Janez Kramberger

A computational model for determination of service life of gears

Abstract A computational model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. The fatigue process leading to tooth breakage is divided into crack initiation and crack propagation period. The strain-life method in the framework of the FEM-method has been used to determine the number of stress cycles N i required for the fatigue crack initiation, where it is assumed that the crack is initiated at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for the further simulation of the fatigue crack growth. The functional relationship between the stress intensity factor and crack length K = f ( a ), which is needed for determination of the required number of loading cycles N p for a crack propagation from the initial to the critical length, is obtained using displacement correlation method in the framework of the FEM-method. The total number of stress cycles N for the final failure to occur is then a sum of N i and N p . The model is used for determination of service life of real spur gear made from through-hardened steel 42CrMo4, where required material parameters have been determined previously by the appropriate test specimens.

Numerical calculation of bending fatigue life of thin-rim spur gears

Abstract Mechanical elements subjected to cyclic loading have to be designed against fatigue. The aim of this paper is to examine the bending fatigue life of thin-rim spur gears of truck gearboxes. The gear service life is divided into the initiation phase of the damage accumulation and the crack growth, respectively. The analysis of thin-rim gear fatigue life has been performed using the finite element method and the boundary element method. The continuum mechanics based approach is used for the prediction of the fatigue process initiation phase, where the basic fatigue parameters of the materials are taken into account. The remaining life of gear with an initial crack is evaluated using the linear-elastic fracture mechanics.

Numerical modelling of fatigue crack initiation of martensitic steel

Numerical simulation of micro-crack initiation that is based on Tanaka-Mura micro-crack nucleation model is presented. Three improvements were added to this model. Firstly, multiple slip bands where micro-cracks may occur are used in each grain. Second improvement deals with micro-crack coalescence by extending existing micro-cracks along grain boundaries and connecting them into a macro-crack. The third improvement handles segmented micro-crack generation, where a micro-crack is not nucleated in one step like in Tanaka-Mura model, but is instead generated in multiple steps. Numerical simulation of crack-initiation was performed with ABAQUS, using a plug-in that was written specially for handling micro-crack nucleation and coalescence. Since numerical model was directed at simulating fatigue properties of thermally cut steel with martensitic structure, edge properties of specimen were additionally inspected in terms of micro-structural properties, surface roughness and residual stresses.

Damage and failure modeling of lotus-type porous material subjected to low-cycle fatigue

The investigation of low-cycle fatigue behaviour of lotus-type porous material is presented in this paper. Porous materials exhibit some unique features which are useful for a number of various applications. This paper evaluates a numerical approach for determining of damage initiation and evolution of lotus-type porous material with computational simulations, where the considered computational models have different pore topology patterns. The low-cycle fatigue analysis was performed by using a damage evolution law. The damage state was calculated and updated based on the inelastic hysteresis energy for stabilized cycle. Degradation of the elastic stifness was modeled using scalar damage variable. In order to examine crack propagation path finite elements with severe damage were deleted and removed from the mesh during simulation. The direct cyclic analysis capability in Abaqus/Standard was used for low-cycle fatigue analysis to obtain the stabilized response of a model subjected to the periodic loading. The computational results show a qualitative understanding of pores topology influence on low-cycle fatigue under transversal loading conditions in relation to pore orientation.

Numerical Analysis of the Crack Growth in a High Loaded Bolt Connection

The present paper deals with the research on the crack growth in a bolt connection of a lug for crane counter weight bars. Counter weight bars are structural elements that are subjected to very heavy loads and therefore special attention must be paid. The main purpose of this research is to determine the number of the load cycles required for a crack to propagate from initial to critical crack length, when the final failure can be expected to occur. All required material parameters and the experimental results were determined in our previous research. The influence of the initial crack size upon the remaining life of the lug is researched numerically by means of finite element analysis and analytically by use of the corrected analytical model.

Fatigue Assessment of High Loaded Bolted Bar Connection Using Strain-Life Approach

The paper deals with the problem of service life evaluation of counterweight bar bolted connection by means of computational analysis and experimental testing. Computational analysis has been performed using the local strain-life approach (ε-N), where appropriate material properties for treated high strength steel S1100Q has been determined previously. Experimental fatigue tests of bars were carried out in a specially constructed hydraulic pulsation machine. Comparison of computational and experimental results shows a reasonable agreement.

