Anti‐symmetrical curved composite laminate subject to delamination induced by thermal cycling

Composite structures usually undergo to temperature variations in aircraft during landing/taking off and when cruising at high altitude. Under these conditions and in combination with curved structures, they can generate severe thermal stresses that induce delaminations. Considering the importance of studying delamination in these conditions, this research imposed an anti‐symmetrical laminate to cyclic temperature variations of 130 °C and ?70 °C with the objective of inducing varied curvatures and, consequently, crack growth. Different from standardized test procedures, this test setup elastically deformed coupons without external forces and forward experimentally and numerically evaluated the strain energy release rate (SERR) during crack propagation. This procedure enabled the assessment of delamination rate (da/dN) as a function of maximum SERR. The experimental results were compared with numerical results obtained by ABAQUS Finite Element code. Despite large scatter in experimental results, a reasonable correlation between experimental and numerical results was obtained in terms of crack growth rate (da/dN) as a function of the maximum SERR.     

Effect of damage levels and curing stresses on delamination growth behaviour emanating from circular holes in laminated FRP composites

This paper deals with the study of the effect of drilling induced delamination damage levels and residual thermal stresses (developed during manufacturing process of cooling the laminate form curing temperature to room temperature) on delamination growth behaviour emanating form circular holes in graphite/epoxy laminated FRP composites. Two sets of full three dimensional finite element analyses (one with the residual thermal stresses developed while curing the laminate and the other without residual thermal stresses i.e. with mechanical loading only) have been performed to calculate the displacements and interlaminar stresses along the delaminated interfaces responsible for the delamination onset and propagation. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of SERR obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply orientation, drilling induced damage levels and material heterogeneity at the delaminated interface dictate the interlaminar fracture behaviour of laminated FRP composites.     

Interlaminar crack onset in co‐cured and co‐bonded composite joints under mode I cyclic loading

Composite joints exhibit different behavior in regard to delamination resistance when dealing with fatigue phenomenon. This research work focuses on an investigation to understand the failure mechanisms on the interfacial strength domain for delamination onset in cocured and cobonded joints. The analysis was based on strain energy release rate versus number of cycles plots that were obtained from fatigue tests in mode I with a stress ratio R = 0.1. The analysis encompassed from the microscopic to mesoscopic level obtained from scanning electron microscopic, and the images processed to extract the most relevant fracture patterns. The main difference between the two technologies was the stress concentration at the crack tip in which the cobonded joint presents a fabric carrier that blunts the adhesive layer, then delaying the delamination. This paper provides important information and guidelines to aid designers in the selection of the best composite joint for high‐performance structural applications.     

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.     

铁素体管线钢的分层裂纹及其对断裂的影响

通过对针状铁素体管线钢缺口根部三维应力状态的有限元分析和不同形式的断裂实验,研究了管线钢分层裂纹产生的条件及其对断裂性能的影响.结果表明裂纹或缺口根部的三维应力状态是产生分层裂纹的必要条件,材料的强度分布影响分层裂纹的形式和方向.分层裂纹均为主裂纹扩展前材料中的弱界面在垂直该弱界面的拉应力作用下产生的,其数量和方向受裂纹端部三维应力场和材料的强度分布状态控制.分层裂纹面上的应力为零,分层裂纹有一定的间距.在断裂过程中产生的分层裂纹使裂纹或缺口根部的构形发生改变,从而对裂尖的应力状态和材料的断裂性能产生巨大的影响.穿透裂纹体的分层裂纹使其有效厚度减小,表面裂纹体的分层裂纹与裂纹扩展方向垂直.在断裂过程中产生分层裂纹需要消耗更多的能量、降低裂端三维应力约束、有效厚度降低或裂尖钝化.这些因素均使断裂扩展更加困难,而使材料韧性得到提高.     

Coupled meshfree and fractal finite element method for mixed mode two‐dimensional crack problems

This paper presents a coupling technique for integrating the element‐free Galerkin method (EFGM) with the fractal finite element method (FFEM) for analyzing homogeneous, isotropic, and two‐dimensional linear‐elastic cracked structures subjected to mixed‐mode (modes I and II) loading conditions. FFEM is adopted for discretization of the domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the EFG and the finite element (FE) shape functions, satisfies the consistency condition thus ensuring convergence of the proposed coupled EFGM–FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no special enriched basis functions or no structured mesh with special FEs are necessary and no post‐processing (employing any path independent integrals) is needed to determine fracture parameters, such as stress‐intensity factors (SIFs) and T‐stress. The numerical results show that SIFs and T‐stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also, a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack length to width ratio on the quality of the numerical solutions. A numerical example on mixed‐mode condition is presented to simulate crack propagation. As in the proposed coupled EFGM–FFEM at each increment during the crack propagation, the FFEM mesh (around the crack tip) is shifted as it is to the new updated position of the crack tip (such that FFEM mesh center coincides with the crack tip) and few meshless nodes are sprinkled in the location where the FFEM mesh was lying previously, crack‐propagation analysis can be dramatically simplified. Copyright © 2010 John Wiley & Sons, Ltd.     

