Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF DYNAMIC DELAMINATION IN COMPOSITES

Abstract A fundamental understanding of dynamic delamination in composites is sought through the application of theoretical and experimental approaches familiar to dynamic fracture mechanics. Analysis of steady-state fracture in an infinite orthotropic strip yields a simple solution which can be used to evaluate numerical procedures and experimental results. The analogous specimen consists of a single edge notched composite strip bonded to stiff steel substrates to enforce the desired displacement boundary conditions. Delamination velocities of the order of 10 to 1000 m/s were measured using a graphite gauge technique. Quasi-static and dynamic finite element methods are applied to investigate the behavior of the specimen and to determine static initiation and dynamic delamination toughness. The experimental observations cannot be explained by linear elastic fracture theory. The absence of a unique G(?) relationship might be rationalized by a simple model relating matrix crack zone size to fiber bridging mechanisms.     

Dynamic delamination fracture toughness of a graphite/epoxy laminate under impact

Dynamic delamination fracture toughness in a [90/0]_5s T300/934 graphite/epoxy laminate was investigated using impact loading. Delamination cracks of three different sizes were embedded at the mid-plane of the composite specimen. The threshold impact velocity that causes propagation of the delamination crack was used in the dynamic analysis with the finite element method. From the finite element solution, the time-history of the strain energy release rate was calculated. The critical strain energy release rate was taken to equal the maximum value of the response history.     

A cut-ply specimen for the mixed-mode fracture toughness and fatigue characterisation of FRPs

The characterisation of mixed-mode fracture toughness and fatigue delamination growth in fibre-reinforced composites is crucial for assessing the integrity of structural elements in service. An asymmetric cut-ply coupon (ACP) loaded in four-point bending is here proposed to carry out the aforementioned characterisations. Analytical expressions of the energy release rate and mode-mixity for the ACP are derived and validated by means of finite element analysis. A fracture toughness and fatigue characterisation of the carbon/epoxy material IM7/8552 is carried out via ACP specimens. It is proved that the material data obtained from ACP specimens match those generated using ASTM standard mixed-mode bending (MMB) coupons. The main reason for the introduction of the ACP test resides in its applicability to characterisation scenarios where measuring the delamination length with optical means, as required for MMB coupons, is difficult. Such scenarios include the investigation of static and fatigue delamination growth at low and high temperatures, which requires the usage of environmental chambers. This poses significant constraints in terms of volume available for the test rigs, and, most importantly, limitations on visual access to observe delamination propagation. However, the manufacturing of ACP coupons is more complex than for MMB specimens and the testing requires several additional precautions that are here discussed in detail.     

用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。     

Computational analysis of dynamically propagating cracks in axisymmetric solids

Dynamic crack propagation behavior in axisymmetric solids is investigated using an effective computational procedure. First, an accurate method to extract energy release rate of a dynamically propagating crack from finite element solutions is formulated for axisymmetric geometries. The method is applied to an analysis of a radially growing circular crack under remote tension in an infinite medium. The computed dynamic energy release rate shows an excellent agreement with the exact solution. Next, we have developed an iterative technique to propagate a crack whose velocity history is initially unknown. With the iterative procedure, the crack propagates according to a condition specified by a dynamic fracture criterion. At each increment of crack growth, an optimum velocity at which the crack growth condition satisfies is obtained by the iterative scheme. This procedure requires no artificial input or no preset crack tip speed in a simulation study. The iterative scheme is employed in a dynamic fracture analysis of ceramics. The computational analysis is carried out for simulation of fracture experiments using circumferentially notched round bars. In the test, a ceramic specimen is subjected to tensile stress wave loading and after crack growth initiation, the external crack propagates to tear the specimen. The computational simulation is carried out for the entire fracture process including the crack growth initiation and the dynamic propagation. The iterative procedure enables us to predict the crack tip velocity which is unmeasurable in the experiment. Suitabilities of proposed fracture toughness criteria for the ceramics are investigated by comparing measured and computed transmitted pulses through the uncracked ligament. This study proves the usefulness of the computational procedures for dynamic fracture analysis. It is most effective in characterizing dynamic fracture toughness where determination of every relevant parameter is difficult in the experiments.     

