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- Duktile Schädigung (2)
- Fatigue (2)
- Laird (2)
- Single crystal (2)
- Striations (2)
- Adiabatic Shear Bands (1)
- Adiabatische Scherbänder (1)
- Bauteilsicherheit (1)
- Blunting and resharpening (1)
- Bruchmechanik (1)
Laird and Smith [(1962). Philosophical Magazine 8, 847857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Lairds plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J2 hypo-elasto-plasticity model with ArmstrongFrederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletauds model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Lairds mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 11551165] on pure copper single crystals.
In this work, the influence of the development of geometrically necessary dislocations (GNDs) at a crack tip in single crystals on the hardening and crack propagation behaviour is investigated. In particular, we are interested in examining the effect of such additional hardening on the development of glide and kink bands at the crack tip as well as on the process of crack opening. To this end, following Nye and many others, local deformation incompatibility in the material is adopted as a measure of the density of GNDs. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening. A thermodynamic formulation of the model in the context of the dissipation principle facilitates the derivation of the corresponding hardening relation. Results suggest that this additional hardening retards kink-band development, but has little or no influence on glide-band development. It also influences the crack tip opening displacement (CTOD). It turns out that the simulated CTOD correlates well with experimentally determined crack-propagation rates for different crack growth direction in the crystal.
Advances in the application of non-local damage models in the simulation of ductile crack-extension
(2004)
Local damage models usually have the disadvantage that results are strongly mesh dependent. The reason is that the type of the underlying partial differential equations changes under quasi-static conditions from elliptic to hyperbolic. Non-local damage models do not exhibit such behaviour under certain conditions. The usage of such non-local damage models in finite element analyses opens the possibility for preserving the ellipticity of the partial differential equations and thus avoiding mesh dependence of numerically obtained results. The loss of ellipticity for local models and its preservation for non-local models are demonstrated for a wide variety of examples enclosing ductile damage. In the present investigation, the non-local damage model is applied to the simulation of ductile crack extension in fracture mechanics specimens. The type of the underlying differential equations is permanently analysed and controlled.
Nicht-lokale, dehnratenabhängige Modellierung adiabatischer Scherbänder an Proben und Bauteilen
(2007)
The purpose of this work is the development and numerical implementation of a non-local extension of existing Gurson-based modeling for isotropic ductile damage and attendant crack growth. In the current work, this extension is based on a generalization of Gurson-based ductile damage modeling formally analogous to that of Needleman and Tvergaard as based on a (local) effective damage parameter f* which accounts in their case in an effective fashion for the effect of void coalescence on yield behaviour. Here, the corresponding generalized effective damage parameter ? is introduced in order to delocalize the model damage process. To this end, ? is modeled in this work as a scalar-valued continuum microstructural field or generalized phase field via a recent thermodynamic approach to the modeling of such fields. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite element method and utilized to investigate the damage behaviour of an inhomogeneous steel block in simple tension. The corresponding simulation results demonstrate in particular that delocalization of the model damage process also leads to minimization of mesh-dependence. For simplicity, the current formulation is restricted to the case of small strain and isothermal conditions.
The purpose of this work is the formulation, numerical implementation and initial application of a non-local extension of existing Gurson-based modelling for isotropic ductile damage and attendant crack growth. It is being carried out under the premise that void coalescence results not only in accelerated damage development (e.g., Needleman and Tvergaard, 1984), but also in damage delocalisation (i.e., via interaction between neighbouring Gurson RVE's). To this end, we proceed by analogy with the approach of Needleman and Tvergaard (1984) who replaced the Gurson void volume fraction f with a (local) effective damage parameter f* in the Gurson yield condition to account for the effect of void coalescence on the material behaviour. In the current case, the role of f* is taken over and generalised by an effective continuum damage field ?. A field relation for ? is formulated here in the framework of continuum thermodynamics. In the simplest case, the resulting relation is formally analogous to the inhomogeneous temperature equation in which void nucleation and growth represent (local) sources for ? and in which void coalescence takes place in a process zone whose dimension is determined by a characteristic material lengthscale. Analogous to temperature, then, ? represents an additional continuum degree-of-freedom here, resulting in a coupled deformation-damage field model. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite-element method on the basis of backward-Euler integration and consistent linearisation. Using this implementation, the behaviour of the current extended Gurson-based damage model is investigated for the case of simple tension of an inhomogeneous steel block. In particular, the corresponding simulation results document quantitatively the dependence of the delocalisation of the model damage process and minimisation of mesh-dependence on the characteristic dimension of the damage process zone.