K.P. Herrmann

Thermal cracking of two-phase composite structures under uniform and non-uniform temperature distributions

Abstract In this paper curved thermal crack growth in self-stressed brittle solids subjected to well-defined temperature fields has been studied. The resulting boundary-value problems of the stationary plane thermoelasticity are solved by means of the finite element method. Moreover, by applying an appropriate crack growth criterion based on the total energy release rate of a quasistatic mixed-mode crack extension the further development of thermal crack paths starting at the external surfaces of disk-like two-phase compounds with circular cross-sections could be predicted. Several specimen geometries consisting of different material combinations have been investigated by considering uniform temperature changes and by applying the relevant methods of fracture mechanics. Further, the corresponding fracture mechanical data like strain energy release rates and stress intensity factors, respectively, have been determined by additional considerations of the influence of inner stress concentrators onto the paths of quasistatic extending thermal cracks. The comparison of those theoretical investigations with associated cooling experiments shows a satisfying agreement. Finally, the influences of additional local temperature changes onto the prospective thermal crack paths have been studied by means of the fracture criterion mentioned already as well as by using the finite element method. Thereby the numerical results have shown some remarkable effects of interference between the local temperature changes located in the vicinity of thermal crack tips and the further crack paths.

Fracture mechanical assessment of interface cracks with contact zones in piezoelectric bimaterials under thermoelectromechanical loadings II. Electrically impermeable interface cracks

Abstract This paper constitutes the second part of a study of interface cracks with contact zones in thermopiezoelectrical bimaterials, and it is concerned with the case of an electrically impermeable interface crack. The principal physical peculiarity of this case in comparison with an impermeable interface crack is connected with the dependencies of the contact zone length and the fracture mechanical parameters on the prescribed electrical flux, and in a mathematical sense the main peculiarity is concerned with the reduction of the problem in question to the joint solution of inhomogeneous combined Dirichlet–Riemann and Hilbert boundary value problems. The exact analytical solutions of the mentioned problems have been found for an arbitrary contact zone length, and the required thermal, mechanical and electrical characteristics at the interface as well as the associated fracture mechanical parameters at the corresponding crack tips are presented. The transcendental equations for the determination of the real contact zone length have been obtained for a general case and for a small contact zone length in an especially simple form. Using the admissible directions of the heat and the electrical fluxes defined in this paper as well, the dependencies of the real contact zone length and the associated fracture and electrical intensity factors on the intensities of the thermal and electrical fluxes are presented in tables and associated diagrams.

MODELING OF THERMAL CRACKING IN ELASTIC AND ELASTOPLASTIC TWO-PHASE SOLIDS

A review is given about fracture mechanical investigations concerning the thermal crack initiation and propagation in one of the segments or in the material interface of two-arid three-dimensional self-stressed two-phase compounds. The resulting boundary value problems of the stationary thermoelasticity and thermoplasticity for the cracked two- and three-dimensional bimaterial structures considered are solved using the finite element method. Furthermore, by applying an appropriate crack growth criterion based on the numerical calculation of the total energy release rate G of a quasistatic mixed-mode crack extension the further development of thermal crack paths starting at the intersection line of the material interface with the external stressfree surface of the two- and three-dimensional elastic bimaterials could be predicted. In the case of the disklike two-phase compounds, the theoretically predicted crack paths show a very good agreement with results gained by associated cooling experiments. Several ...

Theoretical study of formation of pores in elastic solids: particulate composites, rubber toughened polymers, crazing