基于虚拟裂纹闭合技术的应变能释放率分析

基于虚拟裂纹闭合技术(VCCT),建立了复合材料层合板层间裂纹尖端的应变能释放率(SERR)三维有限元计算模型。该模型考虑了裂纹尖端大转动和离散单元形状变化对应变能释放率计算的影响,修正了裂纹尖端应变能释放率的计算方法。利用该模型计算了裂纹长度为15 mm和35 mm时纯Ⅰ型和纯Ⅱ型的应变能释放率,纯Ⅰ型应变能释放率分别为 207 J/m2和 253 J/m2;纯Ⅱ型应变能释放率分别为 758 J / m 2和 1040 J / m2;计算值与试验值吻合得很好。同时,该模型计算了混合型不同比值 R=(G_Ⅱ/G_Ⅰ+G_Ⅱ)的长裂纹层合板层间断裂过程的应变能释放率,其中Ⅰ型和Ⅱ型应变能释放率计算值与试验平均值的最大误差为 11.4%,最小误差为 0.4%。该模型能有效计算裂纹尖端的应变能释放率。     

Analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam specimen using higher order beam theories

Mathematical models, for the stress analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam (DCB) specimen using classical beam theory, first and higher order shear deformation beam theories, have been developed to determine the mode I strain energy release rate (SERR) for unidirectional composites. In the present study, appropriate matching conditions at the crack tip of the DCB specimen have been derived by using variational principles. SERR has been calculated using compliance method. In general, the performance of shear deformation beam models of DCB specimen with variationally derived matching conditions at the crack tip is good in determining the SERR for medium to long crack lengths. Performance of higher order shear deformation beam model (having quadratically varying transverse displacement over the thickness) of DCB specimen, with non-variationally derived matching conditions at the crack tip, is good in determining the SERR for all the crack lengths in comparison with the available theoretical and finite element solutions in the literature. Higher order shear deformation beam theories having varying transverse displacement over the thickness are more appropriate to analyze DCB specimen as they predict the appropriate nature of the interlaminar normal stress at the crack tip and its distribution ahead of the crack tip.     

An enriched element‐failure method (REFM) for delamination analysis of composite structures

This paper develops an enriched element‐failure method for delamination analysis of composite structures. This method combines discontinuous enrichments in the extended finite element method and element‐failure concepts in the element‐failure method within the finite element framework. An improved discontinuous enrichment function is presented to effectively model the kinked discontinuities; and, based on fracture mechanics, a general near‐tip enrichment function is also derived from the asymptotic displacement fields to represent the discontinuity and local stress intensification around the crack‐tip. The delamination is treated as a crack problem that is represented by the discontinuous enrichment functions and then the enrichments are transformed to external nodal forces applied to nodes around the crack. The crack and its propagation are modeled by the ‘failed elements’ that are applied to the external nodal forces. Delamination and crack kinking problems can be solved simultaneously without remeshing the model or re‐assembling the stiffness matrix with this method. Examples are used to demonstrate the application of the proposed method to delamination analysis. The validity of the proposed method is verified and the simulation results show that both interlaminar delamination and crack kinking (intralaminar crack) occur in the cross‐ply laminated plate, which is observed in the experiment. Copyright © 2009 John Wiley & Sons, Ltd.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Mesh‐independent matrix cracking and delamination modeling in laminated composites

The initiation and evolution of transverse matrix cracks and delaminations are predicted within a mesh‐independent cracking (MIC) framework. MIC is a regularized extended finite element method (x‐FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra‐ply MIC opening is implemented by using a mixed‐mode cohesive formulation in a fully three‐dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates withouttextita priori knowledge of damage location or initiation. Good agreement with conventional numerical solutions and/or experimental data was observed in all the problems considered. Published 2011. This article is a US Government work and is in the public domain in the USA.     

Delamination analysis of composites by new orthotropic bimaterial extended finite element method

The extended finite element method (XFEM) is further improved for fracture analysis of composite laminates containing interlaminar delaminations. New set of bimaterial orthotropic enrichment functions are developed and utilized in XFEM analysis of linear‐elastic fracture mechanics of layered composites. Interlaminar crack‐tip enrichment functions are derived from analytical asymptotic displacement fields around a traction‐free interfacial crack. Also, heaviside and weak discontinuity enrichment functions are utilized in modeling discontinuous fields across interface cracks and bimaterial weak discontinuities, respectively. In this procedure, elements containing a crack‐tip or strong/weak discontinuities are not required to conform to those geometries. In addition, the same mesh can be used to analyze different interlaminar cracks or delamination propagation. The domain interaction integral approach is also adopted in order to numerically evaluate the mixed‐mode stress intensity factors. A number of benchmark tests are simulated to assess the performance of the proposed approach and the results are compared with available reference results. Copyright © 2011 John Wiley & Sons, Ltd.     

