Off-axis Fatigue Crack Growth and the Associated Energy Release Rate in Composite Laminates

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

Fatigue crack grovvth in fibre reinforced titanium MMC laminate at room and elevated temperatures

Abstract

The fatigue crack growth resistance of a [0/90°]_2S Ti-6Al-4V (wt-%) SCS-6 cross ply laminate has been assessed as a function of varying the initial nominal stress intensity factor range (?K), the test temperature, and the environment. In all cases, through thickness cracks have been grown from unbridged defects. Fatigue crack growth rates are higher at elevated temperatures of 300 and 450° C in air. However, tests carried out at a temperature of up to 450° C in vacuum have shown that crack arrest conditions are similar to those observed from specimens studied at room temperature and at a temperature of 300° C in air. In these cases, initial ?K_ini transition values between fatigue crack arrest and eventual specimen catastrophic failure are close to 10 MPa m^1/2. In contrast, at a temperature of 450°C in air, even for tests performed at a frequency of 10 Hz, the limiting value of initial ?K_ini to give crack arrest is less than 6 MPa m^1/2. This has been attributed to the action of an aggressive environment, and particularly to the attack of the carbon coating layers. In addition, correlations have been found between fibre pull out lengths and changes in both temperature and environment; these are negligible after tests at 450°C in air. Finally, for such composites, sudden increases in fatigue crack growth rates have been attributed unequivocally to the failure of bridging fi bres, which were detected using acoustic emission.     

Failure behavior of quasi-isotropic carbon fiber-reinforced polyamide composites under tension

In this paper, the microscopic failure behavior of quasi-isotropic carbon fiber-reinforced polyamide-6 (CF/PA6) laminates under tension was investigated experimentally. Laminates of two layups, namely [45°/0°/?45°/ 90°]_s and [45°/0°/?45°/ 90°]_2s, were made from CF/PA6 tapes of two different manufacturers and then subjected to tensile testing. Crack initiation and progression on the polished free edge of specimens were examined using optical microscopy, under several load levels. Crack growth behavior through the specimen width was also traced by observing the crack configurations in different sections in the specimen width direction. The effects of the spatial distribution of fiber on the microscopic damage events were elucidated. The difference in failure behavior between the present CF/PA6 laminates and conventional thermosetting CF/Epoxy laminate is discussed.     

A simple estimation method of stress intensity factors for through-cracks in angle-ply laminates

In the present paper a simple method of estimation of stress intensity factors for through-cracks in angle-ply laminates is developed. In this procedure, Savin's elasticity solution for an elliptical hole in two-dimensional infinite plate is used as a basic solution for the stress distribution in each ply of laminate. The present method is applied to the problems of through cracks in a $\text{(}\text{0°}\text{90}\text{)}$_s laminate and a $\text{(}\text{?45°}\text{+ 45°}\text{)}$_s laminate. Comparison with existing numerical solutions obtained by three-dimensional finite element analysis shows good agreement. The simplicity of the present method gives the design engineer a useful tool for estimating stress concentration due to the presence of a hole or a crack.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

Matrix cracking and stiffness reduction during the fatigue of a (0/90)s GFRP laminate

Stiffness reduction due to matrix cracking in a (0/90)_s glass fibre reinforced plastic (GFRP) laminate has been studied under both quasi-static and fatigue loading. The stiffness reduction is shown to be directly proportional to the density of cracks which accumulate in the transverse ply. A model for the transverse ply crack growth during fatigue gives good agreement with the experimentally determined stiffness reduction curves.     

Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements

Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57–70 2014) to include delamination and simulated additional [45/?45/0/90]_s and [0₂/90_n]_s {n?=?1,2,3} CFRP laminates and a [0/90₃]_s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90_n/0] laminates that as the number of 90° ply increases past n?=?2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.     

Embedded flaws for crack path control in composite laminates

An experimental investigation was conducted on using small flaws purposefully introduced into composite laminates to control growth of interlaminar cracks and through-thickness crack branching. Mode I crack growth specimens were used to study branching through 0°, 90° and 45° plies. The results showed that crack growth through 0° plies could be promoted by a ply gap, but this was not as controllable as combining a ply gap with a pre-crack to create a “crack branch flaw”. Crack branching through 45° plies could be controlled using crack branch flaws, and also promoted controllably using ply gaps. Crack branching through 90° plies was seen without any flaws, but was better controlled with embedded delaminations. Using these outcomes, crack branching through two quasi-isotropic laminates was demonstrated. The results have application to improved damage tolerance and fracture toughness, by taking advantage of high toughness crack growth mechanisms.     

Modeling of permeation and damage in graphite/epoxy laminates for cryogenic tanks in the presence of delaminations and stitch cracks

Composites are extensively used for various aerospace applications and one of its important potential uses is as cryogenic fuel tank material for crew launch vehicles. Composites offer high specific strength and stiffness, and therefore are preferred over many other materials. However under structural mechanical loads and/or thermal loads, transverse micro-cracks develop in the polymer matrix. These cracks along with interlaminar delaminations produced at the crack tips, lead to permeation of cryogenic fuel permeation through the laminates. In this study, mathematical models have been proposed to determine the delaminated crack opening displacement (DCOD) for each ply of a damaged laminate and the permeability associated with it. In addition, a stitch crack model has been proposed to address experimental observations. The through-thickness DCOD distribution for a damaged composite under the action of thermal and/or mechanical load is predicted using a five-layer model which is developed based on first order shear deformation theory. The DCOD predicted by this mathematical model, with and without stitch cracks, shows good agreement with two dimensional finite element analysis. The DCOD values predicted for IM7/5250-4 laminate of lay-up [0/45/−45/90]_S were used to predict permeability using Darcy’s law for fluid flow through porous media. The analysis results were benchmarked using test data from Air Force Research Laboratory. A parametric study for permeability conducted with varying stitch crack lengths shows that the permeability of the composite is sensitive to this form of damage in individual plies.     

