Stress intensity factors for several groups of equal and parallel cracks in finite plates

Several groups of equal and parallel 2D cracks in finite width plates subjected to remote tensile loading have been studied. Formulae for calculating the stress intensity factors of these crack configurations have been proposed from the finite element analysis, and the difference between the formulae and the finite element results is smaller than 3%. On this basis, the influence of crack interactions on stress intensity factors (SIF) is discussed, and it can be seen that interaction between multiple cracks could produce either strong enhancement or shielding effects on the SIF depending on the crack positions and lengths.     

An extended layerwise/solid-element method of stiffened composite plates with delaminations and transverse crack

The stiffened composite plates with the transverse crack and delamination were studied in this paper, and an extended layerwise/solid-element (XLW/SE) method was developed. In the proposed method, the governing equations of composite plates and stiffeners were established based on the extended layerwise method and 3D solid elements, respectively. The final governing equation of stiffened composite plates is assembled by using the compatibility conditions and internal force equilibrium conditions at the joint interface between the plates and stiffeners. For the stiffened composite plates with damages, the XLW/SE method can obtain the local stress and displacement fields accurately and simulate the in-plane transverse cracks and delaminations simultaneously, considering complicated stiffeners without any assumptions. In the numerical examples, the results obtained by the proposed method are compared with those obtained by the 3D elastic models developed in the general finite element code, and the good agreements were achieved for the stiffened composite plates with/without delaminations and/or transverse crack.     

Elastic problem of an adhesion crack in T-junction of two orthotropic thin plates

In this study, the general solution is derived for stresses in a T-junction of two thin plates with an adhesion crack. The plates are orthotropic, and shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the condition of plane stress. The results obtained are verified through numerical calculation using the finite element method. A singular stress field is obtained from the solution in the vicinity of a crack tip.     

含裂纹矩形板的横向振动

本文以“含裂纹零维度单元”模型研究裂纹对矩形动态特性定量的影响，完成一种既能满足工程结构有关设计需要，又比较简单可行的计算模型。     

Buckling behavior of a central cracked thin plate under tension

The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.     

A complex variable boundary element method for solving interface crack problems

The problem of finite bimaterial plates with an edge crack along the interface is studied. A complex variable boundary element method is presented and applied to determine the stress intensity factor for finite bimaterial plates. Using the pseudo-orthogonal characteristic of the eigenfunction expansion forms and the well-known Bueckner work conjugate integral and taking the different complex potentials as auxiliary fields, the interfacial stress intensity factors associated with the physical stress-displacement fields are evaluated. The effects of material properties and crack geometry on stress intensity factors are investigated. The numerical examples for three typical specimens with six different combinations of the bimaterial are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

含面\芯开裂损伤复合材料夹层板考虑几何非线性的能量释放率数值分析

基于一阶剪切变形理论,zig-zag变形假定和von Karman大挠度理论,提出了含不同形状面\芯开裂损伤复合材料夹层板在受压缩载荷作用下的开裂前缘能量释放率研究的有限元分析方法,研究了在轴向应变作用下,具有面\芯开裂损伤复合材料夹层板的分层断裂力学行为,并讨论了在大变形下几何非线性对能量释放率分布规律的影响。通过典型算例分析表明:具有面\芯开裂损伤复合材料夹层板的分层前缘能量释放率的大小和分布规律与开裂面积、开裂形状和受载方向有关。     

The influence of geometry of edge-cracked plates on crack initiation

In this paper the influence of geometry of edge-cracked plates on crack propagate under mixed mode loading conditions is studied. The edge-cracked plates under tension are examined. The crack extension angle and the critical stress of fracture are determined for various values of the crack inclination angle and the ratio of the crack length to specimen's width. The Det.-criterion developed by the author is used.     

Stress intensity factors for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.     

