A generalized damage model for woven ply laminates under static and fatigue loading conditions

A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data.     

The response of a multi-directional composite laminate to through-thickness loading

The through-thickness mechanical response of a carbon fibre/epoxy laminated composite of lay-up [0/45/−45]_ns is measured at low rates of strain. Uniaxial tension and compression experiments are carried out on dogbone specimens cut from a thick laminate along different directions, and failure mechanisms are observed via optical and electron microscopy. The effect of direct and shear stresses at the ply interfaces on the onset of failure is measured, and a failure envelope is constructed. The compressive response of specimens of different shape is investigated. Composite beams of different volume and aspect ratios are tested to failure in three-point bending and these tests reveal a strong dependence of the apparent out-of-plane tensile strength of the composite on the beam volume; this effect is modelled by Weibull theory.     

Constituent damage mechanisms in metal matrix composites under fatigue loading, and their effects on fatigue life

Load controlled fatigue experiments were performed on 8-ply unidirectional ([0]₈) SCS-6-Ti-15-3 metal matrix composites (MMCs) at different temperatures, and the results were interpreted in terms of the overall three-regime framework of fatigue. The emphasis was on understanding the mechanisms and mechanics of constituent damage evolution, and their effects on fatigue life. Most tests were performed at an R-ratio of 0.1, but limited fully-reversed (R = −1) tests were conducted. In regime 1, damage was fiber failure dominated, but the exact mechanisms were different at room and elevated temperatures. In regime 2, observation of matrix cracks and persistent slip bands provided convincing evidence of matrix dominated damage. Weak fiber-matrix interfaces contributed to crack bridging. However, fiber fracture also played an important role in regime 2; tension-tension and tension-compression tests showed similar lives on a maximum fiber stress basis, although the strain range, which primarily controls matrix crack growth, was almost double for R = −1 compared with R = 0 or 0.1. Good agreement was obtained from the different R-ratio tests, between the MMC and matrix data, and data at room and elevated temperatures, when compared based on the strain range in the tension part of a cycle. Analyses and observations of fiber pull-out lengths and fiber fractures in the matrix crack wake provided evidence of fiber damage; the analyses also helped to explain increased fiber bridging with fiber volume fraction. Issues of fatigue life prediction are briefly discussed.     

On the notch sensitivity of flax fibre metal laminates under static and fatigue loading

Damage progression and failure characteristics of open‐hole flax fibre aluminium laminate (flax‐FML) specimens subjected to quasi‐static tensile or tension‐tension fatigue loading were experimentally investigated. Notched and unnotched flax‐FML composites exhibited brittle fracture with little or no fibre pull‐out and minimal delamination at the aluminium/adhesive interface. The flax‐FMLs were tested to failure under tension‐tension fatigue loading conditions (R ratio of 0.1; frequency of 10 Hz; applied fatigue stresses ranging between 30% and 80% of the respective ultimate tensile strength values). The fatigue cycles to failure decreased with the increase in the applied fatigue stress and hole diameter. A phenomenological modelling technique was developed to evaluate the fatigue life of an open‐hole flax‐FML composite. Fatigue tests on specimens subjected to a maximum load equivalent to 35% of the respective tensile failure strength were interrupted at around 85% of the corresponding fatigue life. The accumulated fatigue damage in these specimens was characterised using X‐ray computed tomography. For benchmarking purposes, the fatigue performance and related damage progression in the flax‐FML composite were compared with those of the glass‐FMLs.     

Numerical analysis of fibre bridging and fatigue crack growth in metal matrix composite materials

The analysis of bridged crack configurations in unidirectional fibre-reinforced composites is relevant to a variety of crack growth problems, including the fatigue of metal matrix composites and the study of fibre failure in the wake of a bridged matrix crack. Details of numerical procedures for predicting fibre stresses and their effect on crack tip stress intensity factors are presented here to provide a useful overview of how standard bridging calculations are done. Results are presented and discussed in the context of predicting fatigue crack growth with fibre failure in metal matrix composites.     

Effect of carbon fibres on the static and fatigue mechanical properties of fibre metal laminates

It is crucial to understand the characteristic fatigue crack initiation and its growth mechanisms, as well as the relationship between the mechanical properties and the fatigue damage evolution in fibre metal laminates (FMLs). Two types of FML were studied in this work: a polyacrylonitrile‐based carbon fibre epoxy matrix composite sandwiched by Ti‐6Al‐4V (Ti‐alloy) sheets (IMS60‐Ti) and a pitch‐based carbon fibre epoxy matrix composite sandwiched by Ti‐alloy sheets (K13D‐Ti). The static and fatigue mechanical properties of IMS60‐Ti and K13D‐Ti were investigated. The increased failure strain of the FML was greater than that of carbon fibre‐reinforced polymer (CFRP) matrix composites. The fatigue life of IMS60‐Ti was much longer than that of K13D‐Ti. The fatigue damage process in IMS60‐Ti was related to the fatigue creep behaviour of the Ti‐alloy face sheet and mode II cracking at the CFRP/Ti‐alloy interface, and the damage in K13D‐Ti was related to the K13D CFRP laminate.     

