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- Fatigue (2)
- Fatigue crack propagation (2)
- Residual stresses (2)
- Safe life design (2)
- Combined non-linear hardening with cyclic loading (1)
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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.
A two-dimensional analysis of the Charpy V-notch specimen subjected to impact loading, according to the standard DIN EN 10045-1, is carried out, using a transient explicit dynamic finite element program. An elastic-viscoplastic, temperature dependent, constitutive relation for a porous plastic solid based on the Gurson damage model is developed. Ductile fracture of the matrix material will be described by the nucleation and subsequent growth of voids to coalescence. An updated Lagrange–Jaumann formulation is employed accounting for large strain and rotation. The discretization is based on four-node plane strain solid elements with one Gauss point. The equations of motion are integrated numerically by an explicit integration algorithm utilising a lumped mass matrix. The predictions of the numerical analysis in terms of force deflection response, crack resistance behaviour and deformation energy absorbtion are compared with results from Charpy tests which were carried out according to the low-blow technique.
This paper deals with life prediction by observation and simulation of short fatigue cracks in cyclically loaded smooth and notched specimens made of 0.15 wt-% carbon steel SAE1017. The measured crack behaviour was simulated in a microstructural environment. Reference tests under constant amplitude loading allowed to determine model parameters and hence a reasonable life prediction by simulation resulted even for service loading. Short crack behaviour was a measurable property for damage also to compare smooth and notched specimens.
End of November 2005 strong south-west wind and heavy snowfall were predominant in the region Münsterland, north-western part of Germany. This led to accretion of a considerable quantity of wet snow to overhead electrical lines in form of snow rolls on the conductors. Eighty-two transmission towers failed catastrophically, most of them by buckling, however some by brittle fracture. As a consequence nearly 250,000 people have been cut off from electrical power supply for several days with major media attention.
This paper describes the forensic analysis in order to investigate the failure cause. Therefore extensive materials investigations, mechanical testing of original components and specimens thereof, estimations for the real wind and snow loads and their combinations, structural analyses as well as detailed evaluations on the basis of previous investigations, literature and regulations were conducted. It was revealed that some of the examined components were manufactured from Thomas steel which was partially in embrittled condition. The investigated towers fulfilled the design codes valid at the time of erection. However the present line loads of the wet snow rolls on the conductors exceeded by far the ones given in the design codes valid at that time.
The load case leading to failure was reconstructed by the derived positions of loads mainly caused by unequal and asymmetric distribution of snow rolls on left and right electrical system. The loads and corresponding stresses acting on the structure before failure were estimated. By comparison with the fracture forces from mechanical testing of original members of the collapsed tower the component that primarily failed was localised. The primary fracture occurred on a diagonal member under tension made of Thomas steel which was weakened by embrittlement. The failure cause was a combination of heavy weather conditions (storm, approx. 0 °C and wet snowfall leading to heavy snow rolls on conductors), asymmetric loading conditions and the usage of Thomas steel which was partially embrittled. Finally, recommendations for avoiding future failures are given.
The paper gives an overview on safe life and damage tolerance methods applied to railway axles. It describes failure scenarios due to fatigue crack initiation and propagation. Besides common aspects of design, specific features such as corrosion and impact damage from flying ballast are discussed which may reduce the fatigue strength of axles during service. Potential effects of non-metallic inclusions from the steel manufacturing process are addressed in the context of the very high number of loading cycles railway axles are designed for. With respect to damage tolerance general lines of fracture mechanics residual lifetime analyses are introduced. More specific discussion is provided on aspects such as the threshold value of fatigue crack propagation and reliability aspects of non-destructive inspection.
The safety assessment of railway axles is based on a two-stage approach: fatigue strength design and regular inspections which, in terms of a general safety philosophy refer to safe-life and damage tolerance concepts. Starting with a recent failure case, a broken axle of a German high speed train, a discussion is presented on issues of both safety levels. These include ideas for finite life design, the treatment of in-service effects on the fatigue strength due to flying ballast damage and corrosion pits, the effect of corrosion on fatigue crack initiation and propagation, potential effects of non-metallic inclusions in steels, the way to detect them by quality control measures and reliability aspects of non-destructive testing with respect to the detection of fatigue cracks. Proposals are made how the safety level could be further improved.