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At least 91 records · Page 5

Load redistribution considerations in the fracture of ceramic matrix composites

Using a macroscopic viewpoint, composite laminae are homogeneous orthotropic solids whose directional strengths are random variables. Incorporation of these random variable strengths into failure models, either interactive or noninteractive, allows for the evaluation of the lamina reliability under a given stress state. Using a noninteractive criterion for demonstration purposes, laminate reliabilities are calculated assuming previously established load sharing rules for the redistribution of load as the failure of laminae occur. The matrix cracking predicted by ACK theory is modeled to allow a loss of stiffness in the fiber direction. The subsequent failure in the fiber direction is controlled by a modified bundle theory. Results are compared with previous models which did not permit separate consideration of matrix cracking, as well as to results obtained from experimental data. The effects of variations from the ideal physical geometry which is normally used to depict the matrix cracking are also studied.

Thomas, David J.↗

Characterization of anisotropic mechanical properties of polymer composites from a hybrid additive manufacturing-compression molding process using x-ray computer tomography

In this study, anisotropic stiffness tensors were reconstructed based on fiber orientation distributions obtained from X-ray computer tomography (xCT). A preform was manufactured via a big area additive manufacturing (BAAM) system with carbon fiber (CF) filled acrylonitrile butadiene styrene (ABS). The tailored preform from additive manufacturing (AM) was used in the compression molding (CM) process to produce a low-void high-performance thermoplastic composite panel. An xCT technique was employed to detect the fiber orientations in CF/ABS composites manufactured via three different methods: AM from BAAM, extrusion compression molding (ECM), and AM-CM. The anisotropic stiffness tensor was obtained from the composite panel manufactured via the three manufacturing methods (AM, ECM, and AMCM). A micromechanics theory was used to obtain the orthotropic stiffness tensors of the composite panels and compared with the experimental values. The predicted stiffness tensors of AM and AM-CM composite panels were used to study the deformation characteristics of a steering wheel during airbag deployment by performing finite element analysis (FEA). The approach developed in this study can be utilized for evaluating high-performance composites.

Pokkalla, Deepak↗

Response of composite materials to low velocity impact

Orthotropic and quasiisotropic laminates clamped at the edges were impacted by an instrumented falling weight. Five matrix materials, comprising a baseline epoxy, two toughened thermosets, and amorphous and crystalline thermoplastics were studied. For each material, the projected damage area and residual compression strengths and strains were determined as a function of impact energy. Principal conclusions are: (1) incipient damage associated with a prominent load drop during the impact test seems to be decisive for residual properties; (2) subtle rate effects are present with some materials; and (3) results from the small scale tests parallel those in standard tests and may be adequate for screening purposes.

Srinivasan, K.↗

Response of composite materials to low velocity impact

Orthotropic and quasi-isotropic laminates clamped at the edges were impacted by an instrumented falling weight. Five matrix materials, comprising a baseline epoxy, two toughened thermosets, and amorphous and crystalline thermoplastics were studied. For each material, the projected damage area and residual compression strengths and strains were determined as a function of impact energy. Principal conclusions are: (1) incipient damage associated with a prominent load drop during the impact test seems to be decisive for residual properties; (2) subtle rate effects are present with some materials; and (3) results from the small scale tests parallel those in standard tests and may be adequate for screening purposes.

Srinivasan, K.↗

Verification and Validation of a Three-Dimensional Composite Impact Model with Tabulated Input

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in the commercial transient dynamic finite element code LS-DYNA® has been developed. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure, which allows an arbitrarily shaped failure surface to be defined. A systematic series of validation and verification studies, at a variety of length scales ranging from single element simulations to simulations of a flat panel impact test, have been performed to fully exercise and evaluate the capabilities of the developed model.

Impact↗

Implementation of a Tabulated Failure Model Into a Generalized Composite Material Model Suitable for Use in Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. The aerospace community has identified several key capabilities which are currently lacking in the available material models in commercial transient dynamic finite element codes. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

polymer matrix composites↗

Analysis and Characterization of Damage and Failure Utilizing a Generalized Composite Material Model Suitable for Use in Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in state-of-the art composite impact models is under development. In particular, a next generation composite impact material model, jointly developed by the FAA and NASA, is being implemented into the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage, and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters (such as modulus and strength). The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in the various coordinate directions. Due to the fact that the plasticity and damage models are uncoupled, test procedures and methods to both characterize the damage model and to covert the material stress-strain curves from the true (damaged) stress space to the effective (undamaged) stress space have been developed. A methodology has been developed to input the experimentally determined composite failure surface in a tabulated manner. An analytical approach is then utilized to track how close the current stress state is to the failure surface.

Finite Element Method↗

A simple laminate theory using the orthotropic viscoplasticity theory based on overstress. I - In-plane stress-strain relationships for metal matrix composites

A macromechanics analysis is presented for the in-plane, anisotropic time-dependent behavior of metal matrix laminates. The small deformation, orthotropic viscoplasticity theory based on overstress represents lamina behavior in a modified simple laminate theory. Material functions and constants can be identified in principle from experiments with laminae. Orthotropic invariants can be repositories for tension-compression asymmetry and for linear elasticity in one direction while the other directions behave in a viscoplastic manner. Computer programs are generated and tested for either unidirectional or symmetric laminates under in-plane loading. Correlations with the experimental results on metal matrix composites are presented.

