Jens H. Andreasen

Reliability-based design of ceramics

Abstract A method for reliability-based design of ceramics is developed on the basis of a statistical description of brittle fracture. It is shown that if the crack size distribution is described by the appropriate asymptotic distributions from statistics of extreme values, a two-parameter Weibull distribution for the probability of fracture is obtained. This provides a statistical rationality for choosing this distribution and for disregarding the third Weibull parameter. The method is formulated in general terms such that multiaxial stress states are included. Previous methods for multiaxial stress states, including the Batdorf approach1,2 and the multiaxial elemental strength model3, are reviewed and compared to the present method, and it is shown that if the two-parameter Weibull distribution is adopted the methods are equivalent. A formulation including finite element methods to obtain a probability of fracture for a component of arbitrary shape and loading is discussed as well as the incorporation of proof-testing in production of ceramics and the application of reliability-based design in this context.

Surface cracks in transformation toughening ceramics

Abstract This paper presents a complete R -curve analysis for a single surface crack and an array of equally spaced parallel surface cracks in transformation toughened ceramics (TTC). The problem is reduced to the solution of a pair of singular integral equations in which the dislocation density function and the transformation zone boundary are the unknown functions. The form of the equations does not depend on the number of surface cracks being studied; only the weight functions are different. The singularities of the weight functions and of the dislocation density functions at the crack tip and at the intersection of the crack by the transformation zone wake are analytically isolated for accurate numerical integration of the integral equations.

Interaction Between a Surface Crack and a Subsurface Inclusion

A numerical method for the integration of the singular integral equation resulting from the interaction of a surface crack with a subsurface inclusion is presented. The crack is modelled as a pile-up of dislocations, and the dislocation density function is partitioned into three parts: A singular term due to the load discontinuity imposed by the inclusion, a square root singular term from the crack tip, and a bounded and continuous residual term. By integrating the singular terms explicitly the well behaved residual dislocation density function only has to be determined numerically, together with the intensity of the square root singular term. The method is applied to the determination of the stress intensity factor for a surface crack growing towards and through a circular inclusion whose diameter is equal to the distance from the free surface, and to the determination of the characteristic stress intensity factors when the crack enters the inclusion and leaves it for arbitrary ratios between the inclusion diameter and the distance from the surface.

Interlaminated damping - a method for reduction of vibration and acoustic noise for switched reluctance machines?

This paper investigates a new construction method for the reduction of noise of laminated magnetic structures. One form of the method is to insert damping material between stator laminations having different natural frequencies. The stator laminations with different natural frequencies tend to vibrate at different frequencies thus shearing the interlaminated damping material. Working the damping material absorbs some of the vibrational energy, which would otherwise be emitted as acoustic noise. The work was directed at the switched reluctance motor, which has been viewed as acoustically noisy. Mathematical models and various prototypes are discussed in detail in the paper to assist others in taking advantages of the method.

The solution of an inhomogeneity in a finite plane region and its application to composite materials

A method is described for determining the elastic field in a finite isotropic region containing an isotropic circular inhomogeneity whose elastic constants differ from those of the rest of the region. The method is based on a combination of Muskhelishvili complex potentials and boundary collocation. The method is particularly useful for solving problems of practical interest in the field of composite materials. Two examples are given to illustrate this.

On Lateral Buckling failure of Armour Wires in Flexible Pipes

This paper introduces the concept of lateral buckling of tensile armour wires in flexible pipes as a failure mode. This phenomenon is governed by large deflections and is therefore highly non-linear. A model for prediction of the wire equilibrium state within the pipe wall based on force equilibrium in curved beams and curvature expressions derived from differential geometry is presented. On this basis, a model of the global equilibrium state of the armour layers in flexible pipes is proposed. Furthermore, it is demonstrated how this model can be used for lateral buckling prediction. Obtained results are compared with experiments.Copyright

A novel biaxial specimen for inducing residual stresses in thermoset polymers and fibre composite material

A new type of specimen configuration with the purpose of introducing a well-defined biaxial residual (axisymmetric) stress field in a neat thermoset or a fibre composite material is presented. The ability to experimentally validate residual stress predictions is an increasing need for design engineers when they challenge the material limits in present and future thermoset and composite component. In addition to the new specimen configuration, this paper presents an analytical solution for the residual stress state in the specimen. The analytical solution assumes linear elastic and isotropic material behaviour. Experimental strain release measurements and the analytical solution determine the residual stress state present in the material. A demonstration on neat epoxy is conducted and residual stress predictions of high accuracy and repeatability have been achieved. The precise determination of the biaxial stress state in the specimen after cure makes it suitable for calibrating residual stress models.

A comparison of gel point for a glass/epoxy composite and a neat epoxy material during isothermal curing

Determination of gel point is important for a modelling assessment of residual stresses developed during curing of composite materials. Residual stresses in a composite structure may have a detrimental effect on its mechanical performance and compromise its integrity. In this article, the evolution in bending stiffness of a glass/epoxy composite material during an isothermal curing process is examined to identify different material stages and behaviour. Differential scanning calorimetry and dynamic mechanical analysis are used to analyse the material behaviour. Gelation is identified as a clear onset in bending stiffness, and vitrification is seen as a decrease in the bending stiffness rate. Often gel point predictions for composite materials are based on neat matrix measurements. However, the results presented in this article demonstrate that the gel point is affected by the presence of the fibre reinforcement.

Two practical applications of crack kinking

Abstract This paper illustrates on two examples of practical significance the usefulness of the crack kinking analysis pioneered by Sia Nemat-Nasser and his colleagues. The first example deals with the calculation of the pull-out force of axisymmetric headed anchors embedded deep in concrete blocks and the second with the interaction between the crack deflection and phase transformation mechanisms of toughening in ceramics containing dispersed tetragonal zirconia precipitates.

Experimental investigation of interfacial crack arrest in sandwich beams subjected to fatigue loading using a novel crack arresting device

A recently proposed face-sheet–core interface crack arresting device is implemented in sandwich beams and tested using the Sandwich Tear Test configuration. Fatigue loading conditions are applied to propagate the crack and determine the effect of the crack stopper on the fatigue growth rate and arrest of the crack. Digital image correlation is used through the duration of the fatigue experiment to track the strain evolution as the crack tip advances. The measured strains are related to crack tip propagation, arrest, and re-initiation of the crack. A finite element model is used to calculate the energy release rate, mode mixity and to simulate crack propagation and arrest of the crack. Finally, the effectiveness of the crack arresting device is demonstrated on composite sandwich beams subjected to fatigue loading conditions.