It is difficult to overestimate the multi-functional role and practical meaning of the processes of the formation of pores in solids, especially in polymers and polymer based materials, which are capable to a noticeable plastic deformation. Various mechanisms are responsible for this phenomenon in different systems. Particularly, it is debonding in particulate filled composites, elastomeric inclusions failure in rubber toughened polymers, nucleation of microvoids at defects in glassy polymers. Two main effects of the formation of pores should be underlined. The first is a decrease in the materials stiffness, which is mostly emphasized for composites filled by rigid inclusions. The second is an improvement in the fracture toughness which is widely explored in practice. The nucleation of pores affects the fracture toughness, firstly, absorbing the energy for the new surface formation and, secondly, facilitating of a plastic flow of the basic material. The paper proposed is partly a review of previously obtained results and represents also the novel data and laws. It concerns two aspects of the problem. An analysis of the conditions advantageous for the appearance of a single pore and of the completeness of this event is the first. This part of the paper is mostly a review, but a novel comparable analysis of the regularities of a pore formation by the way of a debonding along the surfaces of rigid particles in particulate filled composites and caused by a failure of rubbery inclusions will be presented. The second aspect of the problem is a spatial cooperation in the nucleation of pores. Some results in this field also have been obtained previously. However, the corresponding part of the paper mostly represents new data as well as a new analysis. Three types of systems will be analyzed from the cooperation point of view: particulate filled composites, rubber toughened plastics and homogeneous polymers for which a formation of micropores in a diffuse or a cooperative manner is a well known phenomenon named as crazing. Certain corrections of the previous conclusions concerning the cooperation arising during the failure of rubbery particles have been performed. Furthermore, the angles of the disposition of porous zones will be estimated. In addition, it will be shown that the conditions advantageous for an individual cavitation as well as the laws of a diffuse or cooperative proceeding of the multiple crazing are qualitatively the same. However, the different features will also be stated.

Stress/strain computation in heterogeneous bodies with discrete Fourier transforms: different approaches

Abstract In recent years the study of heterogeneous bodies, i.e., the computation of local stress–strain fields which may arise due to elastic or thermal mismatches of the constituents or the computation of effective properties (homogenisation), based on the discrete Fourier transformation (DFT) becomes more and more attractive. In fact, several contributions in the field of composite analyses are dedicated to the application of DFT (see [Int. J. Solid Struct. 3 (28) (1999) 3941; C. R. Acad. Sci. Paris 318 (II) (1994) 1417; Proceedings of the IUTAM Symposium on Transformation Problems in Composite and Active Materials, Kluwer Academic Publishers, The Netherlands, 1998, p. 61]). This paper investigates two different approaches to use DFT in order to predict the local stress/strain distribution in externally loaded two-dimensional representative volume elements (RVEs) made out of heterogeneous material. Therefore, the properties of DFT are firstly surveyed and then applied to the solution of a linear elastic material response. By the application of the equivalent inclusion method a functional equation is derived which permits the numerical computation of stresses and strains within an RVE filled with heterogeneities of arbitrary shape and stiffness. Two types of difference schemes which have to be used for the numerical solution of these functional equations are provided. To discuss these different approaches some inhomogeneity problems are numerically solved, and the results are compared to the corresponding analytical results.

Asymptotic crack tip fields for pressure-sensitive materials and dynamic crack growth under plane stress conditions

For the mathematical description of the yield behaviour of elastic-plastic materials the von Mises yield criterion proves to be suitable for the interpretation of the stress and strain curves of metals. However, many materials exhibit a pressure-sensitive yielding. These material properties are not adopted in the von Mises yield criterion. Hence a generalization of the yield criterion is necessary to examine pressure-sensitive materials. In this contribution, a generalization of the von Mises yield criterion is used to investigate the crack tip fields of pressure-sensitive materials like porous metals and certain polymers [1,2]. This extension, which includes a share of the hydrostatic stresses, leads to the so-called Drucker-Prager yield criterion. The factor ~ in this yield criterion is the measure of the pressure-sensitivity and describes the strength of the influence of the hydrostatic stresses on the yield process. A first asymptotic analysis of stress and displacement fields for dynamic crack problems in elastic-plastic solids was performed by Amazigo and Hutchinson [3] by assuming the validity of the J2-flow theory. Achenbach, Kanninen and Popelar [4], Ponte Castaneda [5], Ponte Castarleda and Mataga [6], t3stlund and Gudmundson [7] and Yuan, Yuan and Schwalbe [8,9] generalized those investigations for a dynamic crack propagation including the plastic reloading region on the crack surfaces for a mixed mode loading situation. Studies concerning pressure-sensitive materials using the HRR-field theory were performed by Li and Pan [10], Li [11] and Yuan and Lin [12]. Bigoni and Radi [13,14] advanced the before mentioned investigation [7-9] for pressure-sensitive materials. However, that analysis was restricted to quasistatic crack extension as well as mode I loading. In this paper, the asymptotic stress and velocity crack tip fields for fast running cracks in an elastic-plastic, pressure-sensitive material are determined. The behavior of the singularity exponent s of the stress-singularity was examined for different pressure-sensitivity parameters kt, crack-tip velocities v and hardening coefficients a. The hardening coefficient t~ describes the relation between the shear and the tangent shear modulus. The assumption of homogeneous, isotropic material behaviour showing linear hardening was used. Further, the incremental theory was applied and stationary crack growth under plane stress conditions has been adopted.

