Chihdar Yang

Elastic-plastic model of adhesive-bonded single-lap composite joints

An analytical model for determining adhesive stress distributions within the adhesive-bonded single-lap composite joints was developed. ASTM D3165 ‘‘Strength Properties of Adhesives in Shear by Tension Loading of Single-Lap-Joint Laminated Assemblies’’ test specimen geometry was followed in the model derivation. In the model derivation, the composite adherends were assumed linear elastic while the adhesive was assumed elastic-perfectly plastic following von Mises yield criterion. Laminated Anisotropic Plate Theory was applied in the derivation of the governing equations of the bonded laminates. The adhesive was assumed to be very thin and the adhesive stresses are assumed constant through the bondline thickness. The entire coupled system of equations was determined through the kinematics relations and force equilibrium of the adhesive and the adherends. The overall system of governing equations was solved analytically with appropriate boundary conditions. Computer software Maple V was used as the solution tool. The developed stress model was verified with finite element analysis using ABAQUS by comparing the adhesive stress distributions.

Low-Velocity Impact and Damage Process of Composite Laminates

Several important issues regarding damage simulation of composite laminates due to low velocity impact were investigated including contact law, damage initiation and the corresponding change of stiffness, and damping. Continuum damage mechanics was applied to account for the change of mechanical properties of damaged materials. The Hertzian contact law was modified in order to accommodate the serious damage in the plate. A semi-empirical delamination damage criterion was introduced. A finite element program was written in FORTRAN using twenty-noded solid elements with layered structure to analyze the transient dynamic response of composite laminates. In the simulation computations, variable material damping coefficients were applied to the elements according to damage in order to stabilize the computation. Damage in the forms of matrix cracking, delamination, and fiber breakage were included and analyzed. Results including the force history and delamination areas were found to correlate well with the experiments.

Design and Analysis of Composite Pipe Joints under Tensile Loading

Composite pipe has been used in transporting corrosive fluid in many chemical processes in the petrochemical and pulp and paper industries. More recently, composite pipe has further gained its importance in the offshore oil and gas industry due to its light-weight, corrosion resistance, and the new invention of Tension Leg Platforms (TLPs) for deep-water oil and gas exploration and production. Despite the fact that it has been estimated that there is one joint for every four feet of composite pipe installed for marine applications, the joints are the weakest link in a composite piping system. In order to understand the mechanical behavior and to provide analytical design tools for composite pipe joints, an analytical model was developed based on the first-order laminated anisotropic plate theory. In this developed model, a three-component joint system consisted of coupling, adhesive, and pipe was used to model different types of composite pipe joints such as adhesive-bonded socket joints, butt-and-strap joints, and heat-activated coupling joints. Results obtained from the developed model including adhesive peel stress and shear stress distributions were compared with finite element models. Good correlations were found. With this developed model, the influence of joint length and coupling design on the joint performance was determined.

Stress Model of Composite Pipe Joints under Bending

Recently, composite pipe is becomingpopular in the offshore oil and gas industry due to the new “floating” designs of various platforms which have made deepwater oil and gas exploration and production more economical and affordable. The limited space in platforms emphasizes the needs for composite pipe joints in order to accommodate turns and bends. It has been estimated that there is one joint for every 4 ft of composite pipe installed for marine applications. The joints are the weakest link in a composite pipingsystem. Bending, one of the most common loads in a pipingsystem, was applied to the joint system and analyzed. An analytical model was developed usingthe first-order laminated anisotropic plate theory. Due to the asymmetric nature of the bendingload about the pipe central axis, a twodimensional model is necessary to simulate the system response. In this developed model, a three-component joint system consistingof coupling, adhesive, and pipe was used to model different types of composite pipe joints such as adhesive-bonded socket joints, butt-and-strap joints, and heat-activated couplingjoints. Good correlation was found between results from the developed model and finite element model including adhesive peel stress and shear stress distributions. This investigation has shown the effectiveness of the first-order laminated plate theory in modelingtwo-dimensional tubular geometries, includingthe surface displacements which are important in determiningthe adhesive peel and shear stresses in this study.

A Semi-analytical Method for Determining the Strain Energy Release Rate of Cracks in Adhesively-bonded Single-lap Composite Joints

A semi-analytical method for determining the strain energy release rates due to a prescribed crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rates of the crack are determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUSTM. The results determined using the analytical method correlated well with the results from the finite element analyses.

