Finite Fracture Mechanics at elastic interfaces

In the present paper we provide a method to determine the load causing delamination along an interface in a composite structure. The method is based on the elastic interface model, according to which the interface is equivalent to a bed of linear elastic springs, and on Finite Fracture Mechanics, a crack propagation criterion recently proposed for homogeneous structures. The procedure outlined is general. Details are given for the pull–push shear test. For such geometry, the failure load is obtained and compared with the estimates provided by stress concentration analysis and Linear Elastic Fracture Mechanics. It is seen that Finite Fracture Mechanics provides intermediate values. Furthermore, it is shown that the predictions provided by Finite Fracture Mechanics are almost coincident with the ones provided by the Cohesive Crack Model. As far as we are concerned with the determination of the failure load, the advantage of using Finite Fracture Mechanics with respect to the Cohesive Crack Model is evident, since a troublesome analysis of the softening taking place in the fracture process zone is not necessary. A final comparison with classical fracture criteria based on critical distances, such as the average stress criterion, concludes the paper.     

复合材料层板分层伴以横向裂纹扩展的三维有限元分析

本文采用三维有限元模型,对典型铺设的[0_2/±45_2/90_2]_s碳/环氧复合材料层板中分层伴以横向裂纹的产生和扩展导致的层间应力分布进行了分析。计算结果表明层间裂纹首先在90°层中部出现并开裂至相邻界面处而产生横向裂纹,横向裂纹的出现引起局部分层按三角形状扩展;并指出分层损伤过程是一个主导性的稳定扩展过程,这是导致刚度下降的主要因素。最后,数值计算结果与实验结果比较,两者是吻合的。     

Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading

This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation.     

Intrinsic coupling of near-tip matrix crack formation to mode III delamination advance in laminated polymeric matrix composites

Laminated carbon/epoxy specimens are loaded in anti-plane shear to investigate the relationship between near-tip matrix crack formation and the apparent mode III delamination toughness. Specimens are tested with different insert lengths to various load levels and examined fractographically. Near-tip matrix cracks are found to initiate and propagate intralaminarly before the onset of planar growth. These cracks are inclined at approximately 45° to the delamination plane and are perpendicular to the direction of maximum near-tip tensile stress. It is found that this represents an intrinsically coupled sequence of events for anti-plane shear loading of continuous fiber laminated polymeric composites when a preexisting delamination is bounded by plies that have their fiber direction aligned with the direction of macroscopic advance. This sequence of events violates the assumptions used in the reduction of data from common mode III tests. It therefore invalidates the associated toughness measurements, and may account for or strongly contribute to the common observation that laminated polymeric composites exhibit an apparent mode III delamination toughness that is dependent on test geometry.     

765THE CUT-AND-TRY METHOD IN DETERMINING THE SATURATE SPACING OF TRANSVERSE CRACKS OF COMPOSITE LAMINATES

I.IntroductionTransversecracksfirstoccurinthe9o"plyandspreadalongtheentirewidth.Withstaticorcyclicloadadding,thenumberoftransversecracksinthepliescontinuous1yincreases,lastinguntilthedistributionofcracksreachesasaturatestate.Theoccurrenceoftransversecrack…     

Strain and failure analysis of graphite/epoxy plates with cracks

The objective of this investigation was to study the deformation and failure of uniaxially loaded graphite/epoxy plates with cracks and to determine the influence of notch size on failure. The specimens were quasi-isotropic laminates with cracks of various lengths. They were instrumented with strain gages, photoelastic coatings and moiré grids. Strains near the crack tip show two distinct points of rate change at strain levels of 0.002 and 0.006, the latter corresponding to the ultimate strain of the 90-deg plies. Failure near the crack tip takes the form of a damage zone consisting of ply subcracking along fibers, local delamination and fiber breakage. Failure occurs when this damage zone reaches some critical value. Measured maximum strains at failure exceeded twice the ultimate strain of the unnotched laminate. The average stress over a characteristic distance (5 mm) from the crack tip was used as a criterion to describe the influence of crack length on failure. Comparison of results with those from similar specimens with circular holes showed that strength was nearly independent of notch geometry in this case, i.e., specimens with holes and cracks of the same size had nearly the same strength.     