An experimental investigation of the static and fatigue fracture behaviour of hybrid composite/metal joints for a tilting car body

The hybrid composite joint structures considered in this work, for application in a tilting railroad car body, are subjected to shear and bending loads. Two types of the joint specimens were fabricated and tested under both static and fatigue conditions: a hybrid bolted-joint specimen subjected to a shear loads, and a hybrid beam-joint specimen for the bending tests. The fracture behaviours of these specimens under static loads were different from those under cyclic loads. For the hybrid bolted-joint specimens, static shear loads caused a pure shear fracture in the bolt pin body itself. However, cyclic fatigue shear loads brought about an opening-mode fracture at the local site of the bolt which was the valley of the screwed region of the bolt pin and/or the perpendicularly angled region between the bolt head and the pin body. On the other hand, for the hybrid beam-joint specimens, static bending loads caused shear deformation and fracture in the honeycomb core region, while fatigue cyclic bend loading caused delamination along the interface between the composite skin and the honeycomb core, and/or caused a fracture in the welded part jointed with the steel under-frame. These fracture behaviours could arise in other industrial hybrid joints with similar sub-structures, and were used in developing a design parameter to improve a hybrid joint structure.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

雷击冲击力作用下复合材料层合板动力学响应及损伤特性

采用基于连续介质损伤理论（CDM）的复合材料三维渐进损伤分析模型,以ABAQUS有限元分析软件为平台,结合VUMAT子程序,对雷击冲击力作用下的复合材料层合板进行了三维动力学分析,研究了雷击冲击力作用下层合板的动力学响应及损伤特性。结果表明,在雷击冲击力作用下,层合板做降幅振荡运动,冲击力做功与层合板内能和动能相互转换,同时伴随着黏性耗散能,冲击力做功大小可用雷电流库伦量与作用积分的函数表示;层合板损伤由外力做功大小决定,对于同种材料,基体、纤维及分层损伤分别存在不同的损伤能量临界值,当冲击力做功大于该值,层合板会产生对应的损伤;在相同边界支持条件下,冲击力总功最大值决定了不同损伤类型损伤状态变量的大小,与波形参数和峰值电流无关。     

Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

Intralaminar fatigue crack growth properties of conventional and interlayer toughened CFRP laminate under mode I loading

Intralaminar and interlaminar fatigue crack growth behaviours under mode I loading were investigated with conventional and interlayer toughened unidirectional CFRP laminates. For intralaminar crack growth tests, initial defects were introduced using “intralaminar film insertion method”, in which a release film is inserted inside a single lamina prepreg. A fatigue test under a constant maximum energy release rate, G_max, was carried out using DCB specimens. It was found that the intralaminar fatigue crack growth property of the interlayer toughened CFRP laminates was the same as that of the conventional CFRP laminates. For the interlayer toughened CFRP laminates, the G_max with a given crack growth rate, da/dN, was much lower for intralaminar crack growth than for interlaminar crack growth. The da/dN-G_max curve at zero crack extension, Δa = 0, which was estimated by extrapolating the da/dN-Δa relationship, was not affected by bridging fibres, and most conservative for the interlayer toughened CFRP laminates.     

Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading

In the notch stress intensity approach to the fatigue assessment of welded joints, the weld toe is modelled as a sharp V-notch and the local stress distributions in plane problems are given on the basis of the relevant mode I and mode II notch stress intensity factors (N-SIFs). These factors quantify the magnitude of asymptotic stress distribution obeying Williams’ solution. If the V-notch opening angle at the weld toe is constant and the mode II is not singular, the mode I N-SIF can be directly used to summarize the fatigue behaviour of welded joints. In all the other cases, varying the V-notch angle or including multiaxial loading conditions (where typically both Mode I and Mode III stress distributions are singular), the synthesis can be carried out on the basis of the mean value of the strain energy density over a well-defined volume surrounding the weld toe or the weld root. By using this scalar quantity, two fatigue scatterbands are obtained for structural steels and aluminium alloys, respectively. The material-dependent radius R_C of the control volume (area) is carefully identified with reference to conventional arc welding processes.Sometimes the weld toe radius is found to be very different from zero. The local strain energy approach can be extended as it stands also to these cases, providing a gradual transition from a N-SIF-based approach to a K_t-based approach.     

Notch sensitivity of Ti-based unidirectional metal matrix composites under tensile and fatigue loading

Neuber's rule and the notch equivalent crack length concept were utilized to predict the effect of notches on the fracture strength and fatigue limit of unidirectional metal matrix composites. For the examination of the fracture strength, the strain of the notch is compared to that required for debonding or fracture of the fibres. The notch effect under fatigue loading is determined by examining the ability of the notch to achieve premature debonding.     