Evaluation of the Service Life of Gear in Regard to Bending Fatigue in a Gear Tooth Root

A computational model for evaluation of service life of gears in r ega d to bending fatigue in a gear tooth root is presented. The fatigue process leading to toot h breakage is divided into crack initiation and crack propagation period. The Coffin-Manson relationship is us ed to determine the number of stress cycles Ni required for the fatigue crack initiation, where it is assumed t hat the initial crack is located at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for the further determination of the required number of loading cycles Np for crack propagation from the initial to the critical length, where r quired material parameters have been determined previously with appropriate test specimens. The total number of stress cycles N for the final failure to occur is then a sum N = Ni +Np. Introduction Several classical standardised procedures (DIN, AGMA, ISO, etc.) can be used for the approximate determination of load capacity of gear tooth root. They are commonly ba sed on the comparison of the maximum tooth-root stress with the permissible bending stress and consider only the final stage of the fatigue process in a gear tooth root, i.e. the occurrence of final failure. However, the complete process of fatigue failure of mechanical elements may be divided into the following stages [1, 2]: (1) crack nucleation; (2) short crack growth; (3) long crack growth; and (4) occurrence of final failure. In engineering applications the first two stages are us ually termed as “crack initiation period”, while long crack growth is termed as “crack propagation peri od”. However, the crack initiation period generally accounts for most of the service life, especially in high-cycle fatigue (HCF), see Fig. 1. The total number of stress cycles N can than be determined from the number of stress cycles Ni required for the fatigue crack initiation and the number of stress cycles Np required for a crack to propagate from the initial to the critical crack length:

Fatigue crack initiation and propagation in lotus-type porous material

The investigation of fatigue strength of lotus-type structure with nodular cast iron as a base material using computational model is analysed in present study. The irregular pores distribution in transversal and longitudinal direction, regarding the external loading, is considered in the computational models. The complete fatigue process of analyzed porous structure is then divided into the crack initiation (Ni) and crack propagation (Np) period where the total fatigue life (N) is defined as: N = Ni + Np. The crack initiation period is determined using strain life approach where elastic-plastic numerical analysis is performed to obtain the total strain amplitude in the critical stress fields around the pores. The simplified universal slope method is then used to determine the number of stress cycles, Ni, required for formation of initial cracks. The number of stress cycles, Np, required for crack propagation from initial to the critical crack length is also numerically determined using finite element (FE) models, in the frame of Abaqus computation FEM code. The maximum tensile stress (MTS) criterion is considered when analyzing the crack path inside the porous structure. The performed computational analyses show that stress concentrations around individual pores are higher when external loading is acting in transversal direction in respect to the pore distribution. Therefore, further computational analyses regarding crack initiation and crack propagation period have been done only for pores distribution in transversal direction.

Computational simulation of biaxial fatigue behaviour of lotus-type porous material

A computational simulation of low-cycle fatigue behaviour of lotus-type porous material, subjected to biaxial in-phase loading cycles is presented in this paper. Fatigue properties of porous materials are less frequently published in the literature. This paper evaluates computational analyses, where different pore distribution and biaxial loading conditions in relation to the pore orientations is considered in each simulation. The fatigue analysis is performed by using a damage initiation and evolution law based on the inelastic strain energy. The computational results are subjected to the appropriate statistical analysis, because of different pore topology a different fatigue lives are obtained on the same loading level. Results of computational simulations show also a qualitative understanding of porosity influence on low-cycle fatigue failures of lotus-type porous material under biaxial loading conditions.

Fatigue Crack Initiation and Growth in a High Loaded Bolted Bar Connection

The fatigue crack initiation and growth in a high loaded bolted bar connection made of high strength steel S1100Q is presented. The material parameters for the fatigue crack initiation f’, f’, b and c are determined using low cycle fatigue test according to ASTM E 606 standard. The fracture mechanics parameters C and m are determined according to ASTM E 647 standard. Based on low cycle fatigue parameters the computational analysis is performed to determine the number of stress cycles required for the fatigue crack initiation. The remain service life up to the final failure is than determined using the known parameters C and m and calculated stress intensity factor, where 3D numerical analysis is performed. The bolted bars are also experimentally tested. Comparison of computational and experimental results shows a reasonable agreement.