Micromechanical characterization of local deformation in interlaminar-toughened CFRP laminates

The in situ SEM micro-line/grid methods were applied for quantitative evaluation of microscopic deformation in interlaminar-toughened CFRP cross-ply laminates with transverse cracks. Both the local deformation in the interlaminar region around the transverse crack tip and the crack opening displacement (COD) were observed at different temperatures to evaluate the effect of thermal residual stress. A two-dimensional approximate elastic analysis of stress and displacement fields in interlaminar-toughened cross-ply laminates with transverse cracks was conducted and compared with the experimental results. A reasonable agreement was obtained which implied the applicability of the analysis. The analysis will be a basis for the optimal design of interlaminar-toughened composite laminates.     

Engineering expressions for thermo-elastic constants of laminates with high density of transverse cracks

Thermo-elastic constants of symmetric and balanced laminates with intralaminar cracks in 90-layers depend on the opening displacement (COD) of the crack. The COD dependence on the interaction between cracks in the same layer is studied using FEM. The COD dependence on crack density is described by interaction function in form of tanh(). This interaction function multiplied with COD of non-interactive crack is the input parameter in analytical model for thermo-elastic properties of damaged symmetric and balanced laminates. Predictions performed for cross-ply laminates with cracks in inside and in surface layers and for quasi-isotropic laminates with different position of the 90-layer are in a very good agreement with direct FEM calculations.     

正交异性层板加载孔的变形与断裂分析

本文用云纹法着重对正交异性层板加载孔的变形与断裂行为进行了分析和研究,描述了加载孔的线弹性段、突然起裂段、裂纹稳态扩展段以及失稳扩展段的位移场与应变场的突变,给出了载荷—裂纹长度曲线、载荷—最大应变曲线,载荷—张开位移曲线以及裂纹张开角。在起裂以前,云纹法和线性有限元法的结果较好地吻合;起裂后,云纹法描述了材料的非线性特性。      

Fatigue crack growth in hybrid boron/glass/aluminium fibre metal laminates

The crack growth behaviour of hybrid boron/glass/aluminium fibre metal laminates (FMLs) under constant‐amplitude fatigue loading was investigated. The hybrid FMLs consist of Al 2024‐T3 alloy as the metal layers and a mixture of boron fibres and glass fibres as the fibre layers. Two types of boron/glass/aluminium laminates were fabricated and tested. In the first type, the glass fibre/prepreg and the boron fibre/prepreg were used separately in the fibre layers, and in the second type, the boron fibres and the glass fibres were uniformly mingled together to form a hybrid boron fibre/glass fibre prepreg. An analytical model was also proposed to predict the fatigue crack growth behaviour of hybrid boron/glass/aluminium FMLs. The effective stress intensity factor at a crack tip was formulated as a function of the remote stress intensity factor, crack opening stress intensity factor, and the bridging stress intensity factor. The bridging stress acting on the delamination boundary along the crack length was also calculated based on the crack opening relations. Then, the empirical Paris‐type fatigue crack growth law was used for predicting the crack growth rates. A good correlation between the predicted and experimental crack growth rates has been obtained.     

An analysis of mode I interlaminar deformation ahead of crack front in composite DCB specimens

An analytical model was employed to study mode I interlaminar deformation in double cantilever beam specimens of unidirectional carbon fiber/epoxy laminates. The crack opening displacements experimentally determined by moiré interferometry were compared with the model to evaluate the interlaminar tensile modulus and strain distribution ahead of the crack front. The findings showed that the modulus makes an important contribution to increasing the value of crack opening displacement, and that the strain distribution was dependent on both the modulus and thickness of the specimen. Also, a specific correlation was recognized between the modulus and the maximum strain evaluated at the crack tip.     

Intralaminar Damage Model for Laminates Subjected to Membrane and Flexural Deformations

Prediction of transverse damage initiation and evolution for not necessarily symmetric laminates under membrane and/or bending loads is the subject of this work. The laminate stiffness reduction is computed via crack opening displacement (COD) methods and the generalization to multiple cracking laminas is made via continuum damage mechanics (CDM) concepts. Using available COD solutions combined with homogenization techniques leads to an analytical constitutive model capable of predicting the initiation and evolution of crack density versus applied strain, as well as laminate modulus degradation, not only for symmetric laminates subjected to membrane deformation but also for general laminates subjected to flexural deformations as well. To adjust the model parameters, experimental data is required in the form of crack density, or modulus reduction, versus strain for two laminates of the same material system. Then, the model is capable of predicting crack density and modulus degradation for other laminate stacking sequences. The model takes into account crack closure, which is important under flexure, as well as the case of the center lamina straddling the neutral axis. The effect of thermal stresses is incorporated in the formulation.     