Measurement of the temperature field induced by dynamic crack growth in Beta-C titanium

The temperature increase at the tip of a dynamically propagating crack may have a significant effect on a material's mechanical properties, and hence on its dynamic fracture toughness. In order to start to understand this phenomena, measurements of the temperature field at the tip of a dynamically growing crack in Beta-C titanium alloy were performed using a linear array of high speed infrared detectors. The results show that a maximum temperature of 450°C is reached at the crack tip. In addition, the dynamic fracture toughness was measured for crack speeds from 0 to 500 m/s. In this speed range, the toughness appears to be constant. Estimates of the crack tip energy release rate and plastic strain rate are made using analysis of the experimental data.     

TENSILE IMPACT DELAMINATION OF A CROSS-PLY INTERFACE STUDIED BY MOIRÉ PHOTOGRAPHY

Abstract Impact induced delamination along a cross-ply interface in carbon fiber/epoxy laminates is studied by high resolution moiré photography. The specimens were loaded in a tensile split-Hopkinson bar giving mode I dominated fracture, and a high speed camera captures images during loading and delamination. The resulting moiré fringes are analysed to produce full field displacement maps of the area around the loaded and propagating crack tips. The displacement map prior to failure shows good agreement with numerical solutions, calculated using a 3D self-adaptive p-version of the finite element method. The calibrated finite element solutions are then used to give further information about the matrix cracking zone size around the crack tip and the energy release rate. In comparison to quasi-static loading, tensile impact loading was found to increase the failure load and the resulting energy release rates; some physical explanations for this behaviour are discussed. It was concluded that the procedures presented have good potential for further determination of rate dependent material properties in carbon/fiber epoxy composites.     

双悬臂梁试件裂纹动态扩展的准静态数值分析

本文采用双悬臂梁（DCB）试件研究了复合材料层合板层间插入韧性胶膜（Interleaf）层的Ⅰ型断裂行为。试验结果表明,含和不含Interleaf层试件分别呈现脆性非稳态和脆性稳态分层扩展特性。针对非稳定裂纹扩展问题,依据动态断裂力学中应变能释放率与动能变化率的关系,提出了以断裂韧性值G_IC变化来抵消动能变化对裂纹扩展过程影响的准静态分析方法,根据试验中裂纹扩展的韧性变化,推导出适用于准静态裂纹扩展模拟的等效韧性G_IC*,利用ABAQUS平台和虚裂纹闭合技术（VCCT）建立了三维有限元计算模型;实现了从起裂到止裂的整个裂纹动态扩展过程的数值模拟,揭示了非稳定裂纹扩展过程中一些复杂的力学现象。      

Measuring the rate-dependent mode I fracture toughness of composites – A review

Composite materials are often subjected to mechanical impact causing delamination. For quasi-static loading, measuring the mode I fracture toughness has been standardized. However, for high-rate loading, additional challenges arise. Consequently, no standard test has yet been defined for measuring the mode I fracture toughness under high rates of loading. This article therefore reviews candidate tests for measuring the high-rate mode I fracture toughness. Strength and weaknesses of different specimen designs and test setups are shown. Different approaches to measuring crack growth and loads are presented. The different approaches are compared and recommendations are provided for measuring the mode I fracture toughness of composites under high rates of loading.     

DYNAMIC CRACK PROPAGATION AND CRACK ARREST INVESTIGATED WITH A NEW SPECIMEN GEOMETRY: PART II: EXPERIMENTAL STUDY ON A LOW-ALLOY FERRITIC STEEL

The novel experiment developed in our Institute to investigate crack initiation, rapid crack propagation and crack arrest with one specimen, the ring test, was applied to a ferritic HSLA pipeline steel. The maximum crack speed achieved in these experiments was between 230 m/s and 1165 m/s. The fracture toughness at crack arrest, K_Ia, was determined by a static analysis of this specific test. In all cases, it was found that K_Ia was much lower than K_Ic. The values of K_Ia decrease when the maximum crack speed increases, the results being largely scattered. The fracture toughness at crack arrest is therefore not an intrinsic parameter of the material for a given temperature. Cleavage fracture obtained under these conditions is characterized by the existence of numerous cleavage microcracks, mechanical twins and unbroken ligaments. The decrease in fracture toughness when crack speed increases is related, using the Beremin or the RKR model, to the high strain rates at the tip of a rapid propagating crack. A model which takes into account the effect of unbroken ligaments left in the wake of a propagating crack is developed to account for the large values of K_Ia which were occasionally measured.     

