The fatigue crack propagation characteristics of a friction stir welded AI-Mg-Si alloy, 6082, have been investigated. The electrical potential drop method was used for measurements. A low and a high load ratio (R) level were tested. At low load ratio (R=0.1) and a low stress intensity Delta K the propagation rate in the weld was higher than in the parent material by a factor of 3 to 5. However, the propagation rates were approaching each other close to fracture. At high load ratio (R=0.8) the propagation rate was similar in the parent material and weld. The weld crack growth rate was about the same at low and high R (except close to fracture), while the parent material growth rate increased at high R. Paris law was used to describe the measured crack propagation rates in the weld. In the case of the parent material, showing an R-dependence, Forman's law was used.
Besides stress intensity factors, crack interactions also affect the growth behaviors of multiple cracks, such as crack growth paths and crack growth rates [21,22]. Kishida et al.  researched the growth behaviors of three parallel cracks. Results showed that because multiple cracks experienced interactions, the longest crack might not receive the greatest tangential stress or the SIF at crack tip. Sun et al.  and Jin et al.  found that the double parallel cracks propagated towards each other in the crack growth process because stress redistributions around the crack tip changed the location of the maximum circumferential stress. Wang et al.  conducted experiments on multiple-site damage crack propagation behaviors. Results showed that as cracks grew towards each other, the crack growth accelerated. Gope et al.  found that for the double offset cracks, propagation paths of the inner crack tips exhibited a mutual attraction determined by the positions and sizes of the crack tips, whereas the outer crack tips still propagated perpendicularly to the direction of load. Jin et al.  found that the double collinear cracks and the single crack had different material parameters of Paris equation. Therefore, a new driving force, ΔKn, was introduced, which was obtained from the net section stress range Δσn. Thus, based on the new driving force, ΔKn, Paris equations of the single crack and double collinear cracks showed little difference. Kamaya et al. [29,30] investigated the multiple interacting surface cracks with numerical simulation and fatigue tests. Results showed that for the same ΔKI, the double parallel surface cracks had lower CGRs than the single surface crack. Thus, the crack growth area A is considered to be the representative parameter in crack propagation. Results showed that the new crack growth rate, dA/dN, showed good correlation with the new driving force, σA0.5, between the single surface crack and double parallel surface cracks.
This approach proposed by Newman Jr.  may be used to correlate fatigue crack growth rate data for other materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined.
The crack closure effects may occur due to the surface roughness of the material in the presence of shear deformation at the crack tip [17, 18]. Microstructural studies  indicate that fracture surfaces demonstrate the possibility of crack propagation by the shear mechanism primarily in the near-threshold regime of . In this fatigue regime, the crack closure effects have the greatest influence. Consequently, Hudak and Davidson  proposed a model defined by the following expression:where is a constant related to the pure Mode I fatigue crack growth threshold.
The experimental results from fatigue crack propagation tests can be represented by the following generalized relations (see Figure 2):where is the limiting value above which no detectable closure occurs and is a parameter that can be obtained using the following expression:The and constants are not material properties in the strict sense since they depend on measurements location and measurements sensitivity, resulting from the crack propagation tests aiming at evaluating the crack closure/opening effects. Note that in the limiting condition of approaching zero (13) reduces to (12) thus describing the local measurements.
Ellyin  proposed an approach to define the effective stress intensity range, , taking into account the stress ratio, , and the threshold value of the stress intensity factor range, , with constant amplitude loading (see Figure 3). This approach is a modified version of proposal by Hudak and Davidson . Generally, the crack opening stress intensity factor range, , is smaller than the threshold stress intensity factor range, ; that is, . Besides, the crack opening or closure stress intensities factors are not the same; that is, . Ellyin  proposed the following approach to obtain (see Figure 3):where is the mean stress, is the maximum stress, and is the fatigue strength coefficient.
