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Eingeladener Vortrag
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The failure of composites is initiated by imperfections on microscale. The interface between fiber and matrix is a key parameter concerning failure initiation. In order to get an improved understanding of local failure processes a fracture mechanical analysis of interfacial failure in a composite ply under transverse stresses is performed. The mixed mode energy release rate is calculated. In addition the failure of interfaces under cyclic loading is studied on a single fiber model. The quasistatic debonding process is compared with the interfacial failure under fatigue loading. It is shown that the tan delta can be used as an indicator for the damage propagation.
Epoxy resins are frequently used for advanced fiber reinforced composites applications. Even though the fibers are dominating strength and stiffness of the composites, specifically when loaded in fiber direction, the failure usually initiates in the matrix near or directly at the interface. Especially in plies loaded transverse to the fiber direction, the mechanical behaviour is highly influenced by the mechanical properties of the epoxy matrix. Accordingly the mechanical properties of the matrix are of great importance.
Failure of fiber reinforced composites – role of the matrix behaviour and the interface strength
(2016)
Failure of fiber reinforced composites initiates at microdefects in the matrix or at the interface. The interface strength is calculated from the stress field directly before crack initiation by nonlinear finite element simulations. Large deformations and plastic material behaviour are taken into account. Microscopical inspections of the fibers after failure show only small regions with adhering matrix material. This indicates that the interface strength is below the matrix strength.
The aim of the paper is to analyse the failure process taking place on microscale in fiber reinforced composites. The failure is initiated at microscopical defects presumingly in the interface. The circumferential propagation of interface cracks starting at microdefects in unidirectional plies under transverse loading is studied using a representative volume element. First a linear elastic fracture mechanical analysis of interface cracks in a carbon fiber reinforced epoxy resin is performed by calculating the mixed mode energy release rate using the virtual crack closure method. The influence of the fiber spacing is studied by varying the fiber volume fraction. The total energy release rate rapidly grows after crack initiation indicating an unstable crack propagation. The first phase is dominated by mode I. The mode II energy release rate starts slightly delayed but surpasses the mode I part after a short crack length. By increasing the fiber volume fraction the maximum of the energy release rate shifts to smaller crack angles.
The premise for the development of improved failure criteria for fiber reinforced composites is the understanding of the failure processes on microscale. On microscale the local behaviour of the matrix polymer is crucial. It significantly differs from that found in macroscopic measurements. The present study is focused on the plastic material behaviour of a standard epoxy resin. Local plastic strains are measured in tensile test by using digital image correlation. A multilinear plastic law is implemented by the experimental data. The stress field arising in an idealised representative volume element of a unidirectional ply is analysed by finite element calculations. The change of the stress and strain field due to plastic deformation according to the multilinear plastic law is shown. The change leads to a shift of the critical locations where failure is likely to initiate. In addition, the failure type changes from stress based to strain based failure. The dominant role of the shear strains is shown.
The failure of composites is initiated by imperfections on microscale. The interface between fiber and matrix is a key parameter concerning failure initiation. In order to get an improved understanding of local failure processes a fracture mechanical analysis of interfacial failure in a composite ply under transverse stresses is performed. The mixed mode energy release rate is calculated. In addition the failure of interfaces under cyclic loading is studied on a single fiber model. The quasistatic debonding process is compared with the interfacial failure under fatigue loading. It is shown that the tan delta can be used as an indicator for the damage propagation.
Failure of composite materials is initiated by fracture processes on microscale, especially by interfacial debonding. Failure processes taking place on microscale are studied by single fiber experiments. This is, single fibers embedded in tensile specimen are loaded under various off-axis angles. Starting at microdefects interface cracks propagate circumferentially as well as longitudinally, depending on the loading angle. In addition, finite element simulations of interfacial crack propagation around single fibers as well as fibers embedded in a hexagonal composite are shown based on linear elastic fracture mechanics. The course of the energy release rate is given in dependence of the fiber volume fraction.
