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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 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.
Pore annihilation during hot isostatic pressing (HIP) was investigated in the single-crystal nickel-base superalloy CMSX-4 experimentally by interrupted HIP tests at 1288 °C/103 MPa. The kinetics of pore annihilation was determined by density measurement and quantitative metallography. Transmission electron microscopy of a HIPed specimen showed that the pores shrink via dislocation movement on octahedral glide planes. Theoretically pore closure under HIP condition was modelled by the finite element method using crystal plasticity and large strain theories. The modelling gives a similar kinetics of pore annihilation as observed experimentally, however somewhat higher annihilation rate.
The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed.
Single-crystal components made of nickel base superalloys contain pores after casting and homogenization heat treatment. Hot isostatic pressing (HIP), which is carried above the γ' -solvus temperature of the alloy, is industrially applied to reduce porosity. A modeling of HIP based on continuously distributed dislocations is developed in a 2D setting. Glide and climb of straight-edge dislocations, as well as vacancy diffusion, are the deformation mechanisms taken into account.
Thereby, dislocation glide is controlled by dragging a cloud of large atoms, and climb is controlled by vacancy diffusion. Relying on previous investigations of the creep behavior at HIP temperatures, it is assumed that new dislocations are nucleated at low-angle boundaries (LAB) and move through subgrains until they either reach the opposite LABs or react with other dislocations and annihilate.
Vacancies are created at the pore surface and diffuse through the alloy until they are either consumed by climbing dislocations or disappear at the LABs. The field equations are solved by finite elements. It is shown that pore shrinking is mostly controlled by vacancy diffusion as the shear stresses at the LABs are too low to
nucleate a sufficient amount of dislocations.
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.
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 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.
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 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.
An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one.
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.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
The creep behavior of single crystals of the nickel-based superalloy CMSX-4 was investigated at 1288 °C, which is the temperature of the hot isostatic pressing treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no gammaPrime-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g., the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-sectional area psi of [001] crystals reached nearly 100 pct, while for a [111] crystal psi = 62 pct. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals did not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. The recrystallization degree was found to be correlated with deformation behavior as well as with dwell time at high temperature. From the analysis of the obtained results (creep anisotropy, stress dependence of the creep rate, traces of shear deformation, and TEM observations), it was concluded that the main strain contribution resulted from <01-1>{111} octahedral slip.
The investigation of creep behavior of the single crystal superalloy CMSX-4 at 1288°C is important for the understanding of deformations mechanisms under hot isostatic pressing (HIP). This treatment is used to increase the lifetime of single crystal superalloys by reducing the number of cavities. The understanding of the internal processes during this treatment is still limited due to the material being not single-phase at room temperature, the extreme conditions of HIP and the complexity of the material.
The result of predicting the pore shrinkage rate using classical crystal plasticity was not satisfying. A more complex model has been implemented, now taking the heterogeneity of dislocation sources into account. By introducing a dislocation density, one can describe the transport, nucleation and interaction of dislocations.
The investigation of creep behavior of the single crystal superalloy CMSX-4 at 1288°C is important for the understanding of deformations mechanisms under hot isostatic pressing (HIP). This treatment is used to increase the lifetime of single crystal superalloys by reducing the number of cavities. The understanding of the internal processes during this treatment is still limited due to the material being not single-phase at room temperature, the extreme conditions of HIP and the complexity of the material.
The result of predicting the pore shrinkage rate using classical crystal plasticity was not satisfying. A more complex model has been implemented, now taking the heterogeneity of dislocation sources into account. By introducing a dislocation density, one can describe the transport, nucleation and interaction of dislocations.