Computational Modeling of Fracture Toughness of Al-Si and Al-Zn-Mg-Cu Alloys with Detected Porosity

When defects are detected in the casting part, three possible paths can mainly be taken:

A casting qualified as a scrap is associated with economic losses and entails a series of actions aimed at eliminating the causes or consequences of the defect. The priority action is to determine the causes of the defect and its elimination. This applies in particular to the mass production of low-weight castings. In some cases, repair is a good practice, especially when the price of a single cast is relatively high and the size of the series is small. In the final case (for example, releasing the casting for exploitation), the need to rationalize such a procedure is most visible. However, in the case of the repair decision, it seems important to determine the impact of the “unresolved” defect in the casting (including its durability) and understand the exploitation conditions of the casting.

The solution to the problem outlined above should be based on the theory of elasticity and plasticity, fracture mechanics, and issues related to material fatigue (adequately determined by the specific properties of the materials obtained by the casting methods). The numerical methods seem to be particularly useful in solving the given problem; these are the only ways to correctly determine the field values in the case of time-varying boundary conditions and nonlinear material characteristics.

The authors propose two different FEM calculation models to consider the defects in concentrated porosity or dispersed form.

The research work was conducted for two aluminum alloys: AlSi9 (EN AC-44400) and AlZn6MgCu (EN AW-7010) in the as-cast state. The alloys were subjected to the T6 heat treatment procedure. The static tensile test, fatigue test, determining the critical stress intensity factor, and the Paris test are aimed at determining the relationship between the crack growth and the number of cycles. The test was carried out on an MTS 810 mechanical testing machine. The measurements of the sample elongation and gap dimensions were taken using MTS extensometers. The static tensile test was controlled by the strain rate, while the fatigue tests were controlled by the changes of force value. The measurement of the crack length and the duration of the process were recorded by a video camera. The number of cycles and the test time were controlled by the MTS machine software; this was based on the analysis of images from the computed tomography using ImageJ software. The analysis was performed to determine the areas of reduced density as related to the material of the matrix. The number of cross sections from the computed tomography image allows us to obtain a volumetric proportion of the microporosity in the analyzed casting sample unit. The image analysis of the computed tomography scans was performed in the Nanotom equipment.

