View source for Microstructural Inclusion Influence on Fatigue of a Cast A356 Aluminum Alloy

== Abstract ==
We examine the dependence of fatigue properties on the diﬀerent size scale microstructural inclusions of a cast A356 aluminum alloy in order to quantify the structure-property relations. Scanning electron microscopy (SEM) analysis was performed on fatigue specimens that included three diﬀerent dendrite cell sizes (DCSs). Where past studies have focused upon DCSs or pore size eﬀects on fatigue life, this study includes other metrics such as nearest neighbor distance (NND) of inclusions, inclusion distance to the free surface, and inclusion type (porosity or oxides). The present study is necessary to separate the eﬀects of numerous microstructural inclusions that have a confounding eﬀect on the fatigue life. The results clearly showed that the maximum pore size (MPS), NND of gas pores, and DCS all can inﬂuence the fatigue life. These conclusions are presumed to be typical of other cast alloys with similar second-phase constit¬uents and inclusions. As such, the inclusion-property relations of this work were employed in a microstructure-based fatigue model operating on the crack incubation and MSC with good results.

== Introduction ==
[[Image:Micro_Inclusion_Infl_Fatigue_Cast_A356_Fig_1.jpg|thumb|right|300px|Figure 1 Strain-life curves from horizontally and vertically cast plates.]]
STRUCTURAL aluminum castings give a widely scattered distribution of fatigue data due to the vari¬ances of microstructures, defects, and inclusions present within the material. A widely used alloy is A356 aluminum in which the fatigue behavior was analyzed by Stephens et al.[1,2] <ref> 1. R.I. Stephens, H.D. Berns, R.A. Chernenkoﬀ, R.L. Indig, S.K. Koh, D.J. Lingenfelser, M.R. Mitchell, R.A. Testin, and C.C. Wigant: Low Cycle Fatigue of A356-T6 Cast Aluminum Alloy—A Round-Robin Test Program, SAE Technical Publication SP760, SAE, 1988a, vol. 881701, pp. 1–28, www.sae.org. 

2. R.I. Stephens, B.J. Mahoney, and R.G. Fossman: Low Cycle Fatigue of A356-T6 Cast Aluminum Alloy Wheels, SAE Technical Publication SP760, SAE, 1988b, vol. 881707, pp. 93–102, www.sae.org. 
</ref> In an eﬀort to link the microstructure with varying stages of crack growth of A356 aluminum   , Fan et al.[3] <ref> 3. J. Fan, D.L. McDowell, M.F. Horstemeyer, and K.A. Gall: Eng. Fract. Mech., 2001, vol. 68 (15), pp. 1687–1706. </ref>, Gall et al.[4–6]<ref> 4. K. Gall, N. Yang, M.F. Horstemeyer, D.L. McDowell, and J. Fan: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 3079–88. 5. K. Gall, N. Yang, M.F. Horstemeyer, D.L. McDowell, and J. Fan: Fatigue Fract. Eng. Mater. Struct., 2000, vol. 23, pp. 159– 72. 6. K. Gall, M.F. Horstemeyer, B.W. Degner, D.L. McDowell, and J. Fan: Int. J. Fract., 2001, vol. 198 (3), pp. 207–33
 </ref> , Horstemeyer,[7] <ref> 7. M.F. Horstemeyer: Scripta Mater., 1998, vol. 39 (11), pp. 1491–95. </ref> and Horstemeyer and Gokhale[8] <ref> 8. M.F. Horstemeyer and A.M. Gokhale: Int. J. Solids Struct., 1999, vol. 36, pp. 5029–55. </ref> performed micromechanical ﬁnite element simulations and microstructural analyses. Although many of the microstructure-property studies were focused upon porosity (void volume fraction) or silicon particle size, other aspects such as the interactions between the size eﬀect of pores, nearest neighbor distances (NNDs), number of pores, and void volume fraction (porosity) on the fatigue life have not been elucidated.

