Winfried Dahl

EFFECT OF TRIAXIAL STRESS ON MIXED-MODE FRACTURE

Abstract Triaxial stress has a large influence on fracture behaviour of materials. Present work seeks to investigate effects of triaxial stress on mixed-mode fracture and determines the direction of the crack initiation in dependence on the inclination crack angle with mixed-mode loading. For small scale yielding, based on the three-dimensional (3D) stress field around a crack tip, the distribution of triaxial stress at the inclined crack front in 3D space is obtained. In order to determine the crack initiation angle for a given inclination angle, a criterion is defined by means of maximum triaxial stress: along a contour around a crack tip with equal distance to the crack tip, the crack initiates along the direction where triaxial stress is maximal. According to the criterion the relation between the crack initiation angle and the inclination angle is determined. The maximum triaxial stress around a crack tip increases with increasing the inclination angle and decreases with decreasing Poissons ratio. Experiments to check the theoretical predictions from the criterion have been conducted. CCT-specimens with the same ligament have been designed for the experiments. The steel FeE 550 was tested at temperature −140°C and with loading speed 50 mm/sec. The experimental results have shown a good agreement with theoretical predictions from the present criterion, especially at small inclination angles.

Formation of TiC coatings on steels by a fluidized bed chemical vapour deposition process

Abstract The use of a fluidized bed process for the production of hard wear- and corrosion-resistant coatings of carbides, nitrides and carbonitrides of cementing metals is promising since it can lead to a flexible surface treatment technology combining adaptability with relatively low capital and operational costs. In this paper the feasibility of a fluidized bed process for the formation of titanium carbide coatings using chemical-vapour-deposition-based reactions is discussed. The method involves a treating agent consisting of a powder mixture of Al 2 O 3 with FeTi which is fluidized at elevated temperature with Ar. As an activator of the process NH 4 Cl was used. The use of explosive hydrogen is avoided by the formation of the vapours of the materials to be coated in situ in the reactor. With this method, adherent and dense coatings of TiC were applied on various steel grades.

Modelling of the damage in ductile steels

Abstract The nucleation, growth and coalescence of voids result in ductile fracture of materials. The first coalescence of voids defines crack initiation. In order to describe the initiation behaviour of a controlled rolled structural steel FeE 460 quantitatively, experimental investigations and micromechanical modelling were conducted. The tests were carried out at room temperature with axisymmetric notched tensile specimens under proportional loading. Specimen geometries containing different notch geometries leading to different stress triaxiality ratios were chosen. Taking into consideration the experimental procedure a failure curve which considers the local state of stress and strain at initiation was evaluated. Different criteria concerning initiation of the ductile failure process by reaching a critical void size R c were proved with regard to the reproduction of the material behaviour.

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic–plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation Wdi are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation Wdi which is independent of the stress state during the deformation process. We recommend Wdi as a material property of toughness for testing and engineering purposes.

The influence of strain history on ductile failure of steel

Abstract By comparing the micromechanisms of ductile fracture of metallic materials (void nucleation, void growth and void coalescence) and the loading conditions in terms of local stresses and strains, the fracture behaviour may be described in terms of local properties as, for example, void volume fraction, to find out the damage development during plastic deformation and the conditions of crack initiation. For the damage development due to void growth the stress triaxiality during deformation is thought to be an important parameter. There are different models for void coalescence considering a critical combination of stress triaxiality and plastic strain, a critical void volume fraction and a critical amount of energy added. Experiments on notched tensile specimens had been done to determine the plastic strain at crack initiation. FEM-calculations were used to calculate the parameters stress triaxiality and equivalent plastic strain during deformation at the point of void coalescence taking into regard the loading history. Strongly varying stress triaxiality during deformation was achieved by employing one- and two-step experiments with tensile bars of different notch radii. To find a criterion for void coalescence the following two models are applied: (1) Void growth model: By using this equation to model the damage process a critical size to describe crack initiation by void coalescence is sought. However, it is found that based on this model void coalescence may be described only by a two-parameter-criterion, which in this case is geometrical. (2) Damage work model: To find a one-parameter-criterion the “damage work model” is applied. It takes into account the major influence of stress triaxiality on damage development and the stress-strain-curve of the material. Based on this model crack initiation by void coalescence may be described by one parameter which in this case is an accumulated local energy.