The nonlinear behaviour of epoxy resins is studied on standard tensile tests. A strain field measurement system is applied (Aramis) in order to monitor local strains. The residual strain is measured by recovering the specimens for up to 68 hours after unloading. The time span the specimen is exposed to load has a large influence on the creeping process and the residual strain after recovering. This is studied by comparison of instantaneous unloading with keeping the specimen under permanent load for thirty minutes. It is shown that moderate differences in the initial strain can lead to large differences in the creep behaviour as well as in the residual strain.
The problems of the limits of continuum mechanics are shown on some examples. The fiber-matrix debonding and subsequent crack propagation in fiber reinforced composites is studied. While Finite Element Analyses predict clear crack surfaces, either following the interface or bridging to the neighbouring fiber forming planes, the actual surfaces are very cliffy. Due to the much larger fracture surfaces and the completely different stress states on the cliffy fracture surfaces the continuum mechanical prediction is far from the actual local behaviour. The phenomenon of local high stresses which re much higher than the macroscopically measured strength of the material is also encountered in general fracture mechanics.
The scale dependency of materials is shown on indentation tests conducted on different scales. From a continuum mechanical point of view it makes no difference if the indentation test is performed on a nano-, micro- or macroscale, because it is a matter of self-similarity. However, in nano- or microindentation tests on a pure polymer using e.g. a Berkovic indentor, the extremely high stress concentrations arising at the indentor tip are domination more or less the whole region around the indentor. In case of a macroscopical test, this zone covers only a small part of the material loaded by the indentor. Accordingly, the results of the different test cannot be scaled up.
For the design of laminates the knowledge of the failure behaviour of plies under multiaxial stresses is a necessary precondition. The strength of plies under multiaxial stresses commonly is determined by standard off-axis tests using fixed clamps. By varying the off axis angle the ratio of shear to normal stresses can be prescribed. However, by preventing the rotation a complex stress field develops which strongly varies with the off axis angle as well. While these effects are not crucial when determining the elastic material parameters since the stress state in the center of the specimen is not far from the ideal uniaxial stress state they have a great influence on the failure behaviour.
Verfahren zur Messung der Adhäsion zwischen Faser und Matrix - Einfluss der Faserbeschlichtung
(2015)
Off-axis tests are widely used for the determination of the anisotropic mechanical properties of composite materials, this is, the longitudinal E-modulus and the strength. The mechanical properties are evaluated from the test data under idealising assumptions such as homogeneity of the material as well as a homogeneous stress distribution. In real off-axis tests, however, significant deviations from the idealising assumptions are present. The reduction of the accuracy of the results strongly depends on the off-axis angle.
In this paper a series of off-axis tests is analysed. The stresses on potential failure plane are calculated by finite element analyses. By varying the geometrical parameters it is shown how small deviations from the ideal case influence the measured elastic constants and the strength. Especially at low off-axis angles the mechanical properties strongly vary with the angle. In addition, fracture surfaces for different shear/normal stress combinations are studied and typical phenomena are identified.
The failure behaviour of unidirectional plies tested under off-axis loading is studied. The stress distribution occurring in standard off-axis tests is briefly discussed. The different failure modes, this is, pure fiber breakage, pure inter fiber failure as well as a superposition of both is analysed based on test data and fracture patterns. The large difference of the failure load depending on the failure mode at small off-axis angles is studied by comparison of a short and a long 3° off-axis angle specimen.
The energy release rate delivered during the debonding of a fiber inside a composite ply is analysed using a representative volume element. Two different fiber volume fractions are studied by a linear elastic fracture mechanical analysis by using the finite element method.
The dependency of the mixed mode energy release rate on the length of the crack increment is analysed. It is shown that the same general behaviour found in case of a straight Interface crack is valid also for circular cracks. As a result the discrimination of the energy release rate into mode I and mode II portions is questionable.
The determination of the strength and the failure behaviour of fiber reinforced composites is a complex task. This is mainly due to the anisotropy and the inhomogeneiety of the material on the microscale. The strength or the fracture toughness of the interface between fiber and matrix is the key factor controlling the failure process on microscale, especially under loads transverse to the fiber axes.