Castings made of aluminum alloys usually contain various types of structural discontinuities, which have a significant impact on their strength and fatigue properties. The structural discontinuities may be areas that are not properly filled with metal or include non-metallic inclusions that reduce the mechanical properties of the castings. The liquid aluminum is prone to hydrogen adsorption and oxidation; thus, the inevitable presence of gas porosity and oxide inclusions in aluminum castings is possible. If the casting is not properly fed, then the fatigue strength may be additionally reduced by the presence of shrinkage porosity. It has been confirmed by numerous fractography studies that gas porosity is usually circular in shape, while shrinkage porosity forms in irregular three-dimensional voids (Ref 1). Both types of porosity may occur together with aluminum oxide films. The structural discontinuities of the void type caused by the occurrence of porosity may have different sizes. It is possible to distinguish the microporosity when the diameters of the cavities do not exceed 100 μm as well as the porosity when the diameters of the voids are greater than 100 μm (Ref 2). Porosity and microporosity together greatly reduce the fatigue properties and strength of an alloy, while the occurrence of microporosity alone significantly decreases the fatigue strength within a range of a large number of cycles. The effect of microporosity on fatigue strength should be considered as related to the characteristics of the alloy microstructure, because the location of the microcrack initiation site depends on the mutual dimension relationship and distance between the voids and the microstructure phases. In the case of AlSi alloys, there is a view that the plastic properties of the alloy (like fatigue toughness) are similar depending on the distance between the secondary dendrite arms (SDAS) and the size of the silicon eutectic precipitates (Ref 3). According to research carried out by Wang (Ref 4) for the A356 alloy in the case of a coarse structure (SDAS > 60 μm), the fatigue process is most affected by the distances between the arms of the second-order dendrites. In the case where the microstructure is fine (SDAS < 40 μm), the process is controlled by the size of the dendrite grains. Thus, the critical dimension of the void (which determines the smallest dimension above which microcracking can be initiated) depends on the size of the microstructure components. When solidification takes place slowly in sand molds for example, the critical dimension of the defect should be greater than the distance between the dendrite arms. For castings solidifying during pressure or gravity die casting, the defect may initiate a crack when it is larger than the grain size. The interaction of microstructure and porosity with fatigue strength changes as the number of load cycles increases. In castings made of the AlSi7 alloy, a reduction in the distance between the branches of dendrites (from 50 to 28 μm) and an increase in the porosity fraction (from 0.07 to 0.4%) gives a total effect in the form of increased fatigue strength within the range below 1 × 10⁵ cycles; for comparison, if the number of cycles is greater than 2 × 10⁶, a loss of strength is observed (Ref 5). This can be justified by the fact that, during the low-cycle fatigue (in contrast to high-cycle fatigue), plastic deformation occurs, and as mentioned above, the plastic properties of the alloy depend strongly on the distance between the dendrite arms (as mentioned above). Above the critical dimension of the void, the size of the defect strongly affects the fatigue strength of the alloy. The reason for the crack initiation in the range of the small number of cycles is the presence of a defect constituting a strong stress concentrator. The crack growth velocity is controlled by the cyclic changes of the stress intensity factor, which depends on the amplitude of the stress on the defect position and cross-sectional surfaces (inside or on the surface of the sample). The fatigue strength of light foundry alloys within the range of a large number of cycles with defects within a range of 50-100 μm depends on the surface area of the largest defect and crack propagation velocity in a given alloy. The Wohler curves for the foundry Al alloys tested at ambient temperature are characterized by the fact that the fatigue limit cannot be determined on their basis, even if the number of cycles exceeds 10⁸ or 10⁹ (Ref 6). Studies conducted on eutectic Al-Si alloys show that the cracking mechanisms of castings and processed alloys (plastic processing, forging) differ from each other (Ref 7). According to Murakami (Ref 8), the fracture initiates in the Al matrix in cracked alloys and increases to the critical value according to the II fracture model (which is longitudinal shear). The cracks are arranged at an angle of 45° to the surface of the test sample. Usually, no other types of cracks can be observed. The crack develops rapidly, and the fatigue initiation phase (the lifetime of the structure) has the greatest impact on the crack initiation phase. Cracks of this nature arise before the possible separation of the Si phases and the matrix. Si precipitation may stop the development of a crack to arise. If there is insufficient Si precipitation, a fracture in the Al matrix can easily develop. Casting alloys do not show a clear limit of fatigue, even within a range of more than 10⁸ cycles. If microporosity occurs in the alloy, the fracture initiates in the Al phase next to the defect location and develops according to the II method of fracture. The cracking mechanism within the range of a small number of cycles is the same as for high-cycle fatigue—a similar type of fracture area is observed. This fact is of particular importance in predicting the fatigue life of the casting part that was exposed to stress within the range of high- and low-cycle fatigue. The summarized damage influences the impact on both stages of crack development (initiation and propagation). In the alloy after plastic working, the initiation and cracking mechanisms are substantially different for the cast alloy. The location of the initiation of the crack is the precipitation of Si or the intermetallic surface of the Al matrix and the precipitation of Si. The cracks initiate relatively early within the Si precipitates, and cracking develops according to the first method (i.e., the opening of the fracture surface). This type of mechanism occurs when the number of cycles needed for destruction is fewer than 10⁸. Above this number of cycles, the mechanism of destruction is similar to the cast alloys (i.e., through the shear and initiation of the crack in the Al phase). In the plastic-processed alloys, fatigue strength can be more accurately determined within a range of 10⁷ cycles; this limit becomes even more noticeable when microporosity is present in the alloy. The cracking mechanism for a low number of cycles is the same as for high-cycle fatigue. The conducted research confirms the negative effect of the coarse structure and porosity on the fatigue strength of Al alloys; however, the quantitative methods developed so far do not fully allow us to take into account the influence of the shape, type, and distribution of the defects.