Effects of seawater absorption on fatigue crack development in carbon/epoxy EDT specimens

Fatigue and static edge delamination tests were performed on [45/0/–45/90]_s CFRP laminates. Both dry and seawater presoaked specimens were tested to examine any effect moisture absorption has on fatigue crack development, which was monitored by optical microscopy, scanning electron microscopy and ultrasonic C-scan. Seawater absorption changed the dominant edge-cracking mode from the -45/90 interlaminar delamination in unaged specimens to intralaminar cracking in 90° plies in aged (seawater saturated) specimens. The edge-crack growth rates in both unaged and aged specimens, however, are similar. The effect of moisture absorption on strain energy release rate has been examined, and the change in dominant edge-cracking mode and edge-crack growth have been discussed in terms of strain energy release rate.     

Behavior of a flat internal delamination within a fiber reinforced cross-ply composite

A penny-shaped delamination is modeled as a flat octahedral shaped crack between layers of a cross-ply laminate. The fibers of the laminate intersect the edges of the delamination at angles of 0°/90°, +45°/−45°, 90°/0° and −45°/+45° as one proceeds along the delamination edge. Two lay-ups are considered, a cross-ply consisting of two layers, and a symmetric composite, consisting of three layers. The delamination is always between two of the layers. Both tension and shear are applied to the outer boundary of the body. Stress intensity factors about the delamination edge are calculated by means of a conservative M-integral. These are employed to calculate the interface energy release rate and corresponding phase angles. Use is made of existing experimental results to predict the location of propagation along the edge of the delamination. It was found that the most dangerous regions along the delamination front occurred for the 0°/90° or 90°/0° interfaces.     

复合材料正交层板基体裂纹预测

将断裂力学的能量释放率概念及A.S.D.Wang在90°层横向裂纹情况的方法推广到层板后期复杂基体裂纹情况,对[O₂/90n]s层板内的0°层纵向劈裂、0°—90°界面的两种脱层等裂纹形式进行三维有限元分析并得出其应变能释放率与裂纹尺寸的关系曲线,对每种基体开裂给出载荷的理论预测值,与实验结果比较,吻合较好。      

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.     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

Mode III interlaminar fracture characterization of composite materials

An experimental project was undertaken to develop two interlaminar Mode III tearing test methods. The first was a split cantilever beam test. A laminate, containing a starter crack, was bonded between aluminum bars. The ends of the bars were then loaded in opposite directions, parallel to the plane of the crack and normal to the beam length. Stable crack growth was achieved in carbon fiber material. Unidirectional carbon fiber composites showed Mode III critical strain energy release rates in the range 1·1–1·3 kJ/m². The effects of laminate thickness, beam depth, and data reduction method were investigated. In addition, testing was conducted on angle-ply laminates. Unsuccessful tests were conducted on a tougher matrix thermoplastic composite.An edge delamination specimen was also investigated. [15° _i/ – 15° _i]_S angle-ply laminates were fabricated with four implanted edge starter cracks. Both tension and compression tests were conducted. Difficulties in interpreting the results are discussed. The split cantilever beam and edge delamination results are compared.     

A stress intensity factor approach to the fatigue growth of transverse ply cracks

A model has been developed for the stiffness reduction due to transverse ply crack growth during the fatigue of a (0/90)_s glass-fibre reinforced plastic laminate. A stress intensity factor is derived for a transverse ply crack and related to the stiffness reduction rate by the Paris law. The model gives good agreement with experimental data and can be used to maintain a constant stiffness reduction rate by incremental load-adding. The effect of frequency is considered.     

Experimental characterization of damage behavior in polycyanate CFRP laminates under high temperature atmospheric exposure

This study focuses on the experimental characterization of damage behavior due to thermo-oxidative-induced matrix shrinkage in carbon fiber reinforced plastics (CFRP) with polycyanate ester. To investigate the effects of laminate configuration on matrix shrinkage behavior, [90]₈ and [0]₈ unidirectional laminates, [±45]_2S angle ply laminates, and [45/0/–45/90]_3S quasi-isotropic laminates were exposed to high temperature atmospheric environment at 180 °C to analyze matrix shrinkage up to 2000 h. These samples were removed from convection oven to observe sample side surface changes. The thermo-oxidative-induced matrix shrinkage was measured on the side surface of CFRP sample by confocal laser microscopy. The results suggested thermo-oxidative-induced matrix shrinkage depended on aged hours, fiber-to-fiber distance, and fiber orientation angle. The matrix shrinkage coefficient could be calculated with a tensorial transformation and empirical formula. The model can predict matrix shrinkage tendency of the 45° intra-lamina layer in quasi-isotropic laminate using the data of 0° and 90° matrix shrinkage in the quasi-isotropic laminates.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

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.