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.     

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.     

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.     

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.     

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.     

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.     

Mechanical behavior of glass/epoxy tubes under combined static loading. Part II: Validation of FEA progressive damage model

Experimental results from a series of biaxial static tests of E-Glass/Epoxy tubular specimens [±45]₂, were compared successfully with numerical predictions from thick shell FE calculations. Stress analysis was performed in a progressive damage sense consisting of layer piece-wise linear elastic behavior, simulating lamina anisotropic non-linear constitutive equations, failure mode-dependent criteria and property degradation strategies. The effect of accurate modeling of non-linear shear stress–strain response, dependent on the plane stress field developed, was proved of great importance for the numerical FEA predictions, concerning macroscopic stress–strain response. Ultimate load prediction was influenced more decisively when degradation strategies for the compressive strength along the fiber direction were considered.     

The response of aluminium/GLARE hybrid materials to impact and to in-plane fatigue

Fibre metal laminates (FMLs), such as glass reinforced aluminium (GLARE), are a family of materials with excellent damage tolerance and impact resistance properties. This paper presents an evaluation of the low velocity impact behaviour and the post-impact fatigue behaviour of GLARE laminate adhesively bonded to a high strength aluminium alloy substrate as a fatigue crack retarder. The damage initiation, damage progression and failure modes under impact and fatigue loading were examined and characterised using an ultrasonic phased array C-scan together with metallography and scanning electron microscopy (SEM). After impact on the substrate, internal damage to the GLARE bonded on the opposite side of the substrate occurred in the form of fibre and matrix cracking. No delamination was detected at the GLARE/substrate bond. Before impact the bonded GLARE strap caused reductions in substrate fatigue crack growth rate of up to a factor of 5. After impact the retardation was a factor of 2. The results are discussed in terms of changes to the GLARE stiffness promoted by the impact damage.     

The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part I: Material cracking behaviour

The present paper is the first of a two-part series reporting an experimental and theoretical study of the fracture of circumferentially notched samples of a commercial aluminium alloy, i.e. Al6082, subjected to tension, torsion and mixed tension/torsion loading. The overall aim of the work was to investigate the use of a particular method of failure prediction, known as the Theory of Critical Distances. This first part reports the experimental data - load-deflection curves and observed material failure modes - and discusses the consequences of these findings for the development of the theory, which is covered in the second part. It was observed that relatively blunt notches loaded in tension failed by a conventional ductile fracture mode similar to plain (unnotched) specimens. However, in tensile specimens containing sharp notches, failure occurred via the initiation, stable propagation and, finally, unstable propagation, of circumferential ring cracks. Under torsional loading, and independent of the notch root radius, static failures of the tested samples always occurred by the formation and stable propagation of ring cracks. Under mixed-mode loading there was a gradual transition between the ductile and brittle modes and between stable and unstable cracking. For all types of loading, it was observed that crack initiation always coincided with peak loading conditions, and that cracks invariably grew on the plane perpendicular to the specimen’s longitudinal axis.     

The effects of loading waveform and microstructure on the fatigue response of titanium aero-engine compressor disk alloys

Microstructural variations produced from manufacturing processes and their influence on fatigue crack growth in titanium disks were investigated. Charpy‐tests on titanium disk material were performed and materials with fracture energy values in the range of 3.8–19.1 J/cm² were selected for tests under cyclic loads. Results of Charpy‐tests were compared with fractographic features related to fatigue crack growth in Ti?6Al?3Mo?0.4Si and Ti?6Al?3Mo?2Cr alloys with a two‐phase (α + β) lamellar structure under various cyclic waveforms using specimens made from compressor disks. The material sensitivity to cyclic load waveform can be seen for in‐service disks using a criteria based on fracture energy values determined in Charpy‐tests. A difference in fatigue crack growth periods of 2.5 times was discovered for specimens made from the disk with a filament type microstructure and the mainly globular two‐phase structure of the Ti?6Al?3Mo?0.4Si alloy. The shorter crack growth period correlated with the mainly facetted pattern formation with local zones of fatigue striations when fatigue crack growth is along the planes of the filaments. Fatigue striations are the major fracture surface relief when crack growth occurs in the perpendicular direction to the plane of the filaments. A quantitative fractographic method for estimating the crack growth period for in‐service failed disks was performed for the case of crack development along planes of such microstructural filaments created during the manufacturing process. Specimen tests involving a hold‐time in the cyclic loads are recommended for in‐service accepted titanium disks using a criteria based on the fracture energy value. Selection of disks based on these criteria can indicate a material sensitivity to cyclic load waveforms.     

Low-velocity impact damage response of fiberglass/magnesium fiber-metal laminates under different size and shape impactors

Low-velocity impact tests are performed on fiberglass/AZ31B-H24 magnesium fiber-metal laminates (FMLs) with various configurations in order to gain a better understanding of the effect of an impactor's features on the response of this type of FML. For that, impactors with two different shapes (hemispherical and sharp-edged) and sizes are used to impact the specimens. The impact response data, such as the deformation of the contact location and energy absorption, is obtained directly during the impact tests through the impact equipment, while mechanical sectioning was carried out to establish the extent of delaminated area and post-impact residual deformation. While the sharp-edged impactor caused the development of cracks on the metal constituent, and delamination within the specimens, the hemispherical ones imposed more influence over the residual deformation. Noticeable differences are observed in response of FML specimens made with two and three layers of magnesium, especially with respect to the energy absorption capacity. Moreover, finite-element analysis, as a major part of this study, has been employed to simulate the low-velocity impact response of FML specimens. The behavior of specimens has been simulated using the commercial finite-element code ABAQUS. The results imply that there is a good agreement between the experimental and numerical results.