In this paper, a theoretical model to obtain the effective stress intensity range, , that takes into account the effects of the mean stress and the crack closure and opening effects is proposed. The starting point for the proposed theoretical model is the initial assumptions proposed by Elber [1, 2] and defined in (1) and (4). The basic fatigue crack propagation law in regime II was initially proposed by Paris and Erdogan , which has the following form:where and are material constants. However, this model does not include the other propagation regimes and does not take into account the effects of mean stress. Many other fatigue propagation models have been proposed in literature, with wider range of application and complexity, requiring a significant number of constants . Nevertheless, the simple modification of the Paris relation in order to take into account the stress ratio effects is assumed, as proposed by Dowling :where , , and are constants. Besides, an extension of the Paris relation is adopted to account for crack propagation regime I, having the following configuration:Based on the foregoing assumptions, the effective stress intensity factor range is given by the following expression:Thus, the expression that allows obtaining the quantitative parameter, , is given by the following formula:If the material parameter, γ, is equal to 1, this means that the material is not influenced by the stress ratio. Thus, (21) is simplified and assumes the same form as (12) proposed by Hudak and Davidson  and is similar to the one proposed by Ellyin .
Low-cycle fatigue test results are very often represented using the relation between the strain amplitude and the number of reversals to failure, , usually assumed to correspond to the initiation of a macroscopic crack. Morrow  suggested a general equation, valid for low- and high-cycle fatigue regimes:where and are, respectively, the fatigue ductility coefficient and fatigue ductility exponent; is the fatigue strength coefficient, is the fatigue strength exponent, and is the Young modulus.
Figures 6(a) and 6(b) represent the experimental data and the Paris law correlations for each tested stress ratio of the P355NL1 steel, , , and . The material constants of the Paris crack propagation relation are presented in Table 3. The crack propagation rates are only slightly influenced by the stress ratio. Higher stress ratios result in higher crack growth rates. The lines representing the Paris law, for and , are approximately parallel to each other.
The stress ratio effects on fatigue crack growth rates may be attributed to the crack closure. Crack closure increases with the reduction in the stress ratio leading to lower fatigue crack growth rates. For higher stress ratios, such as , the crack closure is very likely negligible, which means that applied stress intensity factor range is fully effective. Also, the fatigue crack propagation lines for each stress ratio are not fully parallel to each other which means that crack closure also depends on the stress intensity factor range level.
The proposed theoretical model is applied using an inverse analysis of the experimental fatigue crack propagation rates available for the P355NL1 steel. Using the inverse analysis of the proposed theoretical model, it is possible to obtain the relationship between the effective stress ratio, , and the applied stress intensity factor range, . accounts for minimum stress intensity factors higher than crack closure stress intensity factor. In this case, the effective stress intensity factor results from the relationship between the crack opening stress intensity factor, , and the maximum stress intensity factor, . Figure 8 shows that for stress ratios above 0.5 the crack closure and opening effects are not significant. For the stress ratio equal to 0 a significant influence on the effective stress ratio of the applied stress intensity factor range is observed. Such influence is more significant for the initial propagation phase of region II, decreasing significantly for higher applied stress intensity ranges. Thus, it is concluded that the crack closure and opening effects are more significant for the initial crack propagation phase, in region II, for higher levels of the stress intensity factor ranges along the crack length. Figure 9 shows the results obtained for the relationship between and , using the inverse analysis of the proposed theoretical model. This figure helps to understand the influence of the crack closure and opening effects, as a function of stress ratios. The effective stress ratio, , shown in Figure 9, is the average of the values obtained as a function of , according to what is evidenced in Figure 8.
Figure 13 shows the fatigue crack propagation rates as a function of effective intensity range using the proposed method. The results obtained, using this theoretical model, are similar to results presented in the literature .
Crosslinked ultrahigh molecular weight polyethylene (UHMWPE) has been recently approved by the Food and Drug Administration for use in orthopedic implants. The majority of commercially available UHMWPE orthopedic components are crosslinked using e-beam or gamma radiation. The level of crosslinking is controlled with radiation dose and free radicals are eliminated through heat treatments to prevent long-term degradation associated with chain scission or oxidation mechanisms. Laboratory studies have demonstrated a substantial improvement in the wear resistance of crosslinked UHMWPE. However, a concern about the resistance to fatigue damage remains in the clinical community, especially for tibial components that sustain high cyclic contact stresses. The objective of this study was to investigate both the initiation and propagation aspects of fatigue cracks in radiation crosslinked medical-grade UHMWPE. This work evaluated three levels of radiation, which induced three crosslink densities, on the fatigue crack propagation and total fatigue life behavior. Both as-received UHMWPE, as well as those that underwent an identical thermal history as the crosslinked UHMWPE were used as controls. Fractured crack propagation specimens were examined using scanning electron microscopy to elucidate fatigue fracture mechanisms. The results of this work indicated that a low crosslink density may optimize the fatigue resistance from both a crack initiation and propagation standpoint. 2b1af7f3a8