Issue 35

J. Kramberger et alii, Frattura ed Integrità Strutturale, 35 (2016) 142-151; DOI: 10.3221/IGF-ESIS.35.17 143 Figure 1 : Cross section of lotus-type porous material in transversal (a) and longitudinal (b) direction [6]. Existing research work demonstrates that the most common method for determination of structural properties of porous materials is experimental work [6-9]. Measured mechanical property is usually the compressive yield strength or plateau strength. Other mechanical properties, like elastic modulus, ultimate tensile strength, densification strain and fatigue properties have been less frequently published. In structural applications of porous material, it is necessary to take into account the degradation of strength with cycling loading. However, the fatigue properties of lotus-type porous material have not been clarified in detail, compared with those of metal foams. Seki et al [10] clarified the effect of porosity, anisotropic pore structure, and pore size distribution on the fatigue strength of lotus cooper. They discussed the slip band formation and crack initiation around the pores. Furthermore, fatigue cracks were observed in various cycles of fatigue test, and the crack propagation path was investigated using lotus copper specimens with notch. This paper discuss the low cycle fatigue behavior of lotus-type porous material and evaluates the fatigue crack initiation and propagation with computational simulations. In this study we used two-dimensional structure as a basis for the finite element analysis. Considered computational models of lotus-type porous material had different pore topology patterns, where both a regular and an irregular pores distribution in transversal direction have been taken into account. The alternate tensile load under displacement rate control was applied and deformation response was examined. Furthermore, damage initiation and evolution were performed using the direct cyclic analysis procedure from Abaqus/Standard to compute the stabilized response of the modeled structure directly in low-cycle fatigue [11, 12]. C OMPUTATIONAL METHODS n recent years computational simulations became an important tool for solving problems in general engineering and science. Computational simulations allow for better insight into analysed structure behaviour and can provide information which is sometimes very difficult or even impossible to determine with experimental measurements. The traditional approach for determining the fatigue limit for a structure is to conduct a transient finite element analysis in which the load cycle is repetitively applied until a stabilized state is obtained [13, 14]. This method can be quite expensive, since it may require application of a large number of loading cycles to obtain the steady response. To overcome this problem, the direct cyclic analysis procedure from Abaqus/Standard was used in this work to compute the stabilized response of the structure directly [11, 12], without having to compute a number of sequential cycles that would lead to such stabilized cycle. Abaqus/Standard offers a general capability for modeling the progressive damage and failure of ductile materials due to stress reversals and the accumulation of inelastic strain energy when the material is subjected to sub-critical cyclic loadings. Damage initiation and evolution criteria are adopted to determine the low-cycle fatigue damage. These two criteria are based on the stabilized accumulated inelastic hysteresis strain energy per cycle,  w, as illustrated in Fig. 2. Material failures refer to the complete loss of load-carrying capacity that results from progressive degradation of the material stiffness. The stiffness degradation process is modeled using damage mechanics. The theory of damage mechanics takes into account the process of material degradation due to the initiation, growth and coalescence of micro- cracks/voids in a material element under applied loading. Low-cycle fatigue analysis uses the direct cyclic procedure to directly obtain the stabilized cyclic response of the structure. The direct cyclic procedure combines a Fourier series approximation with time integration of the nonlinear material behavior to obtain the stabilized solution iteratively using modified Newton method. The number of Fourier terms, the number of iterations and the incrementation during the cyclic time period can be controlled to improve accuracy [11]. I (b) (a)