Progressive fracture of laminated composite stiffened plate

Laminated fiber-reinforced composite stiffened plate with [0/90/±45]_S plies made of S-Glass/epoxy are evaluated via computational simulation to study damage and fracture progression. The loads are pressure and temperature which varies from 21 to 65.5 °C (case I) and from 143.3 to 21 °C (case II). An integrated computer code is used for the simulation of the damage progression. Results show that damage initiation begins at low load level, with matrix cracking at the 0° (bottom and top) plies, fiber fracture at the bottom (0°) ply and interply delamination at the top (0°) ply. Increasing the applied pressure, the damage growth is expended resulting in fracture through the thickness of the structure. At this stage, 90% of the plies damage at applied pressure 15.306 MPa for the case I and 15.036 MPa for the case II. After this stage, the cracks propagate rapidly and the structure collapses.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Delaminations induced by constrained transverse cracking in symmetric composite laminates

Transverse ply cracking and its induced delaminations at the φ/90° interfaces in [. . . /φ_i/φ_m/90_n] _s laminates are theoretically investigated. Three cracked and delaminated model laminates, one five-layer model (FLM) laminate [S^L/φ_m/90_2n/φ_m/S^R] _T and two three-layer model (TLM) laminates I and II, [φ_m/90_2n/φ_m] _T and [S′^L/90_2n/S′^R] _T, are designed to examine constraining mechanisms of the constraining plies of the center 90°-ply group on transverse crack induced delaminations, where S^L, S^R, S′^L and S′^R are sublaminates [. . ./φ_i] _T, [φ_i/. . .] _T, [. . ./φ_i/φ_m] _T and [φ_m/φ_i/. . .] _T, respectively. A sublaminate-wise first-order shear laminate theory is used to analyze stress and strain fields in the three cracked and delaminated laminates loaded in tension. The extension stiffness reduction of the constrained 90°-plies and the strain energy release rate for a local delamination normalized by the square of the laminate strain are calculated as a function of delamination length and transverse crack spacing. The constraining effects of the immediate neighboring plies and the remote plies are identified by conducting comparisons between the three model laminates. It is seen for the examined laminates that the nearest neighboring ply group of the 90°-plies primarily affects the stiffness reduction and also the normalized strain energy release rate, whereas the influences of the remote constraining layers are negligible.     

Principles of the mechanics of brittle fracture of materials with initial stresses

Conclusions for Fracture Criteria 1. With an increase in compressive stresses along cracks in materials with initial stresses, there is a reduction in the breaking loads corresponding to brittle fracture for normal-rupture and transverse-shear cracks. 2. When the initial stresses reach values corresponding to surface instability of the half-space (within the framework of plane strain), the breaking loads vanish for normal-rupture and transverse-shear cracks.The mechanical phenomenon corresponding to the second conclusion has the following explanation. Due to the use of the linearized theory at the indicated values of the initial stresses, a body with a crack is in a state of neutral equilibrium. In connection with this, it is not necessary to apply an additional finite load in order to remove the body from this state.Several other results on the mechanics of brittle fracture of materials with initial stresses have been published in studies mentioned in the survey [1].Corresponds to the text of a paper presented at the 6th International Conference on Fracture (New Delhi, India, 1984).Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 23, No. 10, pp. 34–39, October, 1987.     

A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks

A methodology is proposed for the construction of a representative volume element (RVE) for analysis of laminated composites containing two arrays of ply cracks running in different directions. The only requirement is that the cracks in any ply are uniformly spaced, and if more than one ply of a given orientation is cracked, then the crack spacing of individual plies must only be in exact multiples of each other. The spacing of cracks in the two directions can be fully independent. The RVE is constructed through a systematic consideration of translational symmetries present in the cracked laminate. As a result, the boundary conditions on the RVE can be imposed without compromising accuracy. Examples of the application of the RVE methodology are given to illustrate its broad capability and a finite element (FE) stress analysis is performed for these cases to illustrate results such as the crack surface displacements, local stress fields and RVE-averaged elastic properties. For one case, the average properties are compared with experimental results, showing good agreement.     

Delamination crack originating from transverse cracking in cross-ply composite laminates under extension

Based upon the Stroh formalism for anisotropic elastic materials and upon the method of eigenfunction expansion, the stress redistribution due to delamination cracks originating from transverse cracking is examined from [90/0], and [0/90], laminates under extension. The structure of the solution, in the form of a series expansion, is determined from the eigenvalue equation resulting from appropriate near-field conditions. To complete the solution, use is made of a boundary collocation technique in conjunction with the eigenfunction series that includes a large number of terms, enough to represent the elastic state throughout the appropriate domain concerned. The fracture mechanics parameters, such as stress intensity factors and energy release rates, are calculated and the major characteristics of stress distribution are discussed. The stability of delamination cracks is examined for varying ratios of ply thickness in terms of the energy release rate.     