The ultimate failure of a laminate is a complex process consisting of a large number of different subprocesses. Due to its highly dynamic nature on one hand and the microscopical scale on the other it is not possible to observe the ultimate failure directly or even to analyse it theoretically. However, long before ultimate failure occurs a large number of elementary failure processes take place in a rather
static manner or at least at low crack Propagation speed.
The failure of laminates is originated in plies loaded transverse to the fiber direction, e.g. in the 90° ply of a cross ply laminate. The initiation of failure is due to the debonding of individual fibers At some point the interface crack kinks into the matrix and propagates towards the inter-face of the neighbouring fiber. The cracks then continue propagating through the full ply. The interface failure obviously is the dominating process of the failure of plies in high fiber volume fraction composites. Several authors investigated the interfacial crack propagation on model systems. First, Varna and Paris studied the debonding process on a single fiber embedded in pure matrix under transverse ten-sion by fracture mechanical analyses. Correa and Paris performed experimental as well as numerical studies by calculating the mixed mode energy release rate under different loading conditions. These analyses were extended to fibers surrounded by a composite material by the present authors. Among others, Comninou as well as Sun and Jih have shown that the separation into a mode I and mode II energy release rate is not universal but the mixed mode ratio depends on the length of the crack increment. Comninou developed a solution of an interface crack between dissimilar media which reveals the even a small contact zone is found near the crack tip. As a result, the mode I part of the energy release rate vanishes because no opening of the crack takes place. The contact zone, however, is extremely small. If these mathematical phenomena, however, are relevant for physical problems is not verified.
The debonding of a fiber in a glass fiber / epoxy composite under transverse loading
is analysed. The stress field in the interface as well as the energy release rate are
analysed for various fiber volume fractions between 5% and 85%. The circumferential
propagation of an interface crack in a hexagonal fiber array is studied. The analysis
is performed by a finite element simulation under plane stress conditions. The
stress distribution during crack propagation is calculated for different crack phases.
The crack starts under dominating mode I stresses. After propagating some 60° the
mode II part reaches a maximum while the mode I part vanishes and the crack
closes. The further crack propagation is driven by mode II stresses only. In addition,
the stress transfer into the neighbouring fibers during debonding is studied.
The failure of fiber reinforced composites under transverse loading is investigated on a
representative volume element. The volume element is composed of a twelve fiber hexagonal
array. The debonding of the central fiber is studied under transverse shear as well as under
transverse compressive loading by calculating the mode I and mode II part of the energy
release rate. The initiation of failure is assumed to take place at the location of maximum
tensile or maximum shear stresses, respectively. In order to determine the failure initiation
point, the stress field in the interface before crack initiation is calculated.
The failure of laminates usually is initiated by the failure of the plies with the maximum transverse stresses. The failure of those plies generally reduces the load carrying capability of the laminate, even though they carry only a small part of the external load. The analysis of failure under off-axis stresses accordingly is essential for the prediction of the strength of laminates. This is taken into account in the "mechanisms based failure criteria" e.g. by Puck. Most of these inter fiber failure criteria are not based on the micromechanics of the failure process but on prescribed stress interaction functions. The failure of plies under transverse loading obviously is governed by the bond strength between fiber and matrix fiber. The interfacial debonding was studied e.g. by Paris et al. and Corea et al.. The bond strength between fiber and matrix usually is measured by using micromechanical tests e.g. pull-out, push-out or fragmentation tests. Stress analyses as well as fracture mechanical analyses show that the interfacial failure over a large range is dominated by shear stresses (Kim and Mai, Pisanova et al, Marotzke and Qiao). The stress distribution arising in those experiments however differs from the stresses acting in a lamina under transverse loading. In transverse failure of a lamina, radial stresses as well as shear stresses are dominating the failure process of the interface. In addition longitudinal shear stresses are present. Experimental work concerning off-axis loading of single fibers was done e.g. by Tandon and Kim and by Ogihara and Koyanagi. They studied the influence of the fiber alignment by using a specimen in form of a cruciform with skew wings.