Krempl, Erhard↗

The stress distribution in pin-loaded orthotropic plates

The performance of mechanically fastened composite joints was studied. Specially, a single-bolt connector was modeled as a pin-loaded, infinite plate. The model that was developed used two dimensional, complex variable, elasticity techniques combined with a boundary collocation procedure to produce solutions for the problem. Through iteration, the boundary conditions were satisfied and the stresses in the plate were calculated. Several graphite epoxy laminates were studied. In addition, parameters such as the pin modulus, coefficient of friction, and pin-plate clearance were varied. Conclusions drawn from this study indicate: (1) the material properties (i.e., laminate configuration) of the plate alter the stress state and, for highly orthotropic materials, the contact stress deviates greatly from the cosinusoidal distribution often assumed; (2) friction plays a major role in the distribution of stresses in the plate; (3) reversing the load direction also greatly effects the stress distribution in the plate; (4) clearance (or interference) fits change the contact angle and thus the location of the peak hoop stress; and (5) a rigid pin appears to be a good assumption for typical material systems.

Klang, E. C.↗

Parametric study of stress-intensity factors in bonded composite stringer panels

Stress-intensity factors are determined for an infinite cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media which are representative of many fiber-reinforced composite materials. The complex variable theory of elasticity was used to obtain a set of integral equations describing the problem. The integral equations are replaced by an equivalent sheet of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. From these adhesive stresses, the stress-intensity factors are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer, the stress-intensity factor is approximately that of the unstiffened sheet. However, as the crack propagates beneath the stringer, the stress-intensity factor decreases significantly. Increasing the stringer stiffness or the adhesive stiffness also decreases the stress-intensity factor.

Bigelow, C. A.↗

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗

Nonlinear analysis of AS4/PEEK thermoplastic composite laminate using a one parameter plasticity model

A one-parameter plasticity model was shown to adequately describe the orthotropic plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The nonlinear stress-strain relations were measured and compared with those predicted by the finite element analysis using the one-parameter elastic-plastic constitutive model. The results show that the one-parameter orthotropic plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.

Sun, C. T.↗

Simultaneous elastic and photoelastic calibration of birefringent orthotropic model materials

Transmission photoelastic analysis of composite models has been shown in recent years to be a viable stress analysis method for composite structures. However, difficulties in the fabrication of the model materials require the development of efficient mechanical and optical calibration procedures. In this paper, the methods for measuring elastic and photoelastic constants of composites are briefly reviewed. Then a new method, utilizing a relatively small calibration specimen, is described. In this method, electrical resistance strain gauges are mounted at selected points of a half-plane model and photoelastic measurements and strain readings are simultaneously taken. The data are processed by a least-squares procedure to yield the elastic and photoelastic constants. Comparison of results obtained by the proposed method with the results from conventional tests shows good agreement.

Prabhakaran, R.↗

Stability analysis of bridged cracks in brittle matrix composites

The bridging of matrix cracks by fibers is an important toughening mechanism in fiber reinforced brittle matrix composites. This paper presents the results of a nonlinear finite element analysis of the Mode-I propagation of a bridged matrix crack in a finite size specimen. The composite is modeled as an orthotropic continuum and the bridging due to the fibers is modeled as a distribution of tractions which resist crack opening. A critical stress intensity factor criterion is employed for matrix crack propagation while a critical crack opening condition is used for fiber failure. The structural response of the specimen (load-deflection curves) as well as the stress intensity factor of the propagating crack are calculated for various constituent properties and specimen configurations for both tensile and bending loading. By controlling the length of the bridged crack results are obtained which highlight the transition from stable to unstable behavior of the propagating crack.

Ballarini, Roberto↗

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.↗

Numerical Validation of Composite Panel Impact Tests

Researchers have met the challenge of modeling impact events involving composite targets for a variety of applications in a variety of ways. In this paper, the theory and implementation details of an orthotropic visco-elastic-visco-plastic material model with strain rate dependence are discussed. The model is driven by experimental data from quasi-static as well as high strain rate tests, and the data is used in defining the deformation, damage and failure sub-models. Validation data is generated by shooting a hollow 50 g Al-2024 projectile at different velocities against a flat panel target made of unidirectional composite material in a 16-ply [(0/90/45/-45)_(2)]_(S) layup. Explicit dynamic finite element analyses of four high speed tests involving one contained (projectile rebounded) and three uncontained (projectile penetrated) impact tests show that the developed material model and modeling techniques yield reasonable and acceptable predictions.

Orthotropic Composite↗

Stress concentrations in cylindrically orthotropic plates with radial variation of the compliances

The stresses in a circular composite plate with a central circular hole in which the material is cylindrically orthotropic and the compliances vary with distance from the center are calculated. A numerical example shows that an arrangement of the fibers at predominantly + or - 45 deg to the radii in the neighborhood of the hole reduces the stress concentrations significantly in an otherwise quasi-isotropic plate.

Muser, C.↗

Fracture analysis of notched composites

The problem of part-through cracks emanating from a central notch in a composite laminate is considered. The composite laminate is modeled as an orthotropic plate and along the branches, it is assumed that the stresses are carried by the fibers only. The stresses along the uncracked portions are assumed to be proportional to the crack opening displacement at the point. After formulating the branched crack problem, the model is applied to a(+45 deg)25 composite laminate. The stress concentration factors for the fibers are computed for various values of the spring constant K. Sample results showing the crack opening displacement are also displayed.

Deale, F.↗