Off-axis fatigue crack growth and the associated energy release rate in composite laminates

Stable matrix crack growth behaviour under mechanical fatigue loading has been studied in a quasi-isotropic (0/90/-45/+45)_s GFRP laminate. Detailed experimental observations were made on the accumulation of cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finite element model of the damaged laminate has been constructed. This model has been used to relate the energy release rate of growing cracks to the crack growth rate via a Paris relation.     

Experimental observations and finite element modelling of damage initiation and evolution in carbon/epoxy non-crimp fabric composites

Damage in carbon/epoxy non-crimp stitched fabric (NCF) reinforced composites, produced by the resin transfer moulding (RTM) process is described. Formation of the stitching loop results in a certain disturbance of the uniform placement of the fibres. These deviations in fibre placement produce resin-rich zones that can influence the mechanical behaviour of the composite part. Tensile tests on quadriaxial (45°/90°-45°/0°)_s laminates are performed accompanied by acoustic emission (AE) registration and X-ray imaging. Early initiation of damage (matrix cracking) in plies with different fibre orientation has been detected. Damage sites correlate with the resin-rich zones created by the stitching. Finite element (FE) analysis is carried out to develop a model that describes damage of the NCF composites. Numerical multi-level FE homogenization is performed to obtain effective elastic orthotropic properties of NCF composite at micro (unit cell of unidirectional tow) and meso (fabric unit cell) levels. A hierarchical sequence of FE models of different scales is created to analyze in detail the 3D stress state of the NCF composite (meso unit cell). A multi-level submodeling approach is applied during FE analysis. Zones of matrix-dominated damage are predicted. A comparison of non-destructive testing results with computational model is performed. Fracture mechanics parameters of matrix crack are computed and cracks growth stability is studied.     

Damage in NCF composites under tension: Effect of layer stacking sequence

Non-crimp fabric (NCF) cross-ply composites response to tensile loading is investigated showing large effect of the fabric layer stacking sequence: much larger elastic modulus reduction was observed in [0/90/0/90]_S than in [90/0/90/0]_S case. Since transverse cracks in 90°-bundles may give modulus decrease about 5%, the observed 40% stiffness reduction is attributed to failure and delamination of bundles oriented in the direction of the applied load. Analysis of micrographs shows extensive delaminations and 0°-bundle breaks. FE calculations showed that failure of 0°-bundles at the surface is energetically more favorable. However, the fracture resistance of surface bundles is higher due to smaller bundle waviness and the density of bundle cracks on the surface was not larger than inside.Two possible reasons for the higher stiffness reduction in the [0/90/0/90]_S NCF composite were suggested: (a) If two imperfect 0°-bundle layers are separated by a 90°-bundle layer their resistance to failure is lower than when they are situated next to each other; (b) the effect of each surface 0°-bundle break on the composite stiffness is larger (due to less constraint from the surrounding material the opening of surface bundle breaks is much larger).     

Dry sliding wear of an Al2O3 continuous fibre reinforced Al-Cu alloy against steel counterface

The tribological properties of Al₂O₃ continuous fibre reinforced Al-4.43 wt %Cu alloy composites with a fibres' volume fraction of about 0.55 were measured for five types of fibre orientations under a dry sliding contact with a bearing steel. Fibres were in a plain perpendicular to wear surface and parallel to sliding direction, and had the angles 0°, 45°, 90°, or 135° with respect to the direction of motion of the counterface; or were anti-parallel the sliding direction. The results show obvious dependence of wear characteristics on fibres orientation: for the 45°, 90°, and 135° orientations, the larger the fibres' angle, the lower the volume loss; while the 0° orientation resulted in a higher steady-state wear rate than those of the 45°, 90°, and 135°, orientations, except that the anti-parallel orientation caused the highest volume loss at all sliding distances. The wear mechanism was inferred as a oxidation-microgrooving process through the analyses of worn surface and subsurface with the aid of optical microscope and scanning electron microscope. Also it was found that the fibres' broken and subsurface deformation had played an important role in causing wear anisotropy.     

Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Investigation of the kinetics of cracks in polymethyl methacrylate by dynamic photoelasticity

Methods have been developed for experimental investigation of the kinetics of fast cracks in plates of optically active model material making it possible to load by pulsed pressure varying the amplitude and length of the pulse and also to use the photoelastic method for recording dynamic processes with use of a superfast motion picture camera. The relationship of the dynamic stress intensity factor to crack growth rate and plate thickness was obtained taking into consideration the influence of longitudinal and transverse elastic waves. A clear relationship between stress intensity factor and v_cr was established. It was shown that with a fast crack growth rate (v_cr < 270 m/sec) the uniqueness between stress intensity factor and v_cr is disturbed by the action of reflected waves. The character of action on the stress intensity factor and crack growth rate of longitudinal and transverse waves reflected from the boundaries of the plate and also the influence of inertial effects caused by stress waves, high crack growth rates, and a change in the stressed and strained state with an increase in plate thickness were determined. It was determined that in polymethyl methacrylate in incidence on a crack at an angle of 90° a longitudinal wave increases the stress intensity factor and v_cr (with v_cr<625 m/sec) while a transverse wave decreases these characteristics.Translated from Problemy Prochnosti, No. 9, pp. 40–46, September, 1991.     

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.     

Fiber direction and stacking sequence design for bicycle frame made of carbon/epoxy composite laminate

According to the maximum stress theory and the results of strength-to-stress ratios, the fiber direction and stacking sequence design for the bicycle frame made of the carbon/epoxy composite laminates have been discussed in this paper. Three testing methods for the bicycle frame, i.e. torsional, frontal, and vertical loadings, are adopted in the analysis. From the finite element results, the stacking sequences [0/90/90/0]_s and [0/90/45/−45]_s are the good designs for the composite bicycle frames. On the contrary, the uni-directional laminates, i.e. [0/0/0/0]_s, [90/90/90/90]_s, [45/45/45/45]_s and [−45/−45/−45/−45]_s, are the bad designs. In addition, weak regions of failure occur at the fillets and connections of the frame, i.e. the stress concentration regions. All weak points occur at the inner or outer layer of the laminated composite tube. The 0°-ply and 90°-ply located on the inner and outer layer of the tube can effectively resist the higher stress at its location.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.     

Damage development in carbon fibre-reinforced polyimides in fatigue loading as a function of stress ratio

Carbon fibre-reinforced polyimide laminates of lay-up (O₂/±45/O₂/ ±45/90)_s have been fatigue tested at stress ratios of 0.1 and −1. Damage propagation was monitored by recording the storage modulus and rate and amplitude of acoustic emission events. The results of these tests, along with X-ray and optical photographs of damaged specimens, indicate that damage propagates in three stages: the formation of transverse cracks on 45° and 90° plies, delamination from the transverse cracks and sample failure.     

Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading

Transverse cracking behaviour in a quasi-isotropic glass/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°/90°/–45°/45°] _S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the neutral axis position and the residual curvature as a function of the transverse crack density and the in-situ ply stress at first ply failure. Experimental results are obtained with the use of the applied moment – strain data in four-point flexural tests and compared with predictions. Time-dependent behaviour of the residual curvature is also investigated.The theoretical predictions are in reasonably good agreement with the experimental results. It is found that the decrease in the residual curvature after unloading is mainly ascribed to viscoelasticity of the material.     

Modelling of transverse crack growth and saturation in cross-ply laminates

A model of transverse cracking in cross-ply laminates is presented. The model describes the onset of cracking, the development of the number of cracks, the saturation phase of this damage mode and the final crack distribution, as well as the dependency of these phenomena on the 90° ply thickness. This analysis is based on an effective flaw size distribution and a non-linear interlaminar behaviour hypothesis. The theoretical prediction of the process and the saturation of cracking was well correlated with the experiments conducted on [O₂/90 _n ]_s graphite/epoxy. However, there was considerable dispersion in the experimental results concerning the onset of cracking. Experimental work and part of the theoretical investigations were made at ONERA, 29 av. Division, Leclerc 92322, Chatillan, Cedex, France.     