Damage evolution and characterisation of crack types in CF/EP laminates loaded at low temperatures

Tensile testing of CF/EP AS4/8552 cross-ply laminates at room (RT) and cryogenic (around −150 °C) temperatures has been performed to study the effect of temperature on damage (intralaminar cracking) evolution. Microscopy studies of the specimen edges showed a significant difference in damage pattern for the two different temperatures. At the low temperature (LT), more complex crack types were obtained that could not be found in specimens tested at the RT. The effect of these crack types on the laminate tensile modulus was studied by FEM. In analytical stiffness modelling complex shape crack was replaced by an “effective” normal (straight) crack with an “effective” crack opening displacement (COD) that leads to the same reduction in laminate stiffness. A crack efficiency factor was introduced to characterize the significance of complex crack shapes for stiffness reduction. The reduction of tensile modulus for a laminate damaged at low temperature was measured and compared with model predictions.     

The fracture toughness of Ni/Al2O3 laminates by digital image correlation II: Bridging-stresses and R-curve models

A composite of metal and brittle ceramic layers have increased fracture toughness as compared to ceramic monoliths. The property controlling the toughness enhancement is the, ‘bridging-stress’, exerted by the ductile phase astride the crack in the ceramic. This bridging-stress is a function of the crack-opening displacement (COD) which is a function of the size of the crack and the position along its profile. Depending on the accuracy of estimation of the bridging-stress, the modeled R-curve and experimental one match. In this study, a weight function based approach to generate the R-curve is reported and compared with the experimental results for Al₂O₃/Ni multilayer laminates.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.     

J-integral estimate for biaxially stressed Mode I cracks based on COD strain

This paper proposes a simple equation for evaluating J-integral values for biaxially stressed Mode I cracks. Finite element analyses were carried out to obtain the relationship between J-integral and crack opening displacement by varying the inelastic constitutive relationship, crack length and stress/strain biaxiality. A quantitative relationship was derived between the J-integral and crack opening displacement for various kinds of stress–strain relationships. A new equation for estimating the J-integral was proposed based on the crack opening displacement. The equation evaluated J-integral values for biaxially stressed Mode I cracks within a 25% error if the yield stress, strain hardening coefficient and exponent were known.     

Determination of static crack arrest toughness, Ja, from the CTOD test

The significance of low toughness pop-ins in weldment crack tip opening displacement (CTOD) tests is better understood once the relevant crack arrest toughness is known. This paper describes how a static crack arrest toughness, J_a may be derived simply from the CTOD test itself.     

Fatigue crack growth in Haynes 230 single crystals: an analysis with digital image correlation

Fatigue crack growth was investigated in Haynes 230, a nickel‐based superalloy. Anisotropic stress intensity factors were calculated with a least squares algorithm using the displacements obtained from digital image correlation. Crack opening/sliding levels were measured by analysing the relative displacement of crack flanks. Reversed crack tip plastic zones were calculated adopting an anisotropic yield criterion. The strains measured in the reversed plastic zone by digital image correlation showed a dependence on crystallographic orientation. Finally, a finite element model was adopted to examine plasticity around the crack tip. Results were compared with the experimentally observed strains.     

The effect of second principal stress on the fatigue propagation of mode I surface crack in Al2O3/Al alloy composites

Using a plate made of A2017-T6 metal matrix composites reinforced with 10 volume % and 20 volume % Al₂O₃ particles and Al alloy possesses the same composition as matrix alloy, the crack propagation rate da/dN of a mode I surface crack by the simultaneous action of plane bending and cyclic torsion are studied. And the effects of crack tip opening stress σ_top, crack opening displacement COD, biaxial stress ratio C (=second principal stress/first principal stress) and the surface roughness of crack section are examined. When stress intensity factor range ΔK is lower than the specific level, da/dN decreases with the increase of volume fraction of Al₂O₃ in C=0 and C=−0.55. But, da/dN of Al alloy becomes minimum in C=−1 and the effect of Al₂O₃ particles disappears. σ_top rises with the increase of volume fraction of Al₂O₃ particles and the decline of C. On the other hand, COD doesn’t always rise with the decline of C. These phenomena can be explained by the residual compressive stress formed at the surface layer of the specimen by the fatigue test and the surface roughness of crack section.     

