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- Beitrag zu einem Tagungsband (11)
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#### Schlagworte

- Debonding (5)
- Energy release rate (4)
- Fracture mechanics (4)
- Interface (4)
- Laminate (3)
- Composites (2)
- Einkristalllegierung (2)
- Kristallplastizität (2)
- composites (2)
- failure mechanisms (2)

#### Organisationseinheit der BAM

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 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.

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.

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 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.

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.