The static and fatigue strength of bolted joints in composites with hygrothermal cycling

The effects of hygrothermal cycling upon the performance of a bolted composite joint was examined. Bolt torque relaxed as the number of environmental cycles increased. Comparison with analytical results suggested that the bolt torque “zigzag” behavior probably results from the natural sensitivity of bolted composite joints to the existing ambient temperature and moisture. The washer effect and specimen surface finishes were investigated to study the friction effect on joint bearing performance. Fatigue tests of specimens exposed to hygrothermal cycling exhibited greater hole elongation than specimens not exposed. High preload does improve static failure strength and the fatigue life of specimens under room conditions. Tests run on IM6/3501-6 material specimens with hygrothermal cycling show reasonable declines in fatigue life. The moisture weight gains of composites under hygrothermal cycling exposure were measured and compared to numerical results; good correlation was obtained. As a result, bolt failure occurred in some fatigue tests and is most frequently associated with large thickness-to-diameter ratio. The peak-to-peak stress was defined to study the effect of the R-ratio on bolts for the bolt failure problem.     

Experimental analyses of SFRP material under static and fatigue loading by means of thermographic and DIC techniques

The mechanical properties of injection moulded short glass fibre-reinforced polyamide composites was investigated using experimental techniques. The Digital Image Correlation technique was applied during the tensile tests in order to obtain the stress–strain curves and to identify the fracture location at the early stages of the tests. Moreover, the thermographic technique was used during the static tests in order to identify the fracture zone and also during the fatigue tests, carried out at different frequencies, to study the temperature evolution of the specimen. A theoretical model was developed to analyze the temperature evolution during the fatigue test and the effect of the test frequency. The aim of this study is the application of the Thermographic Method for the fatigue assessment of short glass fibre-reinforced polyamide composites.     

The peak stress method applied to fatigue assessments of steel and aluminium fillet-welded joints subjected to mode I loading

The aim of this work is to present an engineering method based on linear elastic finite element (FE) analyses oriented to fatigue strength assessments of fillet‐welded joints made of steel or aluminium alloys and subjected to mode I loading in the weld toe region where fatigue cracks nucleate. The proposed approach combines the robustness of the notch stress intensity factor approach with the simplicity of the so‐called ‘peak stress method’. Fatigue strength assessments are performed on the basis of (i) a well‐defined elastic peak stress evaluated by FE analyses at the crack initiation point (design stress) and (ii) a unified scatter band (design fatigue curve) dependent on the class of material, i.e. structural steel or aluminium alloys. The elastic peak stress is calculated by using rather coarse meshes with a fixed FE size. A simple rule to calculate the elastic peak stress is also provided if a FE size different from that used in the present work is adopted. The method can be applied to joints having complex geometry by adopting a two‐step analysis procedure that involves standard finite element (FE) models like those usually adopted in an industrial context. The proposed approach is validated against a number of fatigue data published in the literature.     

The influence of fatigue on the stiffness and remaining static strength of self-piercing riveted aluminium joints

Self piercing riveting (SPR) is one of the major joining technologies for aluminium structures due to its advantages over some of the more traditional joining technologies. In this paper, the mechanisms of crack initiation and growth during fatigue and the influence of fatigue on the stiffness and remaining static strengths of SPR joints in both lap shear and T peel configurations were studied. The results showed that cracks could initiate and develop from different locations on the substrate materials depending on load levels and test types. Fatigue increased the remaining static lap shear strength and stiffness of specimens due to the increased friction force at the top/bottom sheet interfaces around the tip of punched hole through fretting; however, fatigue reduced the remaining static T peel strength of specimens due to crack initiation and development; T peel fatigue at high load levels also increased the stiffness of specimens due to geometry change through large plastic deformation.     

A novel predictive model for mechanical behavior of single-lap GFRP composite bolted joint under static and dynamic loading

Mechanical connection of composite is critical due to its complicated meso-structure and failure mode, which has become a bottleneck on reliability of composite material and structure. Although many researches on composite bolted joints have been carried out, the theory and experiment on mechanical behavior of such a joint structure under dynamic loading were rarely reported. Here, we propose a novel predictive model for quasi-static and dynamic stiffness of composite bolted joint by introducing the strain rate dependent elastic modulus into the mass spring model. Combined with the composite laminate theory and Tsai-Hill theory, the present model was capable of predicting the strain rate dependent stiffness and strength of the composite bolted joint. Quasi-static and impact loading experiments were carried out by Zwick universal hydraulic testing machine and split Hopkinson tension bar, respectively. The stiffness and strength predicted by our model showed good accordance with the experiment data with errors below 12% under quasi-static loading and below 30% under impact loading. The results indicated that under impact loading, stiffness and strength of the composite bolted joint were significantly higher than their quasi-static counterparts, while the failure mode of the joint structure trended towards localization which was mainly bearing failure. Among various lay-up ratios studied, the optimal lay-up ratio for quasi-static and dynamic stiffness was 0:±45:90 = 3:1:1.