Probabilistic analysis of linear elastic cracked structures with uncertain damage

This paper presents a simple and reliable method for the probabilistic characterization of the linear elastic response of cracked structures with uncertain damage. In particular, truss and frame structures with edge cracks of uncertain depth and location are considered. The method of analysis originates from an approach recently appeared in the literature, which is generalized to treat structures with cracks affected by uncertainty. According to this approach, the uncertainties are transformed into superimposed deformations depending on the distribution of internal forces and an iterative procedure is established to solve the resultant equations. The procedure is optimally tuned based on the convergence analysis. Several numerical tests evidence excellent accuracy and convergence qualities also in the case of multicracked structures with large fluctuation of damage.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

An anisotropic linear elastic boundary element formulation for masonry wall analysis

This work presents an application of a Boundary Element Method (BEM) formulation for anisotropic body analysis using isotropic fundamental solution. The anisotropy is considered by expressing a residual elastic tensor as the difference of the anisotropic and isotropic elastic tensors. Internal variables and cell discretization of the domain are considered. Masonry is a composite material consisting of bricks (masonry units), mortar and the bond between them and it is necessary to take account of anisotropy in this type of structure. The paper presents the formulation, the elastic tensor of the anisotropic medium properties and the algebraic procedure. Two examples are shown to validate the formulation and good agreement was obtained when comparing analytical and numerical results. Two further examples in which masonry walls were simulated, are used to demonstrate that the presented formulation shows close agreement between BE numerical results and different Finite Element (FE) models.     

Effect of clamping force on the delamination onset and growth in bolted composite laminates

Clamping force is a key element that alters the mechanism and sequence of failure in bolted joints of composite laminates. The mode of failure in bolted joints can be controlled by geometrical parameters and the preferred fail safe mode of failure is ‘bearing’ which generally consists of matrix cracks, delamination and fibre microbuckling. Three-dimensional (3-D) pinned (without clamping force) and bolted (1 kN clamping force) joint models were developed in [0/90]_s carbon fibre reinforced plastic (CFRP) laminates to show the clamping force effect on the onset and growth of delamination. It is shown that delamination was resulted from the shear stress components (Mode II & III) at the interface and the contribution of the out-of-plane component (Mode I - opening), so the clamping force, was negligible without modelling the in-plane failure modes and their coupling with delamination, which will be considered in future work.     

Post-buckling analysis of non-uniform elastic columns

A numerical method for the second-order analysis of elastic beam-columns is described. For nominated values of axial load and end moments the deformed states and stress distribution can be determined by an automatic iterative procedure. For centrally loaded columns of non-uniform section, the method can be used to predict the critical loads from the grossly deformed equilibrium states above the first critical load. Axial and shear strains may be accounted for as well as flexural strains. Solutions for the shape of the elastica can be obtained for non-uniform columns. The method requires a small digital computer and is demonstrated for several plane, uniform and stepped elastic members. It can be readily extended to deal with transverse and distributed axial loading as well as flexural-torsional behaviour.     

Buckling analysis of pretwisted composite columns

Summary Through the principle of total potential energy the equilibrium equations and related boundary conditions for buckling analysis of pretwisted laminated columns are derived and solved analytically. It is shown that the coupling between bending and stretching actions has a significant effect on the critical loads —the critical loads increase as the coupling term increases. Numerical results for pinned-pinned composite columns with square cross sections are computed and the effects of natural twist and bending-stretching coupling on the buckling loads are investigated.     

An asymptotic general model for linear elastic homogeneous anisotropic rods

This paper covers the mathematical justification and generalization of classical anisotropic rod theories using asymptotic analysis as the area of the cross-section tends to zero in the three-dimensional elasticity model after a rescaling in the unknowns and data, together with convergence results.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

A nonlinear viscoelastic fracture analysis of concrete/FRP delamination in aggressive environments

In this paper, the durability of the bondline between concrete and FRP reinforcement was characterized at various temperature and humidity levels. The linear and nonlinear viscoelastic constitutive behavior of the epoxy bondline was characterized and used for a nonlinear viscoelastic fracture analysis of delamination. A hygrothermal nonlinear viscoelastic pseudo-stress model was developed and calibrated in order to compute a generalized J integral. Driven wedge tests were conducted for examining the fracture behavior of the interface. A finite element analysis was developed for determining the cohesive zone size and the generalized J integral at various temperature and humidity levels. The fracture energy obtained from these parameters greatly depended upon crack growth rate, temperature and humidity.     