The strength of laminates distinctly depends on the transverse strength of the laminas. The transverse failure is dominated by the adhesion between fiber and matrix. Usual strength criteria however do not take into account the adhesive strength explicitly. The determination of the interface strength is performed on the micromechanical scale using single fiber specimens. The fibers are loaded under off-axis loading while the debonding is monitored under a microscope. The stresses acting in the Interface are calculated by finite element analyses. It is found that for off-axial angles up to 35° interfacial debonding is the dominant failure mode while fiber breakage takes place at lower angles. The occurrence of fiber breakage and debonding under off-axis loading shows that the restriction to two potential failure planes - perpendicular or parallel to the fibers - as applied in common failure criteria has to be put in question.
The debonding of a fiber in a glass fiber / epoxy composite under transverse loading is studied. The stress field in the interface as well as the energy release rate are analysed for two fiber volume fractions.
The circumferential propagation of an Interface crack starting at the center of a fiber which is located within a hexagonal fiber array is studied. The analysis is performed by a finite element Simulation under plane stress conditions. Two fiber volume fractions are considered, this is 30% and 70%. The stress distribution before and during crack propagation is calculated for different stages of the
crack. The crack opens by dominating tensile stresses in the first phase while it closes when propagating along the interface. The total energy release rate as well as the mode I and mode II parts are calculated. In the first phase the crack is driven by an increasing mode I energy release rate, indicating an unstable crack propagation. Then the mode II energy release rate increases rapidly and dominates the debonding process while the mode I part decreases and finally vanishes. Subsequently also the mode II part decreases, indicating stable crack propagation. In the last phase the crack becomes unstable again due to a strongly increasing mode I energy release rate. During the debonding process a remarkable change the mode ratio takes place.
The main features of the debonding process are similar for low and high fiber volume fraction. In case of the high fiber content, however, the mode I part is more pronounced and the maximum of the total energy release rate is shifted to lower crack angles.
The debonding of fibers under mixed-mode loading is studied on model composites containing fibers with different orientations with respect to the loading direction. The spacing of the fibers is large, accordingly no significant fiber interaction takes place. For any fiber orientation, interfacial debonding occurs, even though at different load levels. Only for the low off-axis angle, additional fiber fracture is found. Using a rectangular specimen, the interface crack starts at the edges propagating into the center at low speed. In the first phase, only the central part of the interface debonds. After the whole fiber is debonded, the crack propagates in circumferential direction. The superimposition of fiber breakage and debonding shows that the restriction of two potential failure planes - perpendicular or parallel to the fibers - has to be put in question.
The breakage of a fiber and its effect on the strain energy is studied in a model composite, this is, a single fiber embedded in a dogbone specimen. The fracture process is recorded by an acoustic emission device, the crack patterns are monitored under a microscope. A finite element analysis is performed in order to estimate the energy released by different failure scenarios. The abilities and limitations of the acoustic emission analysis in characterizing different failure types in fiber reinforced composites are evaluated.
Widely-used methods for characterising the fibre/matrix interface in polymeric composites are the fragmentation test and the droplet test as a special kind of the single-fibre pull-out test. A severe disadvantage of these tests is that non-realistic model samples are investigated which contain only one fibre in the matrix. In order to obtain data about the effect of the different residual stress situations for fibres in such samples and in composites, pull-out tests of E-glass fibres in polystyrene and polycarbonate are performed using samples, where the investigated fibre is surrounded by 0 to 3 other near fibres. Neighbouring fibres can increase the pull-out forces by a factor of three and the interfacial toughness by a factor of four. This has to be taken into account, if the tests are performed not only for comparison reasons but for measuring interface properties.
Bruchmechanische Analyse des Grenzflächenversagens bei Einzelfaser Pull-out und Fragmentation Tests
(2000)
Influence of the Interface Strenght on Local Failure Processes in Fiber Reinforced Composites
(1999)
The Energy Release Rate of the Fiber/Polymer Matrix Interface: Measurement and Theoretical Analysis
(1997)