Crack propagation in glass coatings under expanding spherical contact

The growth of transverse cracks under expanding spherical contact in a model system consisted of soda-lime glass bonded to a polycarbonate substrate is observed in situ from below or from the polished edge of the bilayer. Abrasion or chemical etching is employed on the coating surfaces to control the initial fracture. In the limit case of monoliths, the crack mouth becomes fully engulfed by the expanding contact, which results in a much steeper crack angle compared to the classical Hertzian cone case. As the coating thickness is reduced, flexure stresses are set in the coating which drive the cone crack to well away from the contact circle and initiate semi-elliptical-like radial cracks at the subsurface, right under the contact. Common to all three fracture modes is an initial unstable propagation phase following by a stable growth, with detrimental failure associated with severe damage to the top surface and/or delamination at the coating/substrate interface taking place at loads several times the fracture initiation loads.LEFM in conjunction with a large-strain FEM contact code is used to study the post-initiation fracture, with the crack path controlled by the principal stress trajectory or zero-mode II S.I.F. The analysis exposes the leading geometric and material parameters in each fracture mode, which may be useful in the design of bilayer structures for optimal mechanical performance. The well-known Auerbach law governing the initial fracture of monoliths is found to apply also to the bilayer crack systems within a certain range of the problem parameters. The numerical prediction for the crack profiles and the fracture envelopes generally collaborate well with the tests.     

A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites

An element-failure algorithm is proposed and incorporated into a finite element code for simulating dynamic crack propagation and impact damage in laminated composite materials. In this algorithm, when a crack is propagating within a finite element, the element is deemed to have partially failed, but not removed from the computations. Consequently, only a fraction of the stresses that were computed before the crack tip entered the element contribute to the nodal forces of the element. When the crack has propagated through the element, the element is completely failed and therefore can only resist volumetric compression. This treatment of crack propagation in isotropic solids allows fracture paths within individual elements and is able to accommodate crack growth in any arbitrary direction without the need for remeshing. However, this concept is especially powerful when extended to the modeling of damage and delamination in fibre-reinforced composite laminates. This is because the nature of damage in composite laminates is generally diffused, characterized by multiple matrix cracks, fibre pullout, fibre breakage and delaminations. It is usually not possible to define or identify crack tips in the tradition of fracture mechanics. Since parts of a damaged composite structure are often able to partially transmit load despite the presence of some damage, it is advantageous to model the damaged portions with partially failed elements. The damage may be efficiently modeled and tracked using element-failure concepts, with the application of appropriate failure criteria and damage evolution laws. The idea is to embody the effects of damage into the effective nodal forces of the finite element. In this paper, we report the novel use of element-failure concepts in the analysis of low-velocity impact damage of composite laminates. The initiation and propagation of delaminations arising from the impact are predicted and the results show qualitative agreement with experimental observation of the formation of multiple delaminations in impact-damaged specimens. While such delaminations do not permit transmission of tensile stress waves across the cracked surfaces, transmission of compressive stress waves are allowed in the simulation. It is further shown that, when elements are allowed to fail, the dynamic stress wave distributions are altered significantly. In the element-failure algorithm, the issue of interpenetration of delamination surfaces in the model does not arise. This is a significant advantage over the conventional method of explicitly modeling the delamination surfaces and crack front, where generally, much computational time must be spent in employing contact algorithms to ensure physically admissible solutions. Finally, we also demonstrate the simulation of crack propagation of pre-notched specimens of an isotropic material under initial conditions of mode II loading using the element-failure algorithm. The numerical results showed that the cracks propagated at an angle of about 70° with respect to the notches, in agreement with the experimental results of Kalthoff.     

任意斜裂纹转子的耦合振动研究

对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征.对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵.在此基础上,采用纽马克-β数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征.与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下,弯曲振动与扭转振动幅度都更大.而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性.所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.     

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.     

复合材料正交叠层板最终拉伸强度的细观统计分析

本文对复合材料正交叠层板［０／９０／０］的最终拉伸破坏行为进行了研究．首先，提出一种修正的剪滞分析方法，求解叠层中由９０°层的基体开裂和０°层的部分纤维断裂相互作用所导致的应力重新分布；然后，采用随机临界核统计模型，对叠层板的最终破坏进行了细观统计分析．对［Ｏ＿２／９０＿ｍ］＿ｓ、［Ｏ＿４／９０＿ｍ］＿ｓ碳／环氧和［Ｏ＿４／９０＿ｍ］＿ｓ玻璃／环氧的计算结果表明，估计的最终拉伸强度与现有的实验结果有较好的符合．     

Fracture initiation in the contact region under shear

In the contact region between sliding elastic bodies, there are subregions where the interacting shores are bonded and subregions where they can slide along each other. It is convenient to interpret the latter as transverse shear cracks with slip resistance forces acting on their closed shores. In the end regions of such a crack, stress concentration may lead to fracture initiation in the contacting bodies. Experimental results and an analytic model of the phenomenon are given for a situation where the fracture intersects the contact plane tilted with respect to the direction of the loads.