The Effect of Transverse Shear in Symmetric and Asymmetric End Notch Flexure Tests–Analytical and Numerical Modeling

This paper focuses on the effects of transverse shear and root rotations in both symmetric and asymmetrical end-notched flexure (AENF) interlaminar fracture toughness tests. A theoretical model is developed, whereas the test specimen is subdivided into four regions joined by a rigid interface. The differential equations for the deflection and rotations of each region are solved within both the Euler–Bernoulli simple beam theory (SBT) and the more refined Timoshenko beam theory (TBT). A concise analytical equation is derived for the AENF deflection profile, compliance, and transverse shearing forces as a function of the specimen geometry, stacking sequence, delamination length, and fixture span. Modeling results are compared with numerical finite element analyses, obtaining a very good agreement. Performed analyses suggest that even in the case of symmetrical and unidirectional laminates considered as pure mode II fracture, a complex compression/tension and bending moment state is present, as well as a slight contribution of anti-planar shear at the vicinity of the crack tip.

Experimental Study on Crushing Resistance of Square CFRP Frusta under Axial Loading

Fibre-reinforced composite materials and structures have been extensively used as energy dissipating components in industries. The crashworthiness of square and circular CFRP (Carbon Fiber Reinforced Plastics) tubes have been widely studied. This paper investigates the deformation and energy absorption of square CFRP frusta under axial quasi-static crushing. The effects of various geometry parameters such as height-to-mean width (H/B) and thickness-to-mean width (t/B) ratios on the crushing resistance for square CFRP frusta with an apical angle of 10 ° have been examined experimentally. Finally the crashworthiness metrics of square CFRP frusta and square tube are compared and evaluated. The results show that the experimentally observed deformation mode of CFRP square frusta can be classified into three types, namely progressive folding collapse; splaying crushing mode characterized by a combination of progressive splaying and transverse shearing failure; and transition mode respectively. The initial peak force, mean crushing force and energy absorption of square CFRP frusta deformed in splaying mode increase with the increasing of wall thickness and width. For the desirable progressive splaying mode, three energy dissipated mechanisms have been identified as crack propagation, transverse shearing and friction energy.

Three-dimensional solutions for free vibration of variable stiffness laminated sandwich plates with curvilinear fibers

This paper is concerned with the free vibration of variable stiffness laminated sandwich plates with curvilinear fibers. The three-dimensional elasticity theory and the p-version of the finite element method are adopted for the analysis. The skin is composed of one or more plies with curvilinear fibers. The fiber path orientation angle in a ply is assumed to vary linearly with the x coordinate. The plies may be stacked symmetrically or anti-symmetrically with respect to the middle surface of the plate. Each layer is modeled as one brick p-element. The principle of virtual displacements is used to derive the element stiffness and mass matrices. The generalized displacements at vertices, edges, and faces shared by elements are matched to ensure inter-element compatibility. Since no solutions are available for the free vibration of such variable stiffness laminated sandwich plates, the validity, convergence, and accuracy of the present three-dimensional method are established by comparing with existing three-dimensional frequencies for constant stiffness laminated sandwich plates with rectilinear fibers. The study reveals that inter-layer modal bending stresses are discontinuous; modal transverse shearing stresses are constant in the core; the sign of modal transverse shearing stresses can change through the thickness of the skin; and the shape of modal cross-sectional warping is influenced by the mode number and stacking sequence of plies. Three-dimensional frequencies are presented for different fiber orientation angles, boundary conditions, aspect ratios, thickness ratios, core/skin thickness ratios, and stacking sequences of plies. The accurate results presented here will serve as a benchmark for future investigations.

One-dimensional models of fourth and sixth orders for rods derived from three-dimensional elasticity

The displacement field in rods can be approximated by using a Taylor–Young expansion in transverse dimension of the rod. These involve that the highest-order term of shear is of second order in the transverse dimension of the rod. Then we show that transverse shearing energy is removed by the fourth-order truncation of the potential energy and so we revisit the model presented by Pruchnicki. Then we consider the sixth-order truncation of the potential which includes transverse shearing and transverse normal stress energies. For these two models we show that the potential energies satisfy the stability condition of Legendre–Hadamard which is necessary for the existence of a minimizer and then we give the Euler–Lagrange equations and the natural boundary conditions associated with these potential energies. For the sake of simplicity we consider that the cross-section of the rod has double symmetry axes.

Crush Zone Morphology of Epoxy-Glass Fiber-Aluminium Composite Columnar Tube due to Longitudinal Crushing Force

Epoxy–glass fiber–aluminium composite may be of interest for energy absorption application due to their improved crashworthiness. In the current study, the hybrid–composite columnar tube specimen has been fabricated by a hand lay–up method using epoxy–glass fiber with aluminium columnar tube as a core material. An experimental quasi–static crush test has been performed on the specimen under axial loading. The post–crushing of composite lay–up configuration was observed during and after interaction of the axial loading with the specimen. The result of crush morphology analysis on final mode of failure of the specimen was carried out using SEM and showed combination of several failure modes such as matrix–fiber interfacial fracture, fiber breakage and hackles. However, the main failure mode is brittle type fracture comprising transverse shearing and splaying modes.

Displacement Governing Equations of Moderately Thick Cylindrical Shallow Shells by Transverse Shearing Deformation and the General Solution

Displacement fundamental equations of the moderately thick cylindrical shallow shells concerning five independent variables, i.e. five middle surface displacements are established based on the displacement fundamental equations of the moderately thick shells by transverse shearing deformation and basic hypothesis on shallow shells. Three assistant displacement functions are introduced to solve the equations, which are tenth-order differential equations with variable coefficient; and then five second-order differential equations are converted into a second-order differential equation and two fourth-order transition differential equations using the Cauchy-Riemann condition, afterwards another assistant displacement function is introduced to build its decoupled governing differential equations, finally five displacement components through four assistant displacement functions are obtained.