermal cycling as well as the feasibility of using Thermography and Ultrasound Spectroscopy technology (UT) to detect and measure such micro-cracking. Carbon/epoxy laminated composite panels were built and cut into strips. These specimens were partially submerged in liquid nitrogen while subjected to various loads on a test machine. Edges of some specimens were polished and etched to determine the degree of micro-cracking. The rest of specimens were then examined with Thermography and Ultrasound Spectroscopy NDE systems to investigate the feasibility of finding such micro-cracking in the laminated composites. Thermography is utilized to determine changes in thermal diffusivity. The degree of cracking may reduce the apparent thermal diffusivity and therefore change the thermal response on the surface. Thermography testing was conducted on a group of specimens where it is desired to have some correlation between the predetermined stress and the thermography data. Ultrasound Spectroscopy was used to determine peak changes between the pre-stressed and stressed samples. Data from the inspections were analyzed and the results are presented in this paper.

Chu, Tsuchin↗