Free Edge Stresses in Elastic and Viscoelastic Composites Under Uniaxial Extension, Bending, and Twisting Loadings

Time-dependent interlaminar stresses in elastic and viscoelastic laminated composites subjected to arbitrary combinations of axial extension, bending and/or twisting loads are obtained based on integral constitutive relations and Pipes and Pagano’s displacement field for laminates under a generalized plane deformation state. Numerical results obtained from the present formulation are compared against experimental data and excellent agreement within two percent was obtained between these results. Time-dependent interlaminar stresses for cross-ply and angle-ply laminates subjected to uniaxial extension, bending and twisting are also presented. Appreciable stress relaxation occurred during the loading period resulting in decreased magnitudes of residual stresses. It is seen that the rate of interlaminar shear stress relaxation is greater than the normal one, since the relaxation of shear moduli is larger than that of the normal moduli.

Download Full-text

Free-Edge Interlaminar Stresses in Angle-Ply Laminates: A Family of Analytic Solutions

Journal of Applied Mechanics ◽

10.1115/1.4032766 ◽

2016 ◽

Vol 83 (5) ◽

Cited By ~ 3

Author(s):

Johnathan Goodsell ◽

R. Byron Pipes

Keyword(s):

Uniaxial Extension ◽

Free Edge ◽

Analytic Solutions ◽

Thermomechanical Loading ◽

Interlaminar Stresses ◽

The Family ◽

Stress Components ◽

Complete Set ◽

Interlaminar Shear ◽

Angle Ply Laminates

A family of analytic solutions for the prediction of interlaminar stresses in angle-ply laminates has been developed and is presented in a unified form and as a unique set of solutions. The uniqueness of the formulation is demonstrated for the class of thermomechanical states of deformation for which the solutions are valid. These are shown to be limited to the specific cases wherein only two in-plane stress components and one interlaminar stress components are nonzero. Interlaminar shear stress in the angle-ply laminate subjected to thermomechanical loading conditions of uniaxial extension, uniform temperature change, and anticlastic bending is shown to make up the family of solutions in the unified formulation. Further, these are shown to comprise the complete set of the solutions and the conditions which control the limitations of this family of solutions are articulated.

Download Full-text

Simple Solutions of the Free-Edge Stresses in Composite Laminates under Thermal and Mechanical Loads

Journal of Composite Materials ◽

10.1177/002199839402800605 ◽

1994 ◽

Vol 28 (6) ◽

pp. 573-586 ◽

Cited By ~ 11

Author(s):

Wan-Lee Yin

Keyword(s):

Composite Laminates ◽

Constitutive Relations ◽

Free Edge ◽

Normal Derivative ◽

Boundary Region ◽

Material Behavior ◽

Interlaminar Stresses ◽

Inelastic Material ◽

Stress Functions ◽

Temperature Loads

Intense and localized interlaminar stresses generally occur in a narrow boundary region near the free edge of a multilayered anisotropic laminate under mechanical and temperature loads. Quantitative measures of interlaminar action across interfaces may be readily obtained through purely algebraic operations, even if nonlinear and inelastic material behavior becomes significant in the boundary region due to severe strain concentration. These measures are the limiting values of the Lekhnitskii stress functions F and $$ (and of the normal derivative of F) along interfaces and toward the interior region of the laminate. In the present work, they are used as the basis of an exceedingly simple and efficient method of interlaminar stress analysis that is potentially applicable to free-edge problems involving nonlinear thermoelastic constitutive relations. Example solutions are obtained for symmetric, four-layer, cross-ply and angle-ply laminates under a temperature load and two different types of strain loads, and the results are found to be in reasonable agreement with the existing numerical and analytical solutions based on elaborate analysis methods.

Download Full-text

Delamination of Laminates Governed by Free Edge Interlaminar Stresses Using Interface Element

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.385-387.821 ◽

2008 ◽

Vol 385-387 ◽

pp. 821-824 ◽

Cited By ~ 3

Author(s):

Hossein Hosseini-Toudeshky ◽

Meisam Jalalvand ◽

Bijan Mohammadi

Keyword(s):

Free Edge ◽

Constitutive Law ◽

Interface Element ◽

Shear Stresses ◽

Interlaminar Stresses ◽

Finite Element Program ◽

Element Program ◽

Failure Loads ◽

The Difference ◽

Interlaminar Shear

In this paper, interface element with de-cohesive constitutive law is used to predict the delamination progress of laminates in which delamination is the prominent failure mode. For this purpose, a finite element program is developed to perform nonlinear damage analysis. The analyses are carried out based on the interlaminar constitutive law of elastic-plastic-damage proposed before in the literature. Delamination initiation and propagation of several laminates with dominant interlaminar shear stresses at free edges are investigated to find the failure load. It is shown that the difference between the predicted failure loads using the present study and the experimental results are 3.1% to 19.4% for various laminates.

