The mechanical properties of sintered porous 316L austenitic stainless steel have been a subject of research in recent years. However, the available publications mainly deal with the high-density case (porosity of an order of several percent), while it is also desirable to determine the mechanical properties of low-density agglomerates [1, 2].

There is a group of publications devoted to the preliminary study of the fatigue life of sintered porous 316L steel. These works describe the fatigue life of 316L steel in comparison with the stability of other biomaterials used in implants. The corresponding results are rather qualitative than quantitative [3]. Some publications present the obtained values of the selected strength parameters, such as compressive strength and Young’s modulus, although these results are incomplete [4–6]. There are only a few publications dealing with the quantitative analysis of crack propagation but they use solely the finite-element simulation. Models of this kind are used mainly to determine the effect of size, the size of pores, or the distance between the pores [7, 8]. The test results that could describe the mechanism of formation and development of defects in the material (on the basis of which it would be possible to propose a computational model and, hence, to predict the state of the damaged material and its fatigue life) are still missing [9].

The aim of the present study is to develop the methodology and implementation of the experimental evaluation of strength and fatigue life of sintered 316L stainless steel and, hence, to obtain the fatigue characteristics for different degrees of porosity of the material. These characteristics form a basis for the development of the computational procedure based on the fatigue life that can be be used in the engineering practice.

Experimental Fatigue Testing of Sintered Specimens of 316L Stainless Steel

The test specimens made of sintered 316L stainless steel were created in the multistage powder metallurgy process. The powder with a grain size of 125–250 μm was cold-pressed in a matrix in a specially constructed EDZ-100 testing machine. Numerous solutions are innovative due to the fact that their application was assigned exclusively to the needs of the present research. Sintered specimens with three degrees of porosity 41, 33 and 26% were used in this test.

The prepared compacts were sintered for 1 h in an oven equipped with a vacuum device at a temperature of 1230°C. After this procedure, the specimens were subjected to the last stage of the process of preparation, which gave their final shape by cutting with water and machining.

The monotonic tensile and appropriate tests were carried out in an MTS-858 Mini Bionix fatigue-testing machine with FlexTest SE digital control (Fig. 1). To measure displacements and, in order to control the dynamic load, we used an Instron 2620-601 extensometer with a measurement base of 20 mm and a range of ±2.5 mm. The specimens were mounted in the testing machine by using specially designed handles.

Fig. 1
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Schematic diagram of the test bench: (1) MTS-858 Mini Bionix testing machine; (2) computer software; (3) FlexTest SE digital control; (4) Instron 2620-601 dynamic extensometer.

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Prior to strength testing, a monotonic tensile test was performed on specimens prepared from sintered 316L steel with different degrees of porosity. The nominal stress-strain curves were obtained (Fig. 2). To compute the stress, we take into account only the original cross-sectional area of the specimen. Due to the shape of the specimen, we had no technical possibilities to measure its displacements in the process of loading. The basic mechanical properties of the investigated material were determined (Table 1).

Fig. 2
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Monotonic tensile curves of sintered 316L stainless steel with different porosities: (1) p = 41%; (2) 33; (3) 26%.

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Table 1 Values of the Parameters for the 316L Porous Sintered Material with Three Degrees of Porosity as Compared with the Solid Material
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We applied the uniaxial cyclic (symmetric) oscillating loading. This is explained by the fact that the sintered porous 316L stainless steel for joint components of the endoprostheses is exposed to compressive and bending stresses with dangerous tensile zones. In the course of our investigations, we recorded the following parameters: the loading force applied to the specimen, the elongation of the extensometer base, and the number of cycles to crack initiation. The averaged deformation of the measurement base was the control variable. The frequency of variations of the load f = 0.5 Hz. In our study, we analyzed various ranges of the control variable (strain amplitude ε a ): 0.01, 0.008, 0.007, 0.005, 0.004, 0.0035, and 0.002 [11]. Each trial was repeated three times.

The performed investigations make it possible to get the plots of fatigue life. They reveal the dependence of the strain amplitude ε a on the number of cycles N f0 to complete fracture of the specimen.

The comparison of the plots of fatigue life for three degrees of porosity shows that, as the porosity increases, the fatigue life measured as the number of cycles to complete fracture becomes about three times smaller for the total assumed load range (Fig. 3).

Fig. 3
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Comparison of the plots of fatigue life for the three degrees of porosity: (1) p = 41%; (2) 33; (3) 26%.

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The study of the fatigue life of sintered porous 316L steel with various degrees of porosity reveals the specific nature of the material. Significant changes in the appearance of the hysteresis loop in the process of cyclic loading were observed (Fig. 4). Noticeable visible changes in the shape of the hysteresis loop are explained by the fact that the tests were carried out in the lower measuring range of the extensometer.

Fig. 4
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Hysteresis loops recorded for the strain amplitude ε a = 0.005 in sintered 316L stainless steel with porosities of: 41 (a); 33 (b); 26% (c).

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Further, we performed the analysis of variations of the elastic Young’s modulus E (induced by the development of fatigue failure) both in the stage of tension and the in the stage of compression. In Fig. 5, we present the comparison of Young’s moduli for the sintered specimens with porosities of 41, 33, and 26% (for the strain amplitude ε a = 0.005). The values of Young’s modulus were determined with a relatively low accuracy resulting from the measurement errors of the extensometer (operation within the lower range). It can be also affected by the nonlinear behavior of the material (plasticizing of the material near the pores even for small levels of loading).