In the case of aluminum alloys containing zinc (like the AlZn6MgCu alloy), the construction of high-strength castings still remain at the stage of initial testing and are described in Ref 9-14. The 7XXX series alloys usually used for plastic processing are characterized by high strength (over 500 MPa) and good plasticity (reaching as high as 20%). The lack of plastic working (forging, rolling) eliminates one of the strengthening mechanisms (which is mechanical hardening). In this case, the microstructure of the alloy is determined by the solidification and heat treatment process. The high strength of the 7XXX series alloys results from the mechanism of precipitation of the intermetallic phase particles within the saturated solid solution αAl (precipitation strengthening). However, the dynamics of the separation as well as the formation of phases such as η (AlZn₂), T (Al₆CuMg₄), and S (Al₂CuMg), which significantly affect the properties of the alloy, depends on its chemical composition and cooling rate (Ref 15). To increase the strength of the alloy, a high content of zinc is preferred, as it causes a reduction in the number of T-phase precipitates; however, an excessive amount makes it difficult to obtain fair plasticity. The casting part usually has a variable wall thickness, where the solidification rates differ significantly. This problem is particularly important in the case of the analyzed alloys because of the wide solidification range (above 150 °C). This phenomenon is conducive to the formation of shrinkage porosity and shrinkage gas microporosity. The appropriate balance of three important elements (Zn, Mg, and Cu), the reduction of impurities such as Fe and Si, and a suitably selected heat treatment process all have an impact on the optimal structure and properties of the alloy. Depending on the type of porosity present in the cast and its percentage, the following calculation models are proposed as well as examples of their use (supported by experimental research).

The experimental laboratory trials included static tensile tests, low-fatigue cycle tests, fracture mechanics tests, fatigue crack propagation tests, the so-called Paris test, a microscopic examination of the sample fracture area, and an x-ray tomographic analysis. The selection of the tests carried out depends on the types of defects found in analyzed alloys.

Depending on the size and shape of the defect, different calculation models were proposed that can be used to determine the stress state in the area of the defect as well as the K_I value in order to predict the durability of castings with discontinuities. In the computational models, the results of the conducted experimental tests were used.

The examples presented below are the application of the calculation models discussed above and used in the analysis of the fatigue life or cracking resistance of the two analyzed alloys. In the computational models, the experimental results were used.

The article presents the methodology for determining the impact of the defects detected in the casting on cracking resistance and strength. The carried-out research mainly concerns the methods of applying fracture mechanics and constitutive models of the material in the assessment of fatigue life and resistance to cracking. The method of analyzing the impact of the defect on the reduction of the strength of the cast depends on the type and size of the defect as well as the method of loading the structure. If the detected defect can be described as a void in the material (as illustrated in the example of the casting of the AlSi9 alloy rotor blade), the strength of the casting can be assessed based on the fracture mechanics methods. In this case, the value of stress intensity factor K_I can be determined and compared to its critical value K_IC (which is a material constant) using Eq 7 for cyclic variables or Eq 1 or 2 for static loads. The occurrence of scattered defects in the form of microporosity can be described by the GTN model, which takes into account the influence of microporosity on the strengthening of the material (Fig. 6). The relationship between the fatigue life and the percentage of microporosity is shown in Table 5. There is a visible relationship between the number of cycles needed for destruction and the percentage of microporosity revealed by x-ray tomography examinations. Regardless of the value of the amplitude of the stress, a higher proportion of microporosity results in a decrease in the number of cycles.

The tests show the significant effect of casting defects on the fatigue properties of the tested AlSi9 and AlZn6MgCu alloys. The obtained results present the great differences in the number of cycles to failure between samples loaded with the same stress amplitude (depending on the size and position of the defect). The number of fatigue cycles prior to the rupture of the sample was also influenced by the number of fatigue points identified on the surface of the fracture. In the case when the initiation of the crack was caused by the presence of a defect, its geometrical model was determined and calculated to determine the value of stress intensity factor K_I. In the case of the samples where casting defects were identified, it was found that the stress intensity factor has a higher value when the number of fatigue cycles decreases (regardless of the stress amplitude). This relationship occurred in all of the analyzed cases regardless of the adopted calculation model despite the differences in the determined values of the stress intensity factors using analytical and numerical calculations. The adoption of a defect model in the form of a crack results in the fact that the calculated stress intensity factor has a much greater value in some cases than that calculated by means of FEM or dependence Eq 3. This difference is caused by the discrepancy between the actual shape of the defect and the model of the gap. The paper also presents the results of determining the fatigue life of a rotor blade casting based on a stress field analysis using the FEM method as well as on the basis of material tests and strength calculations based on fracture mechanics methods. On the basis of this procedure, the influence of porosity on the durability of a casting can be determined.