Accuracy assessment of a three-dimensional,crack tip element based approach for predicting delamination growth in stiffened-skin geometries

Experimental observations of delamination growth in two stiffened-skin geometries are compared to predictions made using a three-dimensional crack tip element based approach. Each geometry consists of a six-ply graphite/epoxy skin co-cured to a six-ply, hat-shaped stiffener containing a preimplanted teflon delamination between the skin and stiffener at the stiffener termination point. One stiffened-skin geometry was loaded in three-point bending and the other had in-plane tension loads applied to the skin. To predict delamination growth, a three-dimensional crack tip element analysis was first performed on each geometry in order to determine the total energy release rate, G, as well as its mode I, II and III components, G_I, G_II and G_III, respectively. These results were used to define a mode mix at each point along the delamination front, G_s/G, where G_s=G_II + G_III. To obtain the delamination toughness, G_c, it was assumed that G_c exhibits the same dependence on G_s/G as on G_II/G, where the results for G_c versus G_II/G were taken from an earlier experimental study. Next, a comparison of the energy release rate to the toughness at each position along the delamination front was performed, and these results were scaled appropriately in order to predict the sequence of loads and corresponding locations at which the delamination will advance. The predictions were then compared to experimental results that included c-scan images of the test specimens taken at each increment of observed growth, and very good quantitative and qualitative correlations were obtained for both geometries. These results indicate the practicality of, and considerable computational savings that may be achieved by, employing crack tip element analyses for delamination growth predictions in realistic structural geometries.     

A numerical approach to subsurface crack propagation assessment in rolling contact

Subsurface crack mode II propagation parallel to the contact surface is a damage mechanism leading to dramatic failure in many components subjected to cyclic loading. A weight function (WF) was elaborated for calculating the applied mode II stress intensity factor (SIF) of a crack in a two‐dimensional half‐space in plane strain condition, for crack completely closed and frictionless contact between the crack faces. With respect to other methods, the WF allows faster SIF calculation, thus being suitable for simulation of many repeated load cycles and fatigue crack propagation. The WF was applied for simulating a case of rolling contact experiments found in the literature, and good agreement between experimental and numerical results was obtained, showing the effectiveness of the WF method in damage tolerant design.     

Effect of initial crack length on the measured bridging law of unidirectional E-glass/epoxy double cantilever beam specimens

In this paper, the effect of initial delamination length is experimentally investigated on obtaining the mode I bridging law of unidirectional E-glass/epoxy double cantilever beam (DCB) specimens manufactured by hand layup method. To this end, an experimental test set-up is established for accurate measurement of crack tip opening displacement (CTOD) using digital image processing method. DCB tests are performed for three different delamination lengths and the corresponding bridging laws are calculated using J-integral approach. Results showed that the maximum bridging stress, the shape of bridging law and energy dissipation in bridging zone are slightly affected by changing initial crack length. In other words, the measured bridging law acts independent of initial delamination length. Therefore, the obtained bridging law can be used with the cohesive elements available in the commercial finite element software to simulate the delamination propagation behavior in unidirectional DCB specimens.     

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

3D fracture mechanics investigation on surface fatigue crack propagation

Surface fatigue crack propagation is the typical failure mode of engineering structures. In this study, the experiment on surface fatigue crack propagation in 15MnVN steel plate is carried out, and the crack shape and propagation life are obtained. With the concept of ‘equivalent thickness’ brought into the latest three‐dimensional (3D) fracture mechanics theory, one closure model applicable to 3D fatigue crack is put forward. By using the above 3D crack‐closure model, the shape and propagation life of surface fatigue crack in 15MnVN plates are predicted. The simulative results show that the 3D fracture mechanics‐based closure model for 3D fatigue crack is effective.     

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

Three‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.     

Effect of mode mixity on K-dominance and three dimensionality in cracked plates

The method of Coherent Gradient Sensing (CGS) in transmission, in conjunction with two and three dimensional finite element methods, is used to study the effect of mode mixity on crack tip stress fields. Using a two dimensional finite element analysis the outer bounds of the region of K-dominance were determined. A three dimensional finite analysis was utilized to study the effect of mode mixity on the three dimensional nature of the stress field in the immediate vicinity of the crack tip and to obtain an inner bound of the region of K-dominance. It was noted that increasing mode mixity leads to an increased rotation of the three dimensional zone, keeping its shape and size unchanged. In contrast, the region of K-dominance is seen to dramatically depend on mode mixity, both in shape and size. In addition, an analysis of the CGS interferograms was conducted to obtain an estimate of the regions of K-dominance experimentally. A least squares fit data analysis technique was used to extract fracture parameters, namely the stress intensity factors K _I, K _II and subsequently the crack tip phase angle, . The data points used for the least square fitting were obtained from the determined regions of K-dominance. The same fracture parameters were also evaluated from the finite element analysis, and good agreement was found between experimental measurements and finite element predictions.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.