Fangsheng Ji

Damage probability in laminated glass subjected to low velocity small missile impacts

The probability of damage at the impact site in the outer glass ply of laminated glass units subjected to low velocity small missile impacts is investigated. A dynamic, non-linear finite element analysis is applied to compute the stress response on impacts. Based on the cumulative damage theory, a damage factor is introduced and related to Weibulls distribution of probability to characterize the probability of damage. In conjunction with the finite element analysis, controlled experiments are conducted to determine the material constants appearing in the damage model and Weibulls distribution of probability. A parametric study involving impact velocity, glass ply thickness and interlayer thickness is presented.

Dynamic strains in architectural laminated glass subjected to low velocity impacts from small projectiles

An experimental validation of a mechanics-based finite element model for architectural laminated glass units subjected to low velocity, two gram projectile impacts is described. The impact situation models a scenario commonly observed during severe windstorms, in which small, hard projectiles, such as roof gravel, impact windows. Controlled experiments were conducted using a calibrated air gun to propel a steel ball against simply supported rectangular laminated glass specimens. Dynamic strains on the inner glass ply were measured using foil strain gages and a high speed data acquisition system. Impact speed, interlayer thickness, glass ply thickness, and glass heat treatment conditions were varied. Dynamic strains predicted by the finite element model were in close agreement with those measured in the laboratory.

DYNAMIC ANALYSIS OF NORMAL IMPACT OF OCCUPANT HEAD ON LAMINATED GLASS

The paper discusses a study that applied a dynamic, nonlinear finite element method to investigate the mechanical behavior of a human head normally impacting on laminated glass plate. The head used is modeled as a solid aluminum sphere covered with a viscoelastic skin; both the aluminum sphere and the viscoelastic are deformable. The study computes the resultant accelerations in the head and maximum principal stresses in laminated glass plates under various impact speeds and laminated glass configurations. Also examined is the effect of impact speed and laminated glass configuration on the maximum resultant head acceleration before the failure of the laminated glass plate.

Saturation of Transverse Cracking with Delamination in Polymer Cross-Ply Composite Laminates

Delamination along the 0°/90° interface following transverse cracking in the 90° plies of a cross-ply composite laminate is analyzed based on the principle of minimum potential energy. The laminate is subjected to longitudinal applied tensile loading and internal residual thermal stresses. The strain energy release rate criterion has been employed to evaluate the critical applied stresses for transverse cracking and interface delamination. The effect of delamination along the 0°/90° interface on laminate stiffness and thermal property is presented for E-glass/epoxy and graphite/epoxy composite laminates. The longitudinal tensile stress in the 90° plies decreases gradually as the transverse crack density increases and thereby decreasing the tendency for transverse crack multiplication. For a given laminate configuration there exists a saturation (limit) crack density. Continued loading beyond this limit, delamination at the 0°/90° interface would occur. The analytical results are compared with the available experimental data.

Failure analysis of laminated architectural glass panels subjected to blast loading

A 3-D nonlinear finite element model is used to predict the probability of failure of laminated architectural glass subjected to blast loading. A uniformly distributed pressure, simulating blast loading generated by a shock wave from the discharge of a bomb, is applied to one of the exposed surfaces of the laminate. In the analysis, the glass ply is modeled as an elastic material while the polymer interlayer is treated as a viscoelastic material. Two-parameter Weibull distribution is adopted to describe the cumulative probability of failure of the unloaded glass ply. A parametric study is presented showing the effect geometric and material properties of the laminate and the blast load parameters. These analytical results can be used in evaluating the blast performance of new laminated architectural glazing systems and in the design of retrofit or upgrade schemes for the existing glazing systems.

