Fatigue assessment of welded gear components under variable amplitude loading and multiaxial loading conditions (#10)
J. Baumgartner1, R. Waterkotte2, J. Hesseler1
1 Fraunhofer Institute for Structural Durability and System Reliability LBF, Darmstadt, Hesse, Germany
Gear components have to endure complex loading conditions during service. From a mechanical point of view, these are variable amplitudes, multiaxial loading conditions at gears with a helical cut and a very high number of load cycles.
In the paper, the fatigue assessment of two weld lines in a differential is presented. The assessment is based on notch stresses derived from FE-analysis at the weld root notch for a reference radius of rref = 0.05mm. The stresses through one revolution of the differential show different number of cycles and a high degree of local multi-axial stressing. The local shear and normal stresses change non-proportional and subsequently lead to a change of the direction of the main principal stresses. Additionally, a load spectrum that approximates the service loads is considered.
The local multi-axial loading conditions are assessed with the modified Gough-Pollard hypothesis using a comparison value of CV=0.5 as recommended for non-proportional loading in the IIW-recommendations. For the assessment of the service loads for each node in the weld notch a local stress-time history was derived for each stress component. By using the linear damage accumulation hypothesis according to Palmgren-Miner modified according to Haibach and applying an allowable damage sum of D=0.5 equivalent constant amplitude stress ranges have been derived for both stress components as input for the modified Gough-Pollard equation and evaluation of the fatigue life.
The results of the numerical assessment are presented and compared to results from component tests. The numerical assessment using the IIW-design line for the reference radius rref = 0.05 mm with the FAT-value 630 MPa for the probability of survival Ps= 97.7% underestimates the in-service life of the weld to a high extent. The design lines are for the worst case and do not consider the beneficial compressive residual stresses which are induced into the weld during the post case hardening of the component. If the design lines are upgraded to Ps = 50%, still a quite conservative assessment is reached. Only by consideration of the compressive residual stresses, a good agreement between assessment and experiment is achieved. The particular results are displayed and discussed.
Keywords: Fatigue assessment, Multiaxial loading, Case hardening, Welded joint, Component test
Fatigue Simulation of Welds Using the 'Total Life' Method (#72)
A. Halfpenny1, S. Vervoort1, P. Roberts1
1 HBM United Kingdom Ltd., nCode Products, Catcliffe, United Kingdom
"Fatigue is the progressive weakening of a material caused by cyclic or otherwise varying loads, even though the resulting stresses are well within the static strength limits"
Fatigue cracks initiate and grow as part of a two-stage process, with Stage 1 - crack initiation, and Stage 2 - crack growth. Historically, crack initiation has typically used either a stress-life (SN) or strain-life (EN) model, whereas crack growth has used either a Linear Elastic Fracture Mechanics (LEFM) or an Elastic-Plastic Fracture Mechanics (EPFM) model.
The Total Life model combines aspects of these models into a unified model for fatigue life estimation. The model can produce fatigue life estimates that are considerably more accurate than the classical approaches. This is particularly apparent with welded structures and lightweight structures, such as thick welded steel structures or lightweight aluminium panels with riveted joints. It is also apparent in lightweight cast structures where fatigue cracks often initiate from gas-entrapped pores caused by the manufacturing process, or by the relatively low-quality surfaces in the as-manufactured condition.
The Total Life model described in this paper is based on the work of Glinka and Mikheevskiy . The paper presents a contextual overview with a detailed review of the mathematical model. The paper describes how the Total Life method has been implemented in a CAE environment, including required inputs for FE modelling, material properties, residual stresses, and applied loading.
A case study is provided illustrating how the model was applied to an engineered weld. Recently the SAE Fatigue Design and Evaluation committee evaluated and validated the Total Life method. By combining crack initiation with crack growth, and including Glinka’s cyclic crack-tip multiaxial plasticity model, the new Total Life technology was shown to estimate fatigue life to within a factor of 2 through simulation alone.
 Mikheevskiy, S., 2009, “Elastic-Plastic Fatigue Crack Growth Analysis Under Variable Amplitude Loading Spectra,” PhD thesis, University of Waterloo.
Keywords: Total Life, Strain-Life (EN), Linear Elastic Fracture Mechanics (LEFM), Cyclic multiaxial elastic-plastic crack-tip residual stress model
Damage Assessment In A Welded Tubular Joint Under Random Loading (#86)
C. Ronchei1, S. Vantadori1, A. Carpinteri1, F. Giordani2, G. Giordani3, I. Iturrioz3, R. Issopo Rodrigues3, D. Scorza1, A. Zanichelli1
1 University of Parma, Department of Engineering & Architecture, Parma, Italy
In agriculture, herbicides and fungicides are distributed on the plants by a pulverization process performed by machines named agricultural sprayers. The most common of such sprayers is the arm sprayer, which is composed by a metallic bearing structure equipped of spray nozzles (Fig. 1(a)). The bearing structure is guided in the vertical movements by a structural component, called ‘‘H” component due to its shape (see the arrow in Fig.1(a)).