聚丙烯纤维水泥稳定碎石断裂性能试验研究

通过30个尺寸为100mm×100mm×515mm的聚丙烯纤维水泥稳定碎石和普通水泥稳定碎石三点弯曲试件断裂试验,探讨了聚丙烯纤维对水泥稳定碎石断裂韧度(KIC)、断裂能(GF)、临界裂缝嘴张开位移(CMODC)、临界裂缝尖端张开位移(CTODC)、极限裂缝嘴张开位移(CMODmax)和极限裂缝尖端张开位移(CTODmax)的影响。试验结果表明:聚丙烯纤维的掺入可增大水泥稳定碎石的断裂韧度、断裂能、临界裂缝嘴张开位移、极限裂缝嘴张开位移、临界裂缝尖端张开位移和极限裂缝尖端张开位移;随着聚丙烯纤维体积掺量的增加,断裂韧度、临界裂缝嘴张开位移和临界裂缝尖端位移的变化无明显规律,但断裂能、极限裂缝嘴张开位移和极限裂缝尖端位移基本上呈线性增加的。     

A simplified analysis of transverse ply cracking in cross-ply laminates

This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.     

Experimental study of damage propagation in Over-height Compact Tension tests

This paper describes an experimental investigation into progressive damage development in notched fibre-reinforced composites laminates. The Over-height Compact Tension (OCT) test captures the behaviour of laminates typical of large structures and permits the stable formation of a process zone ahead of the crack tip. This allows a study of the influence of sub-critical damage on progression of fibre failure. A range of lay-ups have been tested using dispersed and blocked plies in the thickness direction. The load vs. pin opening displacement (POD) curve is used to characterise the progressive failure of specimens. A number of interrupted tests were performed for each lay-up to capture the sub-critical damage process before the onset of fibre fracture. Results show that dispersed plies promote fibre failure and crack growth whilst blocked plies promote a larger amount of splitting and delamination which in turn causes a larger process zone and ultimately a tougher laminate.     

Automated estimation of fatigue crack length and closure/opening stress

An experimental technique is proposed for the estimation of crack length as well as crack closure/opening stress during fatigue crack growth. A specially designed, single cantilever, crack opening displacement gauge is used to monitor these variables during fatigue crack propagation testing. The technique was experimentally validated through electronfractography.     

Effect of the loading rate on mode I interlaminar fracture toughness of laminated composites

The objective of the present study is to determine the influence of the loading rate on the critical energy release rate G_Ic of fibre-reinforced epoxy laminates. In order to perform pure mode I loading at higher opening velocities, a new test device is developed. The approach is based on a symmetrical opening displacement applied to a DCB specimen. In the data reduction, the influence of the kinetic energy has to be taken into account. The results obtained on the unidirectional carbon-epoxy laminate T300/914 at crack opening rates up to 1.6 m/s show a slight effect of the loading rate on G_Ic.     

Effect of fiber bridging on the fatigue crack propagation in carbon fiber-reinforced aluminum laminates

A superior crack propagation resistance was observed on various carbon fiber-reinforced aluminum laminates (CARALL) under tension-tension fatigue. It might be attributed to the restraint on the crack opening imposed by intact fibers in the crack wake. These fibers bridging the crack could reduce the effective stress intensity factor actually experienced by the crack tip. Based on the measurement of crack length and delamination size, the effective stress intensity range, ΔK_eff, of fatigue-damaged CARALL laminate was calculated by using a simplified analytical model. It was shown that the fatigue crack propagation rate in CARALL could be expressed as a unique function of the calculated ΔK_eff, which agree well with the Paris equation for the unreinforced aluminum alloy. This result confirmed the applicability of this simplified analytical model in CARALL laminates.     

Improvement of interlaminar mechanical properties of CFRP laminates using VGCF

In order to improve the interlaminar mechanical properties of CFRP laminates, hybrid CFRP/VGCF laminates have been fabricated by using a newly-developed method, i.e., powder method, where the powder of vapor grown carbon fiber (VGCF) is added at the mid-plane of [0°/0°]₁₄ CFRP laminates. Experimental results of double cantilever beam (DCB) tests indicate the improvement on the interlaminar mechanical properties of Mode-I fracture behavior with much higher critical load P_C and fracture toughness G_IC with VGCF interlayer. Crack propagation and fracture surface have also been observed to interpret this improvement mechanism. Moreover, based on experimental G_IC, numerical simulations using finite element method (FEM) with cohesive elements have been carried out to analyze the delamination propagation. The interlaminar tensile strength of hybrid CFRP/VGCF laminates, which is obtained by matching the numerical load–COD (crack opening displacement) curves to experimental ones, is higher than that of base CFRP laminates.