Interaction of dynamic mode-I cracks with inclined interfaces

In this paper, we report on an experimental study of the deflection/penetration behavior of dynamic mode-I cracks propagating at two different crack velocities (slower and faster) toward inclined weak interfaces of three dissimilar angles (α): 30°, 45° and 60°. A simple wedge-loading specimen configuration as proposed by Xu et al. [Xu LR, Huang YY, Rosakis AJ. Dynamic crack deflection and penetration at interface in homogenous materials: experimental studies and model predictions. J Mech Phys Solids 2003;51:461-86], made of brittle Homalite-100, is used. A modified Hopkinson bar setup is used to achieve well-controlled impact loading conditions. Dynamic photoelasticity in conjunction with high-speed photography is used to capture real-time isochromatics associated with deflected/penetrated cracks.     

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

High-temperature mechanical behaviour of multidirectional Nicalon/CAS-II composite

High-temperature mechanical behaviour of Nicalon/CAS-II composite has been investigated. Oxidation of the exposed interfaces along matrix cracks at 1000 °C lowered the longitudinal unidirectional strength to the stress level at which matrix cracking began to occur. The strength of cross-plied composites was also severely reduced in 800 °C air. Transverse plies cracked prior to 0° ply matrix cracking. However, embrittlement did not occur until the matrix in the 0° plies cracked. It was established that oxidation does not take part in crack growth parallel to the fibres, except adjacent to exposed edges. Neither does oxygen enter 90° ply cracks in cross-plied composites in sufficient quantity to produce oxidation embrittlement, at least up to the 0° matrix cracking strain.The work was established while the author was at the Department of Chemical Engineering at Montana State University.     

INITIATION AND GROWTH OF SMALL CRACKS IN DIRECTIONALLY SOLIDIFIED MAR-M247 UNDER CREEP-FATIGUE PART II: EFFECT OF ANGLE NETWEEN STRESS AXIS AND SOLIDIFICATION DIRECTION

This paper deals with the effect of anisotropy on fracture processes of a directionally solidified superalloy, Mar-M247, under a push–pull creep-fatigue condition at high-temperature. Three kinds of specimen were cut from a cast plate such that their axes possess angles of 0°, 45° and 90° with respect to the 〈001〉 orientation that is aligned parallel to the solidification direction (also to the grain boundaries and primary dendrite axis); these specimens being denoted the 0° specimen, the 45° specimen, and the 90° specimen, respectively. The tests were conducted at 1273  K (1000 °C) in air under equal magnitudes of the range of a Δ J -related parameter, Δ W _c , which represents the driving force for crack growth in creep-fatigue. Although the grain boundaries are macroscopically parallel to the solidification direction, they are wavy or serrated microscopically. Small cracks nucleate along parts of the grain boundaries perpendicular to the stress axis in all specimens. The 90° specimen has the shortest crack initiation life and the 0° specimen has the longest. In the 90° and 45° specimens, intergranular cracks continue to nucleate and a main crack is formed along the grain boundary due to the frequent coalescence of small cracks. In the 0° specimen, cracks grow into the grain, and transgranular cracks coalesce along the primary dendrite or grain boundary. The 0° specimen exhibits the slowest crack growth rate and the 90° specimen the fastest. These differences in the initiation and growth behaviour of small cracks cause the longest failure life in the 0° specimen and the shortest in the 90° specimen.     

An elastic–plastic and residual stress analysis steel reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. Although it starts first at the upper surface for 15°, 30° and 45°, it starts first at the lower surface for 60° and 75° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the х-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles.