Microstructure-based multistage fatigue modeling of a cast AE44 magnesium alloy

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== Abstract ==
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{{template:Research_Paper
The multistage fatigue model developed by McDowell et al. was modified to study the fatigue life of a magnesium alloy AE44 for automobile applications. The fractographic examination indicated three distinct stages of fatigue damage in the high cycle fatigue load¬ing regime: crack incubation, microstructurally small crack growth, and long crack growth. Cracks incubated almost exclusively at the cast pores that were near the free surface, located near sharp geometry changes of the test specimen, or at extremely large pores inside the specimens. Microstructurally small cracks grew in the eutectic region along the weak boundaries of the grains and dendrites or at very closely packed microstructural discontinuities. Long cracks were observed to grow in a transgranular fashion. Specimens fabricated from as-cast bars and extracted from a cast engine cradle were tested at room temperature and an elevated temperature typically required for automotive powertrain applications.Alarge variation of fatigue life in the high cycle fatigue region was observed in specimens from both conditions due to the sensitivity from microstructural discontinuities. The microstructure-based multistage fatigue model was generalized for the AE44 magnesium alloy to capture the network of porosity and temperature dependence. The modified multistage fatigue model was also used to estimate the upper and lower bounds of the strain-life curves based on the extreme microstructural discontinuities.
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== Introduction ==
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|abstract=
 
[[Image:Figure_1_MSF_AE44.jpg‎|thumb|right|300px|Fig. 1. Optical images from polished cross-sections present an overview of size and distribution of casting pores in the AE44 magnesium alloy: (a) as-cast bar, (b) extracted from an engine cradle.]]
 
[[Image:Figure_1_MSF_AE44.jpg‎|thumb|right|300px|Fig. 1. Optical images from polished cross-sections present an overview of size and distribution of casting pores in the AE44 magnesium alloy: (a) as-cast bar, (b) extracted from an engine cradle.]]
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The multistage fatigue model developed by McDowell et al. was modified to study the fatigue life of a magnesium alloy AE44 for automobile applications. The fractographic examination indicated three distinct stages of fatigue damage in the high cycle fatigue load¬ing regime: crack incubation, microstructurally small crack growth, and long crack growth. Cracks incubated almost exclusively at the cast pores that were near the free surface, located near sharp geometry changes of the test specimen, or at extremely large pores inside the specimens. Microstructurally small cracks grew in the eutectic region along the weak boundaries of the grains and dendrites or at very closely packed microstructural discontinuities. Long cracks were observed to grow in a transgranular fashion. Specimens fabricated from as-cast bars and extracted from a cast engine cradle were tested at room temperature and an elevated temperature typically required for automotive powertrain applications.Alarge variation of fatigue life in the high cycle fatigue region was observed in specimens from both conditions due to the sensitivity from microstructural discontinuities. The microstructure-based multistage fatigue model was generalized for the AE44 magnesium alloy to capture the network of porosity and temperature dependence. The modified multistage fatigue model was also used to estimate the upper and lower bounds of the strain-life curves based on the extreme microstructural discontinuities.
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|authors=Y. Xue,, M.F. Horstemeyer, D.L. McDowell, H. El Kadiri, J. Fan
  
Magnesium alloys have received increased interest for automotive applications because of their attractive low density, the possible benefit of weight reduction, and con-sequent reduction in fuel consumption. The rather high specific strength, the good castability, the improved corro¬sion resistance of high purity alloys, and the possibility of recycling are additional advantages of these materials [1– 6] <ref> [1] Mordike BL, Ebert T. Magnesium properties – applications – potential. J Mater Sci Eng A 2001;302:37–45.
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Corresponding author: Y. Xue
[2] Aghion E, Eliezer D, editors. Proceedings of the first Israeli international conference on magnesium science and technology. Dead Sea, Israel: Magnesium Research Institute; 1997.
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[3] Mordike BL, Kainer KU, editors. Magnesium alloys and their applications. Wolfsburg, Germany: Werkstoff-Info GmbH Frankfurt; 1998.
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[4] Kainer KU, editor. Magnesium alloys and their applications. Weinheim, Germany: Wiley–VCH Verlag GmbH; 2004.
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[5] Goodenberger DL, Stephens RI. J Eng Mater Technol 1993;115:391–7.
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[6] Stephens RI, Schrader CD, Lease KB. Corrosion-fatigue of AZ91E¬T6, Cast magnesium alloy in A 3.5 percent NaCl aqueous environ¬ment. J Eng Mater Technol 1995;117(3):293–8.
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</ref>. Cast magnesium alloys are used in several automotive applications such as covers, door structures, and heavier load-bearing components like wheels, housings and frames. Vehicle components are subjected to variable and repeated mechanical straining, where the number of load cycles may be on the order of <math>10^9</math> cycles in car wheels. When magnesium alloys are considered for powertrain components, such as crankcases or gearbox casings, fatigue properties at elevated temperatures are of great interest.
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In this work, the fatigue behavior of an AE44 Mg alloy is explored using test samples extracted from as-cast bars and cast automotive components. The strain-life behavior of the AE44 magnesium alloy was studied for two types of specimens at room temperature and at 121 °C, a tempera¬ture range typical of automotive powertrain applications. The as-cast bars have a more consistent porosity level from specimen to specimen but can have large casting pores. The average dendrite cell size (DCS) for as-cast bars is small and relatively uniform from specimen to specimen. The engine cradle specimens have a wider vari¬ety of defect discontinuities from the thin section to the thick section of the cradle and can have very large pores. The microstructure-based multistage fatigue (MSF) model of McDowell et al. [21] <ref> [21] McDowell DL, Gall K, Horstemeyer MF, Fan J. Microstructure-based fatigue modeling of cast A356-T6 alloy. Eng Fract Mech 2003;70:49–80. </ref> was generalized for the AE44 Mg alloy.
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|animation=
  
== Results ==
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|images=
[[Image:Figure_3_MSF_AE44.jpg|thumb|left|300px|Fig. 3. Stress–strain curves of the AE 44 magnesium alloy: (1) as-cast bar,
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(2) extracted from engine cradle tested at room temperature (RT) and 121 C (HT).]]
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[[Image:Figure_4_MSF_AE44.jpg|thumb|right|300px|Fig. 4. Uniaxial strain-life of AE44 Mg alloy specimens machined from as-cast bars and from an engine cradle tested at room temperature (RT) and 121 �C (HT) under strain-controlled, constant amplitude with
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{{paper_figure|image=Figure 3 MSF AE44.jpg|image caption=fig. 3. Stress–strain curves of the AE 44 magnesium alloy: (1) as-cast bar, (2) extracted from engine cradle tested at room temperature (RT) and 121 C (HT).}}
completely reversed strain amplitude experiments.]]
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Uniaxial tension tests were conducted at room tempera¬ture and 121 °C with a loading rate of 0.005 min-1. The stress–strain curves are shown in Fig. 3. The elastic modulus, yield strength, ultimate strength and strain-to-failure of the as-cast AE44 bars were higher than those extracted from the engine cradle.
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{{paper_figure|image=Figure 4 MSF AE44.jpg|image caption=fig. 4. Uniaxial strain-life of AE44 Mg alloy specimens machined from as-cast bars and from an engine cradle tested at room temperature (RT) and 121 C (HT) under strain-controlled, constant amplitude with
The uniaxial strain-life results are shown in Fig. 4. A large variation of fatigue lives in the HCF regime was observed on specimens from both conditions, due to the sensitivity to microstructure. The large scatter in the HCF regime could be induced by the sub-sized ASTM specimens in which the above stated detrimental pore was almost one tenth of the specimen diameter. The fatigue lives at 121 °C are longer, in general, than those at the room temperature under the constant strain amplitude loading condition with the strain-controlled experiments, which maybe is induced by the increasing ductility at the elevated temperature.
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completely reversed strain amplitude experiments.}}
  
Fractographic analyses
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{{paper_figure|image=Figure_9_MSF_AE44.jpg|image caption=Fig. 9. The multistage fatigue model (MSF) correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle.}}
  
Typical specimens loaded in the strain amplitude of 0.075% (HCF) and 0.3% (LCF) were selected for fractographic analyses. At <math>{\Delta}{\epsilon}</math>/2 = 0.075%, some specimens did not fail at 107 cycles. A sample of medium life, S1 (Nf = 1.3 · 106, at 121 °C), and samples with the shortest lives, S2 (Nf = 1.78 · 105, at 121 °C), and S3 (Nf = 1.83 · 105, at 25 °C) were examined under the SEM.
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{{paper_figure|image=Figure_10_MSF_AE44.jpg|image caption=Fig. 10. The multistage fatigue model correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle at high temperature.}}
Most cracks formed at casting pores at or near the specimen surfaces or at a very large pore within the specimen as shown in Fig. 6. A strong interaction of two pores that were about 25 lm in diameter near the free surface formed a fatigue crack that produced the fatigue failure. A few relatively larger pores were scattered inside this specimen but no damage was formed. Even though S2 and S3 had similar low fatigue lives, the life incubation sites were quite different: the damage in S2 formed at the interaction of two pores that were 65 lm in diameter with one right at the edge while the damage in S3 formed at a large pore of 500 lm in diameter in the middle of the specimen.
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|methodology=  
[[Image:Figure_6_MSF_AE44.jpg|thumb|center|300px|Fig. 6. SEM images of fatigue crack formation sites for samples: (a) S1: interaction of two casting pores of approximately 25 lm diameter near the edge; (b) S2: interaction of two cast pores of approximately 60 lm diameter at the edge; (c) S3: a large casting pore of approximately 0.5 mm in a linear dimension at the center of the specimens.]]
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The experiments were conducted using an MTS servo- controlled electro-hydraulic system. Monotonic and cyclic hardening experiments were conducted using the same specimens and test setup as the fatigue tests. The tests were conducted under strain-controlled, constant strain ampli- tude conditions, with the strain measured using a 0.5 in. axial fatigue rated extensometer attached within the gage length. Cyclic loading was applied at frequencies of 0.5 Hz for the first 43,000 cycles and 20 Hz, thereafter. A 50% drop in the peak cyclic load was used to determine the final failure of the specimens according to ASTM stan- dards. A temperature chamber was employed for a con- stant elevated temperature during the fatigue test at 121 °C. The strain amplitudes ranged 0.05% strain to above the yield strength 0.6%. The remotely applied strain ratio of Re = emin/emax = 􏰀1 was employed in all experiments. At least three replicated tests were conducted for each load- ing condition.
  
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|material model=
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[[Image:Figure_11_MSF_AE44.jpg|thumb|right|300px|Fig. 11. Multistage fatigue model estimation for the upper bound (UB) and lower bound (LB) of fatigue lives of the AE44 magnesium alloys machined from as-cast bars.]]
 
Multistage fatigue model
 
Multistage fatigue model
A microstructure-based multistage fatigue (MSF) model that incorporates different microstructural discontinuities (pores, inclusions, etc.) on physical damage progression was implemented to model the fatigue life of the AE44 Mg alloy. This model partitions the fatigue life into three stages based on the fatigue damage formation and propagation mechanisms: crack incubation, microstructurally small crack (MSC) and physically small crack (PSC) growth, and long crack (LC) growth.
+
A microstructure-based multistage fatigue (MSF) model<ref> McDowell DL, Gall K, Horstemeyer MF, Fan J. Microstructure- based fatigue modeling of cast A356-T6 alloy. Eng Fract Mech 2003;70:49–80.</ref> that incorporates different microstructural discontinuities (pores, inclusions, etc.) on physical damage progression was implemented to model the fatigue life of the AE44 Mg alloy. This model partitions the fatigue life into three stages based on the fatigue damage formation and propagation mechanisms: crack incubation, microstructurally small crack (MSC) and physically small crack (PSC) growth, and long crack (LC) growth.
  
 
Figs. 9 and 10 show the multistage fatigue model correlations for AE44 magnesium alloy in the as-cast and cradle specimens at room and elevated temperatures, respectively. Assuming a large pore size of 500 lm as the site of damage incubation and high porosity near the pore, the lower bound of fatigue life of AE 44 in the as-cast condition was estimated. Assuming an extremely small pore size of 10 lm as the site of damage incubation and no abnormal porosity near the pore, the upper bound for fatigue lives of AE44 as-cast bar specimens were estimated as shown in Fig. 11. The capability of estimating correct upper and low bounds demonstrates the robustness of the multistage fatigue model, which includes the key microstructure features that affect the fatigue life.
 
Figs. 9 and 10 show the multistage fatigue model correlations for AE44 magnesium alloy in the as-cast and cradle specimens at room and elevated temperatures, respectively. Assuming a large pore size of 500 lm as the site of damage incubation and high porosity near the pore, the lower bound of fatigue life of AE 44 in the as-cast condition was estimated. Assuming an extremely small pore size of 10 lm as the site of damage incubation and no abnormal porosity near the pore, the upper bound for fatigue lives of AE44 as-cast bar specimens were estimated as shown in Fig. 11. The capability of estimating correct upper and low bounds demonstrates the robustness of the multistage fatigue model, which includes the key microstructure features that affect the fatigue life.
  
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||input deck=See experiment results
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 +
|results=
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Uniaxial tension tests were conducted at room tempera¬ture and 121 °C with a loading rate of 0.005 min-1. The stress–strain curves are shown in Fig. 3. The elastic modulus, yield strength, ultimate strength and strain-to-failure of the as-cast AE44 bars were higher than those extracted from the engine cradle.
 +
The uniaxial strain-life results are shown in Fig. 4. A large variation of fatigue lives in the HCF regime was observed on specimens from both conditions, due to the sensitivity to microstructure. The large scatter in the HCF regime could be induced by the sub-sized ASTM specimens in which the above stated detrimental pore was almost one tenth of the specimen diameter. The fatigue lives at 121 °C are longer, in general, than those at the room temperature under the constant strain amplitude loading condition with the strain-controlled experiments, which maybe is induced by the increasing ductility at the elevated temperature.
 +
 +
Fractographic analyses
 +
 +
Typical specimens loaded in the strain amplitude of 0.075% (HCF) and 0.3% (LCF) were selected for fractographic analyses. At <math>{\Delta}{\epsilon}</math>/2 = 0.075%, some specimens did not fail at 107 cycles. A sample of medium life, S1 (Nf = 1.3 · 106, at 121 °C), and samples with the shortest lives, S2 (Nf = 1.78 · 105, at 121 °C), and S3 (Nf = 1.83 · 105, at 25 °C) were examined under the SEM.
 +
Most cracks formed at casting pores at or near the specimen surfaces or at a very large pore within the specimen as shown in Fig. 6. A strong interaction of two pores that were about 25 lm in diameter near the free surface formed a fatigue crack that produced the fatigue failure. A few relatively larger pores were scattered inside this specimen but no damage was formed. Even though S2 and S3 had similar low fatigue lives, the life incubation sites were quite different: the damage in S2 formed at the interaction of two pores that were 65 lm in diameter with one right at the edge while the damage in S3 formed at a large pore of 500 lm in diameter in the middle of the specimen.
  
[[Image:Figure_9_MSF_AE44.jpg|thumb|left|300px|Fig. 9. The multistage fatigue model (MSF) correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle.]]
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Samples of high-pressure die cast AE44 magnesium alloys extracted from as-cast bars and from an engine cra- dle were tested until failure under strain control at room and elevated temperatures. The initial microstructure and fatigue fractographs were examined using optical micros- copy and SEM. A multistage fatigue model originally pro- posed by McDowell et al. [21], was modified for greater porosity interaction and temperature dependence. The model captured the following microstructural phenomena in fatigue crack growth:
 +
(1) Fatigue damage formed at large cast pores near the free surfaces with an average size greater than 25 lm; the most detrimental microstructural disconti- nuity to fatigue life were the largest pores greater than 400 lm and the interaction between large pores.
 +
(2) The multistage fatigue model was able to explain the extreme limiting conditions for the strain-life of the AE44 Mg alloy. The upper and lower bounds for fatigue life were estimated using observed extreme microstructure features that coincided with the exper- imental results.
  
[[Image:Figure_10_MSF_AE44.jpg|thumb|none|300px|Fig. 10. The multistage fatigue model correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle at high temperature.]]
 
  
[[Image:Figure_11_MSF_AE44.jpg|thumb|none|300px|Fig. 11. Multistage fatigue model estimation for the upper bound (UB) and lower bound (LB) of fatigue lives of the AE44 magnesium alloys machined from as-cast bars.]]
 
  
== References ==
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|acknowledgement=The authors would like to express appreciation for sup- port from the United States Automotive Materials Partner- ship (USAMP) under the United States Council for Automotive Research (USCAR) and the Center for Ad- vanced Vehicular Systems at Mississippi State University. We would like to extend our thanks to Westmoreland Mechanical Testing and Research Inc., who conducted the static and fatigue experiments for AE44. We would like to thank Andrew Oppedal and Thomas Williams at Missis- sippi State University for conducting the measurements on the DCS and pore size distributions.
<references/>
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 +
|references=The model was initially used in following paper:
 +
}}
  
  

Latest revision as of 12:12, 5 May 2015

AbstractMethodologyMaterial ModelInput DataResultsAcknowledgmentsReferences

Abstract

Fig. 1. Optical images from polished cross-sections present an overview of size and distribution of casting pores in the AE44 magnesium alloy: (a) as-cast bar, (b) extracted from an engine cradle.

The multistage fatigue model developed by McDowell et al. was modified to study the fatigue life of a magnesium alloy AE44 for automobile applications. The fractographic examination indicated three distinct stages of fatigue damage in the high cycle fatigue load¬ing regime: crack incubation, microstructurally small crack growth, and long crack growth. Cracks incubated almost exclusively at the cast pores that were near the free surface, located near sharp geometry changes of the test specimen, or at extremely large pores inside the specimens. Microstructurally small cracks grew in the eutectic region along the weak boundaries of the grains and dendrites or at very closely packed microstructural discontinuities. Long cracks were observed to grow in a transgranular fashion. Specimens fabricated from as-cast bars and extracted from a cast engine cradle were tested at room temperature and an elevated temperature typically required for automotive powertrain applications.Alarge variation of fatigue life in the high cycle fatigue region was observed in specimens from both conditions due to the sensitivity from microstructural discontinuities. The microstructure-based multistage fatigue model was generalized for the AE44 magnesium alloy to capture the network of porosity and temperature dependence. The modified multistage fatigue model was also used to estimate the upper and lower bounds of the strain-life curves based on the extreme microstructural discontinuities.

Author(s): Y. Xue,, M.F. Horstemeyer, D.L. McDowell, H. El Kadiri, J. Fan

Corresponding author: Y. Xue


fig. 3. Stress–strain curves of the AE 44 magnesium alloy: (1) as-cast bar, (2) extracted from engine cradle tested at room temperature (RT) and 121 C (HT). (click on the image to enlarge).
fig. 4. Uniaxial strain-life of AE44 Mg alloy specimens machined from as-cast bars and from an engine cradle tested at room temperature (RT) and 121 C (HT) under strain-controlled, constant amplitude with completely reversed strain amplitude experiments. (click on the image to enlarge).
Fig. 9. The multistage fatigue model (MSF) correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle. (click on the image to enlarge).
Fig. 10. The multistage fatigue model correlation for magnesium alloy AE44 of as-cast bar specimens and specimens extracted from an engine cradle at high temperature. (click on the image to enlarge).

Methodology

The experiments were conducted using an MTS servo- controlled electro-hydraulic system. Monotonic and cyclic hardening experiments were conducted using the same specimens and test setup as the fatigue tests. The tests were conducted under strain-controlled, constant strain ampli- tude conditions, with the strain measured using a 0.5 in. axial fatigue rated extensometer attached within the gage length. Cyclic loading was applied at frequencies of 0.5 Hz for the first 43,000 cycles and 20 Hz, thereafter. A 50% drop in the peak cyclic load was used to determine the final failure of the specimens according to ASTM stan- dards. A temperature chamber was employed for a con- stant elevated temperature during the fatigue test at 121 °C. The strain amplitudes ranged 0.05% strain to above the yield strength 0.6%. The remotely applied strain ratio of Re = emin/emax = 􏰀1 was employed in all experiments. At least three replicated tests were conducted for each load- ing condition.

Material Model

Fig. 11. Multistage fatigue model estimation for the upper bound (UB) and lower bound (LB) of fatigue lives of the AE44 magnesium alloys machined from as-cast bars.

Multistage fatigue model A microstructure-based multistage fatigue (MSF) model[1] that incorporates different microstructural discontinuities (pores, inclusions, etc.) on physical damage progression was implemented to model the fatigue life of the AE44 Mg alloy. This model partitions the fatigue life into three stages based on the fatigue damage formation and propagation mechanisms: crack incubation, microstructurally small crack (MSC) and physically small crack (PSC) growth, and long crack (LC) growth.

Figs. 9 and 10 show the multistage fatigue model correlations for AE44 magnesium alloy in the as-cast and cradle specimens at room and elevated temperatures, respectively. Assuming a large pore size of 500 lm as the site of damage incubation and high porosity near the pore, the lower bound of fatigue life of AE 44 in the as-cast condition was estimated. Assuming an extremely small pore size of 10 lm as the site of damage incubation and no abnormal porosity near the pore, the upper bound for fatigue lives of AE44 as-cast bar specimens were estimated as shown in Fig. 11. The capability of estimating correct upper and low bounds demonstrates the robustness of the multistage fatigue model, which includes the key microstructure features that affect the fatigue life.

Input Data

See experiment results

Results

Uniaxial tension tests were conducted at room tempera¬ture and 121 °C with a loading rate of 0.005 min-1. The stress–strain curves are shown in Fig. 3. The elastic modulus, yield strength, ultimate strength and strain-to-failure of the as-cast AE44 bars were higher than those extracted from the engine cradle. The uniaxial strain-life results are shown in Fig. 4. A large variation of fatigue lives in the HCF regime was observed on specimens from both conditions, due to the sensitivity to microstructure. The large scatter in the HCF regime could be induced by the sub-sized ASTM specimens in which the above stated detrimental pore was almost one tenth of the specimen diameter. The fatigue lives at 121 °C are longer, in general, than those at the room temperature under the constant strain amplitude loading condition with the strain-controlled experiments, which maybe is induced by the increasing ductility at the elevated temperature.

Fractographic analyses

Typical specimens loaded in the strain amplitude of 0.075% (HCF) and 0.3% (LCF) were selected for fractographic analyses. At {\Delta}{\epsilon}/2 = 0.075%, some specimens did not fail at 107 cycles. A sample of medium life, S1 (Nf = 1.3 · 106, at 121 °C), and samples with the shortest lives, S2 (Nf = 1.78 · 105, at 121 °C), and S3 (Nf = 1.83 · 105, at 25 °C) were examined under the SEM. Most cracks formed at casting pores at or near the specimen surfaces or at a very large pore within the specimen as shown in Fig. 6. A strong interaction of two pores that were about 25 lm in diameter near the free surface formed a fatigue crack that produced the fatigue failure. A few relatively larger pores were scattered inside this specimen but no damage was formed. Even though S2 and S3 had similar low fatigue lives, the life incubation sites were quite different: the damage in S2 formed at the interaction of two pores that were 65 lm in diameter with one right at the edge while the damage in S3 formed at a large pore of 500 lm in diameter in the middle of the specimen.

Samples of high-pressure die cast AE44 magnesium alloys extracted from as-cast bars and from an engine cra- dle were tested until failure under strain control at room and elevated temperatures. The initial microstructure and fatigue fractographs were examined using optical micros- copy and SEM. A multistage fatigue model originally pro- posed by McDowell et al. [21], was modified for greater porosity interaction and temperature dependence. The model captured the following microstructural phenomena in fatigue crack growth: (1) Fatigue damage formed at large cast pores near the free surfaces with an average size greater than 25 lm; the most detrimental microstructural disconti- nuity to fatigue life were the largest pores greater than 400 lm and the interaction between large pores. (2) The multistage fatigue model was able to explain the extreme limiting conditions for the strain-life of the AE44 Mg alloy. The upper and lower bounds for fatigue life were estimated using observed extreme microstructure features that coincided with the exper- imental results.

Acknowledgments

The authors would like to express appreciation for sup- port from the United States Automotive Materials Partner- ship (USAMP) under the United States Council for Automotive Research (USCAR) and the Center for Ad- vanced Vehicular Systems at Mississippi State University. We would like to extend our thanks to Westmoreland Mechanical Testing and Research Inc., who conducted the static and fatigue experiments for AE44. We would like to thank Andrew Oppedal and Thomas Williams at Missis- sippi State University for conducting the measurements on the DCS and pore size distributions.

References

The model was initially used in following paper:

  1. McDowell DL, Gall K, Horstemeyer MF, Fan J. Microstructure- based fatigue modeling of cast A356-T6 alloy. Eng Fract Mech 2003;70:49–80.


Citation: Microstructure-based multistage fatigue modeling of a cast AE44 magnesium alloy, Y. Xue a, M.F. Horstemeyer, D.L. McDowell, H. El Kadiri, J. Fan, International Journalof Fatigue 29 (2007) 666–676

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