Analysis of transverse cracking in cross-ply composite laminates

An analytical model based on the principle of minimum potential energy is developed and applied to determine the two-dimensional thermoelastic stress state in cross-ply composite laminates containing multiple equally spaced transverse cracks in the 90° plies and subjected to tensile loading in the longitudinal direction. The model provides full field solution for displacements and stresses including the residual thermal stresses which in turn are used to calculate the strain energy release rate associated with various failure modes. The strain energy release rate criterion has been employed to evaluate the critical applied stresses for two of the possible fracture modes; self-similar extension of a pre-existing flaw and the formation of a new parallel crack. The computed results indicate that formation of new cracks never takes place until pre-existing cracks extend through the entire thickness of the 90° plies. The predicted results of transverse crack density are in good agreement with the available exp...

Stress analysis of a multilayered composite cylinder with defects

The stress analysis of a multilayered composite cylinder with a local delamination is considered. The cylinder comprises an internal thin-walled metal cylinder wrapped in layers formed by winding a unidirectional fiber bundle round it while simultaneously adding epoxy. A realistic analytical model is proposed and a system of differential-difference equations is developed. The problem is reduced to a system of linear ordinary differential equations with constant coefficients by introducing a transformation of super-subscripts. The normal method of solving this kind of system of differential equations is then adopted. The numerical calculations were conducted for a composite cylinder with a local delamination that initiates at the front of a surface notch. The results indicate that the stress distributions are subjected to disturbance due to the delamination in composite cylinder and the stress concentrations occur near the surface notch or the front of the delamination. Also, all stresses in the composite layers are lower than that in the internal metal cylinder.

Effect of transverse cracking on stiffness reduction of cross-ply laminates

An analytical model based on the principle of minimum potential energy is developed and applied to study the effect of multiple cracks in cross-plies on the stiffness of a laminated composite. The transverse cracks are assumed to span the thickness of the cross-ply group only partially unlike in the previous studies in which they were assumed to span the entire thickness of the cross-ply group. This arrangement facilitates the study of competition between the self-similar extension of an inherent flaw within the cross-plies and the multiple parallel cracking. The numerical results for the axial stiffness as a function of both the crack density and the crack length are presented for three different composite material systems (glass/epoxy, graphite/epoxy and ceramic/ceramic) or which experimental results are available so as to validate the model.

Non-axisymmetric matrix cracking in unidirectional brittle matrix composites

Abstract A model is presented for the analysis of a composite cylinder subjected to an axial tensile load in the fiber direction and containing a non-axisymmetric matrix crack. Considering the non-axisymmetry of the crack within the matrix, a three-dimensional stress analysis based on the consistent shear-lag theory is introduced into the above model. The variational approach founded on the principle of minimum potential energy is applied to the above model to obtain the numerical results for the stress and displacement fields. On the basis of the Irwin-Kies compliance calibration formulation and the strain energy release rate criterion, the fracture analysis of the matrix cracking is carried out. The critical loads for various crack sizes and configurations are presented. Some observations on the role of various model parameters on the matrix cracking are made. It is shown that the crack may grow in two stages; the crack first grows unstably in the radial direction up to the interface, then extends through the entire matrix cross-section around the fiber. It is also found that during the transition from the first to the second stage, the crack growth may be arrested.

Non-axisymmetric matrix cracking and interface debonding in unidirectional brittle matrix composites

Abstract A discrete fiber model is developed in this paper and applied to study the problem of non-axisymmetric matrix cracking and interface debonding in unidirectional brittle-matrix fiber-reinforced composite materials subjected to an axial tensile load in the fiber direction. In this model, it is assumed that the interface debond remains open. Considering the non-axisymmetry of the matrix crack and interface debond, a three-dimensional stress analysis is introduced into the above model. The variational approach based on the principle of minimum potential energy is employed to obtain the numerical results for stress and displacement fields. On the basis of Irwin—Kies compliance calibration formulation, the strain energy release rates associated with the matrix crack and the interface debond are calculated. The competition between these two modes is then assessed by comparing the corresponding toughnesses. It is shown that the magnitude of the toughness of the fiber/matrix interface plays a predominant role on the debond initiation and extension. The stabilities of the debond and the matrix crack extension are investigated.