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Eingeladener Vortrag
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The Kitagawa-Takahashi (KT) diagram is a well-established tool in the fatigue community for the prediction of the fatigue limit of metallic materials in presence of defects. Nevertheless, its determination is associated with a large number of fatigue tests carried out on specimens with artificial defects (notches) to describe the fatigue limit-defect size relationship in the short crack regime. The preparation of the specimens and the execution of the tests is time expensive. Therefore, few phenomenological models have been introduced in the past to provide a first approximation of the KT diagram based solely on the fatigue limit for smooth specimen and the fatigue crack propagation threshold for long cracks. Despite the use of such models is widely spread, these suffer from problems related to the uncertainties of the material parameters. Furthermore, the mechanics of short cracks, which is the physical mechanism behind the concept of the fatigue limit, is not considered. This work discusses the advantages and drawbacks of using short fatigue crack propagation models for predicting the fatigue limit of flawed metallic materials. The KT diagrams for a EA4T railway axle steel in as-received and full-hardened condition are approximated by means of the cyclic R-curve method.
This study addressed a 7017 Al-alloy tailored for powder bed fusion – laser beam (PBF-LB) process. The alloy was prepared by mixing 3 wt% Zr and 0.5 wt% TiC powder to standard pre-alloyed 7017 grade aluminium powder. This made printing of the alloys possible avoiding solidification cracking in the bulk and achieving high relative density (99.8 %). Such advanced alloys have significantly higher Young’s modulus (>80 GPa) than conventional Al-alloys (70–75 GPa), thus making them attractive for applications requiring high stiffness. The resulting microstructure in as-printed condition was rich in particles originating from admixed powders and primary precipitates/inclusions originating from the PBF-LB process. After performing a T6-like heat treatment designed for the PBF-LB process, the microstructure changed: Zr-nanoparticles and Fe- or Mg/Zn- containing precipitates formed thus providing 75 % increase in yield strength (from 254 MPa to 444 MPa) at the cost of decreasing ductility (∼20 % to ∼9 %). In-situ tensile testing combined with SXCT, and ex-situ tensile testing combined with fracture analysis confirmed that the fracture initiation in both conditions is highly dependent on defects originated during printing. However, cracks are deflected from decohesion around Zr-containing inclusions/precipitates embedded in the Al-matrix. This deflection is seen to improve the ductility of the material.
Al-Si alloys produced by Laser Powder Bed Fusion (PBF-LB/M) techniques allow the fabrication of lightweight free-shape components. Due to the extremely heterogeneous cooling and heating, PBF-LB/M induces high magnitude residual stress (RS) and a fine Si microstructure. As the RS can be deleterious to the fatigue resistance of engineering components, great efforts are focused on understanding their evolution before and after post-process heat treatments (HT).
An overview of the BAM funed Focus Area Materials Project "AGIL" will be presented. AGIL focussed on the stdiy of the ageing characteristics of additively manufactured austenitic stainless steel with a "powder to mechanical failure" Approach. Recent Highlights are presented and a perspective for future studies.
Modelling of environmentally assisted material degradation in the crack phase-field framework
(2019)
The simulation of crack propagation was conducted with a diffusive crack model in a variational framework. Moreover, the physically sound introduction of mass transport and coupling mechanisms due to environmentally assisted effects could be realised in this framework. The objective consists of the application of the phase-field Approach towards the simulation of environmentally assisted material degradation with the advantage of a non-required predefined crack path and a mesh-independent non-local formulation that facilitates the damage evolution with respect to material softening. The sharp crack is regularised by the introduction of a phase-field order parameter leading to a diffusive crack formulation.
Besides the equations originating from the linear momentum balance an additional evolution equation for the crack phase-field is introduced. Furthermore, mass transport is simulated by a Diffusion equation. The description delivered by the variational phase-field framework is able to simulate crack propagation according to published numerical test cases.
Additionally, the calculation of stress intensity factors is possible as well as crack resistance curves that describe stable crack propagation.
The present paper provides a discussion on all these topics and it offers solutions for it. The authors present an analytical solution of a Delta J based crack driving force based on an R6 type approach but modified for cyclic loading. The gradual build-up of the crack closure effect is modelled by the so-called cyclic R curve which describes the crack size dependency of the fatigue crack propagation threshold in the short crack regime. It is explained how the cyclic R curve is experimentally determined and how it can be estimated by a modified Kitagawa-Takahashi approach.
With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented.
The damage process of short glass fibre (30% weight) reinforced polyamide caused by mechanical loading was investigated from the beginning on micro cracking level to the incipient crack of mm-dimension. Based on high resolution computer tomography and the X-ray-refraction technique the inner surface due to micro-cracking at the short fibre ends and the fibre matrix debonding of the skin surface of the filament was determined quantitatively. With the knowledge of the fatigue crack propagation rate and fracture toughness of the material from former research projects, it was derived that the total inner surface due to micro cracks measured by X-ray refraction is much higher than the specimen could have withstand the load, supposed the surface is in a localized crack. Hence, the damage process could be described from micro to macro level. Accompanying fractographic investigations endorse the modelling based on the NDT-techniques.
The damage process of short glass fibre (30% weight) reinforced polyamide caused by mechanical loading was investigated from the beginning on micro cracking level to the incipient crack of mm-dimension. Based on high resolution computer tomography and the X-ray-refraction technique the inner surface due to micro-cracking at the short fibre ends and the fibre matrix debonding of the skin surface of the filament was determined quantitatively. With the knowledge of the fatigue crack propagation rate and fracture toughness of the material from former research projects, it was derived that the total inner surface due to micro cracks measured by X-ray refraction is much higher than the specimen could have withstand the load, supposed the surface is in a localized crack. Hence, the damage process could be described from micro to macro level. Accompanying fractographic investigations endorse the modelling based on the NDT-techniques.
The determination of the fatigue life in technical alloys containing large and small defects must rely on a propagation model which accounts for short and long crack growth. Recently an analytical model which incorporates propagation in the short crack regime and plastic correction for the crack driving force has been presented by two of the authors.
This work is intended to show further validation of the model, taking into account data sets for different materials with different testing conditions.
Despite the assumptions about missing parameters, the value of which had to be taken from the literature, the predictions showed a fairly good approximation of the fatigue lives. A possible interpretation of the results in terms of multiple crack initiation and propagation at higher loads is proposed.