Therefore, the contribution of this study is the emphasis of experimental observations relating to inclusions and their collective roles to the number of cycles until failure. The particular focus here is evidence observed by failed specimens using scanning electron microscopy (SEM) along with microstructure-based fatigue modeling. 
In trying to determine inclusion-property relations for fatigue, scatter must be considered in the modeling eﬀort. Given the high levels of scatter in cast alloys, statistical methods are often employed. However, upon further examination of the microstructure-inclusion morphology present within a casting, a deterministic approach might well be in order ﬁrst. 
We will show that in modeling fatigue failure with diﬀerent microstructures/inclusions, one should not just independently assign the ﬁnal number of cycles to one parameter, for example, the pore size. Although one might examine just the pore size as the major inclusion for failure in one case, the other parameters/inclusions could play a much larger role in the outcome of the fatigue life for that particular specimen. Furthermore, other specimens may have experienced failure from an oxide.

== Results ==
Fractography and Mechanical Behavior

Figure 1 shows the strain-life curves from the hori-zontally and vertically cast plates. Note that as the DCS increased, the number of cycles (reversals) to failure decreased. Although one might be tempted to attribute the diﬀerences just to DCS, we try to distinguish the eﬀects as a function of diﬀerent microstructural inclu¬sions. As such, strain-life specimens tested at a strain amplitude of 0.0015 were analyzed under SEM and energy-dispersive X-ray spectroscopy to quantify the size and type of the fatigue crack initiation site. Parameters of interest shown in Table I were the inclusion microstructural inclusion type (pore, oxide, silicon particle, or intermetallic), size, distance to free edge, volume fraction, and NND. When more than one pore was present, an average was taken to determine the pore (inclusion) size.

[[Image:Micro_Inclusion_Infl_Fatigue_Cast_A356_Tab_1.jpg|thumb|center|800px|Figure 1 Strain-life curves from horizontally and vertically cast plates.]]

Fatigue Model

The MultiStage fatigue model (MSF) ﬁrst employed by McDowell et al.[22] has been used to model fatigue behavior of cast[22] and wrought[24] aluminum alloys. The governing equations in the MSF are listed as follows:

[[Image:Micro_Inclusion_Infl_Fatigue_Cast_A356_Eqs.jpg|thumb|center|700px|]]


The total fatigue life (Eq. [1]) is comprised of incubation, microstructurally small crack growth (MSC)/physically small crack growth (PSC), and long crack growth (LC). Equation [2] is employed to model the incubation life due to cyclic plastic deformation from micronotches and is based on a modiﬁed Coﬃn– Manson law that links microplasticity to incubation life. The MSC/PSC growth is a function of the crack tip displacement (Eq. [7]) and describes the crack growth regime, where <math>\Delta</math>CTD is the crack tip displacement range, <math>\chi</math> is a material constant, and <math>\Delta</math>CTDth is the threshold for crack tip displacement.

Analysis and MSF Model

In trying to determine the inclusion-property relations with the most pertinent defects, we can nondimension¬alize the deleterious entities. The ﬁrst of the two nondimensionalized parameters is the MPS normalized by the NND. A second nondimensionalized parameter is the MPS normalized by the dendrite cell spacing. When we combine these two nondimensionalized parameters into the incubation (Eq. [3]) and MSC (Eq. [8]) rates and plot them with respect to fatigue life, we can see in Figure 9 that a clear nonlinear relationship

[[Image:Micro_Inclusion_Infl_Fatigue_Cast_A356_Fig_9.jpg|thumb|left|400px| Figure 9 Number of cycles vs (MPS 9 MPS)/(NND 9 DCS) measured for specimens tested at a strain amplitude of 0.0015.]]

Table II presents the constants associated with the MSF model. Figure 10 displays the data presented in Figure 1 along with the MSF model for the upper and lower bounds of the nondimensionalized term. The upper and lower bounds of the model represent the extreme deleterious effect of the MPS, NND, and DCS and correlate well to the experimental data.

[[Image:Micro_Inclusion_Infl_Fatigue_Cast_A356_Tab_2.jpg|thumb|center|500px|]]

== References ==
<references/>



Citation:
Microstructural Inclusion Inﬂuence on Fatigue of a Cast A356 Aluminum Alloy,  J.B. JORDON, M.F. HORSTEMEYER, N. YANG, J.F. MAJOR, K.A. GALL, J. FAN, and D.L. McDOWELL, METALLURGICAL AND MATERIALS TRANSACTIONS A, VOLUME 41A, FEBRUARY 2010

[[Category:Research Paper]]
[[Category:Fatigue]]
[[Category:Aluminum]]