Nonlinear viscoelastic analysis of composite plates and shells

A finite element analysis is developed for treating nonlinear viscoelastic response of laminated composites. The analysis uses an eight-node layered shell element. The transient creep compliance in the viscoelastic model is represented as an exponential series plus a steady-flow term. This allows for a simplification of the numerical procedure for handling hereditary effects. Calculations are performed to study the time-dependent redistribution of stress in a flat plate under uniform pressure, a spherical cap under a point load, and a cylindrical shell pinched between two concentrated forces.     

Transient dynamic crack analysis in piecewise homogeneous, anisotropic and linear elastic composites by a spatial symmetric Galerkin-BEM

Transient elastodynamic analysis of two-dimensional, piecewise homogeneous, anisotropic and linear elastic solids containing interior and interface cracks is presented in this paper. To solve the initial boundary value problem, a spatial symmetric time-domain boundary element method is developed. Stationary cracks subjected to impact loading conditions are considered. Elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are implemented. The piecewise homogeneous, anisotropic and linear elastic solids are modeled by the multi-domain technique. The spatial discretization is performed by a symmetric Galerkin-method, while a collocation method is utilized for the temporal discretization. An explicit time-stepping scheme is obtained for computing the unknown boundary data. Numerical examples are presented and discussed to show the effects of the interface cracks, the material anisotropy, the material combination and the dynamic loading on the dynamic stress intensity factors.     

Numerical and experimental analysis of delamination in the T-stiffener integrated composite structure

In this article, two kinds of cohesive zone models (CZMs; exponential and bilinear) are used to evaluate the delamination behaviors of a composite T-stiffener integrated structure. First, based on the analysis of the bilinear CZM using maximum nominal stress damage initiation criterion and power law energy criterion, both the macroscopic mechanical response and the failure process are predicted, which analyzed the influences of the various cohesive zone parameters on the failure load and the damage patterns. Second, both the strength and the fracture characterizations about various T-stiffener integrated composite structures are studied in the experiment, which have a good agreement between the numerical result and the experimental data. Finally, the relationships among the failure load and the thickness of the skin, and the clamp distance are established; also, the energy release rates of the T-stiffeners for the failure process are predicted. These results will play an important role for designing and evaluating the strength and reliability of composite T-stiffener integrated structures.     

Relaxation in elastic and viscoelastic materials

The mechanical compliance and modulus retardation/relaxation functions are examined in terms of a general behaviour which contains more than one process. An analytical approach to the transformation in the anelastic response between the compliance and the modulus is derived and applied to a cooperative model of relaxation behaviour. In particular it is shown that mechanical viscoelasticity is equivalent to the anomalous low frequency dispersion process that has been observed in dielectrics containing quasifree charges. Comparison with published experimental data over a wide range of solid materials shows the validity of the cooperative model to mechanical relaxation.     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

含分层损伤复合材料等三角形格栅加筋板的起裂和扩展过程研究

对在压缩载荷下先进复合材料等三角形格栅加筋板结构 (AGS) 后屈曲阶段的分层起裂和扩展过程进行了研究。基于一阶剪切变形理论和 Von2 Karman几何非线性关系 , 提出了 AGS结构后屈曲有限元分析模型 ;基于总能量释放率准则 , 并利用虚裂纹闭合法 (VCCT) 及自适应网格的生成和移动技术分析了分层损伤的扩展过程 , 在分析过程中考虑了分层前缘的接触效应。并通过典型算例 , 讨论了不同的初始分层尺寸、 肋骨刚度对等三角形格栅加筋板结构的分层起裂和扩展过程的影响 , 通过与具有相同几何尺度的正交格栅加筋板结构的比较 ,说明等三角形格栅加筋板结构具有较高的抗分层能力。本文方法和所得结论对 A GS结构的承载能力预测和设计将具有参考价值。      

An analysis of interface delamination mechanisms in orthotropic and hybrid fiber-metal composite laminates

The onset and propagation of interlaminar defects is one of the main damage mechanisms in composite materials. This is even more the case when considering layered materials comprising metallic laminae (typically Aluminium) and FRP laminae. Propagation of delamination mainly depends on the initial crack extension and its loading mode.This work presents some results of a combined analytical-numerical-experimental study on the onset and propagation mechanisms regarding interlaminar defects. Two cases have been analysed in particular, the first consisting of a glass-fibre reinforced epoxy resin laminate, and the second consisting of a hybrid laminate where a lamina of aluminium is layered between FRP laminae.