Fig. 5
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Values of Young’s moduli for sintered specimens with different porosities: (1) compression p = 26%; (2) tension p = 26% (N f0 = 205); (3) compression p = 33%; (4) tension p = 33% (N f0 = 93); (5) compression p = 41%; (6) tension p = 41% (N f0 = 90) (strain amplitude ε a = 0.005).

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In addition, the behaviors of the maximum and minimum stresses in various duty cycles were analyzed. Some of these results are shown in Fig. 6.

Fig. 6
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The maximum and minimum stresses in a loading cycle for specimens with different porosities: (a) 41% [(1) σmax = 43.37 MPa, N ∗ f = 50]; (b) 33% [(2) σmax = 87.16 MPa, N ∗ f = 75]; (c) 26% [(3) σmax = 124.91 MPa, N ∗ f = 195] (strain amplitude ε a = 0.005).

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Damage Accumulation Analysis for Sintered 316L Stainless Steel with Various Porosities

The Manson–Coffin relationship (strain amplitude ε a as a function of the number of cycles to failure N f0) was used to determine the fatigue life of the tested porous material (sintered 316L steel) [12–14]:

$$ {\upvarepsilon}_a=\frac{\varDelta {\upvarepsilon}_e}{2}+\frac{\varDelta {\upvarepsilon}_p}{2}=\frac{\upsigma_{f0}}{E}{\left(2{N}_{f0}\right)}^{b0}+{\upvarepsilon}_{f0}{\left(2{N}_{f0}\right)}^{c_0}, $$

where N f0 is the number of cycles to failure for a specimen of porous material, σ f0 and ε f0 are the coefficients of dependence specifying the fracture of the porous material, and b 0 and c 0 are the exponents in this dependence.

After necessary transformations, it is possible to propose the dependences Δε e (N ∗ f ) and Δε p (N ∗ f ), where N ∗ f is the number of cycles to crack initiation (corresponding to a decrease in the maximum values of stresses in a loading cycle):

$$ \log \frac{\varDelta {\upvarepsilon}_e}{2}= \log \frac{\upsigma_f^{\ast }}{E}+{b}^{\ast } \log 2{N}_f^{\ast },\kern1em \log \frac{\varDelta {\upvarepsilon}_p}{2}= \log {\upvarepsilon}_f^{\ast }+{c}^{\ast } \log 2{N}_f^{\ast }, $$

where σ ∗ f and ε ∗ f are the coefficients of the dependence used to describe the crack initiation in a porous material and b * and c * are the exponents in this dependence.

It should be noted that the value of N ∗ f was found from the point of intersection of two approximating straight lines, namely, from the dependence of the maximum axial stress in a loading cycle on the number of loading cycles under the assumption that the first of these lines approximately describes a constant value of these stresses. The results of finding the parameters ε f0, c 0, ε ∗ f , and c * for different porosities by the leastsquares method are presented in Table 2.

Table 2 Values of the Parameters According to the Manson–Coffin or Crack Initiation Curve and the Fatigue Life of Sintered 316L Stainless Steel (up to the Total Fracture)
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The fatigue-life plots, i.e., the fracture of the specimens Δε p (N f0 ) and the crack initiation Δε p (N ∗ f ) in the sintered 316L stainless steel obtained for three different degrees of porosity have a similar behavior. It is worth paying attention to the physical interpretation of these plots. The relationship Δε p (N ∗ f ) obtained by recording the number of cycles in which a sharp decrease in the maximum stress was observed is a crack-initiation curve for the porous material (Fig. 7a).

Fig. 7
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Schematic diagram of the areas of initiation and propagation of microcracks in the sintered porous 316L stainless steel; (a): (1) damage accumulation in the bridges between pores, (2) crack initiation Δε p (N ∗ f ), (3) crack propagation, (4) fracture of the specimens Δε p (N f0 ) (sintered 316L stainless steel with a porosity of 33%); (b): damage accumulation in the bridges between pores; (c): cracking of bridges identified with the crack initiation; (d): subsequent development of cracks.

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This relationship describes both the process of merging of pores and crack initiation. This completes the period of damage accumulation in the bridges between pores. Crack growth is intensified because the pores do not have sharp edges (as classical cracks) and the situation is similar to the case of cracks propagating at the edge of the hole. This effect is definitely stronger for materials with higher porosities. Basically, the relationship Δε p (N f0 ) describes the curve of specimen failure, i.e., the time when the cracks reach their critical dimension and the specimen is not able to sustain any additional strain (we observe its fracture accompanied by the formation of a cross-sectional crack) (Figs. 7b–d).

Conclusions

In analyzing the results of fatigue testing of sintered 316L stainless-steel specimens with various densities (their porosity varies from 26 to 41%), it is possible to draw important conclusions concerning the prediction of the damaged state and cracking processes in the material. In the process of modeling of the development of fatigue damage in the specimens made of sintered porous 316L stainless steel, we can distinguish two stages. The first stage is connected with damage accumulation in the bridges between pores that takes place on the microscale. It is crucial to take into account the stress concentration and plastic strains formed in the bridges (on the mesoscale). The second stage is connected with the merging of pores (cracking of the bridges between them), which should be considered on the mesoscale. This gives a similar effect of increase in the susceptibility of the material (decrease in Young’s modulus and the maximum values of stresses in a loading cycle) for the case of growth of evenly spaced cracks in the material, which can be attributed to the fatigue loading of constant amplitude.

The presented paper was supported by the Bialystok University of Technology under the Research Project No. MB/WM/6/2013.