Thomas Seelig

Linear fracture mechanics

We now turn to the description of the crack behavior. From a macroscopic, continuum mechanical viewpoint, we consider a crack as a cut in a body. Its opposite boundaries are the crack surfaces which are also called crack faces or crack flanks (Fig. 4.1). In general they are traction-free. The crack ends at the crack front or crack tip.

Micromechanics and homogenization

On close inspection, e.g., through a microscope, all real materials show a multitude of heterogeneities even if they macroscopically appear to be homogeneous. These deviations from homogeneity may exist in form of cracks, voids, particles, or regions of a foreign material, layers or fibers in a laminate, grain boundaries, or irregularities in a crystal lattice. Here they shall be referred to as defects in a generalized sense. Subject ofmicromechanical investigations is the behavior of these heterogeneities or defects as well as their effect on the overall properties and performance of amaterial. For instance, heterogeneities of any kind can locally act as stress concentrators and thereby lead to the formation and coalescence of microcracks or voids as a source of progressive material damage (see Section 3.1.2 and Chapter 9).

Computational modeling of rubber-toughening in amorphous thermoplastic polymers: a review

The fracture behavior of rubber-toughened polymers is governed by two dissipative microscopic deformation and damage mechanisms: matrix shear yielding and crazing. These mechanisms are strongly interconnected with the eventual cavitation of the fine dispersed rubber particles. The present work summarizes and discusses a variety of micromechanical–computational modeling approaches undertaken over the past twenty years aiming at an improved understanding of the relation between microstructure and toughening in this class of materials. The focus is on materials such as ABS where both mechanisms are prevalent.

Classical fracture and failure hypotheses

In this chapter, a brief outline on classical fracture and failure hypotheses for materials under static loading will be given. The word classical this context means in that most of these so-called strength hypotheses are already quite old. Partially they date back to considerations made at the end of the 19th or the beginning of the 20th century and they are inseparably associated with the development of solid mechanics at that time. Through modern fracture mechanics they have been pushed into the background, as far as research is regarded. However, because of their wide spreading which, last but not least, is due to their simplicity, they are still of remarkable importance.

Dynamic fracture mechanics

So far, our investigations of crack initiation and propagation have always been based on the assumption of quasistatic conditions. This is no longer justified when inertia forces or high strain rates significantly affect the fracture behavior. It is, for instance, well known that a material is more likely to fail under impulsive dynamic loading than in case of a slowly applied load. One reason for this is the different material behavior: plastic or viscous flow is increasingly suppressed at higher loading rates and a material often behaves more brittle in the dynamic case than in the static case. This and possibly different failure mechanisms in the process zone may lead to a change of the fracture toughness. Another reason is due to the fact that the inertia forces in case of dynamic loading can cause higher stresses in the vicinity of a crack tip than in the corresponding quasistatic case.

Mikromechanik und Homogenisierung

Reale Materialien weisen bei genauem Hinsehen, z. B. durch ein Mikroskop, eine Vielzahl von Heterogenitaten auf, auch wenn sie makroskopisch homogen erscheinen mogen. Solche Abweichungen von der Homogenitat konnen zum Beispiel durch Risse, Hohlraume, Bereiche aus einem Fremdmaterial, durch einzelne Schichten oder Fasern eines Laminates, durch Korngrenzen oder auch durch Unregelm asigkeiten in einem Kristallgitteraufbau gegeben sein. Wir wollen sie im Weiteren als Defekte in einem verallgemeinerten Sinne bezeichnen. Gegenstand mikromechanischer Untersuchungen ist das Verhalten solcher Inhomogenitaten oder Defekte sowie ihre Wirkung auf die globalen Eigenschaften eines Materials. So konnen Heterogenitaten jeder Art aufgrund ihrer lokalen Wirkung als Spannungskonzentratoren beispielsweise zur Bildung und Vereinigung von Mikrorissen oder Mikroporen fuhren und damit den Ausgangspunkt einer fortschreitenden Materialschadigung bilden (vgl. Abschnitt 3.1.2 sowie Kapitel 9).

Investigations of Cruciform Specimen Designs for Biaxial Tensile Testing of SMC

This proceedings paper presents the investigation of different cruciform specimen designs for the characterization of Sheet Molding Compounds under biaxial loading. Biaxial tensile tests allow the investigation of damage evolution under multiaxial stress states, which is particularly interesting due to the different damage phenomena in composite materials. A key challenge is to find a suitable specimen shape, because typical cruciform specimens fail in the arms before damage occurs in the area of interest which is the area of the biaxial stress state in the center region of the specimen. For all of the introduced designs the stiffness degradation is analyzed more in detail and compared to that of a uniaxial bone specimen. For the best performing specimen which is reinforced by unidirectional reinforced tapes on the arms, the strain field is analyzed by finite element simulations, taking into account the mechanical properties of the different layers of the specimen. Especially in the center area and at critical points, strain concentrations and non-symmetrical strain distributions are analyzed and evaluated.

Analysis of Hertzian indentation fracture in the framework of finite fracture mechanics

The concept of finite fracture mechanics which assumes the spontaneous formation of a small, yet finite, crack and employs as stress-based as well as an energetic criterion is applied to the problem of indentation fracture initiation in brittle solids. In evaluating the energetic part of the fracture criterion a semi-analytical and a numerical approach, the latter involving detailed finite element simulations, are compared. The functionality of the hybrid (two-part) criterion in application to indentation fracture is analyzed in principle and, moreover, its predictive capabilities are illustrated by comparison with experimental findings.

Elastic-plastic fracture mechanics

When a test specimen or a structural component consisting of a ductile material and containing a crack is loaded, plastic flow starts in the vicinity of the crack tip. As a consequence, the crack tip becomes increasingly blunted with increasing load and the crack opens. At the same time the plastic zone grows and may, depending on the material and geometry, extend over large regions or the entire specimen until at some critical load crack initiation takes place. In such a situation of large-scale yielding linear elastic fracture mechanics can no longer be applied and parameters and fracture concepts such as the K–concept based on linear elastic material behavior become meaningless. Fracture parameters and concepts then are needed which account for plastic flow of the material in larger regions outside the process zone.

Elements of solid mechanics

This chapter summarizes basic concepts and equations of solid mechanics. It is selfevident that this outline cannot be complete but is limited to a necessary minimum. For more detailed descriptions the reader is referred to the literature, and selected textbooks are listed at the end of the chapter (Section 1.6). The reader with some knowledge of elasticity and plasticity may skip this part and jump directly to the next chapter.