Dynamic crack propagation analysis of orthotropic media by the extended finite element method

Dynamic crack propagation of composites is investigated in this paper based on the recent advances and development of orthotropic enrichment functions within the framework of partition of unity and the extended finite element method (XFEM). The method allows for analysis of the whole crack propagation pattern on an unaltered finite element mesh, defined independent of the existence of any predefined crack or its propagation path. A relatively simple, though efficient formulation is implemented, which consists of using a dynamic crack initiation toughness, a crack orientation along the maximum circumferential stress, and a simple equation to presume the crack speed. Dynamic stress intensity factors (DSIFs) are evaluated by means of the domain separation integral method. The governing elastodynamics equation is first transformed into a standard weak formulation and is then discretized into an XFEM system of time dependent equations, to be solved by the unconditionally stable Newmark time integration scheme. A number of benchmark and test problems are simulated and the results are compared with available reference results.     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite

An investigation of the effects of moisture on mixed-mode I/II delamination growth in a carbon/epoxy composite is presented. Experimental quasi-static and fatigue delamination tests were carried out on composite specimens. The quasi-static fracture test results showed that exposure to moisture led to a decrease in mode II and mixed-mode delamination toughness while mode I toughness was enhanced. The fatigue tests revealed an adverse effect of moisture on delamination growth under mixed-mode loadings. Existing delamination criteria and growth rate models were evaluated to determine which ones best predict delamination toughness and growth, respectively, at any given mixed-mode ratio. Quasi-static and fatigue simulations with a cohesive zone-based finite element model that incorporated the selected mixed-mode delamination models were performed and good agreement between experimental and numerical data was shown for dry and moisture-exposed specimens.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

Modeling of the dynamic delamination of L-shaped unidirectional laminated composites

One of the widely used geometrically complex parts in advanced commercial aircraft is the L-shaped composite. Due to the sharp curved geometry, interlaminar opening stresses are induced and delamination occurs under considerable mode-mixities in L-shaped beams. Dynamic phenomena during delamination initiation and propagation of L-shaped beams are investigated using dynamic (explicit) finite element analysis in conjunction with cohesive zone methods. The 2-D model consists of 24 plies of unidirectional CFRP laminate with an initial 1 mm crack at the center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading type yields different traction fields and mode-mixities in the two sides of the crack in which delamination occurs under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed of the delamination under shear dominated loading at one side is 800 m/s and under normal stress dominated loading is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, a different failure mode is observed in which a secondary crack nucleates at the arm and propagates towards the center crack.     

Composite toughness enhancement with interlaminar reinforcement

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.     

A new mode I fracture test for composites with translaminar reinforcements

A new test method is presented for Mode I delamination fracture toughness testing of laminated composites containing a high density of stitches or translaminar reinforcements. The test set up, which is similar to the standard Double Cantilever Beam test, induces an axial tension in the specimen in addition to the transverse forces responsible for propagation of delamination. The tensile stresses reduce the compressive stresses in the vicinity of the crack tip caused by the large bending moments required for crack propagation. The nonlinear differential equations of equilibrium of the new specimen are solved using an iterative procedure to obtain the strain energy release rate as a function of load and crack length. Experiments were conducted using carbon/epoxy specimens containing 6.2 stitches per square centimeter (40 stitches per square inch). Results include Mode I fracture toughness, crack tip bending moment, transverse deflection and slope as a function of crack length. It is found that the apparent fracture toughness of the specimens tested remains constant as the stitches break and crack propagates, and is about sixty times that of unstitched specimens.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Crack branching in Homalite-100 sheets

Crack branching in Homalite-100 sheets of 1/8-in. and 3/8-in. thickness was studied by dynamic photoelasticity. Dynamic stress intensity factors, crack velocities and branching angles were measured and corresponding static stress intensity factors were determined by the method of finite element analysis. Dynamic stress intensity factors which preceded the actual branching reached a peak value of approximately three times the fracture toughness. The dynamic stress intensity factor drops prior to branching and then increases again to the maximum stress intensity factor at which point branching could occur again. Roughness of the fracture surface can be related to large dynamic stress intensity factors and crack velocities prior to branching and also after branching. Average branching angle was 26 deg.The results of this series of tests thus suggest that large dynamic stress intensity factors are necessary but not sufficient to cause crack branching.