Two- and three-dimensional elastic-plastic stress analysis for a double edge notched tension specimen

Abstract This paper describes an elastic-plastic stress analysis for a double edge notched tension specimen, a specimen used for the determination of the microscopic cleavage fracture stress. The analysis was performed numerically using the finite element method. First, a study of the finite element modelling is presented in order to demonstrate the requirements on a three-dimensional finite element structure leading to accurate stress distributions in the whole specimen. On the other hand possible restrictions are shown, if only a certain parameter, e.g. the maximum tensile stress has to be evaluated. Then the global response of the three-dimensional structure is compared with results of two-dimensional calculations assuming plane stress and plane strain, respectively. Subsequently the most interesting stress and strain distributions are discussed. The maximum value of stress concentration in front of the notch is given as a function of the applied stress. Additionally the state of deformation at fracture load is characterized by the plastic zone size, too. All three-dimensional results are compared with results of a plane strain model.

Influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress

Abstract The aim of this work is to determine the influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress σf*. Besides, the dependence of the initiation temperature for shear fracture Ti and the temperature for general yield Tgy on strain rate is investigated. Finally, the local values of stress triaxiality and equivalent plastic strain at the occurrence of cleavage fracture for several steels and specimen types are compared with the failure curve for ductile fracture to check the validity of the theory of stress controlled cleavage fracture and the strain/triaxiality controlled shear fracture in the transition region. Based on experimental tests, the results are obtained by finite element analyses. The investigation shows, that σf* is dependent on temperature and strain rate and increases with decreasing test temperature and increasing strain rate. The transition temperatures Ti and Tgy increase with increasing strain rate. The theories of stress controlled cleavage fracture and of shear fracture controlled by equivalent plastic strain and stress triaxiality seem to be valid. That fracture mechanism occurs for which the critical condition is reached first.

Determination of crack resistance curves under static and dynamic loading by analysis of load displacement relationship

Abstract The key curve method according to Ernst et al. (Fracture Mechanics, ASTM STP677, pp. 581–599, 1979) was applied for the determination of JR-curves. Steels with different yield strength and toughness were investigated. The method requires a calibration curve, which has to be determined for each material and specimen type. It was shown for CT-specimens that crack extensions calculated by the key curve method are in good agreement with those observed on the fracture surfaces. The J1-values determined coincided well with values derived from ‘stretched-zone’ measurements and the equation for the ‘blunting-line’ according to Shih (J. Mech. Phys. Solids29, 305–326,1981). It was demonstrated that the key curve method can be applied even at high loading rates. 1 CT-25-specimens were tested at ram speeds up to 4 m s . First results of instrumented charpy impact tests showed that crack propagation can be monitored in charpy V-notch specimens, too. On the other hand, crack initiation is difficult to detect in the latter case because of superimposed oscillations in the load signal.

Modelling of sheet metal testing

Abstract Flow stress, work hardening rate and anisotropy characterize plastic behavior of sheet metals during pressforming operations. This paper concentrates on modelling forming limits and limiting drawing ratios by using a new flow curve description. The flow curve description is based on the dislocation theory and allows the separate analysis of yield stress and work hardening rate effects. The theoretical investigations are compared with experiments.

Der Kurzrisseffekt bei der bruchmechanischen Prüfung: A unified method to treat fatigue damage

Kurzfassung Unter dem ausgeprägten Kurzrisseffekt versteht man den Anstieg von zähbruchmechanischen Initiierungskennwerten bei reduzierter Ermüdungsrisslänge. Für Bruchmechanikproben mit niedrigem a/W-Verhältnis, also geringer Ermüdungsrisslänge, werden bei Vorliegen eines ausgeprägten Kurzrisseffekts demnach höhere Initiierungskennwerte ermittelt als für Proben mit größerem a/W-Verhältnis. In mehreren Forschungsarbeiten der Vergangenheit wurden teilweise unterschiedliche Ergebnisse zum Kurzrisseffekt bei Stahl erzielt. Ein im vergangenen Jahr durchgeführtes gemeinsames Forschungsprojekt der Materialprüfungsanstalt Uni Stuttgart (MPA) und des Instituts für Eisenhüttenkunde der RWTH Aachen (IEHK) sollte die Ursachen für die unterschiedlichen Ergebnisse klären.