The use of coupled nonlocal damage-plasticity to predict crack growth in ductile metal plates

A nonlocal coupled damage-plasticity model is presented for predicting crack growth within plates made from a ductile metallic alloy. The damage law is explicitly defined in terms of the accumulated nonlocal plastic strain ensuring efficient numerical implementation. On the basis of this model, a UMAT for the finite element (FE) package ABAQUS (implicit) is developed. Thin plates of different geometries were modelled and analysed using this model, and the numerical stability of the model has been verified. The model shows the ability to capture the post-peak softening behaviour, shows mesh independence, and requires calibration of parameters against experimental data. The suitability of the model for crack path prediction is discussed.     

General solution of stresses due to an adhesion crack for T-shaped junction of two plates

In this study, the general solution of stresses is derived for a T-shaped junction consisting of two thin plates with an adhesion crack. A shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the plane stress condition. The results obtained are verified by a numerical calculation based on the finite element method. Moreover, a singular stress field is obtained from the solution for the vicinity of the crack.     

Extended finite element fracture analysis of a cracked isotropic shell repaired by composite patch

An extended finite element method (XFEM) is developed to study fracture parameters of cracked metal plates and tubes that are repaired on top of the crack with a composite patch. A MATLAB® stand‐alone code is prepared to model such structures with eight‐noded doubly curved shell elements in the XFEM framework. Crack trajectory studies are performed for a diagonally cracked panel under fatigue loading. Verification studies are investigated on different shell type structures such as a cracked spherical shell and cracked cylindrical pipe with different crack orientations. The effects of using patch repairs with different fibre orientations on the reduction of stress intensity factors (SIFs) is also studied which can be useful for design purposes. XFEM is selected as any crack geometry can be embedded in the finite element mesh configuration with no need to coincide the crack geometry with meshed elements and so re‐meshing with fine mesh generation is not needed in the current method.     

Delamination vs matrix cracking in layered composites subjected to transverse loading

An algorithm is presented to compute the distribution of the strain energy release rate along the crack front of a penny-shaped delamination in a layered orthotropic body. The method applies a finite element recently proposed for three-dimensional analysis of layered orthotropic circular plates. The algorithm is economical even though it treats a full three-dimensional state of stress. The method requires only a single virtual crack extension to accurately compute the strain energy release rate at a point along the crack front. The method is applied to the study of delamination crack growth in a nine layer cross-ply laminate. The variation of strain energy release rate, G, along the crack front, is determined. The significance of the plate aspect ratio, as well as length scale, on the fracture process is studied. The establishment of a loading case where a distributed transverse compressive loading causes delamination growth is given.     

Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load

The stress intensity factors (SIFs) for through-transverse crack in the China Railway Track System (CRTS II) slab track system under vehicle dynamic load are evaluated in this paper. A coupled dynamic model of a half-vehicle and the slab track is presented in which the half-vehicle is treated as a 18-degree-of-freedom multi-body system. The slab track is modeled as two continuous Bernoulli–Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The model is applied to calculate the vertical and lateral dynamic wheel–rail forces. A three-dimensional finite element model of the slab track system is then established in which the through-transverse crack at the bottom of concrete base is created by using extended finite element method (XFEM). The wheel–rail forces obtained by the vehicle-track dynamics calculation are utilized as the inputs to finite element model, and then the values of dynamic SIFs at the crack-tip are extracted from the XFEM solution by domain based interaction integral approach. The influences of subgrade modulus, crack length, crack angle, friction coefficient between cracked surfaces, and friction coefficient between faces of concrete base and subgrade on dynamic SIFs are investigated in detail. The analysis indicates that the subgrade modulus, crack length and crack angle have great effects on dynamic SIFs at the crack-tip, while both of the friction coefficients have negligible influences on variations of dynamic SIFs. Also the statistical characteristics of varying SIFs due to random wheel–rail forces are studied and results reveal that the distributions of dynamic SIFs follow an approximately Gaussian distribution with different mean values and standard deviations. The numerical results obtained are very useful in the maintenance of the slab track system.     