Three-dimensional thermal crack growth in self-stressed bimaterial joints: Analysis and experiment

A systematic examination of the initiation and growth of thermal cracks in three-dimensional self-stressed bimaterial joints has been performed by using special models consisting of two segments of different materials, for example of glass and aluminum, and by using a well-defined cooling procedure. Besides, the initiation and development of these thermal cracks originating at one corner of such a bimaterial joint have been measured by means of a special image-processing technique. The corresponding mixed boundary value problem has been formulated, and the fracture mechanical assessment of the three-dimensional thermal crack growth has been evaluated by applying the finite element method. Fracture mechanical parameters have been obtained by two different numerical approaches both based on the FE-method. The first approach is based on Irwins modified crack closure integral by using the so-called 3DMVCCI-technique. As a second method, the well-known J-integral has been implemented in a FE-postprocessor on the basis of the equivalent domain integral (EDI) technique. An appropriate crack growth criterion has been established in accordance with the experimental results obtained.

Interfacial crack growth in thermomechanically loaded bimaterial joints

This paper considers quasi-static and dynamic propagation of straight and curvilinear interface cracks in brittle bimaterials subjected to mechanical crack surface loads and/or superimposed thermal strains acting along the ligament. Explicit stress intensity vector formulae are introduced and discussed in view of interface mechanics features: applied loading, interface, crack-tip velocity and curvature of the interface. In addition, the role of a bulk interphase layer between the adherent bimaterial components is addressed by assessing numerically calculated mixed-mode energy release rates. Finally, crack kinking out of the bulk interlayer (interphase) and the prospective kinking angle are investigated.

Asymptotic analysis for temperature fields induced by dynamic crack growth in pressure-sensitive materials

In this paper the thermic effects of a rapidly propagating crack are investigated. In the case of a dynamic crack propagation, a large portion of the work of inelastic deformation near the crack tip is dissipated as heat. As a result of the rapid propagation the heat conduction from the crack tip is negligibly small. In this paper, the induced asymptotic temperature crack tip fields for fast running cracks in an elastic-plastic and particularly pressure-sensitive material are determined. The calculation of the temperature field (thermal problem) follows from the corresponding asymptotic stress and velocity fields (mechanical problem). Therefore, the mechanical problem has to be solved before the thermal problem. The asymptotic stress and velocity fields were calculated from a corresponding boundary value problem considering the mathematical consequences of a mode I-loading and associated symmetry effects. Then, the asymptotic temperature field can be calculated directly from the received results of the stress and velocity fields. For the calculation of the crack tip fields an asymptotic analysis is used as shown in [1‐8]. Further, for the calculation of the asymptotic crack tip fields the incremental theory of plasticity was applied and stationary crack growth under mode I-loading and plane stress conditions have been adopted. The modelling of the pressure-sensitive properties of the material [9‐11] was performed by the Drucker-Prager yield function. Studies concerning pressure-sensitive materials and asymptotic analysis have been performed in [1, 2] using the assumptions of the HRR-field theory. In [3, 4] the stress and velocity fields for a quasistatic crack growth under mode I-loading conditions are investigated.

Nonideal Interface of a Bimaterial with Defects under Thermal Load

Thermal cracking is often observed in bimaterial compounds as well as in composite materials due to thermal mismatch of materials (Herrmann [1]). In addition, interfaces, defects and their interactions play an important role in understanding the fracture behavior of multiphase solids, and have received considerable attention (Theotokoglou and Tsamasphyros [2], Han et al. [3]). Numerous investigations reveal that the interface strength influences especially also the strength of a bimaterial as a whole.