Such a component (Fig.1(b)) is constituted from welded tubular elements, the intersections of which represent geometrical discontinuities like T-joints. Under service condition, the “H” component is subjected to forces which are random in nature, and cracks are frequently observed in the stress concentration regions after 2000 hours of sprayer service condition.
In order to define the above random load histories applied to the “H” component, firstly the strain history has been experimentally measured at some locations, named control locations. The service condition investigated consists of the following maneuvers: travel on unpaved road, application of the herbicide (perimeter), application of the herbicide (cultivated area), U-curves, perimeter curves, and braking. Then, random load histories applied to the “H” component are computed by means of a linear elastic finite element model, so that the numerical strain histories are equal to the experimental ones.
By exploiting the numerical stress field coming from the numerical model, the purpose of the present paper is to develop a novel approach to evaluate the fatigue damage under service condition, based on the joint application of the hot-spot stress approach and the multiaxial critical plane-based criterion proposed by Carpinteri et al. [1-3].
Comparison between experimental and numerical damage value is quite satisfactory, making the novel approach useful for industrial applications.
 Andrea Carpinteri, Andrea Spagnoli, Sabrina Vantadori, A multiaxial fatigue criterion for random loading. Fatigue & Fracture of Engineering Materials and Structures, Vol. 26, No. 6, pp. 515-522, 2003.
 Andrea Carpinteri, Andrea Spagnoli, Sabrina Vantadori, A review of multiaxial fatigue criteria for random variable amplitude loads, Fatigue and Fracture of Engineering Materials and Structures, Vol. 40, pp.1007–1036, 2017.
 Sabrina Vantadori, Ignacio Iturrioz, Camilla Ronchei, Discussion on fatigue life estimation under multiaxial random loading: comparison between time- and frequency-domain approach, Theoretical and Applied Fracture Mechanics, Vol. 96, pp.134-145, 2018.
Keywords: damage, multiaxial fatigue, high-cycle fatigue, welded joint
Comparison of Different Assessment Methods of Weld Seams Applied to Automotive Suspension ComponentsVergleich verschiedener Bewertungsmethoden von Schweißnähten anhand der Anwendung bei automotiven Fahrwerkskomponenten (#117)
H. Dannbauer1, K. Hofwimmer1, W. Hübsch1
1 Magna Powertrain, Engineering Center Steyr GmbH & CoKG, St. Valentin, Germany
Chassis components are subject to complex multiaxial loads, whereby vibration phenomena also play a role in some cases. These loads can be determined by measurements and simulations with sufficient accuracy to obtain valuable results for design and optimization by means of a numerical fatigue analysis.
Many chassis components consist of formed individual steel and aluminum sheets which are welded using suitable processes. Experience shows that joint areas usually represent the weak points of the component, so accurate assessment of the weld seams is of high importance during the development process.
Globally, those components are geometrically thin-walled with sheet thicknesses of approximately 2-4 mm, that is why finite element models from shell elements are widely used for structural analysis. The evaluation is carried out with different concepts which are based either on structural stresses of the elements or on nodal forces.
The advantage of this procedure lies in the manageable model size and the simple variation of different parameters such as welding penetration degrees. Disadvantages are necessary hypotheses for combined perpendicular, shear and longitudinal loading, inaccurate representation of the local stiffness of the weld seam due to shell modelling and difficult meshing of the geometry if, for example, several weld seams meet.
A very detailed representation of the sheets and weld seams by volume elements - including representative notch radii - provides good results, but is - due to the difficult geometry creation and large FE models - only feasible locally and with high computational effort.
Due to progresses in meshing and analysis of complex FE models, modelling with 3D elements has become feasible for welded chassis components. Here, sheets and weld seams are sufficiently fine meshed in the sense of structural stress, but the representative radii method is not used. The modeling effort for such models is limited due to elimination of middle plane generation and new preprocessor options.
For the evaluation of weld toe, root and end, an algorithm based on the effective stress method was developed. In this case, stress values below the surface are determined which also contributes to reduced mesh sensitivity. Together with modeling guidelines and calibrated Master-S/N curves, a detailed evaluation of weld seams for complex load histories can be carried out within acceptable analysis times.
A further advantage of this volume-based method is the clear interpretation of the fatigue life results, e.g. with regard to the crack location at the end of a weld seam.
Using chassis components, the methods described above are compared with regard to fatigue strength and application. There are partly considerable differences in the results which can be explained both by the FE modelling as well as by the evaluation method.
Keywords: Assessment Methods, Weld Seams, Suspension Components