Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth

Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems

Buckling of a sublaminate in a quasi-isotropic composite laminate

The buckling of an elliptic delamination embedded near the surface of a thick quasi-isotropic laminate was predicted. The thickness of the delaminated ply group (the sublaminate) was assumed to be small compared to the total laminate thickness. Finite-element and Rayleigh-Ritz methods were used for the analyses. The Rayleigh-Ritz method was found to be simple, inexpensive, and accurate, except for highly anisotropic delaminated regions. Effects of delamination shape and orientation, material anisotropy, and layup on buckling strains were examined. Results show that: (1) the stress state around the delaminated region is biaxial, which may lead to buckling when the laminate is loaded in tension; (2) buckling strains for multi-directional fiber sublaminates generally are bounded by those for the 0 deg and 90 deg unidirectional sublaminates; and (3) the direction of elongation of the sublaminate that has the lowest buckling strain correlates with the delamination growth direction

Strain-energy release rate analysis of a laminate with a postbuckled delamination

The objectives are to present the derivation of the new virtual crack closure technique, evaluate the accuracy of the technique, and finally to present the results of a limited parametric study of laminates with a postbuckled delamination. Although the new virtual crack closure technique is general, only homogeneous, isotropic laminates were analyzed. This was to eliminate the variation of flexural stiffness with orientation, which occurs even for quasi-isotropic laminates. This made it easier to identify the effect of geometrical parameters on G. The new virtual crack closure technique is derived. Then the specimen configurations are described. Next, the stress analyses is discussed. Finally, the virtual crack closure technique is evaluated and then used to calculate the distribution of G along the delamination front of several laminates with a postbuckled delamination

ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies

ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented

Prediction of impact force and duration during low velocity impact on circular composite laminates

Two simple and improved models--energy-balance and spring-mass--were developed to calculate impact force and duration during low velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data

An equation for bolt clampup relaxation in transient environments

An equation for bolt clampup relaxation for transient temperature-moisture (T-M) conditions was derived starting with a relaxation equation for steady-state conditions, and then using an incremental time approach that exploits the superposition principle for linear viscoelasticity. The resulting equation uses the initial T-M condition (at the time of clamping), the T-M history after clamping, and elastic clampup coefficients for temperature and moisture changes. For a given material and joint configuration, the clampup coefficients are constants that can be calculated by elastic analyses. The clampup equation was used to calculate the changes in clampup occurring in a T300/5208 graphite/epoxy joint exposed to a one-year history of temperature and moisture. Two cases were considered: one was a dry joint exposed to a relatively humid environment and the other was a nearly saturated joint exposed to an arid environment

Bolt clampup relaxation in a graphite/epoxy laminate

A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. A viscoelastic finite element analysis of a double-lap joint with a steel bolt was conducted. Clampup forces were calculated for various steady-state temperature-moisture conditions using a 20-year exposure duration. The finite element analysis predicted that clampup forces relax even for the room-temperature-dry condition. The relaxations were 8, 13, 20, and 30 percent for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, higher temperatures and moisture levels each increased the relaxation rate. The combined viscoelastic effects of steady-state temperature and moisture appeared to be additive. From the finite-element analysis, a simple equation was developed for clampup force relaxation. This generalized equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well