Stress and Failure Analyses of Adhesive-Bonded Composite Joints Using ASTM D3165 Specimens

An analytical model was developed to determine the stress and strain distributions of single-lap adhesive-bonded composite joints under tension. Both the adherend and the adhesive were assumed linear elastic in the derivations. The Laminated Plate Theory was used in defining the mechanical behavior of the composite adherends, whereas the linear elasticity theory was applied to describe the material response of the adhesive. By doing so, the stresses in the adhesive can vary through the bondline thickness. After the overall system of governing equations was determined by energy method, it was solved by using a symbolic solver—Maple with appropriate boundary conditions. Results from the analytical model were verified with finite element analysis using commercial software ABAQUS. Single-lap composite joint experiments were conducted following ASTM D3165, Strength Properties of Adhesives in Shear by Tension Loading of Single-Lap-Joint Laminated Assemblies. Although all three failure modes of bonded joints, substrate, cohesive, and adhesive failure, were present as the experimental results, the substrate failure mode was the major failure mode observed. Therefore, only substrate failure mode was analyzed using the developed model in the present paper. Four failure criteria, Tsai-Hill failure criterion, von Mises failure criterion, maximum interlaminar tensile stress criterion, and maximum normal stress criterion, were used to correlate the stresses and failure load. Nonlinear regression was conducted to determine the necessary parameters in the failure criteria. Based on the experimental results, thicker bondlines result in weaker joints. The variation of failure load for joints with various bondline thicknesses was consistent with the predicted results.

Evaluation and Adjustments for ASTM D 5656 Standard Test Method for Thick-Adherend Metal Lap-Shear Joints for Determination of the Stress-Strain Behavior of Adhesives in Shear by Tension Loading

Adhesive-bonded joints have been used widely for composite materials as a necessary alternative to conventional mechanical joint designs. In a bonded joint, the load is transferred from one substrate to the other mainly through adhesive shear stress. One of the greatest drawbacks to predicting the mechanical behavior of bonded joints has been the lack of reliable data on the mechanical properties of adhesives. Among many test methods that have been developed to test structural adhesives in thin film geometries, the ASTM D 5656 “thick-adherend lap shear test” is used frequently to determine the shear properties of adhesives while the samples are loaded in tension. Due to the nonuniformity of adhesive shear stress distribution within the joint, through both the bondedline thickness and overlap length, and the measurement method described in the test method, some errors will be introduced if corrections are not made. A finite element analysis was conducted in order to provide a clear picture of the mechanical behavior of the ASTM D 5656 specimen under loading. Based on the results from finite element analysis, the sources of error were analyzed and three correction factors were introduced to recover the adhesive shear modulus of the specimen. Suggestions of mounting the KGR-1 measurement device are also given in order to avoid some of the errors. Because results from linear finite element analysis were used, only adhesive shear modulus within the linear range is discussed in this article.

STRAIN ENERGY RELEASE RATE ANALYSIS OF ADHESIVE-BONDED COMPOSITE JOINTS WITH A PRESCRIBED INTERLAMINAR CRACK

Thesis [M.S] - Wichita State University, College of Engineering, Dept. of Aerospace Engineering

Stress model and strain energy release rate of a prescribed crack in scarf joint/repair of composite panels

An analytical model for stress distribution was derived and an analytical model for determining the strain energy release rate of a prescribed crack in a scarf joint or a bonded scarf repair of a composite panel was developed. The crack closure method was used to calculate the strain energy release rate at the crack tip after a prescribed crack was inserted at high adhesive stress locations. In the stress model, the first-order laminated plate theory was applied to the composite panels, including the following: (1) scarfed parent substrate and corresponding repair panel for a bonded scarf repair or (2) both adherend panels for a scarf joint, assuming a linear elastic adhesive. The bondline was presumed to be thin, so the adhesive stresses were presumed to be uniform through the thickness. The coupled second-order differential equations obtained via kinematics and force equilibrium were solved semi-numerically using the symbolic computational tool Maple. Finite element analyses using the commercial software ABAQUS™ were conducted for comparison purposes, and results correlated well with the developed analytical model. Experimental strain data of the bonded scarf repairs was also used to verify the developed model. It can be seen that the highest adhesive stresses occur at locations where high-stiffness plies are discontinued. The obtained strain energy release rate can be used for failure analysis if appropriate critical energy release rates in conjunction with proper mode mixture rule are used.

Adhesive-Bonded Composite Joint Analysis with Delaminated Surface Ply Using Strain-Energy Release Rate

This paper presents an analytical model to determine the strain energy release rate due to an interlaminar crack of the surface ply in adhesively bonded composite joints subjected to axial tension. Single-lap shear-joint standard test specimen geometry with thick bondline is followed for model development. The field equations are formulated by using the first-order shear-deformation theory in laminated plates together with kinematics relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. The system of second-order differential equations is solved to using the symbolic computation tool Maple 9.52 to provide displacements fields. The equivalent forces at the tip of the prescribed interlaminar crack are obtained based on interlaminar stress distributions. The strain energy release rate of the crack is then determined by using the crack closure method. Finite element analyses using the J integral as well as the crack closure method are performed to verify the developed analytical model. It has been shown that the results using the analytical method correlate well with the results from the finite element analyses. An attempt is made to predict the failure loads of the joints based on limited test data from the literature. The effectiveness of the inclusion of bondline thickness is justified when compared with the results obtained from the previous model in which a thin bondline and uniform adhesive stresses through the bondline thickness are assumed.