Coplanar perturbation of a crack lying on the mid-plane of a plate

Several groups have studied experimentally the deformation of the front of mode I cracks propagating quasistatically along the interface between bonded plates. The theoretical interpretation of such experiments has always been based up to now on a formula of Rice (ASME J Appl Mech 52:571–579, 1985); this formula provides the first-order variation of the local mode I stress intensity factor resulting from some small, but otherwise arbitrary coplanar perturbation of the front of a semi-infinite crack in an infinite body. To be applicable to bonded plates, this formula requires that the characteristic distance of variation of this perturbation in the direction of the crack front be small compared to all other characteristic dimensions of the problem, and first of all the thickness of the plates. This condition is unfortunately frequently violated in practice. The purpose of this paper is therefore to provide a more exact formula for the variation of the local stress intensity factor, for the specific cracked geometry and boundary conditions used in experiments; this should allow for more accurate theoretical interpretations. This is done in two steps. The first one consists in adapting Rice’s (ASME J Appl Mech 52:571–579, 1985) treatment, applicable to the extreme case of plates of infinite thickness, to the other extreme one of plates of infinitesimal thickness, using the standard Love-Kirchhoff plate theory. An interesting outcome of the analysis is that the distance from the crack front to the boundary of the plate acts as a “cutoff length”, in the sense that when the distance between two points on the crack front gets larger than it, the influence of the crack advance at the first point upon the stress intensity factor at the second diminishes quickly; the plate thickness, however, plays no similar role. The second step consists in supplementing the theoretical expressions applicable to extreme values of the plate thickness with finite element computations providing results for intermediate values. These computations lead to the definition of a simple, approximate but accurate “interpolation formula” for the variation of the local stress intensity factor, applicable to plates of arbitrary thickness.     

Experimental and nonlinear finite element studies of RC beams strengthened with FRP plates

This paper presents a joint experimental–analytical investigation aimed at studying the brittle failure modes of RC members strengthened in flexure by FRP plates. Both midspan and plate end failure modes are studied. The finite element analyses are based on nonlinear fracture mechanics. The model considered the actual crack pattern observed in the tests by using a smeared and an interface crack model. This paper shows how concrete cracking, adhesive behavior, plate length, width and stiffness affect the failure mechanisms. The numerical and experimental results show that debonding and concrete cover splitting failure modes occur always by crack propagation inside the concrete.     

Determination of dynamic fracture toughness for PMMA

A dynamic FEM (finite element method) and a strain gage method are applied to analyze the dynamic fracture toughness and SIF (stress intensity factor) for PMMA (polymethyl methacrylate). The analyses are carried out for plates with an edge crack subjected to one-point bending in a plane of the plate. A simple procedure that the present author has proposed is applied to the problem of using a triangular element of assumed constant strain on finite element analysis. The numerical simulation by FEM provides values for the applied forces as measured with the strain gages. Also, a crack initiation time is measured with the strain gage mounted around the crack tip. The dynamic fracture toughness is determined by adapting the crack initiation time to the simulation curve of the dynamic SIF calculated by the FEM. In this study, the usefulness of the method to determine the dynamic fracture toughness is investigated by comparing predictions with the experimental results for dynamic stresses and SIFs.     

SIFs of CCT plate repaired with single‐sided composite patch

Constant amplitude load fatigue tests are performed to obtain crack propagation data for LF2‐aluminium centre crack tension (CCT) plates un‐repaired and repaired with single‐sided composite patches. Then, the James–Anderson method, an experimental method, is used to obtain the stress intensity factor (SIF) formula for the repaired CCT plates with carbon–fibre composite patches. At last, crack propagation life prediction and finite element (FE) calculation are carried out to validate the experimental SIF formula. It is shown that the present SIF formula can exactly predict the fatigue‐crack propagation life of the patched CCT plates and is close to the FE results, which implies the effectivity of the experimental SIF formula in the present paper.