Download Full-text

Multiscale analysis of interlaminar stresses near a free-edge in a [±45/0/90]s laminate

Journal of Composite Materials ◽

10.1177/0021998319883918 ◽

2019 ◽

Vol 54 (13) ◽

pp. 1627-1638

Author(s):

M Keith Ballard ◽

John D Whitcomb

Keyword(s):

Normal Stress ◽

Homogeneous Model ◽

Uniaxial Extension ◽

Local Stress ◽

Multiscale Model ◽

Free Edge ◽

Complex Stress ◽

Computational Effort ◽

Interlaminar Stresses ◽

Local Stress State

A multiscale model for a [±45/0/90]s tape laminate under uniaxial extension was used to investigate the effect of modeling the heterogeneous microstructure near a free-edge. A random fiber arrangement was used for the 0° and 90° plies and homogenized properties for the 45° and −45° plies. The predicted interlaminar normal stress was compared to the prediction using a classical homogeneous model. When fibers and matrix were modeled discretely, the local stress state was shown to be sensitive to the proximity of fibers, which caused a complex stress distribution along the 0–90 ply interface. Next, the effect of reducing the size of region modeled at the microscale was investigated, since this would significantly reduce the computational effort. Reducing the region modeled at the microscale in the direction normal to the 0–90 ply interface to a size that was 25% and 10% of the ply thickness only changed the peak stresses by 3% and 8%, respectively. Reducing the microscale region in the direction normal to the free-edge to be one and two ply thicknesses in size did not have a significant effect on the predicted interlaminar normal stress at points within 75% of a ply thickness of the free-edge.

Download Full-text

Stress Relaxation in Prestressed Composite Laminates

Journal of Applied Mechanics ◽

10.1115/1.1460909 ◽

2002 ◽

Vol 69 (4) ◽

pp. 459-469 ◽

Cited By ~ 3

Author(s):

A. P. Suvorov ◽

G. J. Dvorak

Keyword(s):

Stress Relaxation ◽

Composite Laminates ◽

Constitutive Relations ◽

Tensile Load ◽

Free Edge ◽

Laminated Plates ◽

Curing Temperature ◽

Field Analysis ◽

Viscoelastic Deformation ◽

Transformation Field Analysis

Viscoelastic deformation caused in symmetric laminated plates by release of fiber prestress and by uniform thermomechanical loads is analyzed on the constituent, ply and overall laminate scales with the Transformation Field Analysis (TFA) method (G. J. Dvorak, Proc. R. Soc. Lond., 1992, A437, pp. 311–327). Fiber prestress is applied in individual plies prior to matrix cure and released after matrix consolidation. Linear or nonlinear viscoelastic constitutive relations are used to evaluate the inelastic deformation rates in terms of current constituent stress averages. The TFA method regards both thermal and inelastic strains as piecewise uniform eigenstrains acting in superposition with mechanical loads and fiber prestress release on an elastic laminate. Interactions between the eigenstrains at the three different size scales are described by certain influence functions derived from micromechanical analysis of the plies and laminates. Applications describe stress relaxation in two carbon/epoxy laminates after cooling from the curing temperature and release of optimized fiber prestress, that allows maximum tensile load application while keeping both interior and free-edge stresses within prescribed strength limits. Subsequent viscoelastic deformation under constant rate loading, and stress relaxation caused by a sustained application of an elevated temperature to a laminate without prestress are also analyzed. Results are presented in the form of initial failure maps that identify overall stress states which may or may not initiate a specific damage mode in the laminate.

Download Full-text

Time-Dependent Response of a Recycled C&D Material-Geotextile Interface under Direct Shear Mode

Materials ◽

10.3390/ma14113070 ◽

2021 ◽

Vol 14 (11) ◽

pp. 3070

Author(s):

Fernanda Bessa Ferreira ◽

Paulo M. Pereira ◽

Castorina Silva Vieira ◽

Maria de Lurdes Lopes

Keyword(s):

Shear Stress ◽

Stress Relaxation ◽

Shear Displacement ◽

Time Dependent ◽

Shear Behaviour ◽

Displacement Rate ◽

Shear Mode ◽

Direct Shear ◽

Constant Displacement ◽

Shear Box

Geosynthetic-reinforced soil structures have been used extensively in recent decades due to their significant advantages over more conventional earth retaining structures, including the cost-effectiveness, reduced construction time, and possibility of using locally-available lower quality soils and/or waste materials, such as recycled construction and demolition (C&D) wastes. The time-dependent shear behaviour at the interfaces between the geosynthetic and the backfill is an important factor affecting the overall long-term performance of such structures, and thereby should be properly understood. In this study, an innovative multistage direct shear test procedure is introduced to characterise the time-dependent response of the interface between a high-strength geotextile and a recycled C&D material. After a prescribed shear displacement is reached, the shear box is kept stationary for a specific period of time, after which the test proceeds again, at a constant displacement rate, until the peak and large-displacement shear strengths are mobilised. The shear stress-shear displacement curves from the proposed multistage tests exhibited a progressive decrease in shear stress with time (stress relaxation) during the period in which the shear box was restrained from any movement, which was more pronounced under lower normal stress values. Regardless of the prior interface shear displacement and duration of the stress relaxation stage, the peak and residual shear strength parameters of the C&D material-geotextile interface remained similar to those obtained from the conventional (benchmark) tests carried out under constant displacement rate.

Download Full-text

Reduction of Free-Edge Stress Concentration

Journal of Applied Mechanics ◽

10.1115/1.3169149 ◽

1985 ◽

Vol 52 (4) ◽

pp. 801-805 ◽

Cited By ~ 15

Author(s):

P. R. Heyliger ◽

J. N. Reddy

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Finite Element Model ◽

Three Dimensional ◽

Element Model ◽

Free Edge ◽

Shear Stresses ◽

Normal Stresses ◽

Interlaminar Shear ◽

Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

Download Full-text